Research ArticleTargeted Double Negative Properties in SilverSilica RandomMetamaterials by Precise Control of Microstructures

Peitao Xie12 Zidong Zhang2⋆ Zhongyang Wang2 Kai Sun1 and Runhua Fan12⋆

1College of Ocean Science and Engineering Shanghai Maritime University Shanghai 201306 China2Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education) Shandong UniversityJinan 250061 China

⋆Correspondence should be addressed to Zidong Zhang zhangzidongsdueducn and Runhua Fan fansdueducn

Received 23 November 2018 Accepted 25 December 2018 Published 15 January 2019

Copyright copy 2019 Peitao Xie et al Exclusive Licensee Science and Technology Review Publishing House Distributed under aCreative Commons Attribution License (CC BY 40)

The mechanism of negative permittivitypermeability is still unclear in the random metamaterials where the precise control ofmicrostructure and electromagnetic properties is also a challenge due to its random characteristic Here silver was introduced intoporous SiO2 microsphere matrix by a self-assemble and template method to construct the randommetamaterials The distributionof silver was restricted among the interstices of SiO2 microspheres which lead to the precise regulation of electrical percolation(fromhoping toDrude-type conductivity) with increasing silver content Negative permittivity came from the plasma-like behaviorof silver network and its value and frequency dispersion were further adjusted by Lorentz-type dielectric response During thisprocess the frequency of epsilon-near-zero (ENZ) could be adjusted accordingly Negative permeability was well explained bythe magnetic response of eddy current in silver micronetwork The calculation results indicated that negative permeability hasa linear relation with 12059605 showing a relaxation-type spectrum different from the ldquomagnetic plasmardquo of periodic metamaterialsElectromagnetic simulations demonstrated that negative permittivitymaterials and ENZmaterials with the advantage of enhancedabsorption (40dB) and intelligent frequency selection even in a thin thickness (01 mm) could have potentials for electromagneticattenuation and shielding This work provides a clear physical image for the theoretical explanation of negative permittivity andnegative permeability in random metamaterials as well as a novel strategy to precisely control the microstructure of randommetamaterials

1 Introduction

Metamaterials with unique negative electromagnetic param-eters (eg negative refraction permeability andpermittivity)have gained extensive research attention due to their originalapplications in cloaking waveguide wireless power transferelectromagnetic shielding and high-permittivity capacitoretc [1ndash5] Metamaterials typically consist of artificially peri-odic array structure with different geometrical configuration(split-ring resonators wires fishnet or cut-wire pairs) [1]Rather than originating from the component materials theunique property ofmetamaterials is fundamentally attributedto the resonance in these array structures [6 7] By designingthe size and arrangement of the array units according to theapplied wavelength the electromagnetic resonance can beefficiently controlled to achieve the desirable electromagneticproperties of the metamaterials

In fact negative electromagnetic parameters have alsobeen observed in some conventional materials such as

semiconductors and ferrite [6 8] By introducing these mate-rials with optimal negative electromagnetic parameters intometamaterials according to the specific application require-ment the artificial difficulty in designing the geometricalconfiguration and arrangement mode of metamaterials aswell as achieving the multifunctionalization of metamaterialscan be obviously reduced for physicists and informationscientists Therefore how to combine the conventional mate-rials with metamaterials also becomes a hot issue in thefield of materials science and engineering At the sametime this can also expand the scope of metamaterials anddevelop the design methods of metamaterials Zhou et alpioneered this idea by introducing ferromagnetic materialsand Mie resonance into metamaterials or photonic crystalto realize negative permeability or refraction [9ndash11] Penget al observed the negative electromagnetic parameters inamorphous-metal sensors and transducers a great success ofmultifunctionalization of the devices [12 13]

AAASResearchVolume 2019 Article ID 1021368 11 pageshttpsdoiorg103413320191021368

2 Research

with 2 PVA asbinder

Impregnation and calcine Centrifugation and molding

Equipped withdisc-shapedmold

Alcohol+Ammonia+Deionized water

StOumlbermethod

TEOS+Alcohol

Sintered at

Vacuumization

Dry and calcine

Preparation of SiO spheres

SiO microspheres Porous SiO matrix

SiO suspension

AgSiO composites∘ C

at ∘ C

AgNO solution

m m52 2m

Figure 1 Schematic diagram of fabrication process of the AgSiO2 composites

Specifically Fan et al investigated negative permittivityandor negative permeability in random percolative com-posites where conductive functional fillers were randomlydistributed in the insulatingmatrix [14ndash16] In these so-calledintrinsicrandom metamaterials the sizes of the metamate-rials are no longer dependent on wavelength because thenegative electromagnetic parameter directly originates fromthe intrinsic property of component materials Besides therandom metamaterials different from the periodic meta-materials can be fabricated via the typical processing ofmaterials where their properties can be efficiently controlledby changing the chemical compositions and microstructuresof the component materials which develops a novel andflexible way of adjusting negative electromagnetic parametersin the metamaterials [17ndash19] As a result random metama-terials have aroused tremendous interests in recent years[20 21] However the distribution of functional fillers isusually random in percolative composites a characteristic ofpercolation phenomenon [22]The obtained electromagneticproperties therefore cannot be precisely controlled whichis not beneficial to the design and application of randommetamaterials Moreover themechanism of negative permit-tivity and permeability is still not clear enough in randommetamaterials as the random microstructure leads to thedifficulty in studying their mechanisms To address theseissues a novel strategy needs to be developed to preciselycontrol the microstructure of random metamaterials wherethe functional fillers can be accurately introduced into thetargeted positions in the random metamaterials

Herein we employed a self-assemble and templatemethod to fabricate the AgSiO2 composite to achieve nega-tive permittivity and permeability Ag is a perfect candidate toprovide the electromagnetic response as it is an outstandingconductor due to the high electric conductivity (6305times105Ssdotcmminus1) To provide the porous template the insulatingSiO2 microspheres are used where the silver is introducedin and its microstructure can be precisely controlled bya facile (lt450∘C) impregnation-calcination process Nega-tive permittivity is attributed to the low-frequency plas-monic state of the low-dimensional silver network and canbe adjusted by Lorentz-type dielectric resonance Negative

permeability comes from magnetic behavior of induced cur-rent loops in the silver networkThese randommetamaterialsare potential candidates to innovate some traditional elec-tromagnetic industries Electromagnetic shielding of ultra-thinAgSiO2 randommetamaterials herein was investigatedby electromagnetic simulation showing the advantage ofrandom metamaterials that its size is no longer restrictedby applied wavelength The shielding effectiveness of theAgSiO2 composite can be greatly enhanced to 40 dB withonly 01 mm thickness near the epsilon-near-zero (ENZ)frequency range (520MHz) Compared to the typical electro-magnetic shielding material a better electromagnetic inter-ference (EMI) shielding performance can be expected whenusing the negative permittivitymaterials or ENZmaterials forthe EMI shielding applications

2 Results and Discussion

Figure 1 shows the main steps to fabricate the AgSiO2composites (1) The SiO2 microspheres were prepared by thetypical Stober method [23] (2) The SiO2 microspheres wereultrasonicated in polyvinyl alcohol solution followed by acentrifugation process to obtain a porous bulk sample (3)Theporous bulk sample was put into AgNO3 solution which canfill in the interstices among the SiO2microspheres After thatthe precursor composites were calcined to obtain theAgSiO2composites

21 Phase Characterization and Microstructure The XRDpatterns of the AgSiO2 composites illustrated the high purityof fabricated silver by the impregnation-calcination process(discussed in supporting information and Fig S1) The SEMimages of AgSiO2 composites are shown in Figure 2 Thediameter of SiO2 microsphere is about 700 nm and SiO2microspheres are closely arranged in the SiO2 bulk material(in Figure 2(a)) As we can see the porous matrix can beconstructed by the self-assembly method the pore structure(size shape and connectivity) is no longer random butstable and repeatable After the silver was introduced intothe composites the silver can only be distributed in theinterstices among these SiO2 microspheres where the silver

Research 3

m

Silver particles

m

Silver agglomeration

m

Formation of silver network

m m

Enhanced silver network

m

(a) (b) (c)

(d) (e) (f)

Figure 2 SEM image of SiO2 bulk (a) and AgSiO2 composites with 17 wt (b) 28 wt (c) 32 wt (d) 35 wt (e) and 37 wt (f) silvercontent

nanoparticles will nucleate and grow during the calcinationprocess That is the silver could be introduced into thetargeted positions of the composites which provides the fea-sibility to precisely control the microstructure of compositesand adjust their electromagnetic property [19 23] Whensilver content is low silver particles are isolated and randomlydistributed in the composites with 17wt silver (Ag17) (inFigure 2(b)) With increasing silver content the interconnec-tion of silver particles is enhanced and silver agglomeration isformed (Figure 2(c))Then three-dimensional silver networkis formed in the channels among SiO2 microspheres inthe composites with 32wt silver (Ag32) (Figure 2(d)) Thenetwork is gradually enhanced with increasing silver content(Figures 2(e)-2(f)) The conduction behavior is very sensitiveto its microstructure according to percolation theory hencetheir conduction behaviors are investigated as follows [24]

22 Ac Conductivity and Percolation Figure 3 shows thevariation of alternating current (ac) conductivity (120590ac) (at10MHz) of AgSiO2 composites with different silver con-tents The 120590ac gradually increases with increasing silvercontent when silver volume fraction f lt008 but shows anabrupt increase near f=8 vol This is a typical percolationphenomenon and the percolation threshold (119891c) is near 8vol [14 24] The percolative behavior is attributed to thevariation of microstructure as discusses above when silvercontent is below 119891c the silver particles are isolated by theSiO2 matrix and pore while a continuous network couldbe formed when silver content is above 119891c In this workthe percolative threshold was relatively low compared withthe typical granular composites whose percolative thresholdis usually 16 [22] In fact the percolative threshold isinfluenced by the intrinsic property shape size surface

000 002 004 006 008 010 012Silver Volume Fraction

10 MHz

t = -0366

Insulator-likeConductor

-like

minus

minus

minus

ac

(cm

)minus

minus minus minus minus

minus

minus

minus

minus

Log

(ac

)

c=0082

ac prop (c-)

Log c -

Figure 3 The variation of 120590ac (at 10 MHz) for AgSiO2 compositeswith silver volume fraction The inset shows the calculation resultsusing percolation theory the percolation threshold is 0082 thepercolation critical exponent is t=0366

state and dimension of the fillers If the fillers are one-dimensional conductors such as carbon nanotubes carbonnanofibers and silver nanowires the percolative thresholdcan be decreased accordingly [22] After the silver wasdistributed in the interstices among the SiO2 microspheresthe silver to some extent had a one-dimensional shape inthe silverSiO2 composites Besides the distribution of silverwas restricted by the porous SiO2microspheres templateThepercolative threshold was therefore only about 8 in thesilverSiO2 composites The abrupt change of conductivitycan be expressed by classical percolation theory [22]

120590119886119888 prop 1003816100381610038161003816119891119888 minus 1198911003816100381610038161003816119905 (1)

4 Research

10M 100M 1G

5

10

15

20

25

Frequency (Hz)

Large Capacitor

Ag17SiO bulk Ag23

Ag28

(a) (b)

(c) (d)

10M 100M 1G

0

20k

40k

400M 600M 800M 1G

0

150

Frequency (Hz)

minusk

minusk

minusk

minus

minus

minus

Ag32Ag35

Ag37

100M 1G

0

10k

Frequency (Hz)

Lorentz Model

Drude Model

Drude+Lorentz Model

minus4k

minus3k

minus2k

minus1k

Experimental data of Ag35

10M 100M

Positivepermittivity

region

1G

0

20

Frequency (Hz)

Negative permittivity region

minus

minus

minus

(d

egre

e)

Ag32Ag35

Ag37

Figure 4 Frequency dispersion of real permittivity (1205761015840) for AgSiO2 composites (a b) permittivity dispersion of Ag35 with calculation results(c) Frequency dependence of phase angle 120579 for AgSiO2 composites with different silver content (d) The dashed line is the calculated curveonly by Drude model the dash-dotted line is the calculated curve only by Lorentz model and the solid line is calculated curve by both Theinset in (d) is the equivalent circuit of composites when the silver content is above percolation threshold

where f is the volume fraction of silver filler 119891c is thepercolation threshold and t is the corresponding criticalexponent The calculation results (inset of Figure 3) usingExpression (1) show good agreement with experimentaldata suggesting that percolation theory is applicable tothe AgSiO2 composites The frequency dispersion of 120590acindicates that hopping conductivity behavior below the per-colation threshold while a metal-like conduction behavioris observed above the percolation threshold (detailed in thesupporting information and Fig S3) Therefore the changeof electricalmechanismoccurs inAgSiO2 composites whichcan provide the feasibility of achieving the desirable negativepermittivity property studied in the following section

23 Permittivity and Impedance Frequency dispersions ofreal permittivity (1205761015840) are shown in Figure 4 Permittivityshows obvious dependence on silver content When silver

content is belowpercolation threshold119891c (in Figure 4(a)) 1205761015840 ispositive and increases with increasing silver content becausethe polarization across the silverSiO2 interface indicates thatany pairs of adjacent silver particles separated by an insu-lating gap can work as a microcapacitor [23] The AgSiO2composites can be regarded as a network of microcapacitors(inset of Figure 4(a)) which enables the composites to havea higher permittivity with increasing silver content Thisbehavior is also known asMaxwell-Wagner-Sillars effect [23]which is responsible for the enhancement of permittivity inheterogeneous composites It is worth noting that the SiO2bulk and composites with 17 wt and 23 wt silver contenthave potentials as novel high-permittivity materials over abroad frequency range as their 1205761015840 keeps steady in the wholetest frequency region and their dielectric loss is relativelysmall with dielectric loss tangent tan 120575 lt001 (in Fig S4b)When the silver content increases to 28 wt the 1205761015840 of thecomposites shows obvious frequency dispersion

Research 5

When silver content is above the percolation threshold119891c negative 1205761015840 is achieved and shows obvious frequencydispersion (in Figure 4(b)) The 1205761015840 is sim -5000 at 6 MHzfor composites with 32 wt silver content and graduallyincreases with increasing frequency As for the compositeswith 35 wt silver content the 1205761015840 is sim -50000 at 6 MHz andincreases with increasing frequency reaches the maximum(sim8000) at 150 MHz and then decreases with increasingfrequency As for the composites with 37 wt silver contentthe 1205761015840 is sim -10000 at 6 MHz and keeps increasing to the maxi-mum (sim21000) at 68MHz but then decreases with increasingfrequency The 1205761015840 of Ag32 equals zero at 520 MHz while at57 MHz for the composite with 35wt silver (Ag35) and 11MHz for the composite with 37wt silver (Ag37)That is theepsilon-zero-point shifts to lower frequency with increasingsilver content which provides the feasibility of adjustingepsilon-near-zero properties The AgSiO2 composites cannot only be the promising candidate for negative permit-tivity but also be the epsilon-near-zero materials at radio-frequency region [25] Generally the plasma-type negativepermittivity of metals can be expressed by the Drude model[17]

1205761015840 = 1 minus1205962119901

1205962 + Γ1198632(2)

where ΓD is the damping constant 120596p=2120587119891p is the plasmonsangular frequency Equation (2) is a monotonic increasingfunction while the experimental data are not monotonic buthave maximum (in Figure 4(b)) Because the experimentalresults cannot be perfectly explained by the Drude modelonly there must be other mechanism contributing to thedielectric behavior of the composites [24] The Drude modeldescribes the simple harmonic motion of free electrons ataltering electromagnetic field Besides the Drude model isusually used at the optical and infrared region to describethe negative permittivity The frequency is very high that isperiod time is short so the movement distance of the freeelectrons is also short As a result the plasma oscillation canbe induced even in small metal particles However whenthe frequency of external electrical filed is low even in theradio-frequency region free electrons will be localized insome small metal particles or agglomeration leading to thedeviation from the Drude model The Drude model candescribe the dielectric behavior of silver network only butis not applicable to isolated silver particles [21] Since theisolated silver particles or agglomeration can lead to Lorentz-type dielectric behavior [24] the formula is modified afterconsidering Lorentz-type dielectric resonance [24]

1205761015840 = 1 minus1205962119901

1205962 + Γ2119863+

1198701205962119871 (1205962119871 minus 1205962)(1205962119871 minus 1205962)2 + Γ21198711205962

(3)

where ΓL is the damping constant of Lorentz resonance120596L=2120587119891L is the Lorentz resonance angular frequency andK is the dc electric susceptibility As we can see fromFigure 4(c) and Table S3 the calculation results (solid linesin Figure 4(c)) of Ag35 using Expression (3) show goodagreement with experimental data with high reliability factor

R2=099589TheDrude-type calculation results (dashed linesin Figure 4(c)) indicate that negative permittivity derivesfrom the plasma-type dielectric behavior of free electronsin the silver network while the Lorentz-type calculationresults (dash-dotted lines in Figure 4(c)) indicate that thefrequency dispersion of negative permittivity can be effec-tively adjusted by Lorentz-type dielectric resonance Thesecalculation results were made via the iterative method byusing the respective model Although Lorentz-type dielec-tric resonance can generate negative permittivity in someferroelectric materials and composites containing carbonnanotubes [26 27] the Lorentz-type dielectric behaviors haveno contribution to the negative permittivity in Figure 4(b) Infact it is a relaxation-type curve rather than resonance-typecurve shown as dash-dotted lines in Figure 4(c) as the damp-ing factor is much larger than resonance frequency (shownin Table S3) a common phenomenon at low-frequencyregion in metal optics The Lorentz-type dielectric behaviorcan be attributed to the interfacial imperfection (holes andvoids) and the inhomogeneous silver distribution (isolatedagglomeration and network) formed during adding silverinto SiO2 matrix It can come into the conclusion that thesilver content plays an important role in controlling thefrequency dispersion of negative permittivity

Negative permittivity behavior is further investigated byphase angle (120579) as the positive permittivity is regarded asa capacitive character where the resistance current (119868R) lagsthe capacitive current (119868C) by 90∘ When the silver contentis above 119891c the 120579 of Ag32 is positive below 520 MHz below55 MHz for Ag35 and 102 MHz for Ag37 (in Figure 4(d))while the negative value of 120579 is above these frequency pointsIt shows that the inductive current (119868L) lags the resistivecurrent (119868R) by 90∘ which indicates that negative permittivityexhibits inductive character and the electric energy is storedin inductance [24] Therefore there were usually inductorsin the equivalent circuit of negative permittivity materialsbecause of the inductive character The equivalent circuitanalysis was performed by the ZSimpwin software Theoptimal equivalent circuit was chosen with the smallestChi-square value (usually 10minus3-10minus5) The Chi-square valuerepresents the correlation between experimental data andsimulated data In the previous study we have demonstratedthat the distribution of conductive functional fillers canadjust the frequency dispersion of negative permittivity byLC resonance [23 24] In Figure 4(d) we can see that thesilver content is crucial to the control of LC resonancebecause the value of 120579 is sensitive to the silver content Theabsolute value of 120579 is very small in negative permittivityregion indicating that negative permittivity behavior hashuge dielectric loss and potential application as lossmaterialsBesides the absolute value of 120579 increases with increasingfrequency in positive permittivity region indicating theenergy storage efficiency in capacitance is obviously higherthan that in inductance [28] Interestingly the frequencypoints of 120579=0 correspond with the epsilon-zero points Thatis there is no energy storage but energy loss at epsilon-zeropoint indicating that AgSiO2 composites can function asresistor in metaelectronics circuits at radio-frequency region[29]

6 Research

00

03

06

09

12

Negative permeability region

Frequency (Hz)200M 400M 600M 800M 1G

Fitting data using prop

minus

Ag28Ag32Ag35Ag37

Ag23Ag17

SiO

External magnetic fieldInduced magnetic field by current loop

The space between microspheres is filled with silver

Current loops

(a) (b)

(c) (d)

Pores and gaps among SiO microspheres

1

10

100

near 1 GHz

starts to be remarkableEddy current loss

Frequency (Hz)200M 400M 600M 800M 1G

Slope = 0 at ~520 MHz

Ag28Ag32

(

) (

ns)

2

Frequency (Hz)

Complicatedloss response

Eddy current loss shiftsto lower frequency

Slope = 0 at ~251 MHzand ~355 MHz

200M 400M 600M 800M 1G

Ag35Ag37

(

) (

ns)

2

Figure 5 Frequency dependence of real permeability (1205831015840) for AgSiO2 composites (a) the schematic diagram of magnetic response due tothe induced current loops in AgSiO2 composites (b) and frequency dependence of 12058310158401015840(12058310158402f ) for AgSO2 composites with different silvercontent (c d) The red solid lines in (a) are the calculation results by the relation of 1205831015840 prop radic120596 with high reliability

