Formation of Dense Nanoparticle Monolayers Mediated by Alternating

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J. Phys. Chem. C 2010, 114, 8800–8805

Formation of Dense Nanoparticle Monolayers Mediated by Alternating Current Electric Fields and Electrohydrodynamic Flows Myung-Geun Song, Kyle J. M. Bishop, Anatoliy O. Pinchuk, Bartlomiej Kowalczyk, and Bartosz A. Grzybowski* Department of Chemical and Biological Engineering & Department of Chemistry, Northwestern UniVersity, 2145 Sheridan Road, EVanston, Illinois 60208 ReceiVed: January 27, 2010; ReVised Manuscript ReceiVed: March 8, 2010

Monolayers comprising oppositely charged metal nanoparticles are deposited onto conductive surfaces upon application of ac fields of frequency ranging from 0.1 to 800 kHz. It is found that surface coverage depends on the frequency and is maximal at ∼300 kHz, for which the deposited coatings feature large, hexagonally close packed domains. The observed trends are rationalized by a model in which ac forcing induces hydrodynamic flows around the particles. These flows, in turn, translate into additional interparticle attractions facilitating dense particle packing. Introduction Self-assembly of nanoparticles (NPs) into ordered, twodimensional (2D) lattices provides an interesting route to nanostructured thin films with applications in sensors,1,2 optical or electronic devices,3–6 and magnetic data-storage media.7–9 To date, most strategies for making NP superlattices have relied on evaporation-induced10–20 ordering or Langmuir-Blodgett techniques.21–24 In the former, formation of ordered NP arrays is usually driven by the combination of attractive van der Waals (vdW) forces25 between the NPs and by the reduction of available volume due to the evaporation of an organic solvent (e.g., mesitylene,10 THF11 toluene,11–13,15,16,19,20 chloroform,17 hexane,16,17 etc.). While for equally sized particles these procedures typically yield hexagonally close-packed arrays, other types of orderings are possible by using mixtures of NPs of different sizes,13 by the introduction of additional interactions (e.g., electrostatic20), or by Marangoni-type instabilities in the evaporating/dewetting fluid.26 An interesting extension of evaporation-based methods relies on the self-assembly of the NPs at a liquid-air interface, evaporation of the liquid, and transfer of the NP array thus formed onto a solid substrate such as PDMS.6,27,28 Langmuir-Blodgett techniques21–24 are conceptually similar but the confinement is achieved by reducing the area of a two-dimensional trough and thus “squeezing” the NPs into closely packed arrangements. While confinement-based methods appear attractive in laboratory practice, the need to evaporate organic solvents or to use specialized LB equipment limits their scalability and might raise environmental concerns (if, for example, evaporation were to be performed on a large scale). From a practical perspective, it would be desirable to develop methods that deposit large 2D superlattices from aqueous solutions under mild chemical conditions. In this context, electrophoretic deposition (EPD) under constant voltage (dc field) is one promising strategy, and the electroosmotic or electrohydrodynamic (EHD or “lateral”) interparticle forces induced by the applied field29,30 have been shown to assemble ordered superlattices of both micro-29–33 and nanoparticles,29,34–37 albeit often with poor control of the * Correspondence should northwestern.edu (B.A.G.).

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thickness or structural ordering of the deposited layers.31,35–37 As an alternative, deposition mediated by ac fields has been investigated29 yielding high-quality monolayers of micrometersized particles on conductive electrodes; at the same time, application of ac to solutions of nanoscopic particles has so far produced only sparse coatings or small clusters comprising several to tens of closely packed NPs.29 In this work, we use ac fields to deposit large (several square millimeters), densely packed monolayers from aqueous suspensions of oppositely charged metal NPs. We have recently shown38 that such suspensions spontaneously form coatings (via a cooperative electrostatic adsorption mechanism39) on a variety of materials including polymers, glasses, metals, and semiconductors. Although the electrostatic forces between the particles control the coating’s thickness precisely (adsorption selfterminates after deposition of an electroneutral monolayer), they do not evolve the NPs into ordered arrangements and give maximal surface coverages of only ca. 65%. When, however, the electrostatic interactions are combined with electrohydrodynamic flows induced by ac fields, they produce dense (up to ∼84% surface coverage) NP monolayers with large hexagonally close-packed domains. Remarkably, the degree of ordering and the surface coverage depend on the ac frequency and are maximized for frequencies around ∼300 kHz. A theoretical model based on electrohydrodynamic flows induced by the dynamic polarization of the NPs’ double layers explains the observed frequency dependence and close-packed lattices. These results illustrate the potential importance of hydrodynamic effects in the formation of nanoscale assemblies and may prove useful in the development of other frequency-tunable deposition techniques. Experimental Section i. Nanoparticles and Their Electroneutral Suspensions. We used Au (average metal core diameter 6.1 nm, dispersity σ ) 8.4%) and/or Ag (5.8 nm, σ ) 28.8%) nanoparticles (Figure 1a) stabilized with self-assembled monolayers (SAMs40) of mercaptoundecanoic acid (HS(CH2)10COOH, MUA from Aldrich) or N,N,N-trimethyl(11-mercaptoundecyl)ammonium chloride (HS(CH2)11NMe3+Cl-, TMA from ProChimia, Poland).41–43,38 An electroneutral NP suspension containing approximately equal

