MINISTRY OF EDUCATION AND TRAINING

VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY

GRADATE UNIVERSIY OF SCIENCE AND TECHNOLOGY

Luu Huu Nguyen

THE CHARACTERISTICS OF

MAGNETIC INDUCTIVE HEATING

AND THEIR IMPACTS BY

THE PARTICLE ANISOTROPY AND FERROFLUID VISCOSITY

Major: Electronic materials

Code: 9.44.01.23

SUMMARY OF DOCTORAL THESIS IN MATERIAL SCIENCE

Ha Noi - 2019

This thesis was done at: Laboratory of Magnetism and Superconductivity, Institute of Materials and

Sciene, Vietnam Academy of Science and Technology.

Supervisor: Prof., Dr. Nguyen Xuan Phuc Assoc. Prof., Dr. Pham Thanh Phong

Reviewer 1: ...................................................... Reviewer 2: ...................................................... Reviewer 3: ...................................................... The dissertation will be defended at Graduate University of Science and Technology, 18 Hoang Quoc Viet street, Hanoi. Time: ...h..., .../.../2019 This thesis could be found at National Library of Vietnam, Library of Graduate University of Science and Technology, Library of Institute of Materials and Science, Library of Vietnam Academy of Science and Technology.

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INTRODUCTION In recent decades, nanotechnology and nanoscience have been of great interest so they are

considered as a revolution in the 21st century. Nanotechnology encompasses design, analysis, fabrication and application of structures, devices or systems by controlling the shape, size on a nanometer scale. The subject of these technologies is nanomaterialsNanomaterials with very small sizes (about 1-100 nm) exhibit exciting properties that are different from those of the bulk materials. Based on their size effects, nanomaterials have open new applications in electronics, mechanics, environmental remediation, especially in biomedicine.

For dielectric and magnetic materials, inductive heating is the physical phenomenon by which the materials become thermo-seeds when they are irradiated by proper alternating electromagnetic field. In the case of bulk magnetic materials, the Magnetic Inductive Heating (MIH) using alternative magnetic field (AMF) relies on two mechanisms of energy dissipation, which are energy losses due to Joule heating and energy losses associated with magnetic hysteresis. In nano scale, it is generally known that the energy losses associated with magnetic properties such as hysteresis loss and relaxation loss mainly contribute to the heating.

For biomedical applications, magnetic nanoparticles (MNPs) have to be dispersed in a solvable solvent to create nano ferrofluids. MNPs are coated by a surfactant for preventing the nanoparticles from aggregation and keeping them well dispersed for many years. So, the nano ferrofluids in fact consist of core, shell and solvent. Various magnetic nanoparticles such as magnetic metal nanoparticles, magnetic alloy nanoparticles or magnetic metal oxide nanoparticles have been used as the core of nanofluids. The shell materials can be polymer, copolymer or an oxide material. The fabrication of a magnetic nanofluids may be realized using water or other solvents such as benzyl ether, phenyl ether. It is generally known that there are many methods such as co-precipitation, sol – gel, solvo-thermal, hydrothermal, thermal decomposition or reverse micelle, normally used in synthesing MNPs . The size and size distribution or magnetic properties of nanoparticles depend on the synthesis method. Therefore, it is difficult to experimentally study the effect of one or more parameters of a nano ferrofluid on the physical phenomenon.

Besides, the nano ferrofluids must satisfy two main conditions: they should have large heating power with minimum amount of nanoparticles, they should have good biocompatability. In order to achieve these goals, the so far studies focused on improving the heating power of magnetic nanoferrofluids. Based on previous works, the heating power depends on several physical and magnetic parameters of the particles including: particle size (D) – size distribution, saturation magnetization (Ms), magnetic anisotropy constant (K), viscosity of magnetic fluid (η) as well as the AMF frequency and amplitude. Because there are so many parameters affecting the heating power, experimental studies of optimizing MIH effect are difficult to realize. Therefore, theoretical studying the role of physical parameters of different nanomaterials could be a good approach to provide guidelines for experimental works, becausetheoretical calculations in fact play the role as a “Digital experiment”, which contributes to predicting experimental results. Based on these theoretical results, the experimental parameters can be adjusted to search for suitable materials according to the researchers' goals.

In Vietnam, the basic and application works associated with magnetic nano materials are concerned by a number of research groups at Institute of Materials Science (IMS), Institute for Tropical Technology, Ho Chi Minh city Institute of Physcis - Vietnam Academy of Science and Technology, Hanoi University of Science and Technology, Faculty of Physics in Hanoi University of Science, etc. However, only the research

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group of Prof., Dr. Nguyen Xuan Phuc at IMS permomed theoretical and experimental studies of MIH and focus on both aspects: the synthesis method such as magnetic metal nanoparticles (Fe), magnetite nanoparticles (Fe3O4), doped magneitc nanoparticles (Mn0.3Zn0.7Fe2O4, Mn0.5Zn0.5Fe2O4, La0.7Sr0.3MnO3) or core – shell magnetic nanoparticles - Fe3O4@ poly(styrene-co-acrylic acid), Fe3O4@ poly (Nisopropylacrylamide-co-acrylic acid) and the physical mechanism of MIH.

Up to now, the experimental results on MIH are abudant and diverse. These results indicated the advantage of particular materials, which is used as a core, shell or solvent of biomedical nano ferrofluids. Besides, the experimental results of studying physical parameters on MIH contributed to explain its physical mechanism. However, the dependence of MIH on the ferrofluid physical parameters has not been detailly mentioned in recent experimental works and systematically considered in theoretical reports. So, a series of questions should have satisfactory answers in the research process. Firstly, the heating efficiency of MIH is optimal at which critical size of each mangnetic nano materials? Secondly, the same question for saturation magnetization, hydrodynamic diameter and especially in magnetic anisotropy (K). How the characteristic parameters of MIH are affected in low K or high K magnetic nanofluids? In other words, how can we classify materials based on this parameter or other physical factors in MIH? How the heating efficiency of MIH is affected when the particle is not monodispersive or the viscosity changes? These answers will contribute to optimizing the MIH in each materials and orienting the applicability of these materials. It is a challenge for us and other groups.