24 Permeability Figure 5 depicts the frequency dependenceof real permeability (1205831015840) property for AgSiO2 composites Asshown in Figure 5(a) the 1205831015840 of SiO2 bulk almost keeps 1 dueto its nonmagnetism After silver is added to SiO2 matrixthe value of 1205831015840 is smaller than 1 indicating negative sus-ceptibility The negative susceptibility is obviously enhancedwith increasing silver content and frequencyWhen the silvercontent reaches 37 wt negative permeability is achievedin the range of 760-1000 MHz Since SiO2 and silver areboth nonmagnetic the negative susceptibility and negativepermeability cannot be attributed to the magnetic resonanceof component materials It is worth noting that the previousinvestigations demonstrate that negative permeability is dif-ficult to be realized in metalceramics randommetamaterialsthat only contain nonmagnetic metal [17 18] Thereforethe generation of negative permeability indicates that the

precise control of silver is in favor of the magnetic responseof induced current which improves the response efficiencyand the possibility of realizing negative permeability Wecan get some inspiration from periodic metamaterials asnegative permeability is the unique property of periodicmetamaterials and its mechanism is derived from the law ofelectromagnetic induction [7 30] The split-ring resonatorsare the typical building blocks of magnetic response inperiodic metamaterials while the silver can work as buildingblocks of magnetic response in the AgSiO2 composites Asshown in the schematic diagram in Figure 5(b) the intersticesamong the SiO2 microspheres are filled with silver and thecurrent loops can be induced around the SiO2 microsphereswhen the composites are put under an alternating currentmagnetic field The direction of the induced magnetic fieldfrom these current loops is opposite to the external magnetic

Research 7

field which would cancel part of external magnetic field andthus leads to negative susceptibility [5] When the inducedmagnetic field is even dominant negative permeabilitywill beachieved [7 31]Moreover there are alsomany pores and gapsinside the silver network where the microcurrents (smallloops in Figure 5(b)) can also be induced to generate negativesusceptibilitypermeability

According to the mechanism of negative permeabilityin typical periodic metamaterials also known as ldquomagneticplasmardquo the permeability of classical split-ring resonators(SRRs) can be expressed as follows [31]

1205831015840119890119891119891 = 1 +1198651205962 (12059620 minus 1205962)

(12059620 minus 1205962)2 + Γ21205962(4)

where F is a geometrical factor1205960 is the resonance frequencyand Γ is the resistive damping factor The calculation datausing magnetic plasma model are shown in Fig S7 and TableS5 the low reliability factors indicate that ldquomagnetic plasmardquocannot be the mechanism here As shown in Table S5 thedamping factors Γ are larger than resonance frequency byseveral orders of magnitudes indicating a relaxation-typeresponse in the view of ldquomagnetic plasmardquo [14 15 18] Therelaxation-type behavior results in the huge deviation fromldquomagnetic plasmardquo primarily because of the great differencein shape and dimension between SRRs (typical ldquomagneticplasmardquo structure) and silver network (building blocks inthis work) The capacitance from the split in SRRs leads to aresonance-type magnetic response while no split structuresare available in the silver network In addition it is well-known that the reported periodic metamaterials have 120582lvalue between 2 and 12 where 120582 is the wavelength and l isthe size of the building block while it is not applicable tothis work [31] Moreover the relaxation-type response canbe partly due to the small size of the silver network sincethe damping factor is inversely proportional to the size ofbuilding blocks [32]

The ldquomagnetic plasmardquo cannot explain the negative per-meabilitysusceptibility but the magnetic response can onlyresult from the electromagnetic induction in the nonmag-netic composites According to the Faradayrsquos law the inducedcurrent density can be expressed as follows [33]

119895119894 = 120590119894119890119894 = minus120590119894119889Φ119894119889119905 = minus120596120590119894119860 cos (120596119905) (5)

where 119895119894 is the localized current density 120590119894 is the ac conduc-tivity of local area 119890119894 is the localized electric field intensityΦ119894is the magnetic flux t is the time and A is the amplitude of119890119894 According to Biot-Savart law the induced current loopscan generate an induced magnetic field whose direction isalways opposite to the external magnetic field The magneticresponse 119861119894 at the axes of circulating current 119895119894d119878119894 can becalculated by the formula [33]

119861119894 =12058301199032119895119894119889119878119894

2120587 (1199032 + 1199092)32(6)

where 119861119894 is the magnetic induction intensity r is the radiusof circulating current d119878119894 is the sectional area of circulating

current and x is the distance to the center of circulatingcurrent When the induced currents cannot keep up with theexternal field at very high frequency the induced currentswould lag and thus lead to an out-of-phase or negativeresponse The linear relationship between 1205831015840 119861119894 j and 120596 canbe obtained 1205831015840 prop 119861119894 prop 119873119895 prop 120596 where N is the windingnumber Fig S8 and Table S6 show the calculation resultsusing linear relationship The reliability factors (about 0975)is fine but still cannot satisfy our expectation Thereforeother factors should also be considered In fact the 120590119894 inExpression (5) should not be dc conductivity but ac con-ductivity Ac conductivity is also the function of frequencyusually explained by skin depth 120575 = (21205830120590119889119888120596)05 [18] Therelationship between 119861119894 j and 120596 can be modified [16]

119861119894 prop 119873119895 prop radic120596

1205831015840 = 119886 + 119887radic120596(7)

where a and b are parameters about the intrinsic propertyof AgSiO2 composites The calculation results using (7) areshown as red solid lines in Figures 5(a) and S9 and theused parameters are in Table S7The calculation results agreewell with experimental data (1198772 asymp 09975) indicating thatthe mechanism of negative susceptibilitypermeability canbe well explained [16] The physical meaning of a is theinitial permeability and its value should be 1 for AgSiO2composites in good agreement with the calculation results(in Table S7) The parameter b is an intrinsic parameterwhich is closely related to the composition microstructureand electromagnetic property of composites [34 35]

Themagnetic loss was also studied to reveal the influenceof eddy current on negative susceptibilitypermeability Theimaginary permeability (12058310158401015840) spectra for AgSiO2 compositesare shown in detail in supporting information and Fig S10aMagnetic loss mainly originates from hysteresis loss eddycurrent effect and natural resonance at the radio-frequencyregion The hysteresis loss is negligible in the weak fieldNatural resonance can also be excluded due to nonmagnetismof AgSiO2 compositesTherefore the eddy current loss is theonly source of magnetic loss and the eddy current loss can beexpressed by [36]

12058310158401015840 =21205871205830 (1205831015840

2) 12059011988911988811986321198913

(8)

where D is the effective diameter of metal particles If themagnetic loss simply derives from the eddy current lossthe value of 12058310158401015840(12058310158402f ) should be nearly constant withoutchanging with frequency Figures 5(c)-5(d) and S10 show thefrequency dispersion of 12058310158401015840(12058310158402f ) When the silver content isbelow 119891c 12058310158401015840(1205831015840

2f ) value obviously decreases with frequency(in Fig S10) there is an evidence of no eddy current lossavailable because the size of the silver particles is very tiny andeven smaller than the skin depth When the silver content isnear 119891c (ie Ag28 and Ag32) the value of 12058310158401015840(12058310158402f ) at thelower frequency region also decreases with increasing fre-quency (in Figure 5(c)) Interestingly the slope of Ag32 curve

8 Research

200M 400M 600M 800M 1GFrequency (Hz)

0102030

6070 0

4050(d

B)EM

I SE T

- +asymp

01 mm025 mm05 mm1 mm

Target LevelCommercial

200M

0

400M 600M 800M 1GFrequency (Hz)

05

1015202530

(dB)

EMI S

E R

- +asymp

01 mm025 mm05 mm1 mm

200M 400M 600M

0

800M 1GFrequency (Hz)

(a) (b) (c)

(d) (e)

30

20

10

40

50

0

(dB)

EMI S

E A

- +asymp

01 mm025 mm05 mm1 mm

5012 MHz

2

19617816014212510789

712534356178

0

Z XY

5559 MHz

The EM shieldingproperty at 5012MHz is obviouslybetter than thatat 5559 MHz

Figure 6 Frequency dispersion of EMI SET (a) SER (b) and SEA (c) for Ag32 metacomposites with different thickness The distribution ofelectric field vector of Ag32 composites at 5012 MHz (d) and 5559 MHz (e) with 025 mm thickness

is zero at sim520MHz and at sim1GHz for Ag28 where 12058310158401015840(12058310158402f )keeps constant indicating that the eddy current loss graduallybecomes dominant in magnetic loss [36] Further increasingsilver content the slope of Ag35 curve is zero at sim355 MHzand at sim 251 MHz for Ag37 (in Figure 5(d)) suggesting thatthe eddy current loss shifts to low-frequency region with theenhanced silver network In fact eddy current loss has a closerelationshipwith the frequency of the externalmagnetic fieldgeometrical configuration and the electrical conductivity ofthe metal The faster the magnetic field changes the strongerthe eddy current loss can cause In this work the frequencyshift of eddy current loss could not be attributed to theelectrical conductivity of the metal as the eddy current lossof all the composites came from the silver network The onlyinfluence factor was the geometrical configuration of thesilver network From the SEM results (in Figure 2) it can beobserved that the silver networkwas obviously enhancedwithincreasing silver contentThat is the thicker silverwires couldbe formed in the silver networkThe electrical conductivity ofthe whole silver network could be enhanced with increasingsilver content and thus the remarkable eddy current losscould be caused at lower frequency region It is worth notingthat 12058310158401015840(12058310158402f ) increases with increasing frequency at higherfrequency region (in Figure 5(d)) In addition there is a losspeak for Ag37 curve at 760 MHz and it also seems to bea peak for Ag35 at higher frequency region (above 1 GHz)These can be attributed to the complicated relaxation-typebehavior from the phase lag of induced eddy current [31] It is

concluded that the eddy current effect is the main reason fornegative susceptibilitypermeability

25 Electromagnetic Simulation and Shielding EffectivenessNegative permittivity and permeability were simultaneouslyachieved in the AgSiO2 composites In order to deter-mine the interaction between electromagnetic wave and thematerials the electromagnetic propagation properties weresimulated using Computer Simulation Technology softwareThe simulationmethod is detailed in supporting informationand Fig S11The shielding effectiveness (SE) is the main eval-uation criterion of suppressing electromagnetic interference(EMI) The SE total (SET) includes SE absorption (SEA) andSE reflection (SER) [37]

The simulated SE results of Ag32 were shown in Figure 6The SET value increased with increasing frequency at 100-520 MHz then the SET value dramatically dropped and kepta small value at 520-1000 MHz Intriguingly the frequencyregion with large SET value corresponds well with that ofnegative permittivity while low SET corresponds well withpositive permittivity region (in Figure 4(b)) Similar resultswere also observed for Ag35 and Ag37 in Fig S12-S13 whichis because the formation of the silver network could leadto high SE value and excellent electromagnetic shieldingproperty [38] The SER value almost kept constant (225-275) at 100-520 MHz (in Figure 6(b)) and is independenton the thickness of composites because the thickness ofsilver network is thicker than the skin depth of metal silver

Research 9

(0064 mm at 100 MHz) In contrast the SEA value obviouslyincreased with higher frequency and thicker slab at 100-520 MHz (in Figure 6(c)) a peak value near 520 MHz Theenhanced SEA value had a close relationship with the epsilon-near-zero property of Ag32 composites because of goodimpedance matching and absorption loss Similar enhancedabsorption phenomenon was also observed in indium tinoxide at infrared band [39] Therefore the epsilon-near-zero property is like an ldquoon-off switchrdquo of electromagneticshielding providing the possibility of intelligent frequencyselection It is further demonstrated by the distributionof the electric field vector in Figures 6(d)-6(e) where theelectromagnetic shielding at 5012 MHz is obviously betterthan that at 5559 MHz It is worth noting that the SET valueof Ag32 can reach the target level of 20 dB for commercialapplication at 100-520 MHz and the thickness can be asthin as 01 mm We can conclude that excellent shieldingeffectiveness with the advantage of enhanced absorptionintelligent frequency selection and thin layer makes theAgSiO2 random metamaterials highly competitive to con-ventional metals and carbon shielding materials [38 40]

3 Discussion

Porous SiO2 template was prepared via self-assemble processSilver was precisely introduced into the interstices amongSiO2 microspheres to construct AgSiO2 random metamate-rials by the impregnation-calcination process functioning asfunctional fillers The electrical conductivity results revealedthat a percolation phenomenon occurred The conductivemechanism changed from hopping conduction to Drude-type conduction owing to the formation of silver networkswith increasing silver content Negative permittivity can bewell explained by plasma-like behavior of the silver networkand Lorentz-type behavior of silver agglomeration Negativepermeability was attributed to the magnetic behavior ofinduced current loops The calculation analysis indicatesthat permeability values have a linear relation with 12059605which is different from the ldquomagnetic plasmardquo of periodicmetamaterials Electromagnetic simulations demonstratedthat negative permittivity materials and epsilon-near-zeromaterials can have potentials for electromagnetic attenuationand shielding

4 Materials and Methods

41 Materials The ammonium hydroxide (28 wt )ethanol tetraethyl orthosilicate (TEOS) polyvinyl alcohol(PVA) and silver nitrate (AgNO3) were all purchased fromthe Sinopharm Chemical Reagent Co Ltd ChinaThe chem-icals are obtained as chemically pure grade products and usedwithout any further treatment

42 The Preparation of SiO2 Microspheres The SiO2 micro-spheres were prepared by the Stober method 25 mL deion-ized water 80 mL ethanol and 20 mL ammonium hydroxidewere mixed as A solution at 40∘C 40 mL TEOS and 80 mLethanol weremixed as B solution B solution was added to the

A solution at a speed of 200 mLh Subsequently the mixturewas kept stirring for 12 h at 40∘CThe SiO2microspheres wereobtained by centrifuging the white precipitation and furthercleaned by deionized water for several times until pH=7

43 The Preparation of AgSiO2 Metacomposites 3g SiO2microspheres were dispersed in 50 mL 2 wt PVA solutionThe SiO2 disks were prepared by centrifugal sedimentationmethod using the SiO2 suspension The SiO2 disks can beobtained in the specially designed mold which placed at thebottom of the centrifuge tube and then dried at 60∘C for 24 hThe obtained SiO2 disks were sintered at 950

∘C for 30 min toprepare porous SiO2 matrix The porosity of SiO2 matrix was32 Porous SiO2 discswere soaked into theAgNO3 solutionsof 2molL and vacuumed for 10 min to ldquopressrdquo the solutioninto porous SiO2 The discs were dried at 70∘C for 3h then100∘C for 8 h Finally the discs were calcined at 450∘C for 30min to obtain AgSiO2 composites The silver mass fractionwas controlled by impregnation-calcination cycles

44 Characterization The XRD patterns were carried out bythe Rigaku DMax-RB-type X-ray diffraction target Cu (K120572diffraction line) The morphologies of the fracture surfacemorphologies were obtained by scanning electron micro-scope (SU-70 Field Emission Scanning Electron MicroscopeFESEM) equipped with energy dispersive X-ray spectroscopy(EDX) Dielectric parameters of the composites were mea-sured by Agilent E4991A Precision Impedance Analyzer with16453A dielectric test fixture from 1MHz to 1 GHz includingimpedance (Z1015840 Z10158401015840) capacitance (C) and resistance (119877p)ac conductivity (120590ac) the phase shift angle (120579) and the real(1205761015840) and imaginary (12057610158401015840) part of complex permittivity Thetest fixture of 16454A was used to measure the complexpermeability The dimension of the samples for permittivitymeasurement is 120601 20 mm times 2 mm The thickness wascontrolled by polishing the samples on abrasive papers (1200mesh) The toroidal samples were used for permeabilitymeasurement with the dimensions of 65 times20 times 2 mm Inorder to prepare the toroidal samples a small pore was madeat the center of the samples by a drill (the diameter 1mm) andthen the small pore was gradually enlarged by a conical file

Data Availability

All data needed to evaluate the conclusions in the paper arepresent in the paper andor the Supplementary MaterialsAdditional data related to this paper may be requested fromthe authors

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Peitao Xie and Zidong Zhang designed experimental proce-dures in detail Peitao Xie performed the characterization anddata analysis and wrote the paper Zhongyang Wang and Kai

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

Research 3

m

Silver particles

m

Silver agglomeration

m

Formation of silver network

m m

Enhanced silver network

m

(a) (b) (c)

(d) (e) (f)

Figure 2 SEM image of SiO2 bulk (a) and AgSiO2 composites with 17 wt (b) 28 wt (c) 32 wt (d) 35 wt (e) and 37 wt (f) silvercontent

nanoparticles will nucleate and grow during the calcinationprocess That is the silver could be introduced into thetargeted positions of the composites which provides the fea-sibility to precisely control the microstructure of compositesand adjust their electromagnetic property [19 23] Whensilver content is low silver particles are isolated and randomlydistributed in the composites with 17wt silver (Ag17) (inFigure 2(b)) With increasing silver content the interconnec-tion of silver particles is enhanced and silver agglomeration isformed (Figure 2(c))Then three-dimensional silver networkis formed in the channels among SiO2 microspheres inthe composites with 32wt silver (Ag32) (Figure 2(d)) Thenetwork is gradually enhanced with increasing silver content(Figures 2(e)-2(f)) The conduction behavior is very sensitiveto its microstructure according to percolation theory hencetheir conduction behaviors are investigated as follows [24]

22 Ac Conductivity and Percolation Figure 3 shows thevariation of alternating current (ac) conductivity (120590ac) (at10MHz) of AgSiO2 composites with different silver con-tents The 120590ac gradually increases with increasing silvercontent when silver volume fraction f lt008 but shows anabrupt increase near f=8 vol This is a typical percolationphenomenon and the percolation threshold (119891c) is near 8vol [14 24] The percolative behavior is attributed to thevariation of microstructure as discusses above when silvercontent is below 119891c the silver particles are isolated by theSiO2 matrix and pore while a continuous network couldbe formed when silver content is above 119891c In this workthe percolative threshold was relatively low compared withthe typical granular composites whose percolative thresholdis usually 16 [22] In fact the percolative threshold isinfluenced by the intrinsic property shape size surface

000 002 004 006 008 010 012Silver Volume Fraction

10 MHz

t = -0366

Insulator-likeConductor

-like

minus

minus

minus

ac

(cm

)minus

minus minus minus minus

minus

minus

minus

minus

Log

(ac

)

c=0082

ac prop (c-)

Log c -

Figure 3 The variation of 120590ac (at 10 MHz) for AgSiO2 compositeswith silver volume fraction The inset shows the calculation resultsusing percolation theory the percolation threshold is 0082 thepercolation critical exponent is t=0366

state and dimension of the fillers If the fillers are one-dimensional conductors such as carbon nanotubes carbonnanofibers and silver nanowires the percolative thresholdcan be decreased accordingly [22] After the silver wasdistributed in the interstices among the SiO2 microspheresthe silver to some extent had a one-dimensional shape inthe silverSiO2 composites Besides the distribution of silverwas restricted by the porous SiO2microspheres templateThepercolative threshold was therefore only about 8 in thesilverSiO2 composites The abrupt change of conductivitycan be expressed by classical percolation theory [22]

120590119886119888 prop 1003816100381610038161003816119891119888 minus 1198911003816100381610038161003816119905 (1)

4 Research

10M 100M 1G

5

10

15

20

25

Frequency (Hz)

Large Capacitor

Ag17SiO bulk Ag23

Ag28

(a) (b)

(c) (d)

10M 100M 1G

0

20k

40k

400M 600M 800M 1G

0

150

Frequency (Hz)

minusk

minusk

minusk

minus

minus

minus

Ag32Ag35

Ag37

100M 1G

0

10k

Frequency (Hz)

Lorentz Model

Drude Model

Drude+Lorentz Model

minus4k

minus3k

minus2k

minus1k

Experimental data of Ag35

10M 100M

Positivepermittivity

region

1G

0

20

Frequency (Hz)

Negative permittivity region

minus

minus

minus

(d

egre

e)

Ag32Ag35

Ag37

Figure 4 Frequency dispersion of real permittivity (1205761015840) for AgSiO2 composites (a b) permittivity dispersion of Ag35 with calculation results(c) Frequency dependence of phase angle 120579 for AgSiO2 composites with different silver content (d) The dashed line is the calculated curveonly by Drude model the dash-dotted line is the calculated curve only by Lorentz model and the solid line is calculated curve by both Theinset in (d) is the equivalent circuit of composites when the silver content is above percolation threshold

where f is the volume fraction of silver filler 119891c is thepercolation threshold and t is the corresponding criticalexponent The calculation results (inset of Figure 3) usingExpression (1) show good agreement with experimentaldata suggesting that percolation theory is applicable tothe AgSiO2 composites The frequency dispersion of 120590acindicates that hopping conductivity behavior below the per-colation threshold while a metal-like conduction behavioris observed above the percolation threshold (detailed in thesupporting information and Fig S3) Therefore the changeof electricalmechanismoccurs inAgSiO2 composites whichcan provide the feasibility of achieving the desirable negativepermittivity property studied in the following section

23 Permittivity and Impedance Frequency dispersions ofreal permittivity (1205761015840) are shown in Figure 4 Permittivityshows obvious dependence on silver content When silver

content is belowpercolation threshold119891c (in Figure 4(a)) 1205761015840 ispositive and increases with increasing silver content becausethe polarization across the silverSiO2 interface indicates thatany pairs of adjacent silver particles separated by an insu-lating gap can work as a microcapacitor [23] The AgSiO2composites can be regarded as a network of microcapacitors(inset of Figure 4(a)) which enables the composites to havea higher permittivity with increasing silver content Thisbehavior is also known asMaxwell-Wagner-Sillars effect [23]which is responsible for the enhancement of permittivity inheterogeneous composites It is worth noting that the SiO2bulk and composites with 17 wt and 23 wt silver contenthave potentials as novel high-permittivity materials over abroad frequency range as their 1205761015840 keeps steady in the wholetest frequency region and their dielectric loss is relativelysmall with dielectric loss tangent tan 120575 lt001 (in Fig S4b)When the silver content increases to 28 wt the 1205761015840 of thecomposites shows obvious frequency dispersion