10.1021/jp1008253  2010 American Chemical Society Published on Web 04/21/2010

Dense Nanoparticle Monolayers

Figure 1. (a) Scheme and average dimensions of AuMUA and AgTMA NPs. (b) Schematic diagram of the experimental cell (the interelectrode distance, H ≈ 340 µm). FG denotes the function generator.

numbers of positively and negatively charged particles was prepared according to the precipitation/redissolution method described previously.38,41 In a typical procedure, a 10 mM suspension of AgTMA (concentration in terms of metal atoms) was added dropwise to 10 mL of a 10 mM suspension of AuMUAs deprotonated by adjusting pH to 11.0 (i.e., above the pKa ≈ 6-8 of the MUA SAM;44 the identity of metal cores did not affect the procedure which was identical for AuTMA/ AuMUA and AgTMA/AgMUA combinations). During this titration, oppositely charged NPs were initially stable in solution and precipitated only at the point of electroneutralitysthat is, when the charges on the NPs were neutralized, ∑QNP(+) + ∑QNP(-) ) 0.42,45,46 The precipitate was then redissolved by washing several times with deionized (DI) water (to remove excess salts) and heating at 65 °C overnight. The suspension thus obtained was diluted to 4 mM, was stable for periods up to several months, and showed no aggregation or precipitation of the constituent NPs. ii. The deposition cell (Figure 1b) was built from borosilicate glass microscope slides. An aluminum electrode (EMD Chemicals Inc., 1 cm × 3 cm) was glued to the bottom slide and was covered by 140 µm of carbon tape and 200 µm glass spacer. The top (deposition) electrode was made of a silicon wafer sputter-coated (using Denton Vacuum DeskIII sputterer) with a 15 ( 5 nm layer of Au/Pd (60%/40%). The volume of the chamber thus formed was approximately 30 µL. The electrodes were connected to a function generator (BK Precision model 3011B), and a sinusoidal ac electric field was applied between the electrodes. The applied voltages, Vpp (peak-to-peak voltage) ranged from 2 to 20 V corresponding to the electric fields E0 ) 59-590 V/cm; the range of frequencies, f, investigated was between 100 Hz and 1 MHz. The values (peak-to-peak) of the applied voltage and field frequencies were monitored independently using a digital oscilloscope (Tektronix, model TDS 360). Deposition was carried out for times ranging from 30 s to 40 min. Afterward, the top electrode was detached from the cell and washed with DI water (18.2 MΩ cm) several times, and the deposited NPs were analyzed by scanning electron microscopy (SEM) for ordering and by X-ray photoelectron spectroscopy (XPS) for elemental composition. Results and Discussion 1. Experimental Trends. The surface coverage and the degree of ordering in the NP monolayers depended on the