Based on the above reasons, we chose the research project for thesis, namely: “The characteristics of magnetic inductive heating and their impacts by the particle anisotropy and ferrofluid viscosity”.

Research targets of the thesis:

(i) To thereticallystudy the overall characteristics of MIH and their impacts based on theoretical calculation

(ii) To carry out experiments on the influence of alternating magnetic field, particle size and viscosity on specific loss power for CoFe2O4 and MnFe2O4, chosen as representative of respectively high K and low K magnetic nanoparticles; and to compare the experimental behavior with that obtained by theroretical calculations. Scientific and practical meaning of the thesis:

Applying Linear Respones Theory (LRT) to find the competition between the Néel and the Brownian relaxation which helps to more clearly understand about the role of magnetic anisotropy for classifying materials in MIH. Research methodology:

The thesis was carried out by theoretical calculation based on LRT (using MATLAB software) and practical experimentation combined with numerical data process. CoFe2O4 and MnFe2O4 samples were fabricated by hydrothermal synthesis at Laboratory of Magnetism and Superconductivity, Institute of Materials and Sciene, Vietnam Academy of Science and Technology. Samples were characterized by electron microscopes (FESEM). The viscosity of magnetic fluids was measured by Sine wave Vibro Viscometer SV 10. DLS was used to determine the hydrodynamic diameter of magnetic fluid. Magnetic properties of materials were investigated by Vibrating-Sample Magnetometer (VSM), and were used to evaluate the presence of functional groups on magnetic nanoparticles. Magnetic Induction Heating was carried out on RDO-HFI-5 kW set up installed at Institute of Materials Science..

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Research contents of the thesis: (i) Overview of Magnetic inductive heating for nano ferrofluids (ii) Investigating the effect of physical parameters on the specific loss power based on LRT (iii) Compare theoretical results with experimental results of the influence of alternating

magnetic field, particle size and viscosity on specific absorption rate power for CoFe2O4 and MnFe2O4 magnetic nanoparticles

Layout of the thesis: The contents of thesis were presented in 3 chapters. • Introduction • Chapter 1. Magnetic inductive heating for nano ferrofluids • Chapter 2. The theoretical results of the specific loss power based on Linear Respones Theory • Chapter 3. Verifying theory by experimental results • Conclusion

Research results of the thesis were published in 06 scientific reports including: 02 ISI reports, 03 national reports, 01 report in international scientific workshop.

CHAPTER 1

MAGNETIC INDUCTIVE HEATING FOR NANO FERROFLUID 1.1. Overview of Magnetic inductive heating 1.1.1. Magnetic nanoparticle and superparamagnetic particle: basic properties 1.1.1.1. Domain of magnetic nanoparticle

In a bulk magnetic material, the magnetic moments are uniformly oriented in regions of certain sizes, which are called “magnetic domains” or “domains”. tIn the absence of external filed, the moments vary from domain to domain to make total magnetization minimized to zero. When the size of bulk material decreases, the domain size decreased and the domain structure, the width of the domain wall changes. When the particle was smaller than a critical size, it could not consist of two domains separated by a domain wall and the particle becomes a single domain particle. The critical size for single domain behavior depends on type of magnetic materials. 1.1.1.2. Superparamagnetism

If single-domain nanoparticles become small enough, thermal energy is larger than anisotropy energy so spontaneously reverse the magnetization of a particle from one easy direction to the other likes a single spin in paramagnetic materials. The spin system can be rotated synchronously and the magnetic state of small size and non-interacting nanoparticles is called “superparamagnetic”.

The temperature at which the transition between the superparamagnetic state and the blocked state occurs is called the blocking temperature TB . The blocking temperature TB also depends on other factors such as magnetic anisotropy, size and the measurement time (τm). So, the blocking temperature depends on size andτm for each materials. While the critical size of single domain is determined by the balance of energy forms, superparamagnetic behavior depends on the measurement time. 1.1.1.3. Dependence of magnetic anisotropy on particle size

The anisotropy energy is the energy required by the external magnetic field to move the magnetic moment from easy to hard direction of magnetization. It is the internal magnetocrystalline energy if saturation magnetization is not oriented towards easy axis. This energy, which is associated with

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magnetocystalline anisotropy and the crystal symmetry of the material is called magnetocystalline anisotropy energy.

For fine or thin flim magnetic nanoparticles, surface anisotropy contributes yet to magnetocystalline anisotropy. The surface anisotropy is caused by the breaking of the symmetry and a reduction of the nearest neighbour coordination. Surface effects in small magnetic nanoparticles are a major source of anisotropy.

The effective anisotropy energy per unit volume is given by:

6eff V SK K K

D= + (1.8)

1.1.2. Nano ferrofluid: synthesis and application The magnetic nanoparticles coated by surfactants and suspended in liquid carrier are called

ferrofluids or magnetic fluids, which is a commonly concept in biomedical applications. The magnetic fluids are distingnuished not only by magnetic properties of nanoparticles (core) but also properties of liquids. For example, the Néel and Brownian relaxations mainly contribute towards MIH of ferrofluids based on superparamagnetic nanoparticles. Therefore, the physical effects of ferrofluid are influenced by magnetic nanoparticles in the core, the shell , the solvent and also the synthesis method used. 1.1.3. Magnetic inductive heating and application

Inductive Heating (IH) is the physical phenomenon by which electromagnetic materials become thermal seeds when they are inserted in proper alternating electromagnetic field. In case of nanosized magnetic materials, it is generally known that the energy losses associated with magnetic properties such as hysteresis loss, relaxation loss, v…v. mainly contribute to the heating. The MIH has been of great interest because of their potential applications such as (i) adsorbent material desorption, (ii) cell activation for insulin regulation, (iii) to characterize the nanoparticle distribution in organs and in tissues, (iv) thawing of cryopreserved biomaterials, (v) hyperthermia-based controlled drug delivery and (vi) hyperthermia-based cancer treatment. 1.2. Magnetic inductive heating mechanisms 1.2.1. Contribution factors to thepower of magnetic inductive heating

MIH of magnetic nanoparticles is derived from the process of adsorbed energy from external alternating magnetic field. The total absorbed energy includes surface Joule loss (PF), hysteresis loss (PH), Néel (PN) and Brown (PB) relaxation losses. Because, most nano materials are of high electrical resistivity and small size, this leads to very low eddy current loss. Thus the MIH of nanoparticles is mainly caused by the hysteresis loss, Néel and Brown relaxation losses.