Research 5

When silver content is above the percolation threshold119891c negative 1205761015840 is achieved and shows obvious frequencydispersion (in Figure 4(b)) The 1205761015840 is sim -5000 at 6 MHzfor composites with 32 wt silver content and graduallyincreases with increasing frequency As for the compositeswith 35 wt silver content the 1205761015840 is sim -50000 at 6 MHz andincreases with increasing frequency reaches the maximum(sim8000) at 150 MHz and then decreases with increasingfrequency As for the composites with 37 wt silver contentthe 1205761015840 is sim -10000 at 6 MHz and keeps increasing to the maxi-mum (sim21000) at 68MHz but then decreases with increasingfrequency The 1205761015840 of Ag32 equals zero at 520 MHz while at57 MHz for the composite with 35wt silver (Ag35) and 11MHz for the composite with 37wt silver (Ag37)That is theepsilon-zero-point shifts to lower frequency with increasingsilver content which provides the feasibility of adjustingepsilon-near-zero properties The AgSiO2 composites cannot only be the promising candidate for negative permit-tivity but also be the epsilon-near-zero materials at radio-frequency region [25] Generally the plasma-type negativepermittivity of metals can be expressed by the Drude model[17]

1205761015840 = 1 minus1205962119901

1205962 + Γ1198632(2)

where ΓD is the damping constant 120596p=2120587119891p is the plasmonsangular frequency Equation (2) is a monotonic increasingfunction while the experimental data are not monotonic buthave maximum (in Figure 4(b)) Because the experimentalresults cannot be perfectly explained by the Drude modelonly there must be other mechanism contributing to thedielectric behavior of the composites [24] The Drude modeldescribes the simple harmonic motion of free electrons ataltering electromagnetic field Besides the Drude model isusually used at the optical and infrared region to describethe negative permittivity The frequency is very high that isperiod time is short so the movement distance of the freeelectrons is also short As a result the plasma oscillation canbe induced even in small metal particles However whenthe frequency of external electrical filed is low even in theradio-frequency region free electrons will be localized insome small metal particles or agglomeration leading to thedeviation from the Drude model The Drude model candescribe the dielectric behavior of silver network only butis not applicable to isolated silver particles [21] Since theisolated silver particles or agglomeration can lead to Lorentz-type dielectric behavior [24] the formula is modified afterconsidering Lorentz-type dielectric resonance [24]

1205761015840 = 1 minus1205962119901

1205962 + Γ2119863+

1198701205962119871 (1205962119871 minus 1205962)(1205962119871 minus 1205962)2 + Γ21198711205962

(3)

where ΓL is the damping constant of Lorentz resonance120596L=2120587119891L is the Lorentz resonance angular frequency andK is the dc electric susceptibility As we can see fromFigure 4(c) and Table S3 the calculation results (solid linesin Figure 4(c)) of Ag35 using Expression (3) show goodagreement with experimental data with high reliability factor

R2=099589TheDrude-type calculation results (dashed linesin Figure 4(c)) indicate that negative permittivity derivesfrom the plasma-type dielectric behavior of free electronsin the silver network while the Lorentz-type calculationresults (dash-dotted lines in Figure 4(c)) indicate that thefrequency dispersion of negative permittivity can be effec-tively adjusted by Lorentz-type dielectric resonance Thesecalculation results were made via the iterative method byusing the respective model Although Lorentz-type dielec-tric resonance can generate negative permittivity in someferroelectric materials and composites containing carbonnanotubes [26 27] the Lorentz-type dielectric behaviors haveno contribution to the negative permittivity in Figure 4(b) Infact it is a relaxation-type curve rather than resonance-typecurve shown as dash-dotted lines in Figure 4(c) as the damp-ing factor is much larger than resonance frequency (shownin Table S3) a common phenomenon at low-frequencyregion in metal optics The Lorentz-type dielectric behaviorcan be attributed to the interfacial imperfection (holes andvoids) and the inhomogeneous silver distribution (isolatedagglomeration and network) formed during adding silverinto SiO2 matrix It can come into the conclusion that thesilver content plays an important role in controlling thefrequency dispersion of negative permittivity

Negative permittivity behavior is further investigated byphase angle (120579) as the positive permittivity is regarded asa capacitive character where the resistance current (119868R) lagsthe capacitive current (119868C) by 90∘ When the silver contentis above 119891c the 120579 of Ag32 is positive below 520 MHz below55 MHz for Ag35 and 102 MHz for Ag37 (in Figure 4(d))while the negative value of 120579 is above these frequency pointsIt shows that the inductive current (119868L) lags the resistivecurrent (119868R) by 90∘ which indicates that negative permittivityexhibits inductive character and the electric energy is storedin inductance [24] Therefore there were usually inductorsin the equivalent circuit of negative permittivity materialsbecause of the inductive character The equivalent circuitanalysis was performed by the ZSimpwin software Theoptimal equivalent circuit was chosen with the smallestChi-square value (usually 10minus3-10minus5) The Chi-square valuerepresents the correlation between experimental data andsimulated data In the previous study we have demonstratedthat the distribution of conductive functional fillers canadjust the frequency dispersion of negative permittivity byLC resonance [23 24] In Figure 4(d) we can see that thesilver content is crucial to the control of LC resonancebecause the value of 120579 is sensitive to the silver content Theabsolute value of 120579 is very small in negative permittivityregion indicating that negative permittivity behavior hashuge dielectric loss and potential application as lossmaterialsBesides the absolute value of 120579 increases with increasingfrequency in positive permittivity region indicating theenergy storage efficiency in capacitance is obviously higherthan that in inductance [28] Interestingly the frequencypoints of 120579=0 correspond with the epsilon-zero points Thatis there is no energy storage but energy loss at epsilon-zeropoint indicating that AgSiO2 composites can function asresistor in metaelectronics circuits at radio-frequency region[29]

6 Research

00

03

06

09

12

Negative permeability region

Frequency (Hz)200M 400M 600M 800M 1G

Fitting data using prop

minus

Ag28Ag32Ag35Ag37

Ag23Ag17

SiO

External magnetic fieldInduced magnetic field by current loop

The space between microspheres is filled with silver

Current loops

(a) (b)

(c) (d)

Pores and gaps among SiO microspheres

1

10

100

near 1 GHz

starts to be remarkableEddy current loss

Frequency (Hz)200M 400M 600M 800M 1G

Slope = 0 at ~520 MHz

Ag28Ag32

(

) (

ns)

2

Frequency (Hz)

Complicatedloss response

Eddy current loss shiftsto lower frequency

Slope = 0 at ~251 MHzand ~355 MHz

200M 400M 600M 800M 1G

Ag35Ag37

(

) (

ns)

2

Figure 5 Frequency dependence of real permeability (1205831015840) for AgSiO2 composites (a) the schematic diagram of magnetic response due tothe induced current loops in AgSiO2 composites (b) and frequency dependence of 12058310158401015840(12058310158402f ) for AgSO2 composites with different silvercontent (c d) The red solid lines in (a) are the calculation results by the relation of 1205831015840 prop radic120596 with high reliability

24 Permeability Figure 5 depicts the frequency dependenceof real permeability (1205831015840) property for AgSiO2 composites Asshown in Figure 5(a) the 1205831015840 of SiO2 bulk almost keeps 1 dueto its nonmagnetism After silver is added to SiO2 matrixthe value of 1205831015840 is smaller than 1 indicating negative sus-ceptibility The negative susceptibility is obviously enhancedwith increasing silver content and frequencyWhen the silvercontent reaches 37 wt negative permeability is achievedin the range of 760-1000 MHz Since SiO2 and silver areboth nonmagnetic the negative susceptibility and negativepermeability cannot be attributed to the magnetic resonanceof component materials It is worth noting that the previousinvestigations demonstrate that negative permeability is dif-ficult to be realized in metalceramics randommetamaterialsthat only contain nonmagnetic metal [17 18] Thereforethe generation of negative permeability indicates that the

precise control of silver is in favor of the magnetic responseof induced current which improves the response efficiencyand the possibility of realizing negative permeability Wecan get some inspiration from periodic metamaterials asnegative permeability is the unique property of periodicmetamaterials and its mechanism is derived from the law ofelectromagnetic induction [7 30] The split-ring resonatorsare the typical building blocks of magnetic response inperiodic metamaterials while the silver can work as buildingblocks of magnetic response in the AgSiO2 composites Asshown in the schematic diagram in Figure 5(b) the intersticesamong the SiO2 microspheres are filled with silver and thecurrent loops can be induced around the SiO2 microsphereswhen the composites are put under an alternating currentmagnetic field The direction of the induced magnetic fieldfrom these current loops is opposite to the external magnetic

Research 7

field which would cancel part of external magnetic field andthus leads to negative susceptibility [5] When the inducedmagnetic field is even dominant negative permeabilitywill beachieved [7 31]Moreover there are alsomany pores and gapsinside the silver network where the microcurrents (smallloops in Figure 5(b)) can also be induced to generate negativesusceptibilitypermeability

According to the mechanism of negative permeabilityin typical periodic metamaterials also known as ldquomagneticplasmardquo the permeability of classical split-ring resonators(SRRs) can be expressed as follows [31]

1205831015840119890119891119891 = 1 +1198651205962 (12059620 minus 1205962)

(12059620 minus 1205962)2 + Γ21205962(4)

where F is a geometrical factor1205960 is the resonance frequencyand Γ is the resistive damping factor The calculation datausing magnetic plasma model are shown in Fig S7 and TableS5 the low reliability factors indicate that ldquomagnetic plasmardquocannot be the mechanism here As shown in Table S5 thedamping factors Γ are larger than resonance frequency byseveral orders of magnitudes indicating a relaxation-typeresponse in the view of ldquomagnetic plasmardquo [14 15 18] Therelaxation-type behavior results in the huge deviation fromldquomagnetic plasmardquo primarily because of the great differencein shape and dimension between SRRs (typical ldquomagneticplasmardquo structure) and silver network (building blocks inthis work) The capacitance from the split in SRRs leads to aresonance-type magnetic response while no split structuresare available in the silver network In addition it is well-known that the reported periodic metamaterials have 120582lvalue between 2 and 12 where 120582 is the wavelength and l isthe size of the building block while it is not applicable tothis work [31] Moreover the relaxation-type response canbe partly due to the small size of the silver network sincethe damping factor is inversely proportional to the size ofbuilding blocks [32]

The ldquomagnetic plasmardquo cannot explain the negative per-meabilitysusceptibility but the magnetic response can onlyresult from the electromagnetic induction in the nonmag-netic composites According to the Faradayrsquos law the inducedcurrent density can be expressed as follows [33]

119895119894 = 120590119894119890119894 = minus120590119894119889Φ119894119889119905 = minus120596120590119894119860 cos (120596119905) (5)

where 119895119894 is the localized current density 120590119894 is the ac conduc-tivity of local area 119890119894 is the localized electric field intensityΦ119894is the magnetic flux t is the time and A is the amplitude of119890119894 According to Biot-Savart law the induced current loopscan generate an induced magnetic field whose direction isalways opposite to the external magnetic field The magneticresponse 119861119894 at the axes of circulating current 119895119894d119878119894 can becalculated by the formula [33]

119861119894 =12058301199032119895119894119889119878119894

2120587 (1199032 + 1199092)32(6)

where 119861119894 is the magnetic induction intensity r is the radiusof circulating current d119878119894 is the sectional area of circulating

current and x is the distance to the center of circulatingcurrent When the induced currents cannot keep up with theexternal field at very high frequency the induced currentswould lag and thus lead to an out-of-phase or negativeresponse The linear relationship between 1205831015840 119861119894 j and 120596 canbe obtained 1205831015840 prop 119861119894 prop 119873119895 prop 120596 where N is the windingnumber Fig S8 and Table S6 show the calculation resultsusing linear relationship The reliability factors (about 0975)is fine but still cannot satisfy our expectation Thereforeother factors should also be considered In fact the 120590119894 inExpression (5) should not be dc conductivity but ac con-ductivity Ac conductivity is also the function of frequencyusually explained by skin depth 120575 = (21205830120590119889119888120596)05 [18] Therelationship between 119861119894 j and 120596 can be modified [16]

119861119894 prop 119873119895 prop radic120596

1205831015840 = 119886 + 119887radic120596(7)

where a and b are parameters about the intrinsic propertyof AgSiO2 composites The calculation results using (7) areshown as red solid lines in Figures 5(a) and S9 and theused parameters are in Table S7The calculation results agreewell with experimental data (1198772 asymp 09975) indicating thatthe mechanism of negative susceptibilitypermeability canbe well explained [16] The physical meaning of a is theinitial permeability and its value should be 1 for AgSiO2composites in good agreement with the calculation results(in Table S7) The parameter b is an intrinsic parameterwhich is closely related to the composition microstructureand electromagnetic property of composites [34 35]

Themagnetic loss was also studied to reveal the influenceof eddy current on negative susceptibilitypermeability Theimaginary permeability (12058310158401015840) spectra for AgSiO2 compositesare shown in detail in supporting information and Fig S10aMagnetic loss mainly originates from hysteresis loss eddycurrent effect and natural resonance at the radio-frequencyregion The hysteresis loss is negligible in the weak fieldNatural resonance can also be excluded due to nonmagnetismof AgSiO2 compositesTherefore the eddy current loss is theonly source of magnetic loss and the eddy current loss can beexpressed by [36]

12058310158401015840 =21205871205830 (1205831015840

2) 12059011988911988811986321198913

(8)

where D is the effective diameter of metal particles If themagnetic loss simply derives from the eddy current lossthe value of 12058310158401015840(12058310158402f ) should be nearly constant withoutchanging with frequency Figures 5(c)-5(d) and S10 show thefrequency dispersion of 12058310158401015840(12058310158402f ) When the silver content isbelow 119891c 12058310158401015840(1205831015840

2f ) value obviously decreases with frequency(in Fig S10) there is an evidence of no eddy current lossavailable because the size of the silver particles is very tiny andeven smaller than the skin depth When the silver content isnear 119891c (ie Ag28 and Ag32) the value of 12058310158401015840(12058310158402f ) at thelower frequency region also decreases with increasing fre-quency (in Figure 5(c)) Interestingly the slope of Ag32 curve

8 Research

200M 400M 600M 800M 1GFrequency (Hz)

0102030

6070 0

4050(d

B)EM

I SE T

- +asymp

01 mm025 mm05 mm1 mm

Target LevelCommercial

200M

0

400M 600M 800M 1GFrequency (Hz)

05

1015202530

(dB)

EMI S

E R

- +asymp

01 mm025 mm05 mm1 mm

200M 400M 600M

0

800M 1GFrequency (Hz)

(a) (b) (c)

(d) (e)

30

20

10

40

50

0

(dB)

EMI S

E A

- +asymp

01 mm025 mm05 mm1 mm

5012 MHz

2

19617816014212510789

712534356178

0

Z XY

5559 MHz

The EM shieldingproperty at 5012MHz is obviouslybetter than thatat 5559 MHz

Figure 6 Frequency dispersion of EMI SET (a) SER (b) and SEA (c) for Ag32 metacomposites with different thickness The distribution ofelectric field vector of Ag32 composites at 5012 MHz (d) and 5559 MHz (e) with 025 mm thickness

is zero at sim520MHz and at sim1GHz for Ag28 where 12058310158401015840(12058310158402f )keeps constant indicating that the eddy current loss graduallybecomes dominant in magnetic loss [36] Further increasingsilver content the slope of Ag35 curve is zero at sim355 MHzand at sim 251 MHz for Ag37 (in Figure 5(d)) suggesting thatthe eddy current loss shifts to low-frequency region with theenhanced silver network In fact eddy current loss has a closerelationshipwith the frequency of the externalmagnetic fieldgeometrical configuration and the electrical conductivity ofthe metal The faster the magnetic field changes the strongerthe eddy current loss can cause In this work the frequencyshift of eddy current loss could not be attributed to theelectrical conductivity of the metal as the eddy current lossof all the composites came from the silver network The onlyinfluence factor was the geometrical configuration of thesilver network From the SEM results (in Figure 2) it can beobserved that the silver networkwas obviously enhancedwithincreasing silver contentThat is the thicker silverwires couldbe formed in the silver networkThe electrical conductivity ofthe whole silver network could be enhanced with increasingsilver content and thus the remarkable eddy current losscould be caused at lower frequency region It is worth notingthat 12058310158401015840(12058310158402f ) increases with increasing frequency at higherfrequency region (in Figure 5(d)) In addition there is a losspeak for Ag37 curve at 760 MHz and it also seems to bea peak for Ag35 at higher frequency region (above 1 GHz)These can be attributed to the complicated relaxation-typebehavior from the phase lag of induced eddy current [31] It is

concluded that the eddy current effect is the main reason fornegative susceptibilitypermeability

25 Electromagnetic Simulation and Shielding EffectivenessNegative permittivity and permeability were simultaneouslyachieved in the AgSiO2 composites In order to deter-mine the interaction between electromagnetic wave and thematerials the electromagnetic propagation properties weresimulated using Computer Simulation Technology softwareThe simulationmethod is detailed in supporting informationand Fig S11The shielding effectiveness (SE) is the main eval-uation criterion of suppressing electromagnetic interference(EMI) The SE total (SET) includes SE absorption (SEA) andSE reflection (SER) [37]

The simulated SE results of Ag32 were shown in Figure 6The SET value increased with increasing frequency at 100-520 MHz then the SET value dramatically dropped and kepta small value at 520-1000 MHz Intriguingly the frequencyregion with large SET value corresponds well with that ofnegative permittivity while low SET corresponds well withpositive permittivity region (in Figure 4(b)) Similar resultswere also observed for Ag35 and Ag37 in Fig S12-S13 whichis because the formation of the silver network could leadto high SE value and excellent electromagnetic shieldingproperty [38] The SER value almost kept constant (225-275) at 100-520 MHz (in Figure 6(b)) and is independenton the thickness of composites because the thickness ofsilver network is thicker than the skin depth of metal silver

Research 9

(0064 mm at 100 MHz) In contrast the SEA value obviouslyincreased with higher frequency and thicker slab at 100-520 MHz (in Figure 6(c)) a peak value near 520 MHz Theenhanced SEA value had a close relationship with the epsilon-near-zero property of Ag32 composites because of goodimpedance matching and absorption loss Similar enhancedabsorption phenomenon was also observed in indium tinoxide at infrared band [39] Therefore the epsilon-near-zero property is like an ldquoon-off switchrdquo of electromagneticshielding providing the possibility of intelligent frequencyselection It is further demonstrated by the distributionof the electric field vector in Figures 6(d)-6(e) where theelectromagnetic shielding at 5012 MHz is obviously betterthan that at 5559 MHz It is worth noting that the SET valueof Ag32 can reach the target level of 20 dB for commercialapplication at 100-520 MHz and the thickness can be asthin as 01 mm We can conclude that excellent shieldingeffectiveness with the advantage of enhanced absorptionintelligent frequency selection and thin layer makes theAgSiO2 random metamaterials highly competitive to con-ventional metals and carbon shielding materials [38 40]

3 Discussion

Porous SiO2 template was prepared via self-assemble processSilver was precisely introduced into the interstices amongSiO2 microspheres to construct AgSiO2 random metamate-rials by the impregnation-calcination process functioning asfunctional fillers The electrical conductivity results revealedthat a percolation phenomenon occurred The conductivemechanism changed from hopping conduction to Drude-type conduction owing to the formation of silver networkswith increasing silver content Negative permittivity can bewell explained by plasma-like behavior of the silver networkand Lorentz-type behavior of silver agglomeration Negativepermeability was attributed to the magnetic behavior ofinduced current loops The calculation analysis indicatesthat permeability values have a linear relation with 12059605which is different from the ldquomagnetic plasmardquo of periodicmetamaterials Electromagnetic simulations demonstratedthat negative permittivity materials and epsilon-near-zeromaterials can have potentials for electromagnetic attenuationand shielding

4 Materials and Methods

41 Materials The ammonium hydroxide (28 wt )ethanol tetraethyl orthosilicate (TEOS) polyvinyl alcohol(PVA) and silver nitrate (AgNO3) were all purchased fromthe Sinopharm Chemical Reagent Co Ltd ChinaThe chem-icals are obtained as chemically pure grade products and usedwithout any further treatment

42 The Preparation of SiO2 Microspheres The SiO2 micro-spheres were prepared by the Stober method 25 mL deion-ized water 80 mL ethanol and 20 mL ammonium hydroxidewere mixed as A solution at 40∘C 40 mL TEOS and 80 mLethanol weremixed as B solution B solution was added to the

A solution at a speed of 200 mLh Subsequently the mixturewas kept stirring for 12 h at 40∘CThe SiO2microspheres wereobtained by centrifuging the white precipitation and furthercleaned by deionized water for several times until pH=7

43 The Preparation of AgSiO2 Metacomposites 3g SiO2microspheres were dispersed in 50 mL 2 wt PVA solutionThe SiO2 disks were prepared by centrifugal sedimentationmethod using the SiO2 suspension The SiO2 disks can beobtained in the specially designed mold which placed at thebottom of the centrifuge tube and then dried at 60∘C for 24 hThe obtained SiO2 disks were sintered at 950

∘C for 30 min toprepare porous SiO2 matrix The porosity of SiO2 matrix was32 Porous SiO2 discswere soaked into theAgNO3 solutionsof 2molL and vacuumed for 10 min to ldquopressrdquo the solutioninto porous SiO2 The discs were dried at 70∘C for 3h then100∘C for 8 h Finally the discs were calcined at 450∘C for 30min to obtain AgSiO2 composites The silver mass fractionwas controlled by impregnation-calcination cycles