J. Phys. Chem. C, Vol. 114, No. 19, 2010 8801 frequency of the ac field, f (Figure 2). For low frequencies, f ≈ 100 Hz, the deposited NPs were sparse irrespective of the field strength. For the range of frequencies f ≈ 1-100 kHz, the NPs showed short-range ordering (islands containing tens of tightly packed NPs) but the monolayer had many large voids. Dense coatings (surface coverage calculated from SEM images ∼0.013 NP/nm2 or ∼84%; cf. Supporting Information for details) were obtained for f ≈ 250-500 kHz. These coatings had large (up to hundreds of NPs) domains of hexagonally close packed NPs. When the frequency was increased further, both the surface coverage and the degree of ordering decreased to give “cellular” patterns shown in the rightmost image in Figure 2. We note that the presence of oppositely charged nanoparticles was essential for the formation of densely packed monolayers. With particles of only one polarity (e.g., only AuTMA or only AuMUA) or with uncharged particles (e.g., Au/HS(CH2)11OH), the deposited filmssif anyswere sparse, and sometimes more than one layer of NPs was deposited. In sharp contrast, oppositely charged NPs never deposited more than a monolayer. As evidenced by the XPS analysis (Figure 3), this monolayer contained equal amounts of the oppositely charged NPs and was therefore electrically neutral. The fact that no further layers were deposited can be attributed to the fact that the interactions between the NPs and the surface (both with and without the applied field; see ref 38) are stronger than those between neighboring NPs. Consequently, the forces mediating the adsorption of a potential second layer are weaker than those mediating the formation of the first layer, and a second layer does not form (except at high field strengths; see Supporting Information). 2. Theoretical Model. The frequency dependence of the monolayer packing/ordering can be explained by the ac fields inducing the motions of both the charged NPs and the ionic species near the electrode. These charge motions give rise to electrohydrodynamic flows that ultimately translate into lateral attraction between the particles and facilitate their tight packing on the electrode surface. To show this we consider the following effects: 2a. Electric Field in the Cell. The time-dependent electric field within the cell may be calculated using the standard electrokinetic model47 and is given by the real part of

Ez(z, t) )

V0 E (z) exp(-iωt) 2h 0

(1)

with

E0(z) ≡

γ cosh[γ(1 - z/h)] cosh(γ) - iγν2 coth(γ) 1 - iγν2 coth(γ)

(2) Here, V0 is the applied voltage difference between the electrodes located at z ) 0 and z ) 2h (cf. Figure 4a), ω ) 2πf is the angular oscillation frequency, and E0 is a complex coefficient. The dimensionless variables, ν and γ, are defined as ν2 ) ω/κ2D and γ2 ) (κh)2(1 - iν2), where D is the ionic diffusivity, and κ-1 ) (ε0εkT/2cse2)1/2 is the so-called screening length for an monovalent electrolyte of concentration cs. Equations 1 and 2 assume that the electrodes are “perfectly polarizable” (i.e., no surface reactions and therefore no flux of ions at the surface) and that the applied voltages are small, φ0 e kT/e. When the screening length, κ-1, is much smaller than the separation between the electrodes (i.e., κh . 1; here, κh ≈ 1.7

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Figure 2. SEM images of typical binary AuMUA/AgTMA NPs coatings deposited with different ac frequencies ranging from 0.1 to 800 kHz. All samples were prepared at the same electric field strength of 150 V cm-1 (i.e., 5 V across 340 µm) and 15 min of field application. Scale bars are 100 nm; the insets are 50 nm × 50 nm.

Figure 3. SEM image (left) of a typical binary AuMUA/AgTMA NPs coating for a frequency of 500 kHz and field strength equal to 150 V cm-1 (scale bar is 100 nm). The XPS spectrum (right) shows that the coating has approximately equal numbers of Au and Ag NPs.

× 104), the field coefficient at the electrodes is well approximated as

E0(0) ) E0(2h) ≈

1 - iν2 1/γ - iν2

(3)

This quantity is plotted in Figure 4b using the experimental parameters. Importantly, the strength of the electric field decreases with increasing frequencysfrom E0 ≈ κh ) 17000 at frequencies less than ∼10 Hz (i.e., ω , κD/h) to E0 ≈ 1 for frequencies greater that ∼100 kHz (i.e., ω . κ2D). The charge density, F, within the cell is related to the field by F ) ε0ε∇ · E; substituting the field from eq 1 and assuming κh . 1, one obtains

F(z, t) ≈

[

ε0εV0γ

2h2 exp[γ(z/h - 1)] - exp[-γ(z/h + 1)] exp(-iωt) (4) 1/γ - iν2

]

