Nanoparticle Self-AssemblyDOI: 10.1002/anie.200705537

Controlling the Growth of Charged-Nanoparticle Chains throughInterparticle Electrostatic Repulsion**Hao Zhang and Dayang Wang*

Nanoparticles (NPs) are envisaged as both building blocks toform advanced materials[1–3] and appropriate models to gaininsight into condensed-matter physics;[4–7] this is because oftheir unique dimensions and the innovative physical proper-ties derived thereof. All these promising applications of theNPs are primarily dependent on the capability of controllingtheir spatial coupling. Self-assembly of NPs is driven byvarious forces, such as van der Waals interactions, which leadto either dense and close-packed clusters or extendedcrystals.[8] The assembled structures are a result of a thermo-dynamic balance between these interactions. By capping theNPs with molecular ligands to minimize the van der Waalsattractions and induce dipolar interactions, it was recentlypossible to tune the anisotropic interactions that dominate thecourse of the self-assembly process, thus leading to aniso-tropic self-assembly of the NPs into one-dimensional (1D)chains,[9–11] two-dimensional (2D) freestanding films,[12] orquasi-2D fractal chain networks.[13] However, the control ofthe anisotropic self-assembly of NPs (for example, the chainlength) has been scarcely studied, which makes the thermo-dynamic picture revealed in the self-assembly studies hard toextend to other self-assembled systems, such as crystallizationor phase transition—this is particularly true in the case ofaqueous media where the electrostatic interactions are not atall negligible.

Electrostatic interactions are long-range interactionswhich ubiquitously exit in aqueous systems. Electrostaticrepulsive and attractive interactions between charged par-ticles are usually regarded as isotropic, thus driving the self-assembly of the particles in an isotropic crystallizationfashion. Recently, Lilly et al. successfully regulated theelectrostatic interactions between aqueous CdTe NPs by

using dimethyl sulfoxide, thus controlling the transformationof the NPs into nanowires.[14] This result suggests an interest-ing but usually ignored effect of the electrostatic interactionson the anisotropic self-assembly of charged NPs in aqueousmedia. Here, we demonstrate the profound anisotropiccharacter of electrostatic repulsions during the self-assemblyof charged NPs in the presence of a short-range anisotropicdipolar interaction, thus endorsing the anisotropic self-assembly of charged NPs into chains. Of particular impor-tance is the fact that tuning the electrostatic repulsionbetween gold NPs by using the ionic strength, and especiallythe polarity, of the colloidal suspensions led to a fine controlof the length of the gold-NP chains, that is, the number of NPsin them.

We chose negatively charged gold NPs (with a size of14 nm and stabilized by citrate) as the model system becausethe transverse configuration of their plasmon resonance ishighly sensitive to the electronic coupling between parti-cles,[15] thus enabling us to monitor the particle-chain growthin situ by using spectroscopic methods. The colloidal stabilityof charged particles in an aqueous medium is estimated byusing the Derjaguin–Landau–Verwey–Overbeek (DLVO)theory.[16] The total interaction potential (VT) is expressed asthe sum of the electrostatic repulsion potential (Velec), the vander Waals attraction potential (VvdW), the dipolar interactionpotential (Vdipole), and the charge–dipole interaction potential(Vcharge–dipole) [Eq. (1)]. For monodisperse spherical NPs, Velec,VvdW, Vdipole, and Vcharge–dipole can be calculated as shown inEquations (2)–(5).

VT ¼ Velec þ VvdW þ Vdipole þ Vcharge�dipole ð1Þ

VelecðrÞ ¼ 2pese0 aY20 lnf1þ exp½�akðR�2Þ�g ð2Þ

VvdWðrÞ ¼ �AH

6

�2

R2�4þ 2R2 þ ln

R2�4R2

�ð3Þ

VdipoleðrÞ ¼ �m2

2pese0 RðR2�4 a2Þ ð4Þ

Vcharge�dipoleðrÞ ¼ �Q2m2

6ð2pese0Þ2 kB T r4ð5Þ

Herein, r is the center-to-center separation of neighboringNPs of radius a (R= r/a), es is the relative dielectric constantof the solvent (about 80 for water), e0 is the dielectric constantof vacuum (8.854 @ 10�12 F m�1), Y0 is the surface potential ofthe particle, k is the inverse Debye length, m is the dipolemoment,Q is the effective surface charge of the NPs, kB is theBoltzmann constant, T is the absolute temperature, and AH isthe Hamaker constant of the particles (about 4 @ 10�19 J for

[*] Dr. H. Zhang,[+] Dr. D. WangMax Planck Institute of Colloids and Interfaces14424 Potsdam (Germany)Fax: (+49)331-567-9202E-mail: dayang.wang@mpikg.mpg.de

[+] Present address: State Key Lab of Supramolecular Structure andMaterialsCollege of Chemistry, Jilin UniversityChangchun 130012 (P.R. China)

[**] The authors thank H. M@hwald for helpful discussion. H.Z. isgrateful to the Alexander von Humboldt Foundation for a researchfellowship. J. Hartmann and R. Pitschke are acknowledged for theirassistance with the TEM studies and K.-H. Fung and C. T. Chan(HKUST) for their assistance with theoretical modeling of theabsorption spectra of the gold-nanoparticle assemblies. This workwas supported by the Max Planck Society.