44 Characterization The XRD patterns were carried out bythe Rigaku DMax-RB-type X-ray diffraction target Cu (K120572diffraction line) The morphologies of the fracture surfacemorphologies were obtained by scanning electron micro-scope (SU-70 Field Emission Scanning Electron MicroscopeFESEM) equipped with energy dispersive X-ray spectroscopy(EDX) Dielectric parameters of the composites were mea-sured by Agilent E4991A Precision Impedance Analyzer with16453A dielectric test fixture from 1MHz to 1 GHz includingimpedance (Z1015840 Z10158401015840) capacitance (C) and resistance (119877p)ac conductivity (120590ac) the phase shift angle (120579) and the real(1205761015840) and imaginary (12057610158401015840) part of complex permittivity Thetest fixture of 16454A was used to measure the complexpermeability The dimension of the samples for permittivitymeasurement is 120601 20 mm times 2 mm The thickness wascontrolled by polishing the samples on abrasive papers (1200mesh) The toroidal samples were used for permeabilitymeasurement with the dimensions of 65 times20 times 2 mm Inorder to prepare the toroidal samples a small pore was madeat the center of the samples by a drill (the diameter 1mm) andthen the small pore was gradually enlarged by a conical file

Data Availability

All data needed to evaluate the conclusions in the paper arepresent in the paper andor the Supplementary MaterialsAdditional data related to this paper may be requested fromthe authors

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Peitao Xie and Zidong Zhang designed experimental proce-dures in detail Peitao Xie performed the characterization anddata analysis and wrote the paper Zhongyang Wang and Kai

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

4 Research

10M 100M 1G

5

10

15

20

25

Frequency (Hz)

Large Capacitor

Ag17SiO bulk Ag23

Ag28

(a) (b)

(c) (d)

10M 100M 1G

0

20k

40k

400M 600M 800M 1G

0

150

Frequency (Hz)

minusk

minusk

minusk

minus

minus

minus

Ag32Ag35

Ag37

100M 1G

0

10k

Frequency (Hz)

Lorentz Model

Drude Model

Drude+Lorentz Model

minus4k

minus3k

minus2k

minus1k

Experimental data of Ag35

10M 100M

Positivepermittivity

region

1G

0

20

Frequency (Hz)

Negative permittivity region

minus

minus

minus

(d

egre

e)

Ag32Ag35

Ag37

Figure 4 Frequency dispersion of real permittivity (1205761015840) for AgSiO2 composites (a b) permittivity dispersion of Ag35 with calculation results(c) Frequency dependence of phase angle 120579 for AgSiO2 composites with different silver content (d) The dashed line is the calculated curveonly by Drude model the dash-dotted line is the calculated curve only by Lorentz model and the solid line is calculated curve by both Theinset in (d) is the equivalent circuit of composites when the silver content is above percolation threshold

where f is the volume fraction of silver filler 119891c is thepercolation threshold and t is the corresponding criticalexponent The calculation results (inset of Figure 3) usingExpression (1) show good agreement with experimentaldata suggesting that percolation theory is applicable tothe AgSiO2 composites The frequency dispersion of 120590acindicates that hopping conductivity behavior below the per-colation threshold while a metal-like conduction behavioris observed above the percolation threshold (detailed in thesupporting information and Fig S3) Therefore the changeof electricalmechanismoccurs inAgSiO2 composites whichcan provide the feasibility of achieving the desirable negativepermittivity property studied in the following section

23 Permittivity and Impedance Frequency dispersions ofreal permittivity (1205761015840) are shown in Figure 4 Permittivityshows obvious dependence on silver content When silver

content is belowpercolation threshold119891c (in Figure 4(a)) 1205761015840 ispositive and increases with increasing silver content becausethe polarization across the silverSiO2 interface indicates thatany pairs of adjacent silver particles separated by an insu-lating gap can work as a microcapacitor [23] The AgSiO2composites can be regarded as a network of microcapacitors(inset of Figure 4(a)) which enables the composites to havea higher permittivity with increasing silver content Thisbehavior is also known asMaxwell-Wagner-Sillars effect [23]which is responsible for the enhancement of permittivity inheterogeneous composites It is worth noting that the SiO2bulk and composites with 17 wt and 23 wt silver contenthave potentials as novel high-permittivity materials over abroad frequency range as their 1205761015840 keeps steady in the wholetest frequency region and their dielectric loss is relativelysmall with dielectric loss tangent tan 120575 lt001 (in Fig S4b)When the silver content increases to 28 wt the 1205761015840 of thecomposites shows obvious frequency dispersion

Research 5

When silver content is above the percolation threshold119891c negative 1205761015840 is achieved and shows obvious frequencydispersion (in Figure 4(b)) The 1205761015840 is sim -5000 at 6 MHzfor composites with 32 wt silver content and graduallyincreases with increasing frequency As for the compositeswith 35 wt silver content the 1205761015840 is sim -50000 at 6 MHz andincreases with increasing frequency reaches the maximum(sim8000) at 150 MHz and then decreases with increasingfrequency As for the composites with 37 wt silver contentthe 1205761015840 is sim -10000 at 6 MHz and keeps increasing to the maxi-mum (sim21000) at 68MHz but then decreases with increasingfrequency The 1205761015840 of Ag32 equals zero at 520 MHz while at57 MHz for the composite with 35wt silver (Ag35) and 11MHz for the composite with 37wt silver (Ag37)That is theepsilon-zero-point shifts to lower frequency with increasingsilver content which provides the feasibility of adjustingepsilon-near-zero properties The AgSiO2 composites cannot only be the promising candidate for negative permit-tivity but also be the epsilon-near-zero materials at radio-frequency region [25] Generally the plasma-type negativepermittivity of metals can be expressed by the Drude model[17]

1205761015840 = 1 minus1205962119901

1205962 + Γ1198632(2)

where ΓD is the damping constant 120596p=2120587119891p is the plasmonsangular frequency Equation (2) is a monotonic increasingfunction while the experimental data are not monotonic buthave maximum (in Figure 4(b)) Because the experimentalresults cannot be perfectly explained by the Drude modelonly there must be other mechanism contributing to thedielectric behavior of the composites [24] The Drude modeldescribes the simple harmonic motion of free electrons ataltering electromagnetic field Besides the Drude model isusually used at the optical and infrared region to describethe negative permittivity The frequency is very high that isperiod time is short so the movement distance of the freeelectrons is also short As a result the plasma oscillation canbe induced even in small metal particles However whenthe frequency of external electrical filed is low even in theradio-frequency region free electrons will be localized insome small metal particles or agglomeration leading to thedeviation from the Drude model The Drude model candescribe the dielectric behavior of silver network only butis not applicable to isolated silver particles [21] Since theisolated silver particles or agglomeration can lead to Lorentz-type dielectric behavior [24] the formula is modified afterconsidering Lorentz-type dielectric resonance [24]

1205761015840 = 1 minus1205962119901

1205962 + Γ2119863+

1198701205962119871 (1205962119871 minus 1205962)(1205962119871 minus 1205962)2 + Γ21198711205962

(3)

where ΓL is the damping constant of Lorentz resonance120596L=2120587119891L is the Lorentz resonance angular frequency andK is the dc electric susceptibility As we can see fromFigure 4(c) and Table S3 the calculation results (solid linesin Figure 4(c)) of Ag35 using Expression (3) show goodagreement with experimental data with high reliability factor

R2=099589TheDrude-type calculation results (dashed linesin Figure 4(c)) indicate that negative permittivity derivesfrom the plasma-type dielectric behavior of free electronsin the silver network while the Lorentz-type calculationresults (dash-dotted lines in Figure 4(c)) indicate that thefrequency dispersion of negative permittivity can be effec-tively adjusted by Lorentz-type dielectric resonance Thesecalculation results were made via the iterative method byusing the respective model Although Lorentz-type dielec-tric resonance can generate negative permittivity in someferroelectric materials and composites containing carbonnanotubes [26 27] the Lorentz-type dielectric behaviors haveno contribution to the negative permittivity in Figure 4(b) Infact it is a relaxation-type curve rather than resonance-typecurve shown as dash-dotted lines in Figure 4(c) as the damp-ing factor is much larger than resonance frequency (shownin Table S3) a common phenomenon at low-frequencyregion in metal optics The Lorentz-type dielectric behaviorcan be attributed to the interfacial imperfection (holes andvoids) and the inhomogeneous silver distribution (isolatedagglomeration and network) formed during adding silverinto SiO2 matrix It can come into the conclusion that thesilver content plays an important role in controlling thefrequency dispersion of negative permittivity

Negative permittivity behavior is further investigated byphase angle (120579) as the positive permittivity is regarded asa capacitive character where the resistance current (119868R) lagsthe capacitive current (119868C) by 90∘ When the silver contentis above 119891c the 120579 of Ag32 is positive below 520 MHz below55 MHz for Ag35 and 102 MHz for Ag37 (in Figure 4(d))while the negative value of 120579 is above these frequency pointsIt shows that the inductive current (119868L) lags the resistivecurrent (119868R) by 90∘ which indicates that negative permittivityexhibits inductive character and the electric energy is storedin inductance [24] Therefore there were usually inductorsin the equivalent circuit of negative permittivity materialsbecause of the inductive character The equivalent circuitanalysis was performed by the ZSimpwin software Theoptimal equivalent circuit was chosen with the smallestChi-square value (usually 10minus3-10minus5) The Chi-square valuerepresents the correlation between experimental data andsimulated data In the previous study we have demonstratedthat the distribution of conductive functional fillers canadjust the frequency dispersion of negative permittivity byLC resonance [23 24] In Figure 4(d) we can see that thesilver content is crucial to the control of LC resonancebecause the value of 120579 is sensitive to the silver content Theabsolute value of 120579 is very small in negative permittivityregion indicating that negative permittivity behavior hashuge dielectric loss and potential application as lossmaterialsBesides the absolute value of 120579 increases with increasingfrequency in positive permittivity region indicating theenergy storage efficiency in capacitance is obviously higherthan that in inductance [28] Interestingly the frequencypoints of 120579=0 correspond with the epsilon-zero points Thatis there is no energy storage but energy loss at epsilon-zeropoint indicating that AgSiO2 composites can function asresistor in metaelectronics circuits at radio-frequency region[29]

6 Research

00

03

06

09

12

Negative permeability region

Frequency (Hz)200M 400M 600M 800M 1G

Fitting data using prop

minus

Ag28Ag32Ag35Ag37

Ag23Ag17

SiO

External magnetic fieldInduced magnetic field by current loop

The space between microspheres is filled with silver

Current loops

(a) (b)

(c) (d)

Pores and gaps among SiO microspheres

1

10

100

near 1 GHz

starts to be remarkableEddy current loss

Frequency (Hz)200M 400M 600M 800M 1G

Slope = 0 at ~520 MHz

Ag28Ag32

(

) (

ns)

2

Frequency (Hz)

Complicatedloss response

Eddy current loss shiftsto lower frequency

Slope = 0 at ~251 MHzand ~355 MHz

200M 400M 600M 800M 1G

Ag35Ag37

(

) (

ns)

2

Figure 5 Frequency dependence of real permeability (1205831015840) for AgSiO2 composites (a) the schematic diagram of magnetic response due tothe induced current loops in AgSiO2 composites (b) and frequency dependence of 12058310158401015840(12058310158402f ) for AgSO2 composites with different silvercontent (c d) The red solid lines in (a) are the calculation results by the relation of 1205831015840 prop radic120596 with high reliability

24 Permeability Figure 5 depicts the frequency dependenceof real permeability (1205831015840) property for AgSiO2 composites Asshown in Figure 5(a) the 1205831015840 of SiO2 bulk almost keeps 1 dueto its nonmagnetism After silver is added to SiO2 matrixthe value of 1205831015840 is smaller than 1 indicating negative sus-ceptibility The negative susceptibility is obviously enhancedwith increasing silver content and frequencyWhen the silvercontent reaches 37 wt negative permeability is achievedin the range of 760-1000 MHz Since SiO2 and silver areboth nonmagnetic the negative susceptibility and negativepermeability cannot be attributed to the magnetic resonanceof component materials It is worth noting that the previousinvestigations demonstrate that negative permeability is dif-ficult to be realized in metalceramics randommetamaterialsthat only contain nonmagnetic metal [17 18] Thereforethe generation of negative permeability indicates that the

precise control of silver is in favor of the magnetic responseof induced current which improves the response efficiencyand the possibility of realizing negative permeability Wecan get some inspiration from periodic metamaterials asnegative permeability is the unique property of periodicmetamaterials and its mechanism is derived from the law ofelectromagnetic induction [7 30] The split-ring resonatorsare the typical building blocks of magnetic response inperiodic metamaterials while the silver can work as buildingblocks of magnetic response in the AgSiO2 composites Asshown in the schematic diagram in Figure 5(b) the intersticesamong the SiO2 microspheres are filled with silver and thecurrent loops can be induced around the SiO2 microsphereswhen the composites are put under an alternating currentmagnetic field The direction of the induced magnetic fieldfrom these current loops is opposite to the external magnetic

Research 7

field which would cancel part of external magnetic field andthus leads to negative susceptibility [5] When the inducedmagnetic field is even dominant negative permeabilitywill beachieved [7 31]Moreover there are alsomany pores and gapsinside the silver network where the microcurrents (smallloops in Figure 5(b)) can also be induced to generate negativesusceptibilitypermeability

According to the mechanism of negative permeabilityin typical periodic metamaterials also known as ldquomagneticplasmardquo the permeability of classical split-ring resonators(SRRs) can be expressed as follows [31]

1205831015840119890119891119891 = 1 +1198651205962 (12059620 minus 1205962)

(12059620 minus 1205962)2 + Γ21205962(4)

where F is a geometrical factor1205960 is the resonance frequencyand Γ is the resistive damping factor The calculation datausing magnetic plasma model are shown in Fig S7 and TableS5 the low reliability factors indicate that ldquomagnetic plasmardquocannot be the mechanism here As shown in Table S5 thedamping factors Γ are larger than resonance frequency byseveral orders of magnitudes indicating a relaxation-typeresponse in the view of ldquomagnetic plasmardquo [14 15 18] Therelaxation-type behavior results in the huge deviation fromldquomagnetic plasmardquo primarily because of the great differencein shape and dimension between SRRs (typical ldquomagneticplasmardquo structure) and silver network (building blocks inthis work) The capacitance from the split in SRRs leads to aresonance-type magnetic response while no split structuresare available in the silver network In addition it is well-known that the reported periodic metamaterials have 120582lvalue between 2 and 12 where 120582 is the wavelength and l isthe size of the building block while it is not applicable tothis work [31] Moreover the relaxation-type response canbe partly due to the small size of the silver network sincethe damping factor is inversely proportional to the size ofbuilding blocks [32]

The ldquomagnetic plasmardquo cannot explain the negative per-meabilitysusceptibility but the magnetic response can onlyresult from the electromagnetic induction in the nonmag-netic composites According to the Faradayrsquos law the inducedcurrent density can be expressed as follows [33]

119895119894 = 120590119894119890119894 = minus120590119894119889Φ119894119889119905 = minus120596120590119894119860 cos (120596119905) (5)

where 119895119894 is the localized current density 120590119894 is the ac conduc-tivity of local area 119890119894 is the localized electric field intensityΦ119894is the magnetic flux t is the time and A is the amplitude of119890119894 According to Biot-Savart law the induced current loopscan generate an induced magnetic field whose direction isalways opposite to the external magnetic field The magneticresponse 119861119894 at the axes of circulating current 119895119894d119878119894 can becalculated by the formula [33]

119861119894 =12058301199032119895119894119889119878119894

2120587 (1199032 + 1199092)32(6)

where 119861119894 is the magnetic induction intensity r is the radiusof circulating current d119878119894 is the sectional area of circulating

current and x is the distance to the center of circulatingcurrent When the induced currents cannot keep up with theexternal field at very high frequency the induced currentswould lag and thus lead to an out-of-phase or negativeresponse The linear relationship between 1205831015840 119861119894 j and 120596 canbe obtained 1205831015840 prop 119861119894 prop 119873119895 prop 120596 where N is the windingnumber Fig S8 and Table S6 show the calculation resultsusing linear relationship The reliability factors (about 0975)is fine but still cannot satisfy our expectation Thereforeother factors should also be considered In fact the 120590119894 inExpression (5) should not be dc conductivity but ac con-ductivity Ac conductivity is also the function of frequencyusually explained by skin depth 120575 = (21205830120590119889119888120596)05 [18] Therelationship between 119861119894 j and 120596 can be modified [16]

119861119894 prop 119873119895 prop radic120596

1205831015840 = 119886 + 119887radic120596(7)

where a and b are parameters about the intrinsic propertyof AgSiO2 composites The calculation results using (7) areshown as red solid lines in Figures 5(a) and S9 and theused parameters are in Table S7The calculation results agreewell with experimental data (1198772 asymp 09975) indicating thatthe mechanism of negative susceptibilitypermeability canbe well explained [16] The physical meaning of a is theinitial permeability and its value should be 1 for AgSiO2composites in good agreement with the calculation results(in Table S7) The parameter b is an intrinsic parameterwhich is closely related to the composition microstructureand electromagnetic property of composites [34 35]

Themagnetic loss was also studied to reveal the influenceof eddy current on negative susceptibilitypermeability Theimaginary permeability (12058310158401015840) spectra for AgSiO2 compositesare shown in detail in supporting information and Fig S10aMagnetic loss mainly originates from hysteresis loss eddycurrent effect and natural resonance at the radio-frequencyregion The hysteresis loss is negligible in the weak fieldNatural resonance can also be excluded due to nonmagnetismof AgSiO2 compositesTherefore the eddy current loss is theonly source of magnetic loss and the eddy current loss can beexpressed by [36]

12058310158401015840 =21205871205830 (1205831015840

2) 12059011988911988811986321198913

(8)

where D is the effective diameter of metal particles If themagnetic loss simply derives from the eddy current lossthe value of 12058310158401015840(12058310158402f ) should be nearly constant withoutchanging with frequency Figures 5(c)-5(d) and S10 show thefrequency dispersion of 12058310158401015840(12058310158402f ) When the silver content isbelow 119891c 12058310158401015840(1205831015840

2f ) value obviously decreases with frequency(in Fig S10) there is an evidence of no eddy current lossavailable because the size of the silver particles is very tiny andeven smaller than the skin depth When the silver content isnear 119891c (ie Ag28 and Ag32) the value of 12058310158401015840(12058310158402f ) at thelower frequency region also decreases with increasing fre-quency (in Figure 5(c)) Interestingly the slope of Ag32 curve

8 Research

200M 400M 600M 800M 1GFrequency (Hz)

0102030

6070 0

4050(d

B)EM

I SE T

- +asymp

01 mm025 mm05 mm1 mm

Target LevelCommercial

200M

0

400M 600M 800M 1GFrequency (Hz)

05

1015202530

(dB)

EMI S

E R

- +asymp

01 mm025 mm05 mm1 mm

200M 400M 600M

0

800M 1GFrequency (Hz)

(a) (b) (c)

(d) (e)

30

20

10

40

50

0

(dB)

EMI S

E A

- +asymp

01 mm025 mm05 mm1 mm

5012 MHz

2

19617816014212510789

712534356178

0

Z XY

5559 MHz

The EM shieldingproperty at 5012MHz is obviouslybetter than thatat 5559 MHz

Figure 6 Frequency dispersion of EMI SET (a) SER (b) and SEA (c) for Ag32 metacomposites with different thickness The distribution ofelectric field vector of Ag32 composites at 5012 MHz (d) and 5559 MHz (e) with 025 mm thickness

is zero at sim520MHz and at sim1GHz for Ag28 where 12058310158401015840(12058310158402f )keeps constant indicating that the eddy current loss graduallybecomes dominant in magnetic loss [36] Further increasingsilver content the slope of Ag35 curve is zero at sim355 MHzand at sim 251 MHz for Ag37 (in Figure 5(d)) suggesting thatthe eddy current loss shifts to low-frequency region with theenhanced silver network In fact eddy current loss has a closerelationshipwith the frequency of the externalmagnetic fieldgeometrical configuration and the electrical conductivity ofthe metal The faster the magnetic field changes the strongerthe eddy current loss can cause In this work the frequencyshift of eddy current loss could not be attributed to theelectrical conductivity of the metal as the eddy current lossof all the composites came from the silver network The onlyinfluence factor was the geometrical configuration of thesilver network From the SEM results (in Figure 2) it can beobserved that the silver networkwas obviously enhancedwithincreasing silver contentThat is the thicker silverwires couldbe formed in the silver networkThe electrical conductivity ofthe whole silver network could be enhanced with increasingsilver content and thus the remarkable eddy current losscould be caused at lower frequency region It is worth notingthat 12058310158401015840(12058310158402f ) increases with increasing frequency at higherfrequency region (in Figure 5(d)) In addition there is a losspeak for Ag37 curve at 760 MHz and it also seems to bea peak for Ag35 at higher frequency region (above 1 GHz)These can be attributed to the complicated relaxation-typebehavior from the phase lag of induced eddy current [31] It is

concluded that the eddy current effect is the main reason fornegative susceptibilitypermeability

25 Electromagnetic Simulation and Shielding EffectivenessNegative permittivity and permeability were simultaneouslyachieved in the AgSiO2 composites In order to deter-mine the interaction between electromagnetic wave and thematerials the electromagnetic propagation properties weresimulated using Computer Simulation Technology softwareThe simulationmethod is detailed in supporting informationand Fig S11The shielding effectiveness (SE) is the main eval-uation criterion of suppressing electromagnetic interference(EMI) The SE total (SET) includes SE absorption (SEA) andSE reflection (SER) [37]