2b. Particle Motion. In an oscillating electric field, a small charged particle moves with a velocity, U, proportional to the local electric field, E(r,t)si.e., U ) µE(r,t) where µ is the electrophoretic mobility of the particle. Here, the mobilities for positive and negatively charged NPssµ+ and µ-, respectivelys were measured experimentally (using a Malvern Zetasizer Nano ZS) to be ca. (2.5 × 10-8 m2 V-1 s-1 (corresponding to ζ-potentials of ca. (50 mV). For a spatially homogeneous, oscillating field (e.g., in the z direction: Ez ) E0 cos(ωt)), the position of the particle, zp, is given by zp ) (µE0/ω) sin(ωt) + z0, where z0 is the initial position. Notice that the amplitude of the oscillatory motion varies inversely with the oscillation frequency. For an inhomogeneous field, such as that described in section 2a, the trajectory of the particle must be integrated numerically

as illustrated in Figure 4c. Here, we find that particles of either polarity are attracted toward the wall and adopt a steady oscillatory motion at the electrode surface (independent of the particle’s initial position). The amplitude of the oscillations, zpmax, decreases with increasing frequency of the applied field (Figure 4d). Importantly, zpmax remains larger than the screening length for frequencies less than ∼100 kHz. For such frequencies, ordering cannot occur owing to the large oscillation amplitudes, which prevent oppositely charged particles from interacting significantly with one another (e.g., favorable electrostatic interactions between oppositely charged NPs are negligible when the particles are separated by one or more screening lengths). Instead, NP ordering becomes possible only for frequencies greater than ∼100 kHz, for which the oscillation amplitude is comparable to the size of the particles and less than the screening length, in which case particles interact favorably with their oppositely charged neighbors. This theoretical prediction is consistent with the experimental results that NP ordering is poor (even more so than in the absence of the field) for frequencies less than ∼100 kHz. 2c. Particle Dipole Moments. In addition to the screened electrostatic fields emanating from the charged NPs (which decay exponentially as ∼exp(-κr)), the particles also create a dipole field due to the polarization of the particle’s double layer in the applied field (Figure 5a). Importantly, these oscillating dipoles are not screened,48,49 and their fields can act over distances much longer than the screening length. The dipole moment generated by a charged NP is given by the real part of p ) RE(z,t), where R is the complex, frequency-dependent polarizability of the particle. Following the approach of Delacey and White,48 we use the standard electrokinetic model to determine R(ω) ) R′(ω) + iR′′(ω)as illustrated in Figure 5b. For applied fields oriented in the z direction, the electric field due to a single polarizable particle, E(d), is given by

E(d)(x, z) )

[(

) (

)]

3x(z - zp) 3(z - zp)2 p 1 e + - 3 ez x 4πε0ε r5 r5 r (5)

where z is the distance from the electrode surface, zp is the distance of the particle center from the surface, x is a radial coordinate (in a cylindrical system; see Figure 6a), and r2 ) (z - zp)2 + x2. For simplicity, we assume that the dipole moment is determined exclusively by the applied field (i.e., p ) Re[REz(z,t)]ez) and neglect the field contributions due to other dipoles. 2d. Electrohydrodynamic Flows. The dipole field due to a particle near the surface creates an additional horizontal component of the electric field (i.e., tangential to the surface), thereby inducing electrohydrodynamic (EHD) flows in the

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fx )

(

3x(z - zp) Fp 2 4πε0ε [x + (z - z )2]5/2 p

)

(6)

Here, we assume that the free charge density is given by eq 4 and is not significantly perturbed by the dipole fields due to the particles. The position of the particle, zp, oscillates in time as illustrated in Figure 4c. To remove the spatial dependence, integration with respect to x and z gives the net force, Fx, on the fluid.

Fx(t) ) 2π

∫ fx(t, x, z)x dx dz

(7)

Here, the integral is carried out numerically over the entire region surrounding the particle. Importantly, Fx(t) is not purely oscillatory but has a steady component, the magnitude and direction of which depends strongly on the frequency of the applied field. The period-averaged force is given by

〈Fx〉 )

1 2π

∫02π Fx d(ωt)

(8)

Finally, using scaling arguments,50 one can estimate the tangential component of the fluid velocity, ux, from the force, 〈Fx〉, as

ux ∼

Figure 4. (a) Schematic illustration of the electrode geometry and pertinent dimensions; in experiments, h ) 170 µm and κ-1 ) 10 nm. (b) Frequency dependence of the real (blue) and imaginary (red) parts of the electric field coefficient at the electrode surface; the electric field is given by Ez(t) ) (V0/2h)Re[E0 exp(-iωt)]. Here, D ) 1.5 × 10-9 m2/s and κ-1 ) 10 nm corresponding to 1 mM TMACl electrolyte. (c) Particle trajectories (i.e., distance, zp, of the particle center from the electrode surface) as a function of dimensionless time, ωt, over one oscillation period for frequencies, f ) 10 kHz (solid) and f ) 100 kHz (dashed). Red curves correspond to positively charged NPs; blue curves are for negatively charged NPs; the black dashed line at zp ) 4 nm corresponds to contact between the NP and the electrode surface. Here, the applied voltage is V0 ) 5 V, the particle radius is a ) 4 nm, and the electrophoretic mobility is µ ) (2.5 × 10-8 m2/(V s) corresponding to experimental conditions. (d) Oscillation amplitude, zpmax, as a function of the applied frequency for voltages V0 equal to 2 and 10 V, respectively. The black dashed lines correspond to the screening length, κ-1 ) 10 nm, and hard sphere contact with the electrode, a ) 4 nm.