Supporting information for this article is available on the WWWunder http://www.angewandte.org or from the author.

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3984 � 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2008, 47, 3984 –3987

gold). The Vdipole of citrate-stabilized gold NPs arises fromsurface defects and nonuniform ligand capping which, how-ever, is usually negligibly small. Thus, the colloidal stability ofsuch particles is usually determined by the balance betweenVelec and VvdW. Weakening the Velec between the particles byadding a tiny amount of salt usually causes aggregates, andeventually precipitates with an irregular shape (see theSupporting Information).

Here, the gold NPs were capped by using thioglycolic acid(TGA) (see the Supporting Information). Besides improvingthe colloidal stability of the gold NPs against salt, TGAcapping also introduced Au�S bonds, which can dramaticallyenhance the dipole moment.[17] When a small amount of NaCl(the NaCl concentration in the NP dispersions was less than30mm) was added to aqueous dispersions of TGA-cappedgold NPs, these dispersions remained stable for several days.Intriguingly, besides the original plasmon absorption at520 nm, a signal found above 600 nm evolved into a pro-nounced band upon increasing the salt concentration. Thelatter signal became stronger than the former one when theNaCl concentration was 30mm (Figure 1a). Transmission

electron microscopy (TEM) imaging of the resulting disper-sions revealed that TGA-capped gold NPs self-assembled into1D chains (Figure 1b–d). Accordingly, the plasmon absorp-tion band in the wavelength region of 600–800 nm shouldarise from a 1D transverse plasmon electron couplingbetween the gold NPs along the chains, similar to thatobserved in gold nanorods.[15] The chain length increased withthe salt concentration, which suggests a correlation between

the growth of the chain and the interparticle electrostaticrepulsion.

According to Equations (2) and (4), a decrease in thedielectric constant of the medium surrounding the chargedNPs can cause a decrease of Velec while Vdipole increases. Thus,various polar organic solvents with a smaller dielectricconstant, such as acetonitrile, ethanol, acetone, and N,N-dimethylformamide (DMF), were added to aqueous disper-sions of the TGA-capped gold NPs. Similarly to NaCl, theaddition of such solvents (for instance, acetonitrile) also led toa noticeable absorption band at longer wavelengths; this bandbecame more and more pronounced as the amount ofacetonitrile increased (Figure 2a). TEM imaging clearly

demonstrated that the length of the gold NP chains increasedin a rather linear way upon increasing the amount ofacetonitrile added (Figure 2b–d). Preliminary modeling ofthe plasmon resonance of the gold-NP chains was fairlyconsistent with the results shown in Figure 2a, thus confirm-ing that the particle chains were formed in the dispersionsrather than during drying (see the Supporting Information).We therefore conclude that the growth of the chain composedof TGA-capped gold NPs can be finely controlled byregulating the interparticle electrostatic repulsion.

To gain insight into the 1D self-assembly of negativelycharged gold NPs, we calculated Velec and VvdW for TGA-capped gold NPs (size: 14 nm) with negatively chargedsurfaces, according to Equations (2) and (3). In our calcu-lations, we assumed a spherical particle shape and aninterparticle distance equal to twice the Debye length (1

k). Ina 30mm NaCl solution, for instance, 1

k = 2 nm, VvdW =

Figure 1. a) UV/Vis absorption spectra of gold-NP solutions (particlesize 14 nm) capped without (c) and with (b) TGA, and absorp-tion spectral evolution of the TGA-capped NPs as a function of theNaCl concentration: 12.5mm (g), 22.5mm (d), 25 mm (dash–dot–dotted), 27.5mm (a), and 30mm (short-dotted). b–d) TEMimages of the TGA-capped gold-NP self-assemblies formed in thepresence of additional NaCl: b) 12.5mm, c) 17.5mm, and d) 22.5mm.

Figure 2. a) UV/Vis spectra of gold-NP dispersions in water–acetoni-trile at volume ratios of 1:1 (g), 1:2 (a), and 1:3 (c). b–d) TEM images of the gold-NP chains obtained using the differentwater–acetonitrile volume ratios: b) 1:1, c) 1:2, and d) 1:3. The corre-sponding high-magnification TEM images are shown in the insets.

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�2.24kBT, and Velec = 4.6kBT (at 300 K). This result indicatesthat Velec and VvdW of the NPs are of the same order ofmagnitude, while the former value remains larger to guaran-tee a better colloidal stability. Once an anisotropic dipolarattraction Vdipole (of the order of several kBT) has beeninduced between the gold NPs (enhanced by the Au�Sbonding of the TGA capping), the attractive forces betweenthe NPs may overcome the electrostatic repulsion, thusleading to coupling of neighboring particles. Because of theanisotropic character of the dipolar interaction, coupling ofthe gold NPs is considered anisotropic, as suggested in theliterature.[9–13]

Here, however, the isotropic electrostatic repulsionbetween the negatively charged gold NPs remained stronger,which should inhibit the growth of the NP chain.[14] Toelucidate the effect of electrostatic repulsions on chaingrowth, we evaluated the electrostatic repulsion potential ateither end of a NP chain in the proximity of an NP, Vend

elec, andthat between the chain side and a neighboring NP, Vside

elec

(Figure 3). We demonstrated that once the gold NPs self-assembled into a chain, the electrostatic double layer wasrearranged into a uniform layer surrounding the wholechain.[18] Based on this fact and the modified model ofelectrostatic interaction between elongated objects,[19] Vend

elec

and Vsideelec between an NP chain composed of n NPs and an NP

can be derived as shown in Equations (6) and (7), where 1 is

the charge density, A is the surface area, n is the number ofNPs (n> 2), and D is the length of the NP chain.