The simulated SE results of Ag32 were shown in Figure 6The SET value increased with increasing frequency at 100-520 MHz then the SET value dramatically dropped and kepta small value at 520-1000 MHz Intriguingly the frequencyregion with large SET value corresponds well with that ofnegative permittivity while low SET corresponds well withpositive permittivity region (in Figure 4(b)) Similar resultswere also observed for Ag35 and Ag37 in Fig S12-S13 whichis because the formation of the silver network could leadto high SE value and excellent electromagnetic shieldingproperty [38] The SER value almost kept constant (225-275) at 100-520 MHz (in Figure 6(b)) and is independenton the thickness of composites because the thickness ofsilver network is thicker than the skin depth of metal silver

Research 9

(0064 mm at 100 MHz) In contrast the SEA value obviouslyincreased with higher frequency and thicker slab at 100-520 MHz (in Figure 6(c)) a peak value near 520 MHz Theenhanced SEA value had a close relationship with the epsilon-near-zero property of Ag32 composites because of goodimpedance matching and absorption loss Similar enhancedabsorption phenomenon was also observed in indium tinoxide at infrared band [39] Therefore the epsilon-near-zero property is like an ldquoon-off switchrdquo of electromagneticshielding providing the possibility of intelligent frequencyselection It is further demonstrated by the distributionof the electric field vector in Figures 6(d)-6(e) where theelectromagnetic shielding at 5012 MHz is obviously betterthan that at 5559 MHz It is worth noting that the SET valueof Ag32 can reach the target level of 20 dB for commercialapplication at 100-520 MHz and the thickness can be asthin as 01 mm We can conclude that excellent shieldingeffectiveness with the advantage of enhanced absorptionintelligent frequency selection and thin layer makes theAgSiO2 random metamaterials highly competitive to con-ventional metals and carbon shielding materials [38 40]

3 Discussion

Porous SiO2 template was prepared via self-assemble processSilver was precisely introduced into the interstices amongSiO2 microspheres to construct AgSiO2 random metamate-rials by the impregnation-calcination process functioning asfunctional fillers The electrical conductivity results revealedthat a percolation phenomenon occurred The conductivemechanism changed from hopping conduction to Drude-type conduction owing to the formation of silver networkswith increasing silver content Negative permittivity can bewell explained by plasma-like behavior of the silver networkand Lorentz-type behavior of silver agglomeration Negativepermeability was attributed to the magnetic behavior ofinduced current loops The calculation analysis indicatesthat permeability values have a linear relation with 12059605which is different from the ldquomagnetic plasmardquo of periodicmetamaterials Electromagnetic simulations demonstratedthat negative permittivity materials and epsilon-near-zeromaterials can have potentials for electromagnetic attenuationand shielding

4 Materials and Methods

41 Materials The ammonium hydroxide (28 wt )ethanol tetraethyl orthosilicate (TEOS) polyvinyl alcohol(PVA) and silver nitrate (AgNO3) were all purchased fromthe Sinopharm Chemical Reagent Co Ltd ChinaThe chem-icals are obtained as chemically pure grade products and usedwithout any further treatment

42 The Preparation of SiO2 Microspheres The SiO2 micro-spheres were prepared by the Stober method 25 mL deion-ized water 80 mL ethanol and 20 mL ammonium hydroxidewere mixed as A solution at 40∘C 40 mL TEOS and 80 mLethanol weremixed as B solution B solution was added to the

A solution at a speed of 200 mLh Subsequently the mixturewas kept stirring for 12 h at 40∘CThe SiO2microspheres wereobtained by centrifuging the white precipitation and furthercleaned by deionized water for several times until pH=7

43 The Preparation of AgSiO2 Metacomposites 3g SiO2microspheres were dispersed in 50 mL 2 wt PVA solutionThe SiO2 disks were prepared by centrifugal sedimentationmethod using the SiO2 suspension The SiO2 disks can beobtained in the specially designed mold which placed at thebottom of the centrifuge tube and then dried at 60∘C for 24 hThe obtained SiO2 disks were sintered at 950

∘C for 30 min toprepare porous SiO2 matrix The porosity of SiO2 matrix was32 Porous SiO2 discswere soaked into theAgNO3 solutionsof 2molL and vacuumed for 10 min to ldquopressrdquo the solutioninto porous SiO2 The discs were dried at 70∘C for 3h then100∘C for 8 h Finally the discs were calcined at 450∘C for 30min to obtain AgSiO2 composites The silver mass fractionwas controlled by impregnation-calcination cycles

44 Characterization The XRD patterns were carried out bythe Rigaku DMax-RB-type X-ray diffraction target Cu (K120572diffraction line) The morphologies of the fracture surfacemorphologies were obtained by scanning electron micro-scope (SU-70 Field Emission Scanning Electron MicroscopeFESEM) equipped with energy dispersive X-ray spectroscopy(EDX) Dielectric parameters of the composites were mea-sured by Agilent E4991A Precision Impedance Analyzer with16453A dielectric test fixture from 1MHz to 1 GHz includingimpedance (Z1015840 Z10158401015840) capacitance (C) and resistance (119877p)ac conductivity (120590ac) the phase shift angle (120579) and the real(1205761015840) and imaginary (12057610158401015840) part of complex permittivity Thetest fixture of 16454A was used to measure the complexpermeability The dimension of the samples for permittivitymeasurement is 120601 20 mm times 2 mm The thickness wascontrolled by polishing the samples on abrasive papers (1200mesh) The toroidal samples were used for permeabilitymeasurement with the dimensions of 65 times20 times 2 mm Inorder to prepare the toroidal samples a small pore was madeat the center of the samples by a drill (the diameter 1mm) andthen the small pore was gradually enlarged by a conical file

Data Availability

All data needed to evaluate the conclusions in the paper arepresent in the paper andor the Supplementary MaterialsAdditional data related to this paper may be requested fromthe authors

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Peitao Xie and Zidong Zhang designed experimental proce-dures in detail Peitao Xie performed the characterization anddata analysis and wrote the paper Zhongyang Wang and Kai

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

Research 5

When silver content is above the percolation threshold119891c negative 1205761015840 is achieved and shows obvious frequencydispersion (in Figure 4(b)) The 1205761015840 is sim -5000 at 6 MHzfor composites with 32 wt silver content and graduallyincreases with increasing frequency As for the compositeswith 35 wt silver content the 1205761015840 is sim -50000 at 6 MHz andincreases with increasing frequency reaches the maximum(sim8000) at 150 MHz and then decreases with increasingfrequency As for the composites with 37 wt silver contentthe 1205761015840 is sim -10000 at 6 MHz and keeps increasing to the maxi-mum (sim21000) at 68MHz but then decreases with increasingfrequency The 1205761015840 of Ag32 equals zero at 520 MHz while at57 MHz for the composite with 35wt silver (Ag35) and 11MHz for the composite with 37wt silver (Ag37)That is theepsilon-zero-point shifts to lower frequency with increasingsilver content which provides the feasibility of adjustingepsilon-near-zero properties The AgSiO2 composites cannot only be the promising candidate for negative permit-tivity but also be the epsilon-near-zero materials at radio-frequency region [25] Generally the plasma-type negativepermittivity of metals can be expressed by the Drude model[17]

1205761015840 = 1 minus1205962119901

1205962 + Γ1198632(2)

where ΓD is the damping constant 120596p=2120587119891p is the plasmonsangular frequency Equation (2) is a monotonic increasingfunction while the experimental data are not monotonic buthave maximum (in Figure 4(b)) Because the experimentalresults cannot be perfectly explained by the Drude modelonly there must be other mechanism contributing to thedielectric behavior of the composites [24] The Drude modeldescribes the simple harmonic motion of free electrons ataltering electromagnetic field Besides the Drude model isusually used at the optical and infrared region to describethe negative permittivity The frequency is very high that isperiod time is short so the movement distance of the freeelectrons is also short As a result the plasma oscillation canbe induced even in small metal particles However whenthe frequency of external electrical filed is low even in theradio-frequency region free electrons will be localized insome small metal particles or agglomeration leading to thedeviation from the Drude model The Drude model candescribe the dielectric behavior of silver network only butis not applicable to isolated silver particles [21] Since theisolated silver particles or agglomeration can lead to Lorentz-type dielectric behavior [24] the formula is modified afterconsidering Lorentz-type dielectric resonance [24]

1205761015840 = 1 minus1205962119901

1205962 + Γ2119863+

1198701205962119871 (1205962119871 minus 1205962)(1205962119871 minus 1205962)2 + Γ21198711205962

(3)

where ΓL is the damping constant of Lorentz resonance120596L=2120587119891L is the Lorentz resonance angular frequency andK is the dc electric susceptibility As we can see fromFigure 4(c) and Table S3 the calculation results (solid linesin Figure 4(c)) of Ag35 using Expression (3) show goodagreement with experimental data with high reliability factor

R2=099589TheDrude-type calculation results (dashed linesin Figure 4(c)) indicate that negative permittivity derivesfrom the plasma-type dielectric behavior of free electronsin the silver network while the Lorentz-type calculationresults (dash-dotted lines in Figure 4(c)) indicate that thefrequency dispersion of negative permittivity can be effec-tively adjusted by Lorentz-type dielectric resonance Thesecalculation results were made via the iterative method byusing the respective model Although Lorentz-type dielec-tric resonance can generate negative permittivity in someferroelectric materials and composites containing carbonnanotubes [26 27] the Lorentz-type dielectric behaviors haveno contribution to the negative permittivity in Figure 4(b) Infact it is a relaxation-type curve rather than resonance-typecurve shown as dash-dotted lines in Figure 4(c) as the damp-ing factor is much larger than resonance frequency (shownin Table S3) a common phenomenon at low-frequencyregion in metal optics The Lorentz-type dielectric behaviorcan be attributed to the interfacial imperfection (holes andvoids) and the inhomogeneous silver distribution (isolatedagglomeration and network) formed during adding silverinto SiO2 matrix It can come into the conclusion that thesilver content plays an important role in controlling thefrequency dispersion of negative permittivity

Negative permittivity behavior is further investigated byphase angle (120579) as the positive permittivity is regarded asa capacitive character where the resistance current (119868R) lagsthe capacitive current (119868C) by 90∘ When the silver contentis above 119891c the 120579 of Ag32 is positive below 520 MHz below55 MHz for Ag35 and 102 MHz for Ag37 (in Figure 4(d))while the negative value of 120579 is above these frequency pointsIt shows that the inductive current (119868L) lags the resistivecurrent (119868R) by 90∘ which indicates that negative permittivityexhibits inductive character and the electric energy is storedin inductance [24] Therefore there were usually inductorsin the equivalent circuit of negative permittivity materialsbecause of the inductive character The equivalent circuitanalysis was performed by the ZSimpwin software Theoptimal equivalent circuit was chosen with the smallestChi-square value (usually 10minus3-10minus5) The Chi-square valuerepresents the correlation between experimental data andsimulated data In the previous study we have demonstratedthat the distribution of conductive functional fillers canadjust the frequency dispersion of negative permittivity byLC resonance [23 24] In Figure 4(d) we can see that thesilver content is crucial to the control of LC resonancebecause the value of 120579 is sensitive to the silver content Theabsolute value of 120579 is very small in negative permittivityregion indicating that negative permittivity behavior hashuge dielectric loss and potential application as lossmaterialsBesides the absolute value of 120579 increases with increasingfrequency in positive permittivity region indicating theenergy storage efficiency in capacitance is obviously higherthan that in inductance [28] Interestingly the frequencypoints of 120579=0 correspond with the epsilon-zero points Thatis there is no energy storage but energy loss at epsilon-zeropoint indicating that AgSiO2 composites can function asresistor in metaelectronics circuits at radio-frequency region[29]

6 Research

00

03

06

09

12

Negative permeability region

Frequency (Hz)200M 400M 600M 800M 1G

Fitting data using prop

minus

Ag28Ag32Ag35Ag37

Ag23Ag17

SiO

External magnetic fieldInduced magnetic field by current loop

The space between microspheres is filled with silver

Current loops

(a) (b)

(c) (d)

Pores and gaps among SiO microspheres

1

10

100

near 1 GHz

starts to be remarkableEddy current loss

Frequency (Hz)200M 400M 600M 800M 1G

Slope = 0 at ~520 MHz

Ag28Ag32

(

) (

ns)

2

Frequency (Hz)

Complicatedloss response

Eddy current loss shiftsto lower frequency

Slope = 0 at ~251 MHzand ~355 MHz

200M 400M 600M 800M 1G

Ag35Ag37

(

) (

ns)

2

Figure 5 Frequency dependence of real permeability (1205831015840) for AgSiO2 composites (a) the schematic diagram of magnetic response due tothe induced current loops in AgSiO2 composites (b) and frequency dependence of 12058310158401015840(12058310158402f ) for AgSO2 composites with different silvercontent (c d) The red solid lines in (a) are the calculation results by the relation of 1205831015840 prop radic120596 with high reliability

24 Permeability Figure 5 depicts the frequency dependenceof real permeability (1205831015840) property for AgSiO2 composites Asshown in Figure 5(a) the 1205831015840 of SiO2 bulk almost keeps 1 dueto its nonmagnetism After silver is added to SiO2 matrixthe value of 1205831015840 is smaller than 1 indicating negative sus-ceptibility The negative susceptibility is obviously enhancedwith increasing silver content and frequencyWhen the silvercontent reaches 37 wt negative permeability is achievedin the range of 760-1000 MHz Since SiO2 and silver areboth nonmagnetic the negative susceptibility and negativepermeability cannot be attributed to the magnetic resonanceof component materials It is worth noting that the previousinvestigations demonstrate that negative permeability is dif-ficult to be realized in metalceramics randommetamaterialsthat only contain nonmagnetic metal [17 18] Thereforethe generation of negative permeability indicates that the

precise control of silver is in favor of the magnetic responseof induced current which improves the response efficiencyand the possibility of realizing negative permeability Wecan get some inspiration from periodic metamaterials asnegative permeability is the unique property of periodicmetamaterials and its mechanism is derived from the law ofelectromagnetic induction [7 30] The split-ring resonatorsare the typical building blocks of magnetic response inperiodic metamaterials while the silver can work as buildingblocks of magnetic response in the AgSiO2 composites Asshown in the schematic diagram in Figure 5(b) the intersticesamong the SiO2 microspheres are filled with silver and thecurrent loops can be induced around the SiO2 microsphereswhen the composites are put under an alternating currentmagnetic field The direction of the induced magnetic fieldfrom these current loops is opposite to the external magnetic

Research 7

field which would cancel part of external magnetic field andthus leads to negative susceptibility [5] When the inducedmagnetic field is even dominant negative permeabilitywill beachieved [7 31]Moreover there are alsomany pores and gapsinside the silver network where the microcurrents (smallloops in Figure 5(b)) can also be induced to generate negativesusceptibilitypermeability

According to the mechanism of negative permeabilityin typical periodic metamaterials also known as ldquomagneticplasmardquo the permeability of classical split-ring resonators(SRRs) can be expressed as follows [31]

1205831015840119890119891119891 = 1 +1198651205962 (12059620 minus 1205962)

(12059620 minus 1205962)2 + Γ21205962(4)

where F is a geometrical factor1205960 is the resonance frequencyand Γ is the resistive damping factor The calculation datausing magnetic plasma model are shown in Fig S7 and TableS5 the low reliability factors indicate that ldquomagnetic plasmardquocannot be the mechanism here As shown in Table S5 thedamping factors Γ are larger than resonance frequency byseveral orders of magnitudes indicating a relaxation-typeresponse in the view of ldquomagnetic plasmardquo [14 15 18] Therelaxation-type behavior results in the huge deviation fromldquomagnetic plasmardquo primarily because of the great differencein shape and dimension between SRRs (typical ldquomagneticplasmardquo structure) and silver network (building blocks inthis work) The capacitance from the split in SRRs leads to aresonance-type magnetic response while no split structuresare available in the silver network In addition it is well-known that the reported periodic metamaterials have 120582lvalue between 2 and 12 where 120582 is the wavelength and l isthe size of the building block while it is not applicable tothis work [31] Moreover the relaxation-type response canbe partly due to the small size of the silver network sincethe damping factor is inversely proportional to the size ofbuilding blocks [32]

The ldquomagnetic plasmardquo cannot explain the negative per-meabilitysusceptibility but the magnetic response can onlyresult from the electromagnetic induction in the nonmag-netic composites According to the Faradayrsquos law the inducedcurrent density can be expressed as follows [33]

119895119894 = 120590119894119890119894 = minus120590119894119889Φ119894119889119905 = minus120596120590119894119860 cos (120596119905) (5)

where 119895119894 is the localized current density 120590119894 is the ac conduc-tivity of local area 119890119894 is the localized electric field intensityΦ119894is the magnetic flux t is the time and A is the amplitude of119890119894 According to Biot-Savart law the induced current loopscan generate an induced magnetic field whose direction isalways opposite to the external magnetic field The magneticresponse 119861119894 at the axes of circulating current 119895119894d119878119894 can becalculated by the formula [33]

119861119894 =12058301199032119895119894119889119878119894

2120587 (1199032 + 1199092)32(6)

where 119861119894 is the magnetic induction intensity r is the radiusof circulating current d119878119894 is the sectional area of circulating

current and x is the distance to the center of circulatingcurrent When the induced currents cannot keep up with theexternal field at very high frequency the induced currentswould lag and thus lead to an out-of-phase or negativeresponse The linear relationship between 1205831015840 119861119894 j and 120596 canbe obtained 1205831015840 prop 119861119894 prop 119873119895 prop 120596 where N is the windingnumber Fig S8 and Table S6 show the calculation resultsusing linear relationship The reliability factors (about 0975)is fine but still cannot satisfy our expectation Thereforeother factors should also be considered In fact the 120590119894 inExpression (5) should not be dc conductivity but ac con-ductivity Ac conductivity is also the function of frequencyusually explained by skin depth 120575 = (21205830120590119889119888120596)05 [18] Therelationship between 119861119894 j and 120596 can be modified [16]

119861119894 prop 119873119895 prop radic120596

1205831015840 = 119886 + 119887radic120596(7)

where a and b are parameters about the intrinsic propertyof AgSiO2 composites The calculation results using (7) areshown as red solid lines in Figures 5(a) and S9 and theused parameters are in Table S7The calculation results agreewell with experimental data (1198772 asymp 09975) indicating thatthe mechanism of negative susceptibilitypermeability canbe well explained [16] The physical meaning of a is theinitial permeability and its value should be 1 for AgSiO2composites in good agreement with the calculation results(in Table S7) The parameter b is an intrinsic parameterwhich is closely related to the composition microstructureand electromagnetic property of composites [34 35]

Themagnetic loss was also studied to reveal the influenceof eddy current on negative susceptibilitypermeability Theimaginary permeability (12058310158401015840) spectra for AgSiO2 compositesare shown in detail in supporting information and Fig S10aMagnetic loss mainly originates from hysteresis loss eddycurrent effect and natural resonance at the radio-frequencyregion The hysteresis loss is negligible in the weak fieldNatural resonance can also be excluded due to nonmagnetismof AgSiO2 compositesTherefore the eddy current loss is theonly source of magnetic loss and the eddy current loss can beexpressed by [36]

12058310158401015840 =21205871205830 (1205831015840

2) 12059011988911988811986321198913

(8)

where D is the effective diameter of metal particles If themagnetic loss simply derives from the eddy current lossthe value of 12058310158401015840(12058310158402f ) should be nearly constant withoutchanging with frequency Figures 5(c)-5(d) and S10 show thefrequency dispersion of 12058310158401015840(12058310158402f ) When the silver content isbelow 119891c 12058310158401015840(1205831015840

2f ) value obviously decreases with frequency(in Fig S10) there is an evidence of no eddy current lossavailable because the size of the silver particles is very tiny andeven smaller than the skin depth When the silver content isnear 119891c (ie Ag28 and Ag32) the value of 12058310158401015840(12058310158402f ) at thelower frequency region also decreases with increasing fre-quency (in Figure 5(c)) Interestingly the slope of Ag32 curve

8 Research

200M 400M 600M 800M 1GFrequency (Hz)

0102030

6070 0

4050(d

B)EM

I SE T

- +asymp

01 mm025 mm05 mm1 mm

Target LevelCommercial

200M

0

400M 600M 800M 1GFrequency (Hz)

05

1015202530

(dB)

EMI S

E R

- +asymp

01 mm025 mm05 mm1 mm

200M 400M 600M

0

800M 1GFrequency (Hz)

(a) (b) (c)

(d) (e)

30

20

10

40

50

0

(dB)