The hysteresis loss refers to the loss due to irreversible magnetization process in AC field. This is the mainly heat generation of ferrite or ferromagnetic multi – domain materials. For the superparamagnetic nanoparticles, it is generally known that Néel and Brown relaxation losses mainly contribute to the MIH of materials. The Néel relaxation loss is originated from relaxation effects of magnetization in magnetic field, the Brown relaxation loss is due to the rotation of the nanoparticles as a whole in ferrofluid.

Nowadays, the theoretical models of MIH such as Rayleigh model, Stoner–Wohlfarth model based theories (SWMBTs), and Linear Response Theory (LRT) depend on the applicable conditions. The dimensionless parameter ξ to indicate the limit of validity of each theoretical model.

0 S

B

M VHk T

µξ = (1.9)

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When ξ < 1, nanoparticles show superparamagnetic behavior or H<<HC. The relationship between M and H can be approximated to a linear function. Therefore, the LRT can be applied. This model is based on two mechanisms: Néel and Brown relaxation losses. In contrast, the hysteresis loss is the mainly heat generation of ferrite or ferromagnetic multi – domain when the parameter ξ > 1. Thus Rayleigh and SWMBTs models are applicable depending on field used. 1.2.2. Hysteresis loss

SW model is a theoretical model based on the hysteresis loss, which can be estimated from the area of the hysteresis loop when the magnetization material is saturated. Note that the hysteresis loop changes with the amplitude and frequency of the AMF.

For low AMF, Rayleigh model has been applied and it has been shown that the law SLP ∝ H3 could describe the hysteresis losses. SWMBTs was built by the hypothesis: single domain ferromagnetic particles with non interaction uniaxial anisotropy and orient randomly. According to the SWMBTs, the loss power was equal to twice the anisotropic energy density. In fact, J. Carey et Al. found that it was equal to 1.92 the anisotropic energy density. 1.2.3. Néel relaxation loss

For single domain particles, the anisotropy energy is smaller than thermal energy so that the particle magnetic moment can rotate freely in the absence of an external magnetic field. Heating is accomplished by rotating the magnetic moment of each particle against an energy barrier. 1.2.4. Brown relaxation loss

The Brown relaxation loss refers to the rotation of particle as a whole in magnetic fluid. This is significant when the direction of the magnetic moment is tightly attached to particle (high magnetic anisotropy) and low viscosity. 1.2.5. Linear Response Theory

LRT describes the ability of the magnetic moment to respond AMF. Based on theoretical results, J. Carey et. al found that the condition of validity for the LRT is ξ < 1. So, LRT based on Néel and Brown relaxation losses is suitable for superparamagnetic nanoparticles or H<<HC.

Loss power of MIH based on relaxation losses is given by:

( ),, 20LRTP f H fµ πχ= (1.20.)

1. 3. Difficulties and challenges in experimental study of optimal MIH of nano ferrofluids In biomedical applications, the preferred size of the nanoparticles (core) is typically around 10–50 nm,

nanoparticles have high saturation magnetization and must satisfy two main conditions: they should have large heating power with minimum amount of nanoparticles and they should have good stability in ferrofluids. Therefore, the major issue that is being investigated is optimal MIH.

Specific Loss Power – SLP or Specific Absorption Rate – SAR is commonly used to describe the MIH capacitance or the ability to absorb energy from AMF of the magnetic nanopaerticles:

/ PSLP SAR

ρ= (1.23.)

1.3.1. Size particle and problem in controlling size and narrow size distribution There are many magnetic nanoparticle synthesis methods such as co-precipitation, sol – gel, solvo-

thermal, hydrothermal, thermal decomposition or reverse micelle. The size and size distribution or magnetic properties of nanoparticles depend on the synthesis method. So, it is difficult to control size particle, size distribution and material crystallization. For example, synthesizing magnetic fluids with a same medium size

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but different size distribution or same size distribution with different medium size is not feasible. Therefore, it is difficult to study of the effect of one or more parameters of nano ferrofluid on a physical phenomenon. 1.3.2. Saturation magnetization and attenuation from saturation magnetization by surface dead layer

The magnetization of a magnetic material is the sum of the magnetic moments per unit volume. Surface effects and finite size effects are responsible for the difference between nanoparticle and bulk material magnetization. The corresponding contributions of the two effects are opposite. The attenuation from magnetic saturation of the nanoparticles is due to the existence of a dead layer or spin canting on the particle surface. 1.3.3. Magnetic anisotropy of nanoparticle

For bulk magnetic materials, magnetic anisotropy depends on composition and crystal field of each material. Because of the increased ratio of surface atoms to core atoms in nanoparticle, surface effects were suggested to have significant role on the properties magnetic anisotropy of nanoparticle.

The magnetic anisotropy depends on shape and crystallization for nanoparticels with a same ingredient. The magnetic anisotropy strongly depends on synthesis method and synthetic conditions of each method. Thus, studying the dependence of MIH on the magnetic anisotropy by controlling the value of magnetic anisotropy is impossible in experimental works 1.3.4. Viscosity of ferrofulids in applications

The value of viscosity changes from 1 to 4 mPa•s in biomedical applications or is equal infinite in other applications such as adsorbent material desorption and thawing of cryopreserved biomaterials. 1.4. Review of magnetic inductive heating 1.4.1. Review of experimental works

Most of experimental studies have focused on the impact of insitric parameters of magnetic fluid (size distribution, saturation magnetization, viscosity …) to loss power because of the limit of AMF in biomedical applications.

There are some interesting experimental results such as the peak behavior of heating power versus diameter, decrease of SLP with expanding size distribution or increasing the value of viscosity. As for the tendencies of heating power decrease, there is the different behavior between the high-K and low-K magnetic nanoparticles. However, the dependence of MIH on physical parameters has not been detailly and systematically mentioned in recent experimental works because of difficulties in experimental study: magnetic properties depend on size and shape of nano ferrofluids. 1.4.2. Review of theoretical works

The LRT is commonly used because of practical requirements in biomedical applications. Based on LRT, the SLP exhibits a peak (SLPmax) at some critical diameter when the condition ωτ = 1 is satisfied and this condition is compared with the experimental works. However, the value of Dcp, SLPmax and ΔDcp depend on which physical parameters have not been mentioned.