surrounding fluid (Figure 6a). Depending on their direction, such flows can act to bring particles together or push them apart. For the experimental conditions described here, we find that these EHD flows are attractive for frequencies greater than ∼300 kHz and their magnitude is maximal at frequencies of ∼400 kHz. To see this, note that the instantaneous, electric force per unit volume on the fluid is given by f ) FE such that its horizontal component is given by

κ〈Fx〉 η

(9)

Figure 5. (a) Schematic illustratation of the dynamic polarization of the particles’ double layers under an applied ac field. (b) Dimensionless dipole coefficients, C0 ) R/4πε0εa3 and C0 ) C′0 + iC′′0, as a function of frequency for positive (blue) and negatively charge (red) nanoparticles. The parameters used in the calculation correspond to those found in the experiments: particle radius, a ) 4 nm; fluid dielectric constant, ε ) 78.55; temperature, T ) 298.16 K; fluid viscosity, η ) 0.8904 cP; electrolyte concentration, cs ) 1 mM; limiting conductance of tetramethylammonium (TMA+) and chloride (Cl-) ions, Λ+∞ ) 44.9 cm2 S mol-1 and Λ-∞ ) 76.4 cm2 S mol-1, respectively; ζ-potential, ζ ) (50 mV. The dielectric constant of the particles was assumed equal to that of the surrounding fluid; in this way, the induced dipoles are due entirely to the polarization of the NPs’ ionic atmospheres, which should be the dominant contribution for κa > 1.

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Song et al. for particle sizes comparable to the screening length and act on both positive and negative particles simultaneously. The model we developed provides a simple starting point from which to explore more electrohydrodynamic phenomena at the nanoscale, where the motion of the particles, themselves, can be just as important as that of the molecular ions. Acknowledgment. This work was supported by the Nonequilibrium Energy Research Center (NERC) which is an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0000989. M.G.S. was partly supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-352-D00042). Supporting Information Available: Additional information on the effects of field strength and surface coverage. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes

Figure 6. (a) Schematic illustration of the dipole field generated by the polarization of a negatively charged NP. This field acts on the free charge in the double layer near the electrode to generate “lateral” electrohydrodynamic flows directed toward the particle. Note that the direction of the applied field, the position of the particles, and the density of free charge all oscillate with time; however, the averaged EHD velocity is nonzero. (b) Electrohydrodynamic velocity, u (as defined in eq 9), plotted as a function of frequency for both positive (red curve) and negative (blue curve) particles. Positive velocities denote fluid flows are directed away from the particle. For frequencies greater than ∼300 kHz, the flows are directed toward the particles and reach their maximal velocity at ∼400 kHz. (c) Electrohydrodynamic flows directed toward the particles results in an effective attraction between particles as illustrated schematically.

This quantity is plotted in Figure 6b. It shows that the electrohydrodynamic flows are attractive for frequencies above ∼300 kHz and that the magnitude of the flow is maximal at frequencies of ∼400 kHz. Importantly, the electrohydrodynamic flows surrounding positive and negatively charged NPs are qualitatively similar (although the former is somewhat stronger in magnitude owing to its larger dipole coefficient; cf. Figure 5b) resulting in attractive interactions between both types of particles (Figure 6c). To first approximation, this attraction is simply the result of particles moving in the EHD flow field of their neighbors (for a more detailed consideration, see ref 51). Such flowinduced interactions combine with the electrostatic interactions present even in the absence of the field and help to organize the NPs into close-packed hexagonal lattices. Conclusions In summary, we demonstrated that ac fields perpendicular to a conductive surface induce lateral EHD flows around charged nanoparticles and that these flows facilitate the packing of nanoparticle monolayers. Since deposition takes place in an aqueous medium, our method provides an environmentally benign alternative to the deposition of NP layers from evaporating organic solvents. The fundamental novelty of this worksone that differentiates it from previous studies of EHD-mediated particle deposition50–52,29,53sis that the observed effects occur

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