EMI S

E A

- +asymp

01 mm025 mm05 mm1 mm

5012 MHz

2

19617816014212510789

712534356178

0

Z XY

5559 MHz

The EM shieldingproperty at 5012MHz is obviouslybetter than thatat 5559 MHz

Figure 6 Frequency dispersion of EMI SET (a) SER (b) and SEA (c) for Ag32 metacomposites with different thickness The distribution ofelectric field vector of Ag32 composites at 5012 MHz (d) and 5559 MHz (e) with 025 mm thickness

is zero at sim520MHz and at sim1GHz for Ag28 where 12058310158401015840(12058310158402f )keeps constant indicating that the eddy current loss graduallybecomes dominant in magnetic loss [36] Further increasingsilver content the slope of Ag35 curve is zero at sim355 MHzand at sim 251 MHz for Ag37 (in Figure 5(d)) suggesting thatthe eddy current loss shifts to low-frequency region with theenhanced silver network In fact eddy current loss has a closerelationshipwith the frequency of the externalmagnetic fieldgeometrical configuration and the electrical conductivity ofthe metal The faster the magnetic field changes the strongerthe eddy current loss can cause In this work the frequencyshift of eddy current loss could not be attributed to theelectrical conductivity of the metal as the eddy current lossof all the composites came from the silver network The onlyinfluence factor was the geometrical configuration of thesilver network From the SEM results (in Figure 2) it can beobserved that the silver networkwas obviously enhancedwithincreasing silver contentThat is the thicker silverwires couldbe formed in the silver networkThe electrical conductivity ofthe whole silver network could be enhanced with increasingsilver content and thus the remarkable eddy current losscould be caused at lower frequency region It is worth notingthat 12058310158401015840(12058310158402f ) increases with increasing frequency at higherfrequency region (in Figure 5(d)) In addition there is a losspeak for Ag37 curve at 760 MHz and it also seems to bea peak for Ag35 at higher frequency region (above 1 GHz)These can be attributed to the complicated relaxation-typebehavior from the phase lag of induced eddy current [31] It is

concluded that the eddy current effect is the main reason fornegative susceptibilitypermeability

25 Electromagnetic Simulation and Shielding EffectivenessNegative permittivity and permeability were simultaneouslyachieved in the AgSiO2 composites In order to deter-mine the interaction between electromagnetic wave and thematerials the electromagnetic propagation properties weresimulated using Computer Simulation Technology softwareThe simulationmethod is detailed in supporting informationand Fig S11The shielding effectiveness (SE) is the main eval-uation criterion of suppressing electromagnetic interference(EMI) The SE total (SET) includes SE absorption (SEA) andSE reflection (SER) [37]

The simulated SE results of Ag32 were shown in Figure 6The SET value increased with increasing frequency at 100-520 MHz then the SET value dramatically dropped and kepta small value at 520-1000 MHz Intriguingly the frequencyregion with large SET value corresponds well with that ofnegative permittivity while low SET corresponds well withpositive permittivity region (in Figure 4(b)) Similar resultswere also observed for Ag35 and Ag37 in Fig S12-S13 whichis because the formation of the silver network could leadto high SE value and excellent electromagnetic shieldingproperty [38] The SER value almost kept constant (225-275) at 100-520 MHz (in Figure 6(b)) and is independenton the thickness of composites because the thickness ofsilver network is thicker than the skin depth of metal silver

Research 9

(0064 mm at 100 MHz) In contrast the SEA value obviouslyincreased with higher frequency and thicker slab at 100-520 MHz (in Figure 6(c)) a peak value near 520 MHz Theenhanced SEA value had a close relationship with the epsilon-near-zero property of Ag32 composites because of goodimpedance matching and absorption loss Similar enhancedabsorption phenomenon was also observed in indium tinoxide at infrared band [39] Therefore the epsilon-near-zero property is like an ldquoon-off switchrdquo of electromagneticshielding providing the possibility of intelligent frequencyselection It is further demonstrated by the distributionof the electric field vector in Figures 6(d)-6(e) where theelectromagnetic shielding at 5012 MHz is obviously betterthan that at 5559 MHz It is worth noting that the SET valueof Ag32 can reach the target level of 20 dB for commercialapplication at 100-520 MHz and the thickness can be asthin as 01 mm We can conclude that excellent shieldingeffectiveness with the advantage of enhanced absorptionintelligent frequency selection and thin layer makes theAgSiO2 random metamaterials highly competitive to con-ventional metals and carbon shielding materials [38 40]

3 Discussion

Porous SiO2 template was prepared via self-assemble processSilver was precisely introduced into the interstices amongSiO2 microspheres to construct AgSiO2 random metamate-rials by the impregnation-calcination process functioning asfunctional fillers The electrical conductivity results revealedthat a percolation phenomenon occurred The conductivemechanism changed from hopping conduction to Drude-type conduction owing to the formation of silver networkswith increasing silver content Negative permittivity can bewell explained by plasma-like behavior of the silver networkand Lorentz-type behavior of silver agglomeration Negativepermeability was attributed to the magnetic behavior ofinduced current loops The calculation analysis indicatesthat permeability values have a linear relation with 12059605which is different from the ldquomagnetic plasmardquo of periodicmetamaterials Electromagnetic simulations demonstratedthat negative permittivity materials and epsilon-near-zeromaterials can have potentials for electromagnetic attenuationand shielding

4 Materials and Methods

41 Materials The ammonium hydroxide (28 wt )ethanol tetraethyl orthosilicate (TEOS) polyvinyl alcohol(PVA) and silver nitrate (AgNO3) were all purchased fromthe Sinopharm Chemical Reagent Co Ltd ChinaThe chem-icals are obtained as chemically pure grade products and usedwithout any further treatment

42 The Preparation of SiO2 Microspheres The SiO2 micro-spheres were prepared by the Stober method 25 mL deion-ized water 80 mL ethanol and 20 mL ammonium hydroxidewere mixed as A solution at 40∘C 40 mL TEOS and 80 mLethanol weremixed as B solution B solution was added to the

A solution at a speed of 200 mLh Subsequently the mixturewas kept stirring for 12 h at 40∘CThe SiO2microspheres wereobtained by centrifuging the white precipitation and furthercleaned by deionized water for several times until pH=7

43 The Preparation of AgSiO2 Metacomposites 3g SiO2microspheres were dispersed in 50 mL 2 wt PVA solutionThe SiO2 disks were prepared by centrifugal sedimentationmethod using the SiO2 suspension The SiO2 disks can beobtained in the specially designed mold which placed at thebottom of the centrifuge tube and then dried at 60∘C for 24 hThe obtained SiO2 disks were sintered at 950

∘C for 30 min toprepare porous SiO2 matrix The porosity of SiO2 matrix was32 Porous SiO2 discswere soaked into theAgNO3 solutionsof 2molL and vacuumed for 10 min to ldquopressrdquo the solutioninto porous SiO2 The discs were dried at 70∘C for 3h then100∘C for 8 h Finally the discs were calcined at 450∘C for 30min to obtain AgSiO2 composites The silver mass fractionwas controlled by impregnation-calcination cycles

44 Characterization The XRD patterns were carried out bythe Rigaku DMax-RB-type X-ray diffraction target Cu (K120572diffraction line) The morphologies of the fracture surfacemorphologies were obtained by scanning electron micro-scope (SU-70 Field Emission Scanning Electron MicroscopeFESEM) equipped with energy dispersive X-ray spectroscopy(EDX) Dielectric parameters of the composites were mea-sured by Agilent E4991A Precision Impedance Analyzer with16453A dielectric test fixture from 1MHz to 1 GHz includingimpedance (Z1015840 Z10158401015840) capacitance (C) and resistance (119877p)ac conductivity (120590ac) the phase shift angle (120579) and the real(1205761015840) and imaginary (12057610158401015840) part of complex permittivity Thetest fixture of 16454A was used to measure the complexpermeability The dimension of the samples for permittivitymeasurement is 120601 20 mm times 2 mm The thickness wascontrolled by polishing the samples on abrasive papers (1200mesh) The toroidal samples were used for permeabilitymeasurement with the dimensions of 65 times20 times 2 mm Inorder to prepare the toroidal samples a small pore was madeat the center of the samples by a drill (the diameter 1mm) andthen the small pore was gradually enlarged by a conical file

Data Availability

All data needed to evaluate the conclusions in the paper arepresent in the paper andor the Supplementary MaterialsAdditional data related to this paper may be requested fromthe authors

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Peitao Xie and Zidong Zhang designed experimental proce-dures in detail Peitao Xie performed the characterization anddata analysis and wrote the paper Zhongyang Wang and Kai

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

6 Research

00

03

06

09

12

Negative permeability region

Frequency (Hz)200M 400M 600M 800M 1G

Fitting data using prop

minus

Ag28Ag32Ag35Ag37

Ag23Ag17

SiO

External magnetic fieldInduced magnetic field by current loop

The space between microspheres is filled with silver

Current loops

(a) (b)

(c) (d)

Pores and gaps among SiO microspheres

1

10

100

near 1 GHz

starts to be remarkableEddy current loss

Frequency (Hz)200M 400M 600M 800M 1G

Slope = 0 at ~520 MHz

Ag28Ag32

(

) (

ns)

2

Frequency (Hz)

Complicatedloss response

Eddy current loss shiftsto lower frequency

Slope = 0 at ~251 MHzand ~355 MHz

200M 400M 600M 800M 1G

Ag35Ag37

(

) (

ns)

2

Figure 5 Frequency dependence of real permeability (1205831015840) for AgSiO2 composites (a) the schematic diagram of magnetic response due tothe induced current loops in AgSiO2 composites (b) and frequency dependence of 12058310158401015840(12058310158402f ) for AgSO2 composites with different silvercontent (c d) The red solid lines in (a) are the calculation results by the relation of 1205831015840 prop radic120596 with high reliability

24 Permeability Figure 5 depicts the frequency dependenceof real permeability (1205831015840) property for AgSiO2 composites Asshown in Figure 5(a) the 1205831015840 of SiO2 bulk almost keeps 1 dueto its nonmagnetism After silver is added to SiO2 matrixthe value of 1205831015840 is smaller than 1 indicating negative sus-ceptibility The negative susceptibility is obviously enhancedwith increasing silver content and frequencyWhen the silvercontent reaches 37 wt negative permeability is achievedin the range of 760-1000 MHz Since SiO2 and silver areboth nonmagnetic the negative susceptibility and negativepermeability cannot be attributed to the magnetic resonanceof component materials It is worth noting that the previousinvestigations demonstrate that negative permeability is dif-ficult to be realized in metalceramics randommetamaterialsthat only contain nonmagnetic metal [17 18] Thereforethe generation of negative permeability indicates that the

precise control of silver is in favor of the magnetic responseof induced current which improves the response efficiencyand the possibility of realizing negative permeability Wecan get some inspiration from periodic metamaterials asnegative permeability is the unique property of periodicmetamaterials and its mechanism is derived from the law ofelectromagnetic induction [7 30] The split-ring resonatorsare the typical building blocks of magnetic response inperiodic metamaterials while the silver can work as buildingblocks of magnetic response in the AgSiO2 composites Asshown in the schematic diagram in Figure 5(b) the intersticesamong the SiO2 microspheres are filled with silver and thecurrent loops can be induced around the SiO2 microsphereswhen the composites are put under an alternating currentmagnetic field The direction of the induced magnetic fieldfrom these current loops is opposite to the external magnetic

Research 7

field which would cancel part of external magnetic field andthus leads to negative susceptibility [5] When the inducedmagnetic field is even dominant negative permeabilitywill beachieved [7 31]Moreover there are alsomany pores and gapsinside the silver network where the microcurrents (smallloops in Figure 5(b)) can also be induced to generate negativesusceptibilitypermeability

According to the mechanism of negative permeabilityin typical periodic metamaterials also known as ldquomagneticplasmardquo the permeability of classical split-ring resonators(SRRs) can be expressed as follows [31]

1205831015840119890119891119891 = 1 +1198651205962 (12059620 minus 1205962)

(12059620 minus 1205962)2 + Γ21205962(4)

where F is a geometrical factor1205960 is the resonance frequencyand Γ is the resistive damping factor The calculation datausing magnetic plasma model are shown in Fig S7 and TableS5 the low reliability factors indicate that ldquomagnetic plasmardquocannot be the mechanism here As shown in Table S5 thedamping factors Γ are larger than resonance frequency byseveral orders of magnitudes indicating a relaxation-typeresponse in the view of ldquomagnetic plasmardquo [14 15 18] Therelaxation-type behavior results in the huge deviation fromldquomagnetic plasmardquo primarily because of the great differencein shape and dimension between SRRs (typical ldquomagneticplasmardquo structure) and silver network (building blocks inthis work) The capacitance from the split in SRRs leads to aresonance-type magnetic response while no split structuresare available in the silver network In addition it is well-known that the reported periodic metamaterials have 120582lvalue between 2 and 12 where 120582 is the wavelength and l isthe size of the building block while it is not applicable tothis work [31] Moreover the relaxation-type response canbe partly due to the small size of the silver network sincethe damping factor is inversely proportional to the size ofbuilding blocks [32]

The ldquomagnetic plasmardquo cannot explain the negative per-meabilitysusceptibility but the magnetic response can onlyresult from the electromagnetic induction in the nonmag-netic composites According to the Faradayrsquos law the inducedcurrent density can be expressed as follows [33]

119895119894 = 120590119894119890119894 = minus120590119894119889Φ119894119889119905 = minus120596120590119894119860 cos (120596119905) (5)

where 119895119894 is the localized current density 120590119894 is the ac conduc-tivity of local area 119890119894 is the localized electric field intensityΦ119894is the magnetic flux t is the time and A is the amplitude of119890119894 According to Biot-Savart law the induced current loopscan generate an induced magnetic field whose direction isalways opposite to the external magnetic field The magneticresponse 119861119894 at the axes of circulating current 119895119894d119878119894 can becalculated by the formula [33]

119861119894 =12058301199032119895119894119889119878119894

2120587 (1199032 + 1199092)32(6)

where 119861119894 is the magnetic induction intensity r is the radiusof circulating current d119878119894 is the sectional area of circulating

current and x is the distance to the center of circulatingcurrent When the induced currents cannot keep up with theexternal field at very high frequency the induced currentswould lag and thus lead to an out-of-phase or negativeresponse The linear relationship between 1205831015840 119861119894 j and 120596 canbe obtained 1205831015840 prop 119861119894 prop 119873119895 prop 120596 where N is the windingnumber Fig S8 and Table S6 show the calculation resultsusing linear relationship The reliability factors (about 0975)is fine but still cannot satisfy our expectation Thereforeother factors should also be considered In fact the 120590119894 inExpression (5) should not be dc conductivity but ac con-ductivity Ac conductivity is also the function of frequencyusually explained by skin depth 120575 = (21205830120590119889119888120596)05 [18] Therelationship between 119861119894 j and 120596 can be modified [16]

119861119894 prop 119873119895 prop radic120596

1205831015840 = 119886 + 119887radic120596(7)

where a and b are parameters about the intrinsic propertyof AgSiO2 composites The calculation results using (7) areshown as red solid lines in Figures 5(a) and S9 and theused parameters are in Table S7The calculation results agreewell with experimental data (1198772 asymp 09975) indicating thatthe mechanism of negative susceptibilitypermeability canbe well explained [16] The physical meaning of a is theinitial permeability and its value should be 1 for AgSiO2composites in good agreement with the calculation results(in Table S7) The parameter b is an intrinsic parameterwhich is closely related to the composition microstructureand electromagnetic property of composites [34 35]

Themagnetic loss was also studied to reveal the influenceof eddy current on negative susceptibilitypermeability Theimaginary permeability (12058310158401015840) spectra for AgSiO2 compositesare shown in detail in supporting information and Fig S10aMagnetic loss mainly originates from hysteresis loss eddycurrent effect and natural resonance at the radio-frequencyregion The hysteresis loss is negligible in the weak fieldNatural resonance can also be excluded due to nonmagnetismof AgSiO2 compositesTherefore the eddy current loss is theonly source of magnetic loss and the eddy current loss can beexpressed by [36]

12058310158401015840 =21205871205830 (1205831015840

2) 12059011988911988811986321198913

(8)

where D is the effective diameter of metal particles If themagnetic loss simply derives from the eddy current lossthe value of 12058310158401015840(12058310158402f ) should be nearly constant withoutchanging with frequency Figures 5(c)-5(d) and S10 show thefrequency dispersion of 12058310158401015840(12058310158402f ) When the silver content isbelow 119891c 12058310158401015840(1205831015840

2f ) value obviously decreases with frequency(in Fig S10) there is an evidence of no eddy current lossavailable because the size of the silver particles is very tiny andeven smaller than the skin depth When the silver content isnear 119891c (ie Ag28 and Ag32) the value of 12058310158401015840(12058310158402f ) at thelower frequency region also decreases with increasing fre-quency (in Figure 5(c)) Interestingly the slope of Ag32 curve

8 Research

200M 400M 600M 800M 1GFrequency (Hz)

0102030

6070 0

4050(d

B)EM

I SE T

- +asymp

01 mm025 mm05 mm1 mm

Target LevelCommercial

200M

0

400M 600M 800M 1GFrequency (Hz)

05

1015202530

(dB)

EMI S

E R

- +asymp

01 mm025 mm05 mm1 mm

200M 400M 600M

0

800M 1GFrequency (Hz)

(a) (b) (c)

(d) (e)

30

20

10

40

50

0

(dB)

EMI S

E A

- +asymp

01 mm025 mm05 mm1 mm

5012 MHz

2

19617816014212510789

712534356178

0

Z XY

5559 MHz

The EM shieldingproperty at 5012MHz is obviouslybetter than thatat 5559 MHz

Figure 6 Frequency dispersion of EMI SET (a) SER (b) and SEA (c) for Ag32 metacomposites with different thickness The distribution ofelectric field vector of Ag32 composites at 5012 MHz (d) and 5559 MHz (e) with 025 mm thickness

is zero at sim520MHz and at sim1GHz for Ag28 where 12058310158401015840(12058310158402f )keeps constant indicating that the eddy current loss graduallybecomes dominant in magnetic loss [36] Further increasingsilver content the slope of Ag35 curve is zero at sim355 MHzand at sim 251 MHz for Ag37 (in Figure 5(d)) suggesting thatthe eddy current loss shifts to low-frequency region with theenhanced silver network In fact eddy current loss has a closerelationshipwith the frequency of the externalmagnetic fieldgeometrical configuration and the electrical conductivity ofthe metal The faster the magnetic field changes the strongerthe eddy current loss can cause In this work the frequencyshift of eddy current loss could not be attributed to theelectrical conductivity of the metal as the eddy current lossof all the composites came from the silver network The onlyinfluence factor was the geometrical configuration of thesilver network From the SEM results (in Figure 2) it can beobserved that the silver networkwas obviously enhancedwithincreasing silver contentThat is the thicker silverwires couldbe formed in the silver networkThe electrical conductivity ofthe whole silver network could be enhanced with increasingsilver content and thus the remarkable eddy current losscould be caused at lower frequency region It is worth notingthat 12058310158401015840(12058310158402f ) increases with increasing frequency at higherfrequency region (in Figure 5(d)) In addition there is a losspeak for Ag37 curve at 760 MHz and it also seems to bea peak for Ag35 at higher frequency region (above 1 GHz)These can be attributed to the complicated relaxation-typebehavior from the phase lag of induced eddy current [31] It is

concluded that the eddy current effect is the main reason fornegative susceptibilitypermeability

25 Electromagnetic Simulation and Shielding EffectivenessNegative permittivity and permeability were simultaneouslyachieved in the AgSiO2 composites In order to deter-mine the interaction between electromagnetic wave and thematerials the electromagnetic propagation properties weresimulated using Computer Simulation Technology softwareThe simulationmethod is detailed in supporting informationand Fig S11The shielding effectiveness (SE) is the main eval-uation criterion of suppressing electromagnetic interference(EMI) The SE total (SET) includes SE absorption (SEA) andSE reflection (SER) [37]

The simulated SE results of Ag32 were shown in Figure 6The SET value increased with increasing frequency at 100-520 MHz then the SET value dramatically dropped and kepta small value at 520-1000 MHz Intriguingly the frequencyregion with large SET value corresponds well with that ofnegative permittivity while low SET corresponds well withpositive permittivity region (in Figure 4(b)) Similar resultswere also observed for Ag35 and Ag37 in Fig S12-S13 whichis because the formation of the silver network could leadto high SE value and excellent electromagnetic shieldingproperty [38] The SER value almost kept constant (225-275) at 100-520 MHz (in Figure 6(b)) and is independenton the thickness of composites because the thickness ofsilver network is thicker than the skin depth of metal silver

Research 9

(0064 mm at 100 MHz) In contrast the SEA value obviouslyincreased with higher frequency and thicker slab at 100-520 MHz (in Figure 6(c)) a peak value near 520 MHz Theenhanced SEA value had a close relationship with the epsilon-near-zero property of Ag32 composites because of goodimpedance matching and absorption loss Similar enhancedabsorption phenomenon was also observed in indium tinoxide at infrared band [39] Therefore the epsilon-near-zero property is like an ldquoon-off switchrdquo of electromagneticshielding providing the possibility of intelligent frequencyselection It is further demonstrated by the distributionof the electric field vector in Figures 6(d)-6(e) where theelectromagnetic shielding at 5012 MHz is obviously betterthan that at 5559 MHz It is worth noting that the SET valueof Ag32 can reach the target level of 20 dB for commercialapplication at 100-520 MHz and the thickness can be asthin as 01 mm We can conclude that excellent shieldingeffectiveness with the advantage of enhanced absorptionintelligent frequency selection and thin layer makes theAgSiO2 random metamaterials highly competitive to con-ventional metals and carbon shielding materials [38 40]

3 Discussion

Porous SiO2 template was prepared via self-assemble processSilver was precisely introduced into the interstices amongSiO2 microspheres to construct AgSiO2 random metamate-rials by the impregnation-calcination process functioning asfunctional fillers The electrical conductivity results revealedthat a percolation phenomenon occurred The conductivemechanism changed from hopping conduction to Drude-type conduction owing to the formation of silver networkswith increasing silver content Negative permittivity can bewell explained by plasma-like behavior of the silver networkand Lorentz-type behavior of silver agglomeration Negativepermeability was attributed to the magnetic behavior ofinduced current loops The calculation analysis indicatesthat permeability values have a linear relation with 12059605which is different from the ldquomagnetic plasmardquo of periodicmetamaterials Electromagnetic simulations demonstratedthat negative permittivity materials and epsilon-near-zeromaterials can have potentials for electromagnetic attenuationand shielding