The difference in the SLP(D) graph shape of nano ferrofluids is mentioned or used to explain the different decrease of SLP with expanding size distribution of the γ-Fe2O3 and CoFe2O4. But, it is still an open issue. In addition, the role of competition between Néel and Brown relaxation losses to MIH has not been studied.

CHAPTER 2 THE THEORETICAL RESULTS OF THE SPECIFIC LOSS POWER

BASED ON LINEAR RESPONES THEORY

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2.1. Characteristic of the specific loss power 2.1.1. The competition between Néel and Brown relaxation losses

It is indicated the existence of three particle diameter (D) regions that: the Néel relaxation dominates in region I (D < DN), the Brownian relaxation dominates in region III (D > DB) and the two dissipation mechanisms contribute simultaneously in region II (DB ≤ D ≤ DN). 2.1.2. The peak behavior of the specific loss power versus diameter

The peak behavior of the specific loss power versus diameter with the value of Dcp and SLPmax indicated that SLP depends strongly on diameter. Parameter of full-width-half-maximum ∆Dcp is introduced to describe these peaks. The vaule of ∆Dcp relates to decrease of SLPmax according to the deviation from Dcp. 2.1.3. Characteristics of optimal parameters in regions with different loss mechanisms

The difference in the SLP (D) graph shape of nano ferrofluids depends on the value of magnetic anisotropy, specifically the low-K magnetic fluids such as FeCo, LSMO, MnFe2O4 and Fe3O4 or the high-K magnetic fluids such as CoFe2O4 and FePt. These two groups are more or less of one rank the value of magnetic anisotropy. We distinguish these nano ferrofluids into two groups: group A consists of low-K magnetic fluids (FeCo, LSMO, MnFe2O4 and Fe3O4) (K < 10 kJ/m3) and group B consists of high-K magnetic fluids (CoFe2O4 and FePt) (K > 100 kJ/m3).

For group A, the peak is narrow and small ∆Dcp. In contrast, the peak is bell-like with a large width ∆Dcp for group B. The cause of this phenomenon is due to the value of Dcp for each group. These values are in regions I and II - group A, and, in region III - group B. 2.2. Effect of physical parameters on optimal parameters 2.2.1. The parameters of alternating magnetic field a. Amplitude of alternating magnetic field

For nano ferrofluid with diameter of 4 nm, SLP depends on the amplitude of AMF as a quadratic form. SLP is linearly dependent on H for nano ferrofluid with diameter of 36 nm. The cause of these different results is due to H affecting SLP by H2 function and imaginary susceptibility χ’’. So, the dependence of SLP on H can be able an exponential (first order, quadratic, or tertiary) function or a complex function.

Figure 2.5. Dependence of ( )

( )( )max

max 50SLP H

SLP H Oe= rate on H

for FeCo, LSMO, MnFe2O4, Fe3O4, CoFe2O4 and FePt with Dcp

The value of SLPmax increases linearly with H for six ferrofluids. The heating power of the MIH increases linearly with H at the critical diameter e even though the heat generation mechanism is Néel or

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Brown relaxation loss. In addition, the optimal parameters Dcp and ∆Dcp do not depend on the the amplitude of AMF. b. Frequency of alternating magnetic field

The value of SLP reaches the maximum SLPmax at the critical size when this condition 1ωτ = is satisfied. The value of Dcp changes when the frequency changes. However, the impact of frequency on the critical diameter is different for two groups (A and B).

For group A, the Dcp changes from 2.5 to 3.5 nm when the frequency changes from 100 kHz to 1 MHz. The Dcp changes from 4.5 to 5.5 nm when the frequency changes from 100 kHz to 1 MHz for CoFe2O4 and FePt ferrofluids. While the Dcp of CoFe2O4 and FePt ferrofluids change 25% - 34%, the Dcp of group A only changes ∼10% - ∼13%. However, the value of ∆Dcp do not depend on the the frequency of AMF.

Figure 2.9. Dependence of ( )

( )( )100SLP f

SLP f kHz= rate on f

for FeCo, LSMO, MnFe2O4, Fe3O4, CoFe2O4 and FePt with Dcp (f=100 kHz) At the critical diameter (f = 100 kHz), the SLP increases linearly with frequency when the value of

frequency is smaller than ≤ 200 kHz – the condition 1ωτ ≈ is satified. These values will be saturated in the high frequency. The value of saturation SLP differs for magnetic fluids and is higher for low-K magnetic nanofluids. 2.2.2. Saturation magnetization

Based on LRT, the value of SLP reaches the maximum SLPmax at the critical size when this condition 1ωτ = is satisfied. At the critical diameter, the value of SLPmax:

( )max 0max .

2LRT

S SP HfSLP M A Mµ π

ρ ρ= ≈ = (2.4.)

The value of SLPmax is an increasing linear function of MS. It can be explained by the independent behavior of MS on the effective relaxation time. Table 2.4. The slope max / SSLP M∆ ∆ for FeCo, LSMO, MnFe2O4, Fe3O4, CoFe2O4 and FePt magnetic fluids

Magnetic fluid K

(kJ/m3) max / SSLP M∆ ∆ R2

FeCo 1,5 2,39 1 La0.7Sr0.3MnO3 2 2,37 1

MnFe2O4 3 2,39 1 Fe3O4 9 2,14 0,99729

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CoFe2O4 180 1,05 0,99879 FePt 206 1,77 0.99985

However, the value of the slope max / SSLP M∆ ∆ for magnetic fluids depend on K. One can note again that the materials having low and high K values behave differently. Namely, the slope of the materials with K< 10 kJ/m3 changes very little with K ( max / SSLP M∆ ∆ ∼ 2.38 for FeCo, LSMO, MnFe2O4,), whereas that of high K materialsis almost halved. The cause of this phenomenon is due to the value of Dcp for each group. These values are in regions I and II - group A, and, in region III - group B. These results demonstrate the role of magnetic anisotropy in explaining the physical mechanism of the MIH.