Vendelec ¼

Xn

QDi¼ZDtotal

0

1ADi

dD ¼ 1A lnDtotal ¼ 1A ln2n a ð6Þ

Vsideelec ¼ 21A ln n a ð7Þ

Comparison of Equations (6) and (7) indicates that Vsideelec is

always bigger than Vendelec, thereby underlining the anisotropic

character of the electrostatic repulsion between the NP chainsand surrounding NPs. Once two NPs have coupled to form adimer—driven mainly by dipolar interactions and van derWaals forces—the difference between Vend

elec and Vsideelec allows

other neighboring NPs to preferentially attach to the ends ofthe dimer, rather than to the sides, thus forming linear NPtrimers, tetramers, and eventually, 1D chains (anisotropic self-assembly of the NPs, see Figure 3). If Vside

elec between NPs andNP chains becomes weaker than VvdW, the NPs will start toattach to the chain sides, thus generating quasi-2D isotropicfractal aggregates, and eventually, 2D sheets (see Figure 3 andthe Supporting Information).

During the endorsed anisotropic growth of the chainscomposed of negatively charged gold NPs (under equilibriumof different forces, namely, VT = 0), the value of Vend

elec shouldbe equal to the sum of VvdW, Vdipole, and Vcharge–dipole [Eq. (8)],while Vside

elec should be kept higher to warrant chain growth anda higher colloidal stability of the chains. Accordingly, we cancalculate the number (n) of NPs composing the chain by usingEquation (9).

Vendelec ¼ �ðVvdW þVdipole þ Vcharge�dipoleÞ ð8Þ

n ¼exp½�ðVvdW þVdipoleÞ=1A�

2 að9Þ

Equation (9) reveals a clear correlation between n and thesurface charge density 1 of the particle. Note that the short-range interactions between NP chains and NPs should beequal to those between two NPs. As a result, the reduction of1 by altering the ionic strength and/or the dielectric constantof the surrounding media can increase n, thus increasing thechain length. This is fairly consistent with our present results.The arguments given here also follow experimental andtheoretical studies of Langmuir monolayers, where dipolarinteractions (that is, anisotropic interactions within a plane)cause elongated lipid domains.[20–22]

In conclusion, we have used long-range electrostaticrepulsions to control the growth of chains composed ofcharged gold NPs. Chain growth was triggered by short-rangeanisotropic dipolar interactions between the NPs. The colloi-dal stability and organization of self-assembled systems inaqueous media are always governed by long-range electro-static repulsion forces. In this scenario, we demonstrate aninteresting and non-negligible contribution of the electro-static repulsion which—albeit usually being regarded asisotropic—can enforce the anisotropic self-assembly ofcharged NPs in the presence of anisotropic interactions.

Figure 3. Self-assembly of charged particles endorsed by a balancebetween isotropic long-range electrostatic repulsion and isotropicshort-range van der Waals attraction between the particles in thepresence of short-range anisotropic dipolar attraction forces.

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Since short-range anisotropic dipolar interactions are oftenencountered in self-assembled systems, our findings can beeasily generalized to the self-assembly of various chargedpieces, thus providing a better elucidation of, for instance, theformation of irregular shapes upon aggregation of chargedparticles and crystallization of charged nuclei.[23]

Experimental SectionAn aqueous suspension of gold NPs (with a size of 14 nm) wasprepared by reduction with citrate, which was then replaced by TGAvia ligand exchange. Prior to directing the self-assembly of the goldNPs using NaCl, the as-prepared gold solution (10 mL) was diluted(to 40 mL) using deionized water (8.6 @ 1010 NPmL�1). Afterwards,aliquots of 1m NaCl were added to diluted solutions of the gold NPs(4 mL) capped with and without TGA. The concentration of NaClranged between 0 and 75mm. Additionally, different solvents—including acetonitrile, ethanol, acetone, and DMF—were added toaqueous solutions of the TGA-capped gold NPs. The additional-solvent-to-water ratios ranged from 3:1 to 1:1. Self-assembly of thegold NPs was analyzed by means of UV/Vis absorption spectroscopy(using a Cary 50 UV/Vis spectrophotometer) and TEM (using a ZeissEM 912 Omega microscope at an acceleration voltage of 120 kV).

Received: December 4, 2007Revised: February 1, 2008Published online: April 11, 2008

.Keywords: anisotropy · electrostatic interactions · gold ·nanostructures · self-assembly

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