4 Materials and Methods

41 Materials The ammonium hydroxide (28 wt )ethanol tetraethyl orthosilicate (TEOS) polyvinyl alcohol(PVA) and silver nitrate (AgNO3) were all purchased fromthe Sinopharm Chemical Reagent Co Ltd ChinaThe chem-icals are obtained as chemically pure grade products and usedwithout any further treatment

42 The Preparation of SiO2 Microspheres The SiO2 micro-spheres were prepared by the Stober method 25 mL deion-ized water 80 mL ethanol and 20 mL ammonium hydroxidewere mixed as A solution at 40∘C 40 mL TEOS and 80 mLethanol weremixed as B solution B solution was added to the

A solution at a speed of 200 mLh Subsequently the mixturewas kept stirring for 12 h at 40∘CThe SiO2microspheres wereobtained by centrifuging the white precipitation and furthercleaned by deionized water for several times until pH=7

43 The Preparation of AgSiO2 Metacomposites 3g SiO2microspheres were dispersed in 50 mL 2 wt PVA solutionThe SiO2 disks were prepared by centrifugal sedimentationmethod using the SiO2 suspension The SiO2 disks can beobtained in the specially designed mold which placed at thebottom of the centrifuge tube and then dried at 60∘C for 24 hThe obtained SiO2 disks were sintered at 950

∘C for 30 min toprepare porous SiO2 matrix The porosity of SiO2 matrix was32 Porous SiO2 discswere soaked into theAgNO3 solutionsof 2molL and vacuumed for 10 min to ldquopressrdquo the solutioninto porous SiO2 The discs were dried at 70∘C for 3h then100∘C for 8 h Finally the discs were calcined at 450∘C for 30min to obtain AgSiO2 composites The silver mass fractionwas controlled by impregnation-calcination cycles

44 Characterization The XRD patterns were carried out bythe Rigaku DMax-RB-type X-ray diffraction target Cu (K120572diffraction line) The morphologies of the fracture surfacemorphologies were obtained by scanning electron micro-scope (SU-70 Field Emission Scanning Electron MicroscopeFESEM) equipped with energy dispersive X-ray spectroscopy(EDX) Dielectric parameters of the composites were mea-sured by Agilent E4991A Precision Impedance Analyzer with16453A dielectric test fixture from 1MHz to 1 GHz includingimpedance (Z1015840 Z10158401015840) capacitance (C) and resistance (119877p)ac conductivity (120590ac) the phase shift angle (120579) and the real(1205761015840) and imaginary (12057610158401015840) part of complex permittivity Thetest fixture of 16454A was used to measure the complexpermeability The dimension of the samples for permittivitymeasurement is 120601 20 mm times 2 mm The thickness wascontrolled by polishing the samples on abrasive papers (1200mesh) The toroidal samples were used for permeabilitymeasurement with the dimensions of 65 times20 times 2 mm Inorder to prepare the toroidal samples a small pore was madeat the center of the samples by a drill (the diameter 1mm) andthen the small pore was gradually enlarged by a conical file

Data Availability

All data needed to evaluate the conclusions in the paper arepresent in the paper andor the Supplementary MaterialsAdditional data related to this paper may be requested fromthe authors

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Peitao Xie and Zidong Zhang designed experimental proce-dures in detail Peitao Xie performed the characterization anddata analysis and wrote the paper Zhongyang Wang and Kai

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

Research 7

field which would cancel part of external magnetic field andthus leads to negative susceptibility [5] When the inducedmagnetic field is even dominant negative permeabilitywill beachieved [7 31]Moreover there are alsomany pores and gapsinside the silver network where the microcurrents (smallloops in Figure 5(b)) can also be induced to generate negativesusceptibilitypermeability

According to the mechanism of negative permeabilityin typical periodic metamaterials also known as ldquomagneticplasmardquo the permeability of classical split-ring resonators(SRRs) can be expressed as follows [31]

1205831015840119890119891119891 = 1 +1198651205962 (12059620 minus 1205962)

(12059620 minus 1205962)2 + Γ21205962(4)

where F is a geometrical factor1205960 is the resonance frequencyand Γ is the resistive damping factor The calculation datausing magnetic plasma model are shown in Fig S7 and TableS5 the low reliability factors indicate that ldquomagnetic plasmardquocannot be the mechanism here As shown in Table S5 thedamping factors Γ are larger than resonance frequency byseveral orders of magnitudes indicating a relaxation-typeresponse in the view of ldquomagnetic plasmardquo [14 15 18] Therelaxation-type behavior results in the huge deviation fromldquomagnetic plasmardquo primarily because of the great differencein shape and dimension between SRRs (typical ldquomagneticplasmardquo structure) and silver network (building blocks inthis work) The capacitance from the split in SRRs leads to aresonance-type magnetic response while no split structuresare available in the silver network In addition it is well-known that the reported periodic metamaterials have 120582lvalue between 2 and 12 where 120582 is the wavelength and l isthe size of the building block while it is not applicable tothis work [31] Moreover the relaxation-type response canbe partly due to the small size of the silver network sincethe damping factor is inversely proportional to the size ofbuilding blocks [32]

The ldquomagnetic plasmardquo cannot explain the negative per-meabilitysusceptibility but the magnetic response can onlyresult from the electromagnetic induction in the nonmag-netic composites According to the Faradayrsquos law the inducedcurrent density can be expressed as follows [33]

119895119894 = 120590119894119890119894 = minus120590119894119889Φ119894119889119905 = minus120596120590119894119860 cos (120596119905) (5)

where 119895119894 is the localized current density 120590119894 is the ac conduc-tivity of local area 119890119894 is the localized electric field intensityΦ119894is the magnetic flux t is the time and A is the amplitude of119890119894 According to Biot-Savart law the induced current loopscan generate an induced magnetic field whose direction isalways opposite to the external magnetic field The magneticresponse 119861119894 at the axes of circulating current 119895119894d119878119894 can becalculated by the formula [33]

119861119894 =12058301199032119895119894119889119878119894

2120587 (1199032 + 1199092)32(6)

where 119861119894 is the magnetic induction intensity r is the radiusof circulating current d119878119894 is the sectional area of circulating

current and x is the distance to the center of circulatingcurrent When the induced currents cannot keep up with theexternal field at very high frequency the induced currentswould lag and thus lead to an out-of-phase or negativeresponse The linear relationship between 1205831015840 119861119894 j and 120596 canbe obtained 1205831015840 prop 119861119894 prop 119873119895 prop 120596 where N is the windingnumber Fig S8 and Table S6 show the calculation resultsusing linear relationship The reliability factors (about 0975)is fine but still cannot satisfy our expectation Thereforeother factors should also be considered In fact the 120590119894 inExpression (5) should not be dc conductivity but ac con-ductivity Ac conductivity is also the function of frequencyusually explained by skin depth 120575 = (21205830120590119889119888120596)05 [18] Therelationship between 119861119894 j and 120596 can be modified [16]

119861119894 prop 119873119895 prop radic120596

1205831015840 = 119886 + 119887radic120596(7)

where a and b are parameters about the intrinsic propertyof AgSiO2 composites The calculation results using (7) areshown as red solid lines in Figures 5(a) and S9 and theused parameters are in Table S7The calculation results agreewell with experimental data (1198772 asymp 09975) indicating thatthe mechanism of negative susceptibilitypermeability canbe well explained [16] The physical meaning of a is theinitial permeability and its value should be 1 for AgSiO2composites in good agreement with the calculation results(in Table S7) The parameter b is an intrinsic parameterwhich is closely related to the composition microstructureand electromagnetic property of composites [34 35]

Themagnetic loss was also studied to reveal the influenceof eddy current on negative susceptibilitypermeability Theimaginary permeability (12058310158401015840) spectra for AgSiO2 compositesare shown in detail in supporting information and Fig S10aMagnetic loss mainly originates from hysteresis loss eddycurrent effect and natural resonance at the radio-frequencyregion The hysteresis loss is negligible in the weak fieldNatural resonance can also be excluded due to nonmagnetismof AgSiO2 compositesTherefore the eddy current loss is theonly source of magnetic loss and the eddy current loss can beexpressed by [36]

12058310158401015840 =21205871205830 (1205831015840

2) 12059011988911988811986321198913

(8)

where D is the effective diameter of metal particles If themagnetic loss simply derives from the eddy current lossthe value of 12058310158401015840(12058310158402f ) should be nearly constant withoutchanging with frequency Figures 5(c)-5(d) and S10 show thefrequency dispersion of 12058310158401015840(12058310158402f ) When the silver content isbelow 119891c 12058310158401015840(1205831015840

2f ) value obviously decreases with frequency(in Fig S10) there is an evidence of no eddy current lossavailable because the size of the silver particles is very tiny andeven smaller than the skin depth When the silver content isnear 119891c (ie Ag28 and Ag32) the value of 12058310158401015840(12058310158402f ) at thelower frequency region also decreases with increasing fre-quency (in Figure 5(c)) Interestingly the slope of Ag32 curve

8 Research

200M 400M 600M 800M 1GFrequency (Hz)

0102030

6070 0

4050(d

B)EM

I SE T

- +asymp

01 mm025 mm05 mm1 mm

Target LevelCommercial

200M

0

400M 600M 800M 1GFrequency (Hz)

05

1015202530

(dB)

EMI S

E R

- +asymp

01 mm025 mm05 mm1 mm

200M 400M 600M

0

800M 1GFrequency (Hz)

(a) (b) (c)

(d) (e)

30

20

10

40

50

0

(dB)

EMI S

E A

- +asymp

01 mm025 mm05 mm1 mm

5012 MHz

2

19617816014212510789

712534356178

0

Z XY

5559 MHz

The EM shieldingproperty at 5012MHz is obviouslybetter than thatat 5559 MHz

Figure 6 Frequency dispersion of EMI SET (a) SER (b) and SEA (c) for Ag32 metacomposites with different thickness The distribution ofelectric field vector of Ag32 composites at 5012 MHz (d) and 5559 MHz (e) with 025 mm thickness

is zero at sim520MHz and at sim1GHz for Ag28 where 12058310158401015840(12058310158402f )keeps constant indicating that the eddy current loss graduallybecomes dominant in magnetic loss [36] Further increasingsilver content the slope of Ag35 curve is zero at sim355 MHzand at sim 251 MHz for Ag37 (in Figure 5(d)) suggesting thatthe eddy current loss shifts to low-frequency region with theenhanced silver network In fact eddy current loss has a closerelationshipwith the frequency of the externalmagnetic fieldgeometrical configuration and the electrical conductivity ofthe metal The faster the magnetic field changes the strongerthe eddy current loss can cause In this work the frequencyshift of eddy current loss could not be attributed to theelectrical conductivity of the metal as the eddy current lossof all the composites came from the silver network The onlyinfluence factor was the geometrical configuration of thesilver network From the SEM results (in Figure 2) it can beobserved that the silver networkwas obviously enhancedwithincreasing silver contentThat is the thicker silverwires couldbe formed in the silver networkThe electrical conductivity ofthe whole silver network could be enhanced with increasingsilver content and thus the remarkable eddy current losscould be caused at lower frequency region It is worth notingthat 12058310158401015840(12058310158402f ) increases with increasing frequency at higherfrequency region (in Figure 5(d)) In addition there is a losspeak for Ag37 curve at 760 MHz and it also seems to bea peak for Ag35 at higher frequency region (above 1 GHz)These can be attributed to the complicated relaxation-typebehavior from the phase lag of induced eddy current [31] It is

concluded that the eddy current effect is the main reason fornegative susceptibilitypermeability

25 Electromagnetic Simulation and Shielding EffectivenessNegative permittivity and permeability were simultaneouslyachieved in the AgSiO2 composites In order to deter-mine the interaction between electromagnetic wave and thematerials the electromagnetic propagation properties weresimulated using Computer Simulation Technology softwareThe simulationmethod is detailed in supporting informationand Fig S11The shielding effectiveness (SE) is the main eval-uation criterion of suppressing electromagnetic interference(EMI) The SE total (SET) includes SE absorption (SEA) andSE reflection (SER) [37]

The simulated SE results of Ag32 were shown in Figure 6The SET value increased with increasing frequency at 100-520 MHz then the SET value dramatically dropped and kepta small value at 520-1000 MHz Intriguingly the frequencyregion with large SET value corresponds well with that ofnegative permittivity while low SET corresponds well withpositive permittivity region (in Figure 4(b)) Similar resultswere also observed for Ag35 and Ag37 in Fig S12-S13 whichis because the formation of the silver network could leadto high SE value and excellent electromagnetic shieldingproperty [38] The SER value almost kept constant (225-275) at 100-520 MHz (in Figure 6(b)) and is independenton the thickness of composites because the thickness ofsilver network is thicker than the skin depth of metal silver

Research 9

(0064 mm at 100 MHz) In contrast the SEA value obviouslyincreased with higher frequency and thicker slab at 100-520 MHz (in Figure 6(c)) a peak value near 520 MHz Theenhanced SEA value had a close relationship with the epsilon-near-zero property of Ag32 composites because of goodimpedance matching and absorption loss Similar enhancedabsorption phenomenon was also observed in indium tinoxide at infrared band [39] Therefore the epsilon-near-zero property is like an ldquoon-off switchrdquo of electromagneticshielding providing the possibility of intelligent frequencyselection It is further demonstrated by the distributionof the electric field vector in Figures 6(d)-6(e) where theelectromagnetic shielding at 5012 MHz is obviously betterthan that at 5559 MHz It is worth noting that the SET valueof Ag32 can reach the target level of 20 dB for commercialapplication at 100-520 MHz and the thickness can be asthin as 01 mm We can conclude that excellent shieldingeffectiveness with the advantage of enhanced absorptionintelligent frequency selection and thin layer makes theAgSiO2 random metamaterials highly competitive to con-ventional metals and carbon shielding materials [38 40]

3 Discussion

Porous SiO2 template was prepared via self-assemble processSilver was precisely introduced into the interstices amongSiO2 microspheres to construct AgSiO2 random metamate-rials by the impregnation-calcination process functioning asfunctional fillers The electrical conductivity results revealedthat a percolation phenomenon occurred The conductivemechanism changed from hopping conduction to Drude-type conduction owing to the formation of silver networkswith increasing silver content Negative permittivity can bewell explained by plasma-like behavior of the silver networkand Lorentz-type behavior of silver agglomeration Negativepermeability was attributed to the magnetic behavior ofinduced current loops The calculation analysis indicatesthat permeability values have a linear relation with 12059605which is different from the ldquomagnetic plasmardquo of periodicmetamaterials Electromagnetic simulations demonstratedthat negative permittivity materials and epsilon-near-zeromaterials can have potentials for electromagnetic attenuationand shielding

4 Materials and Methods

41 Materials The ammonium hydroxide (28 wt )ethanol tetraethyl orthosilicate (TEOS) polyvinyl alcohol(PVA) and silver nitrate (AgNO3) were all purchased fromthe Sinopharm Chemical Reagent Co Ltd ChinaThe chem-icals are obtained as chemically pure grade products and usedwithout any further treatment

42 The Preparation of SiO2 Microspheres The SiO2 micro-spheres were prepared by the Stober method 25 mL deion-ized water 80 mL ethanol and 20 mL ammonium hydroxidewere mixed as A solution at 40∘C 40 mL TEOS and 80 mLethanol weremixed as B solution B solution was added to the

A solution at a speed of 200 mLh Subsequently the mixturewas kept stirring for 12 h at 40∘CThe SiO2microspheres wereobtained by centrifuging the white precipitation and furthercleaned by deionized water for several times until pH=7

43 The Preparation of AgSiO2 Metacomposites 3g SiO2microspheres were dispersed in 50 mL 2 wt PVA solutionThe SiO2 disks were prepared by centrifugal sedimentationmethod using the SiO2 suspension The SiO2 disks can beobtained in the specially designed mold which placed at thebottom of the centrifuge tube and then dried at 60∘C for 24 hThe obtained SiO2 disks were sintered at 950

∘C for 30 min toprepare porous SiO2 matrix The porosity of SiO2 matrix was32 Porous SiO2 discswere soaked into theAgNO3 solutionsof 2molL and vacuumed for 10 min to ldquopressrdquo the solutioninto porous SiO2 The discs were dried at 70∘C for 3h then100∘C for 8 h Finally the discs were calcined at 450∘C for 30min to obtain AgSiO2 composites The silver mass fractionwas controlled by impregnation-calcination cycles

44 Characterization The XRD patterns were carried out bythe Rigaku DMax-RB-type X-ray diffraction target Cu (K120572diffraction line) The morphologies of the fracture surfacemorphologies were obtained by scanning electron micro-scope (SU-70 Field Emission Scanning Electron MicroscopeFESEM) equipped with energy dispersive X-ray spectroscopy(EDX) Dielectric parameters of the composites were mea-sured by Agilent E4991A Precision Impedance Analyzer with16453A dielectric test fixture from 1MHz to 1 GHz includingimpedance (Z1015840 Z10158401015840) capacitance (C) and resistance (119877p)ac conductivity (120590ac) the phase shift angle (120579) and the real(1205761015840) and imaginary (12057610158401015840) part of complex permittivity Thetest fixture of 16454A was used to measure the complexpermeability The dimension of the samples for permittivitymeasurement is 120601 20 mm times 2 mm The thickness wascontrolled by polishing the samples on abrasive papers (1200mesh) The toroidal samples were used for permeabilitymeasurement with the dimensions of 65 times20 times 2 mm Inorder to prepare the toroidal samples a small pore was madeat the center of the samples by a drill (the diameter 1mm) andthen the small pore was gradually enlarged by a conical file

Data Availability

All data needed to evaluate the conclusions in the paper arepresent in the paper andor the Supplementary MaterialsAdditional data related to this paper may be requested fromthe authors

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Peitao Xie and Zidong Zhang designed experimental proce-dures in detail Peitao Xie performed the characterization anddata analysis and wrote the paper Zhongyang Wang and Kai

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

8 Research

200M 400M 600M 800M 1GFrequency (Hz)

0102030

6070 0

4050(d

B)EM

I SE T

- +asymp

01 mm025 mm05 mm1 mm

Target LevelCommercial

200M

0

400M 600M 800M 1GFrequency (Hz)

05

1015202530

(dB)

EMI S

E R

- +asymp

01 mm025 mm05 mm1 mm

200M 400M 600M

0

800M 1GFrequency (Hz)

(a) (b) (c)

(d) (e)

30

20

10

40

50

0

(dB)

EMI S

E A

- +asymp

01 mm025 mm05 mm1 mm

5012 MHz

2

19617816014212510789

712534356178

0

Z XY

5559 MHz

The EM shieldingproperty at 5012MHz is obviouslybetter than thatat 5559 MHz

Figure 6 Frequency dispersion of EMI SET (a) SER (b) and SEA (c) for Ag32 metacomposites with different thickness The distribution ofelectric field vector of Ag32 composites at 5012 MHz (d) and 5559 MHz (e) with 025 mm thickness

is zero at sim520MHz and at sim1GHz for Ag28 where 12058310158401015840(12058310158402f )keeps constant indicating that the eddy current loss graduallybecomes dominant in magnetic loss [36] Further increasingsilver content the slope of Ag35 curve is zero at sim355 MHzand at sim 251 MHz for Ag37 (in Figure 5(d)) suggesting thatthe eddy current loss shifts to low-frequency region with theenhanced silver network In fact eddy current loss has a closerelationshipwith the frequency of the externalmagnetic fieldgeometrical configuration and the electrical conductivity ofthe metal The faster the magnetic field changes the strongerthe eddy current loss can cause In this work the frequencyshift of eddy current loss could not be attributed to theelectrical conductivity of the metal as the eddy current lossof all the composites came from the silver network The onlyinfluence factor was the geometrical configuration of thesilver network From the SEM results (in Figure 2) it can beobserved that the silver networkwas obviously enhancedwithincreasing silver contentThat is the thicker silverwires couldbe formed in the silver networkThe electrical conductivity ofthe whole silver network could be enhanced with increasingsilver content and thus the remarkable eddy current losscould be caused at lower frequency region It is worth notingthat 12058310158401015840(12058310158402f ) increases with increasing frequency at higherfrequency region (in Figure 5(d)) In addition there is a losspeak for Ag37 curve at 760 MHz and it also seems to bea peak for Ag35 at higher frequency region (above 1 GHz)These can be attributed to the complicated relaxation-typebehavior from the phase lag of induced eddy current [31] It is

concluded that the eddy current effect is the main reason fornegative susceptibilitypermeability

25 Electromagnetic Simulation and Shielding EffectivenessNegative permittivity and permeability were simultaneouslyachieved in the AgSiO2 composites In order to deter-mine the interaction between electromagnetic wave and thematerials the electromagnetic propagation properties weresimulated using Computer Simulation Technology softwareThe simulationmethod is detailed in supporting informationand Fig S11The shielding effectiveness (SE) is the main eval-uation criterion of suppressing electromagnetic interference(EMI) The SE total (SET) includes SE absorption (SEA) andSE reflection (SER) [37]

The simulated SE results of Ag32 were shown in Figure 6The SET value increased with increasing frequency at 100-520 MHz then the SET value dramatically dropped and kepta small value at 520-1000 MHz Intriguingly the frequencyregion with large SET value corresponds well with that ofnegative permittivity while low SET corresponds well withpositive permittivity region (in Figure 4(b)) Similar resultswere also observed for Ag35 and Ag37 in Fig S12-S13 whichis because the formation of the silver network could leadto high SE value and excellent electromagnetic shieldingproperty [38] The SER value almost kept constant (225-275) at 100-520 MHz (in Figure 6(b)) and is independenton the thickness of composites because the thickness ofsilver network is thicker than the skin depth of metal silver