Two optimal parameters Dcp and ∆Dcp do not depend on the the frequency of AMF. 2.2.3. Viscosity of magnetic fluids

While all relaxation times depend on diameter, only the Brown relaxation time depends on the viscosity of nano ferrofluids. The value of Dcp for group A is in regions I and II. The value of Dcp for group B is in regions III – the Brown relaxation loss dominates. These are reasons that the optimal parameters change when the viscosity of nano ferrofluids group B changes.

Hình 2.12. Dependence of SLP on D at various η for (a)CoFe2O4 and (b)FePt

For group B: the Brown relaxation loss dominates at the critical diameter. Thus, the critical diameter depend on the viscosity:

3 2 32 2B

cpk T AD

fδ δ

ηπ η= − = − (2.5)

All optimal parameters SLPmax, Dcp and ∆Dcp change with changing the value of the viscosity of magnetic fluids in gropu B. It is easy to see from the figure that the SLPmax of CoFe2O4 and FePt decreases strongly (∼ 50% – ∼ 60%) and the characteristic parameters Dcp and ∆Dcp do insignificantly with increasing the viscosity from 1 mPa•s to 2 mPa•s.

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Hình 2.13. Dependence of SLPmax on MS at various η for (a)CoFe2O4 and (b)FePt

SLPmax was directly proportional to Ms depending not on the viscosity, meanwhile the slope of them decreased with increasing of viscosity. The contrast results between group A and group B continue to confirm that the MIH is primarily derived from the Brown relaxation loss for group B or from the Néel relaxation loss for group A. 2.2.4. Size ditribution

With expanding the size distribution (the value of σ increases), the contribution of magnetic nanoparticles with diameter around the value of Dcp is larger. Thus, the SLPmax decreases with increasing standard diameter deviation σ of size distribution for all magnetic fluids. However, it has a difference between two groups: A and B.

These results found the value of SLPmax of group A decreases stronger than group B with expanding particle the size distribution from 0 (monodispersion) to 0.25. When the value of σ increases from 0.25 to 0.5, the value of SLPmax of group A decreases slower than group B.

Figure 2.15. Dependence of ( )

( )max

max 0SLP

SLPσ

σ = rate on σ for FeCo, LSMO, MnFe2O4, Fe3O4, CoFe2O4 và FePt

The difference in ∆Dcp and heating mechanism between group A and B is the key to explain the decrease of SLPmax with expanding the size distribution. The Néel and Brown relaxation losses are the main heating mechanisms. Depdencce of the Néel relaxation loss on diameter is stronger than depdencce of the Brown relaxation loss on diameter. So, the value of SLP decreases strongly with decreasing of diameter in region I (D < DN). When diameter increases in region III (D > DB), SLP decreases slowly.

For group A, the contribution ratio of nanoparticles from region I is greater than region III when σ increases from 0 to 0.25. So, the value of SLPmax decreases strongly. In constract, the value of SLPmax decreases slowly because the contribution ratio of nanoparticles from region III is greater than region I when σ increases from 0.25 to 0.5.

The value of Dc is near region I, the more obvious this phenomenon is. This explains that the fastest increasing of ∆Dcp for FeCo magnetic fluid and the least increasing of corresponding value for Fe3O4 magnetic fluid in group A.

In contrast, the value of SLPmax for group B decreases slowly because the contribution ratio of nanoparticles from region III is greater than region I when σ increases from 0 to 0.25. The contribution of nanoparticles from region I increase when σ increases from 0.25 to 0.5, resulting in a decrease in the value of SLPmax for group B faster than group A.

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The competition between Néel and Brown relaxation losses is a decisive role in this phenomenon. 2.3. The role of magnetic anisotropy on the competition between Néel and Brown relaxation losses

Two groups of magnetic fluids (group A and group B) exhibit different characteristics of the optimal parameters of MIH. For group A, the value of SLPmax decreases strongly with expanding size distribution and is independent on viscosity. For the B group, the SLPmax value decreases slowly with expanding size distribution and was dependends on the viscosity. The cause of this phenomenon is due to the competition between Néel and Brown relaxation losses. The Néel relaxation loss dominates for group A and the Brown relaxation loss dominates for group B. These results show the important role of magnetic anisotropy with this competition.

Figure 2.18. The plot of SLP(D) for Fe3O4 at various K khác nhau

The plot of SLP(D) for Fe3O4 changes from “sharp” to “bell” and the changing of peak is at 34 kJ/m3. All optimal parameters for Fe3O4 change with changing of K.

Table 2.11. The value of Dcp, ∆Dcp and SLPmax for Fe3O4 Magnetic anisotropy

(kJ/m3) Dcp

(nm) ∆Dcp

(nm) SLPmax

(W/g) 5 23 3 169,9

10 18,5 3 130,5 15 16,5 4 99,9 20 15 8,5 82,4 25 14 11,5 69,5 30 13,5 13,5 60 34 13 15 54,9 35 16 15 54,9 40 16 15,5 54,9 45 16 16 54,9 50 16 16 54,9

When the value of K increases from 5 kJ/m3 to 34 kJ/m3, the value of Dcp changes because the Néel relaxation loss still affects this parameter. When the value of K for Fe3O4 is larger than 35 kJ/m3, Dcp and SLPmax are not changed due to the domination of Brown relaxation loss. So, it changes abruptly at some critical anisotropy KC = 35 kJ/m3.

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For optimal parameter ∆Dcp, the width of peak of SLP does not changes abruptly at K = 35 kJ/ m3. It is continuous process with beginning at the value of K = 15 kJ/ m3 and saturating at K = 35 kJ/ m3. The value of KC is checked by this result: the SLPmax value decreases slowly with expanding size distribution for Fe3O4 with K ≥ 35 kJ/m3 – the Brown relaxation loss dominates.