Research 9

(0064 mm at 100 MHz) In contrast the SEA value obviouslyincreased with higher frequency and thicker slab at 100-520 MHz (in Figure 6(c)) a peak value near 520 MHz Theenhanced SEA value had a close relationship with the epsilon-near-zero property of Ag32 composites because of goodimpedance matching and absorption loss Similar enhancedabsorption phenomenon was also observed in indium tinoxide at infrared band [39] Therefore the epsilon-near-zero property is like an ldquoon-off switchrdquo of electromagneticshielding providing the possibility of intelligent frequencyselection It is further demonstrated by the distributionof the electric field vector in Figures 6(d)-6(e) where theelectromagnetic shielding at 5012 MHz is obviously betterthan that at 5559 MHz It is worth noting that the SET valueof Ag32 can reach the target level of 20 dB for commercialapplication at 100-520 MHz and the thickness can be asthin as 01 mm We can conclude that excellent shieldingeffectiveness with the advantage of enhanced absorptionintelligent frequency selection and thin layer makes theAgSiO2 random metamaterials highly competitive to con-ventional metals and carbon shielding materials [38 40]

3 Discussion

Porous SiO2 template was prepared via self-assemble processSilver was precisely introduced into the interstices amongSiO2 microspheres to construct AgSiO2 random metamate-rials by the impregnation-calcination process functioning asfunctional fillers The electrical conductivity results revealedthat a percolation phenomenon occurred The conductivemechanism changed from hopping conduction to Drude-type conduction owing to the formation of silver networkswith increasing silver content Negative permittivity can bewell explained by plasma-like behavior of the silver networkand Lorentz-type behavior of silver agglomeration Negativepermeability was attributed to the magnetic behavior ofinduced current loops The calculation analysis indicatesthat permeability values have a linear relation with 12059605which is different from the ldquomagnetic plasmardquo of periodicmetamaterials Electromagnetic simulations demonstratedthat negative permittivity materials and epsilon-near-zeromaterials can have potentials for electromagnetic attenuationand shielding

4 Materials and Methods

41 Materials The ammonium hydroxide (28 wt )ethanol tetraethyl orthosilicate (TEOS) polyvinyl alcohol(PVA) and silver nitrate (AgNO3) were all purchased fromthe Sinopharm Chemical Reagent Co Ltd ChinaThe chem-icals are obtained as chemically pure grade products and usedwithout any further treatment

42 The Preparation of SiO2 Microspheres The SiO2 micro-spheres were prepared by the Stober method 25 mL deion-ized water 80 mL ethanol and 20 mL ammonium hydroxidewere mixed as A solution at 40∘C 40 mL TEOS and 80 mLethanol weremixed as B solution B solution was added to the

A solution at a speed of 200 mLh Subsequently the mixturewas kept stirring for 12 h at 40∘CThe SiO2microspheres wereobtained by centrifuging the white precipitation and furthercleaned by deionized water for several times until pH=7

43 The Preparation of AgSiO2 Metacomposites 3g SiO2microspheres were dispersed in 50 mL 2 wt PVA solutionThe SiO2 disks were prepared by centrifugal sedimentationmethod using the SiO2 suspension The SiO2 disks can beobtained in the specially designed mold which placed at thebottom of the centrifuge tube and then dried at 60∘C for 24 hThe obtained SiO2 disks were sintered at 950

∘C for 30 min toprepare porous SiO2 matrix The porosity of SiO2 matrix was32 Porous SiO2 discswere soaked into theAgNO3 solutionsof 2molL and vacuumed for 10 min to ldquopressrdquo the solutioninto porous SiO2 The discs were dried at 70∘C for 3h then100∘C for 8 h Finally the discs were calcined at 450∘C for 30min to obtain AgSiO2 composites The silver mass fractionwas controlled by impregnation-calcination cycles

44 Characterization The XRD patterns were carried out bythe Rigaku DMax-RB-type X-ray diffraction target Cu (K120572diffraction line) The morphologies of the fracture surfacemorphologies were obtained by scanning electron micro-scope (SU-70 Field Emission Scanning Electron MicroscopeFESEM) equipped with energy dispersive X-ray spectroscopy(EDX) Dielectric parameters of the composites were mea-sured by Agilent E4991A Precision Impedance Analyzer with16453A dielectric test fixture from 1MHz to 1 GHz includingimpedance (Z1015840 Z10158401015840) capacitance (C) and resistance (119877p)ac conductivity (120590ac) the phase shift angle (120579) and the real(1205761015840) and imaginary (12057610158401015840) part of complex permittivity Thetest fixture of 16454A was used to measure the complexpermeability The dimension of the samples for permittivitymeasurement is 120601 20 mm times 2 mm The thickness wascontrolled by polishing the samples on abrasive papers (1200mesh) The toroidal samples were used for permeabilitymeasurement with the dimensions of 65 times20 times 2 mm Inorder to prepare the toroidal samples a small pore was madeat the center of the samples by a drill (the diameter 1mm) andthen the small pore was gradually enlarged by a conical file

Data Availability

All data needed to evaluate the conclusions in the paper arepresent in the paper andor the Supplementary MaterialsAdditional data related to this paper may be requested fromthe authors

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Peitao Xie and Zidong Zhang designed experimental proce-dures in detail Peitao Xie performed the characterization anddata analysis and wrote the paper Zhongyang Wang and Kai

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

Research 9

(0064 mm at 100 MHz) In contrast the SEA value obviouslyincreased with higher frequency and thicker slab at 100-520 MHz (in Figure 6(c)) a peak value near 520 MHz Theenhanced SEA value had a close relationship with the epsilon-near-zero property of Ag32 composites because of goodimpedance matching and absorption loss Similar enhancedabsorption phenomenon was also observed in indium tinoxide at infrared band [39] Therefore the epsilon-near-zero property is like an ldquoon-off switchrdquo of electromagneticshielding providing the possibility of intelligent frequencyselection It is further demonstrated by the distributionof the electric field vector in Figures 6(d)-6(e) where theelectromagnetic shielding at 5012 MHz is obviously betterthan that at 5559 MHz It is worth noting that the SET valueof Ag32 can reach the target level of 20 dB for commercialapplication at 100-520 MHz and the thickness can be asthin as 01 mm We can conclude that excellent shieldingeffectiveness with the advantage of enhanced absorptionintelligent frequency selection and thin layer makes theAgSiO2 random metamaterials highly competitive to con-ventional metals and carbon shielding materials [38 40]

3 Discussion

Porous SiO2 template was prepared via self-assemble processSilver was precisely introduced into the interstices amongSiO2 microspheres to construct AgSiO2 random metamate-rials by the impregnation-calcination process functioning asfunctional fillers The electrical conductivity results revealedthat a percolation phenomenon occurred The conductivemechanism changed from hopping conduction to Drude-type conduction owing to the formation of silver networkswith increasing silver content Negative permittivity can bewell explained by plasma-like behavior of the silver networkand Lorentz-type behavior of silver agglomeration Negativepermeability was attributed to the magnetic behavior ofinduced current loops The calculation analysis indicatesthat permeability values have a linear relation with 12059605which is different from the ldquomagnetic plasmardquo of periodicmetamaterials Electromagnetic simulations demonstratedthat negative permittivity materials and epsilon-near-zeromaterials can have potentials for electromagnetic attenuationand shielding

4 Materials and Methods

41 Materials The ammonium hydroxide (28 wt )ethanol tetraethyl orthosilicate (TEOS) polyvinyl alcohol(PVA) and silver nitrate (AgNO3) were all purchased fromthe Sinopharm Chemical Reagent Co Ltd ChinaThe chem-icals are obtained as chemically pure grade products and usedwithout any further treatment

42 The Preparation of SiO2 Microspheres The SiO2 micro-spheres were prepared by the Stober method 25 mL deion-ized water 80 mL ethanol and 20 mL ammonium hydroxidewere mixed as A solution at 40∘C 40 mL TEOS and 80 mLethanol weremixed as B solution B solution was added to the

A solution at a speed of 200 mLh Subsequently the mixturewas kept stirring for 12 h at 40∘CThe SiO2microspheres wereobtained by centrifuging the white precipitation and furthercleaned by deionized water for several times until pH=7

43 The Preparation of AgSiO2 Metacomposites 3g SiO2microspheres were dispersed in 50 mL 2 wt PVA solutionThe SiO2 disks were prepared by centrifugal sedimentationmethod using the SiO2 suspension The SiO2 disks can beobtained in the specially designed mold which placed at thebottom of the centrifuge tube and then dried at 60∘C for 24 hThe obtained SiO2 disks were sintered at 950

∘C for 30 min toprepare porous SiO2 matrix The porosity of SiO2 matrix was32 Porous SiO2 discswere soaked into theAgNO3 solutionsof 2molL and vacuumed for 10 min to ldquopressrdquo the solutioninto porous SiO2 The discs were dried at 70∘C for 3h then100∘C for 8 h Finally the discs were calcined at 450∘C for 30min to obtain AgSiO2 composites The silver mass fractionwas controlled by impregnation-calcination cycles

44 Characterization The XRD patterns were carried out bythe Rigaku DMax-RB-type X-ray diffraction target Cu (K120572diffraction line) The morphologies of the fracture surfacemorphologies were obtained by scanning electron micro-scope (SU-70 Field Emission Scanning Electron MicroscopeFESEM) equipped with energy dispersive X-ray spectroscopy(EDX) Dielectric parameters of the composites were mea-sured by Agilent E4991A Precision Impedance Analyzer with16453A dielectric test fixture from 1MHz to 1 GHz includingimpedance (Z1015840 Z10158401015840) capacitance (C) and resistance (119877p)ac conductivity (120590ac) the phase shift angle (120579) and the real(1205761015840) and imaginary (12057610158401015840) part of complex permittivity Thetest fixture of 16454A was used to measure the complexpermeability The dimension of the samples for permittivitymeasurement is 120601 20 mm times 2 mm The thickness wascontrolled by polishing the samples on abrasive papers (1200mesh) The toroidal samples were used for permeabilitymeasurement with the dimensions of 65 times20 times 2 mm Inorder to prepare the toroidal samples a small pore was madeat the center of the samples by a drill (the diameter 1mm) andthen the small pore was gradually enlarged by a conical file

Data Availability

All data needed to evaluate the conclusions in the paper arepresent in the paper andor the Supplementary MaterialsAdditional data related to this paper may be requested fromthe authors

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Peitao Xie and Zidong Zhang designed experimental proce-dures in detail Peitao Xie performed the characterization anddata analysis and wrote the paper Zhongyang Wang and Kai

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

10 Research

Sun gave important help during the experimental section andwriting this paper Runhua Fan directed the research

Acknowledgments

The authors thank Xueyan Fu for her advice on electro-magnetic simulation usingComputer Simulation Technologysoftware The authors thank Yao Liu Guohua Fan YunpengQu and Yuliang Jiang for their advice for doing exper-iments and measurements The authors acknowledge thesupport of the National Natural Science Foundation of China[Grants nos 51601105 51871146 and 51803119] the YoungElite Scientists Sponsorship Program by CAST (Grant no2017QNRC001) and the Innovation Program of ShanghaiMunicipal Education Commission

Supplementary Materials

Fig S1 XRD patterns (a) of AgSiO2 composites withdifferent silver content and EDX analysis results (b) of sampleAg23 Fig S2 EDX analysis results of sample Ag23 FigS3 the frequency dispersion of 120590ac in 6 MHzndash1 GHz regionThe solid lines are calculation results using the power law andDrude model Fig S4 frequency dependence of imaginarypermittivity 12057610158401015840 (a) and dielectric loss tangent tan 120575 (b)of AgSiO2 composites with different silver content FigS5 frequency dependence of phase angle 120579 for AgSiO2composites with different silver content at 6 MHzndash1 GHzFig S6 Nyquist plots for samples SiO2 bulk Ag17 andAg23 their results of equivalent circuit analysis The inset isthe equivalent circuit for AgSiO2 composites with differentsilver content The solid lines are calculation results usingequivalent circuit Fig S7 the fitting results of permeabilityspectra of Ag32 Ag35 and Ag37 using magnetic plasmaThered solid lines are fitting data Fig S8 the fitting results ofpermeability spectra ofAg32Ag35 andAg37 by linear fittingThe solid lines are fitting data Fig S9 the calculation resultsof permeability spectra of Ag17 Ag23 and Ag28 by (7) Thesolid lines are calculation data with high reliability Fig S10frequency dependence of imaginary permeability (12058310158401015840) (a)and12058310158401015840(12058310158402119891) (b) forAgSO2 composites with different silvercontent Fig S11 the square slab model built for numericalsimulation Fig S12 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag35 composites with differentthickness Fig S13 frequency dispersion of EMI SET (a)SER (b) and SEA (c) for Ag37 composites with differentthickness Table S1 the fitting results of ac conductivity usingpower law Table S2 the fitting results of ac conductivityusing Drude model Table S3 the calculation results of realpermittivity using Lorentz model Table S4 the calculationresults of equivalent circuit Table S5 fitting results using(4) Table S6 fitting parameters of linear fitting Table S7the calculation results of (7) (Supplementary Materials)

References

[1] K Sun R Fan X Zhang et al ldquoAn overview of metamaterialsand their achievements in wireless power transferrdquo Journal ofMaterials Chemistry C vol 6 no 12 pp 2925ndash2943 2018

[2] S Jahani and Z Jacob ldquoAll-dielectric metamaterialsrdquo NatureNanotechnology vol 11 no 1 pp 23ndash36 2016

[3] N K Grady J E Heyes D R Chowdhury et al ldquoTerahertzmetamaterials for linear polarization conversion and anoma-lous refractionrdquo Science vol 340 no 6138 pp 1304ndash1307 2013

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] Z Shi J Wang F Mao C Yang C Zhang and R FanldquoSignificantly improved dielectric performances of sandwich-structured polymer composites induced by alternating positive- K and negative- k layersrdquo Journal ofMaterials Chemistry A vol5 no 28 pp 14575ndash14582 2017

[6] W A Murray and W L Barnes ldquoPlasmonic materialsrdquoAdvanced Materials vol 19 no 22 pp 3771ndash3782 2007

[7] W J Padilla D N Basov and D R Smith ldquoNegative refractiveindexmetamaterialsrdquoMaterials Today vol 9 no 7-8 pp 28ndash352006

[8] S Hussain ldquoNegative permeability from random particle com-positesrdquo Journal of Magnetism andMagnetic Materials vol 428pp 1ndash5 2017

[9] Q Zhao L Kang B Du et al ldquoExperimental demonstration ofisotropic negative permeability in a three-dimensional dielec-tric compositerdquo Physical Review Letters vol 101 no 2 ArticleID 027402 2008

[10] X Liu C Lan K Bi B Li Q Zhao and J Zhou ldquoDualband metamaterial perfect absorber based on Mie resonancesrdquoApplied Physics Letters vol 109 no 6 p 062902 2016

[11] YWen and J Zhou ldquoArtificial nonlinearity generated from elec-tromagnetic coupling metamoleculerdquo Physical Review Lettersvol 118 no 16 Article ID 167401 2017

[12] F X Qin and H X Peng ldquoFerromagnetic microwires enabledmultifunctional composite materialsrdquo Progress in MaterialsScience vol 58 no 2 pp 183ndash259 2013

[13] Y Luo F X Qin F Scarpa et al ldquoLeft-handed metacompositescontaining carbon fibers and ferromagnetic microwiresrdquo AIPAdvances vol 7 no 5 Article ID 056110 2017

[14] Z-C Shi R-H Fan Z-D Zhang et al ldquoRandom Compositesof nickel networks supported by porous alumina toward doublenegative materialsrdquo Advanced Materials vol 24 no 17 pp2349ndash2352 2012

[15] Z-C Shi R-H Fan K-L Yan et al ldquoPreparation of ironnetworks hosted in porous alumina with tunable negativepermittivity and permeabilityrdquo Advanced Functional Materialsvol 23 no 33 pp 4123ndash4132 2013

[16] P Xie W Sun Y Liu et al ldquoCarbon aerogels towards newcandidates for double negative metamaterials of low densityrdquoCarbon vol 129 pp 598ndash606 2018

[17] Z-C Shi R-H Fan X-A Wang et al ldquoRadio-frequencypermeability and permittivity spectra of copperyttrium irongarnet cermet prepared at low temperaturesrdquo Journal of theEuropean Ceramic Society vol 35 no 4 pp 1219ndash1225 2015

[18] P Xie K Sun Z Wang et al ldquoNegative permittivity adjustedby SiO2-coated metallic particles in percolative compositesrdquoJournal of Alloys and Compounds vol 725 pp 1259ndash1263 2017

[19] P Xie Z Zhang K Liu et al ldquoCSiO2 meta-compositeOvercoming the 120582a relationship limitation in metamaterialsrdquoCarbon vol 125 pp 1ndash8 2017

[20] H Gu H Zhang C Ma et al ldquoPolyaniline assisted uniformdispersion for magnetic ultrafine barium ferrite nanorodsreinforced epoxy metacomposites with tailorable negative per-mittivityrdquo The Journal of Physical Chemistry C vol 121 no 24pp 13265ndash13273 2017

Research 11

[21] T Tsutaoka H Massango T Kasagi S Yamamoto and KHatakeyama ldquoDouble negative electromagnetic properties ofpercolated Fe53Ni47Cu granular compositesrdquo Applied PhysicsLetters vol 108 no 19 Article ID 191904 2016

[22] C-W Nan Y Shen and J Ma ldquoPhysical properties of compos-ites near percolationrdquoAnnual Review of Materials Research vol40 pp 131ndash151 2010

[23] P Xie Z Wang Z Zhang et al ldquoSilica microsphere templatedself-assembly of a three-dimensional carbon network withstable radio-frequency negative permittivity and low dielectriclossrdquo Journal of Materials Chemistry C vol 6 no 19 pp 5239ndash5249 2018

[24] P Xie Z Wang K Sun C Cheng Y Liu and R FanldquoRegulation mechanism of negative permittivity in percolatingcomposites via building blocksrdquo Applied Physics Letters vol 111no 11 p 112903 2017

[25] R Maas J Parsons N Engheta and A Polman ldquoExperimentalrealization of an epsilon-near-zero metamaterial at visiblewavelengthsrdquo Nature Photonics vol 7 no 11 pp 907ndash912 2013

[26] K Sun P Xie Z Wang et al ldquoFlexible polydimethylsiloxanemulti-walled carbon nanotubes membranous metacompositeswith negative permittivityrdquo Polymer (United Kingdom) vol 125pp 50ndash57 2017

[27] Z Wang K Sun P Xie Y Liu and R Fan ldquoGeneration mecha-nism of negative permittivity and Kramers-Kronig relations inBaTiO3Y3Fe5O12 multiferroic compositesrdquo Journal of PhysicsCondensed Matter vol 29 Article ID 365703 2017

[28] WChenTheElectrical EngineeringHandbook CRCPress 1992[29] N Engheta ldquoTaming light at the nanoscalerdquo Physics World vol

23 no 9 pp 31ndash34 2010[30] T J Yen W J Padilla N Fang et al ldquoTerahertz magnetic

response from artificial materialsrdquo Science vol 303 no 5663pp 1494ndash1496 2004

[31] C M Soukoulis J Zhou T Koschny M Kafesaki and E NEconomou ldquoThe science of negative index materialsrdquo Journalof Physics Condensed Matter vol 20 no 30 p 304217 2008

[32] J B Prendry A Holden W Stewart and I Youngs ldquoExtremelylow frequency plasmons in metallic mesostructuresrdquo PhysicalReview Letters vol 76 no 25 pp 4773ndash4776 1996

[33] D JonesTheTheory of Electromagnetism Elsevier 2013[34] J E L Bishop ldquoMagnetic domain structure eddy currents and

permeability spectrardquo British Journal of Applied Physics vol 17no 11 pp 1451ndash1460 2002

[35] D-X Chen and J L Munoz ldquoTheoretical eddy-current perme-ability spectra of slabs with bar domainsrdquo IEEE Transactions onMagnetics vol 33 no 3 pp 2229ndash2244 1997

[36] D Ding Y Wang X Li et al ldquoRational design of core-shell CoC microspheres for high-performance microwaveabsorptionrdquo Carbon vol 111 pp 722ndash732 2017

[37] B Zhao and C B Park ldquoTunable electromagnetic shieldingproperties of conductive poly(vinylidene fluoride)Ni chaincomposite films with negative permittivityrdquo Journal of MaterialsChemistry C vol 5 no 28 pp 6954ndash6961 2017

[38] M Han X Yin H Wu et al ldquoTi3C2 MXenes with ModifiedSurface forHigh-Performance ElectromagneticAbsorption andShielding in the X-Bandrdquo ACS Applied Materials amp Interfacesrvol 8 no 32 pp 21011ndash21019 2016

[39] T Y Kim M A Badsha J Yoon S Y Lee Y C Jun and CK Hwangbo ldquoGeneral strategy for broadband coherent perfectabsorption and multi-wavelength all-optical switching basedon epsilon-near-zero multilayer filmsrdquo Scientific Reports vol 6Article ID 22941 2016

[40] P Xie H Li B He et al ldquoBio-gel derived nickelcarbonnanocompositeswith enhancedmicrowave absorptionrdquo Journalof Materials Chemistry C vol 6 no 32 pp 8812ndash8822 2018