Figure 2.20. Dependence of ( )

( )max

max 0SLP

SLPσ

σ = on σ for Fe3O4

Bảng 2.14. The value of KC at various viscosity or frequency

f (kHz) KC (kJ/m3)

η = 1mPa•s η = 2mPa•s η = 3mPa•s η = 4mPa•s η = 5mPa•s 10 2 6 9 11 14

100 20 33 47 60 72 250 50 63 85 119 143 500 59 112 163 >180 >180 750 100 153 >180 >180 >180 1000 102 >180 >180 >180 >180

It can be seen, that the anisotropy boundary of the transition from Néel to Brown domination changes with changing the frequency of AMF, depending yet on the viscosity of the magnetic fluids

Figure 2.22. The plots of KC versus (a) f with fitting function ( ) ( )( )1 01 1 B f f

CK f A e− × −= −

or (b) η with fitting function ( ) 2 2CK A Bη η= + ×

The shift from the main contribution by the Néel relaxation loss to the Brown relaxation loss can occur for nanoparticle fluids with depending on the choice of f and η suitable the value of given K. For example,

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the Néel relaxation loss dominates when f is equal 250 kHz and η is equal 1 mPa•s for magnetic fluid Fe3O4 (K = 40 kJ/m3). For this magnetic fluid, the Brown relaxation loss dominates when f is larger than 400 kHz and η is larger than 4 mPa•s. It is confirm that the role of magnetic anisotropy on the competition between Néel and Brown relaxation losses. 2.4. Some orientations for experimental study

The synthesis requirement for group A is indicated so that the error between size and critical size within 2 nm and the standard deviation of size distribution is smaller than 0.25. For group B, the error between size and critical size can be up to 5 nm and the standard deviation of size distribution is smaller than 0.4.

These results showed that a behavior to analyzing the competition of contribution between Néel and Brown relaxation losses: the different of dependence of SLP on viscosity on two groups A and B. If SLP depends on viscosity, the main heating generation is the Brown relaxation loss. In contrast, the main heating generation mechanism is Néel relaxation loss with independence of SLP on viscosity.

Based on the value of K, the shift from the main contribution by the Néel relaxation loss to the Brown relaxation loss can occur for nanoparticle fluids by changing frequency or viscosity. For example, the main heating generation is the Brown relaxation loss at f ≤ 200 kHz for magnetic fluid with K = 50 kJ/m3. However, the main heating generation mechanism is Néel relaxation loss for this magnetic fluid when f is larger than 400 kHz.

CHAPTER 3 VERIFYING THEORY BY EXPERIMENTAL RESULTS

3.1. Fabrication of CoFe2O4 and MnFe2O4 magnetic fluids 3.1.1. Chemicals and equipment

Synthesis of CoFe2O4 and MnFe2O4 nanoparticles by hydrothermal method was conducted at Laboratory of Magnetism and Superconductivity, Institute of Materials and Science. The chemicals used include CoCl2.6H2O (99.99%), MnCl2.4H2O (99.99%), FeCl3.6H2O (99.99%), and solid NaOH (99.99%) of Merck (Germany), HCl and acetone are of Chinese industrial chemicals with purity of 98.9%. 3.1.2. Process of synthesizing nano particles

CoFe2O4 and MnFe2O4 nanoparticles were fabricated by hydrothermal method described in the following diagram (Figure 3.2.)

Figure 3.2. Process of synthesizing CoFe2O4 and MnFe2O4 nano particles

3.1.3. Fabrication of magnetic fluids

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CoFe2O4 and MnFe2O4 magnetic fluids were formed according to the following process: the magnetic nanoparticles were removed from the thermos flask - it was still in NaOH solution. Then the magnetic nanoparticles were washed several times by pure water. Magnetic nanoparticles were dispersed into solvents by ultrasonic vibrations (2 hours) into magnetic fluids. 3.2. Structure and magnetic property 3.2.1. Structure

Figure 3.4. X-ray diffraction of samples: (a) MnFe2O4 and (b) CoFe2O4

The diffraction peaks at the planes of (220), (311), (222), (400), (422), (511), and (440) confirm the

presence of single-phase face-centered cubic structure. The patterns in (a) and (b) are in good agreement with their corresponding standard patterns of CoFe2O4 (cubic, space group: Fd3m, Z = 8; ICDD PDF: 22–1086) and MnFe2O4 (cubic, space group: Fd3m, Z = 8; ICDD PDF: 73–1964), respectively. The broad peaks in Co and Mn ferrite indicate fine nanocrystalline nature of samples.

For MFO sample, the obtained a = 8.39 Å was smaller than that of bulk counterparts (8.51 Å). Oxidation of Mn2+ to Mn3+ and different cation distributions of Mn ferrite nanoparticles could lead to decrease in the lattice constant. In bulk Mn ferrite, cation distribution is demonstrated as (Mn0.8

2+Fe0.23+)A(Mn0.2

2+Fe1.83+)B, where A and B denote the tetrahedral and octahedral sites in spinel

structure, respectively. Oxidation of Mn2+ (0,81 Å) to Mn3+ (0.72 Å) reduces the lattice parameter. Aslibeiki and Kameli obtained a = 8.34 Å for ∼ 6.5 nm MnFe2O4 nanoparticles prepared by a thermal decomposition method. They explained this result by discussing the difference in the cation distribution between nanoparticles and bulk manganese ferrite. For CFO sample, a = 8,39 Å is approximately equal to the lattice constants obtained from bulk (a = 8.38 Å).

Table 3.2. The value of DXRD and aexp

Sample Mean szie lattice constant

DXRD (nm) DFESEM (nm) aexp (Å) aLT (Å) MFT100 16 19 8.39

8.51 MFT120 18 21 8.39 MFT140 20 22 8.40 MFT160 23 26 8.40 MFT180 29 31 8.41 CFT100 18 20 8.39

8,38 CFT120 21 23 8.39

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CFT140 24 27 8.39 CFT160 28 32 8.41 CFT180 34 38 8.42

3.2.2. Magnetic properti of CoFe2O4 and MnFe2O4 Fig. 3.7 and Fig 3.9. show the typical room-temperature hysteresis loops for two samples. The

enlarged view of M-H in the inset of Fig. 3.7 confirms this superparamagnetic behavior

Figure 3.7. Magnetic hysteresis loops at T=300 K of MnFe2O4 nanoparticles

Table 3.3. The value of MS, Keff and SPMD for MnFe2O4 nanoparticles Sample MS (emu/g) Keff (erg/cm3) SPMD (nm)

MFT100 55 42.77 10× 41 MFT120 59.9 43.01 10× 40 MFT140 63.1 43.18 10× 40 MFT160 65.4 43.29 10× 39 MFT180 68.1 43.29 10× 39

Different from the magnetic nanoparticles MnFe2O4 that all showed the pure superparamagnetism behavior, the CoFe2O4 nanoparticles exhibit significant coercivity. As the particle size increases, the coercivity of these particle systems increases from 1200 to 2650 Oe (Table 3.4). The HC values of CoFe2O4 magnetic nanoparticles were used to determine the value of effective magnetic anisotropy.

Figure 3.9. Magnetic hysteresis loops at T=300 K of CoFe2O4 nanoparticles Table 3.4. The value of MS, HC, MR and Keff for CoFe2O4 nanoparticles

Sample MS (emu/g) HC (Oe) MR (emu/g) Keff (erg/cm3) CFT100 53.8 1200 17.5 61.07 10×

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CFT120 57.6 1400 24 61.33 10× CFT140 61.1 2300 29.5 62.3 10× CFT160 63.9 2400 32 62.46 10× CFT180 73 2650 37 63.09 10×

The value of magnetic anisotropy of CoFe2O4 nanoparticles is range form 61.02 10× to

( )6 33.09 10 /erg cm× . 3.3. Hydrodyamic diameter and viscosity of magnetic fluid 3.3.1. Hydrodyamic diameter of nano particles

The hydrodyamic diameter of the two nanofluids, CFO and MFO nanoparticles, were measured using a dynamic light scattering (DLS) system.

Table 3.5. Distributions of the hydrodynamic diameter

Sample Size distribution

DH (nm) σ MFT100 21 0.18 MFT120 23 0.18 MFT140 24 0.21 MFT160 27 0.17 MFT180 37 0.1 CFT100 25 0.18 CFT120 27 0.12 CFT140 29 0.1 CFT160 38 0.25 CFT180 43 0.27

3.3.2. Viscosity of magnetic fluid Rheological characterization of nanofluids was performed by a Sine wave Vibro Viscometer SV 10,

featuring the vibrating tuning fork measurement method. It measures viscosity by detecting the driving electric current necessary to resonate two sensor plates at constant frequency of 30 Hz and amplitude of less than 1 mm. The temperature dependence of the viscosity was measured at room temperature. 3.4. Magnetic Inductive Heating

Magnetic Inductive Heating was carried out on RDO-HFI-5 kW. The Specific Absorption Rate – SAR is given by:

s

i

m TSAR Cm t

∆=

∆

3.5. Some experimental results for verifying theoretical results 3.5.1. Dependence of MIH on alternating magnetic field

For ferrite nanofluids, eddy current losses are almost negligible because it has low conductivity. For MFT100, the major heating contribution is relaxation loss because magnetic nanoparticles are superparamagnetic. For CFT100, the mainly heating contribution is also relaxation loss because the value of H is smaller than the coercivity (1200 Oe - Table 3.4.

Table 3.6. SAR for MFT100 and CFT100 nanofluids H (Oe) SAR (MFT100) (W/g) SAR (CFT100) (W/g)

50 8.8 6.9

17

60 13.4 9.2 70 20 13.8 80 31.7 21.3

Figure 3.15 shows that SAR depends on the amplitude of AMF as a quadratic form. This experimental result is in good agreement with results of M. Cobianchi, P. M. A. Caeteno and B. B Lahiri. It confirmed that the LRT is suitable for the MIH at low magnetic fields.

As can be seen from figure 3.15, SAR does not depends on the amplitude of AMF as a quadratic form at H = 80 Oe. In other words, LRT is inaccurate with the amplitude of AMF lager than 80 Oe. The value of parameter ξ for MFT100 and CFT100 are 0.85 and 1.24 when H is equal to 80 Oe. While the value of parameter ξ for MFT100 is is the intersection between the two models: SWMBTs and LRT, the value of parameter ξ for CFT100 indicated that the heating contributions are relaxation loss and hysteresis loss. Therefore, to accurately compare the experimental results and the LRT, the SAR value of these two systems is subtracted from the heating contribution from the hysteresis loss. This is method that P. H. Nam and colleagues used in their work.

Figure 3.15. Depenedence of SAR on the amplitude of AMF for MFT100 and CFT100.

The solid lines represent the fitting curve assuming the quadratic function

The dependences of SAR on f are shown in Fig. 3.15, which can be fitted very well by a linear relationship for CFT100 and MFT100. These experimental results are in good agreement with results of M. Cobianchi, Kishimoto and Fortin

Table 3.7. The value of SAR for MFT100 và CFT100

f (kHz) SAR (MFT100)

(W/g) SAR (CFT100)

(W/g) 166 10.5 2.6 178 16.9 8.2 236 31.7 21.3

The dependences of SAR on AMF indicated that the LRT is suitable for the MIH at low AMF for CFT100 and MFT100.

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Figure 3.17. The dependences of SAR on f

The solid lines represent the fitting curve assuming the linear function

3.5.2. Dependence of MIH power on particle size The particle size of sample was changed by changing the synthesis temperature from 100 oC to

180oC. The values of size of samples are in range from 21 nm to 43 nm. The existence of critical particle size was found in many theoretical studies. Surprisingly, not much

experimental work is reported on the influence of particle size. It is known that these were previously published only in two experimental works by Deatsch et al. and Krishnan et al. for Fe3O4 nanoparticles. Krishnan et al. found that the values of Dcp approximately equal to 16 nm at 170 Oe, 376 kHz. By performing data from eight different references, Deatsch et al. indicated that SAR maximized at Dcp ∼ 15-18 nm.

Figure 3.19. The value of SLP/MS and SAR/MS for MnFe2O4 magnetic fluids

As can be seen Fig. 6, the value of SAR/MS maximized for a range of about 25-30 nm. It is interesting that both calculated SLP/MS and experimental SAR/MS of MFO exhibits a peak at Dcp of about 27 nm (MFT160). The experimental data are in good agreement with those data from theory.

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Figure 3.20. The value of SLP/MS and SAR/MS for CoFe2O4 magnetic fluids

For the CoFe2O4 magnetic fluids, the value of size of samples are quite far above the optimal size (Dcp = 16 nm) by calculated based on the LRT (Fig. 3.20). Although most experimental measurement points (CFT 120, CFT140, CFT160 and CFT180) have same tendency with theoretical curve when size is larger than theoretical Dcp (SAR or SLP decreases with increasing of diameter), the experimental data is not enough to comment on the existence of the peak of SLP or SAR.

Besides, we now focus our attention on the large difference in the measured and calculated values. This discrepancy might be due to the following reasons: firstly, the hydrodynamic volume is not a well defined parameter because in colloidal dispersions the particles are coated with dispersants by forming multiple layers on the surface. Secondly, there are magnetic interactions in the samples while non-interacting nanoparticles are assumed in the calculation. In a recent work, Serantes et al. have numerically studied the effect of magnetic interactions in MNPs on the magnitude of SAR. They found that in ferromagnetic MNPs having dipolar interactions, SAR is enhanced (reduced) at low (high) field and is saturated at a higher field than independent MNPs. 3.5.3. Analyze the contribution of Néel and Brown relaxation losses

The SLP value of MFT100 is almost unchanged with the viscosity of the magnetic fluid: this value decreases from 65 W/g to 63.7 W/g when the viscosity increases from 1 to 2 mPa•s. The changing is very small, accounting for only 2% of the SLP value of MFT100 in pure water. In contrast, the changing for CFT100 is account for more than 34% (17 times more than MFT100). Therefore, it is evident that SLP of two ferrites differently respond to viscosity.

Table 3.10. SLP and SAR for CFT100 and MFT100

Sample η

(mPa•s) SAR

(W/g) SLP

(W/g) Sample

η

(mPa•s) SAR

(W/g) SLP

(W/g)

CFT100

1.37 38.7 72

MFT100

1 12 65 1.56 19.9 63.6 1.2 10.6 64.7 1.74 16.7 57.3 1.4 11.3 64.4 1.97 11.5 51.8 1.6 10.9 64.1 2.12 9.1 47.3 1.8 11 63.9

2 10 63.7 It is interesting that both SLP (theoretical results) and (experimental results) SAR of CFT100 are

greatly influenced by the surrounding viscosity while those of MFT100 are almost unaffected.

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Figure 3.22. Dependence of SAR on viscosity for (a) MnFe2O4 and (b) CoFe2O4.

The red lines represent the theoretical results based on LRT.

In case of CFT100 nanofluids, SLP is influenced by the viscosity because due to its higher magnetic anisotropy the “Brown relaxation loss” dominated heating power. In contrast to Co-nanofluid, both the SLP and measured SAR of Mn-nanofluid were independent of the viscosity. This result implies that the nanofluid is soft ferrite in which the “Néel relaxation loss power” dominated.

CONCLUSION

The theoretical results of MIH based on LRT deduce the following conclusions: 1. It is indicated the existence of three particle diameter (D) regions that: the Néel relaxation dominates

in region I (D < DN), the Brownian relaxation dominates in region III (D > DB) and the two dissipation mechanisms contribute simultaneously in region II (DB ≤ D ≤ DN).

2. The peak behavior of heating power (SLP) versus D is characteristic differently in the two different groups of magnetic nanoparticles depending on their anisotropy (K). (i) For group A (K < KC) the peak is narrow (small width ∆Dcp), the value of SLPmax decreases strongly with expanding size distribution and is independent on viscosity. The Néel relaxation dominates totally when K << KC. Then, the contribution of Brownian relaxation became stronger with magnetic anisotropy increasing up to the transition value K = KC. For the B group (K >KC), the peak is bell-like with a large width ∆Dcp, the SLPmax value decreases slowly with expanding size distribution and was dependends on the viscosity. The Brownian relaxation dominates definitely for nanoparticles in the group B.

3. The values of KC depend on the frequency of AMF as exponential function and the viscosity of magnetic fluids as a linear function.

The experimental results of the influence of alternating magnetic field, particle size and viscosity on specific loss power for CoFe2O4 and MnFe2O4 magnetic nanoparticles indicated that:

4. The Linear Response Theory (LRT) is in good agreement with the experimental results when ξ <1. The experimental values of SLP depended linearly on frequency and by quadratic function on the magnetic field. The dependence of SLP on the particle diameter exhibited a peak at Dcp around 27 nm for MnFe2O4 fluid, which is consistent with that obtained by LRT-based calculations. The various experimental results for CoFe2O4 and MnFe2O4 confirmed the different behavior between the high-K and low-K magnetic nanoparticles groups.

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PUBLISHED REPORTS USED IN THIS THESIS

1. P. T. Phong, L. H. Nguyen, L. T. H. Phong, P. H. Nam, D. H. Manh, I. –J. Lee, N. X. Phuc, “Study of specific loss power of magnetic fluids with various viscosities”, Journal of Magnetism and Magnetic Materials 428 (2017) 36

2. P. T. Phong, L. H. Nguyen, I. –J. Lee, N. X. Phuc, “Computer Simulations of Contributions of Néel and Brown Relaxation to Specific Loss Power of Magnetic Fluids in Hyperthermia”, Journal of Electronic Materials 46 (2017) 2393.

3. L. H. Nguyen, P. T. Phong, D. H. Manh, N. X. Phuc, “Tính toán công suất đốt từ phụ thuộc vào kích thước của các hệ hạt nano từ cấu trúc spinel MFe2O4 (M=Fe, Mn, Co)”, Tạp chí Khoa học và Công nghệ 52(3B) (2014) 74.

4. L. H. Nguyen, P. Q. Thong, P. H. Nam, L. T. H. Phong, P. T. Phong, N. X. Phuc, “Influence of saturation magnetization and viscosity on specific loss power for CoFe

2O

4 and MnFe

2O

4 magnetic

nanoparticles”, Vietnam Journal of Science and Technology 54(1A) (2016) 33. 5. L. H. Nguyen, P. T. Phong, P. H. Nam, D. H. Manh, N. X. Phuc, “Influence of particle size

distribution on specific loss power of magnetic nanoparticle”, Vietnam Journal of Science and Technology 56(1A) (2018) 79.

6. L. H. Nguyen, P. T. Phong, P. H. Nam, D. H. Manh, N. T. K. Thanh, L. D. Tung, N. X. Phuc, “How to distinguish a domination of Néel or Brown relaxation contribution to loss power of magnetic inductive heating?”, Proceedings of MSSM2018 (07-10 Aug 2018, UWS, Paisley, UK), ISBN 9781903978634, pp. 188-193.