Dielectrophoretic Growth of Platinum Nanowires: Concentration and

Article pubs.acs.org/Langmuir

Dielectrophoretic Growth of Platinum Nanowires: Concentration and Temperature Dependence of the Growth Velocity A. Nerowski,†,§ M. Poetschke,†,§ M. Bobeth,† J. Opitz,†,‡ and G. Cuniberti*,† †

Institute for Materials Science and Max Bergmann Center of Biomaterials, Dresden University of Technology, 01062 Dresden, Germany ‡ Fraunhofer-Institute for Non-Destructive Testing, 01109 Dresden, Germany S Supporting Information *

ABSTRACT: The growth velocity of platinum nanowires in an aqueous solution of K2PtCl4 is investigated as a function of the metal complex concentration and temperature. The solution is specially prepared to provide mainly the neutral complex cis[PtCl2(H2O)2] for growing nanowires by dielectrophoresis. The measured growth velocities indicate diffusion-limited nanowire growth at low concentration and high temperature in qualitative agreement with a theoretical analysis that includes the diffusion of metal complexes and the dielectrophoretic force on the complexes. At concentrations greater than 100 μM and low temperature, different behavior is observed, suggesting the growth rate to be limited by the deposition reaction of platinum at the nanowire tip. The enhancement of the K+ concentration is found to support nanowire growth. Possible reasons for a rate limitation and for the difference between observed and calculated nanowire growth velocities are discussed.

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INTRODUCTION In the last few years, research on nanoscale devices has intensified and bottom-up processes used to fabricate nanowires have gained in interest.1 In 2001, Hermanson et al.2 demonstrated the growth of metallic microwires from clusters in solution using dielectrophoresis. The wires assemble between two metal electrodes on an insulating substrate. Figure 1 illustrates a schematic setup. This method has several advantages compared to conventional methods: it is costefficient (no expensive equipment is used), fast (the wires grow

within seconds to a few minutes), and most importantly, the wires are already connected to the electrodes. The successful fabrication of nanowires from molecules (Pd(OAc)2) in solution has been reported by Cheng et al.3 and Ranjan et al.4 Recently, arrays of nanowires were also grown in this way.5 For sensor applications and nanoelectronics, the controlled growth of very thin, straight nanowires between electrodes is of high interest. However, dielectrophoretically grown nanowires exhibit branches or kinks. The nanowire growth is controlled by a series of process parameters, for example, the amplitude and frequency of the applied ac voltage, the composition of the solution, and the temperature. As reported in the literature,4,6 the frequency has an important effect on the nanowire morphology. Gierhart et al.,6 who assembled nanowires from gold clusters, observed a major influence of high frequencies on the straightness as well. Bhatt et al.7 reported that an increase in the viscosity of the solution yields straighter microwires. Besides the wire morphology, a further important feature is the nanowire density (number of growing nanowires per Received: January 20, 2012 Revised: April 10, 2012 Published: April 17, 2012

Figure 1. Scheme of the experimental setup for nanowire growth. © 2012 American Chemical Society

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substrate area). Cheng et al.3 found that this density increases upon lowering the frequency of the applied voltage. The difference between our approach and a method called directed electrochemical nanowire assembly (DENA) is worth pointing out. This method basically has the same setup; however, the electrochemically active species in the solution are metallic anions, not neutral complexes.8,9 Ozturk et al.8 established a theory for the diffusion-limited case that was in qualitative agreement with experiments. Furthermore, they showed that with increasing frequency it is possible to tune the nanowire’s diameter. Moreover, Pt nanowires were also grown from an aqueous H2PtCl6 solution by Kawasaki et al.9 To our knowledge, the atomistic mechanisms of the metal deposition at the growing nanowire tip are only poorly understood at present. Deeper insight into these mechanisms could provide a better understanding of the evolving wire morphology. In particular, it could reveal measures to suppress wire branching. We consider in this article the dependence of the wire growth velocity on the composition of the solution and on the temperature. When these parameters were varied, a noticeable transition in the growth rate-limiting process was revealed. To grow Pt nanowires, we use the K2PtCl4 complex because its dissociation behavior was extensively investigated.10,11 On the basis of the known dissociation mechanism of K2PtCl4, we attempted to prepare a solution that contains mainly the neutral platinum complex cis-[PtCl2(H2O)2]. The neutral complexes are strongly attracted by the nanowire tip because of the high inhomogeneous electric field around the tip. To prove our present understanding of nanowire assembly, the experimental measurements of the nanowire growth velocity have been compared with a theoretical analysis of the wire growth that includes the K 2 PtCl 4 diffusion and the effect of the dielectrophoretic force on the complexes. In the following text, we first report on our experimental measurements and present then a theoretical model that allows us to estimate the nanowire growth velocity. Finally, experimental and theoretical results are compared, and possible mechanisms that could explain our experimental observations are discussed.

Figure 2. Simulated concentration evolution of various chloroplatinates for a total concentration of c0 = 10 μM using the data of Elding.10

PtCl2 from 2000 to 3500 min is larger than 92.5%. In this case, the solution was used as is. For K2PtCl4 concentrations larger than 10 μM, the solution contains significant amounts of negatively charged metal complexes that were removed by anion exchangers (Sartorius Sartobind Q75) to achieve well-defined deposition conditions with only neutral platinum complexes. K2PtCl4 concentrations equal to or less than 10 μM would damage the ion exchangers. The resulting cis-PtCl2 concentration will be denoted as c∞ in the following text. We characterized the solution using transmission electron microscopy (TEM) and observed the presence of Pt clusters with an average diameter of around 23 nm. Photoactive cluster formation similar to that reported by Shironita et al.12 might be responsible. Although small platinum clusters were found in the solution, we believe that the major contribution to the growth of Pt nanowires is given by neutral platinum complexes, as explained in more detail in the Supporting Information. The interdigitated electrodes were fabricated lithographically. The spacing between the electrodes ranged from 2 to 4 μm. For further information on the electrode fabrication and structure, see the Supporting Information. The temperature of the glass slide was controlled by a thermoelectric element and measured with a negative temperature-coefficient resistor (NTC EPCOS type B57861S, R/T no. 8016) glued with conductive silver paint on the surface of the thermoelectric element. A dualchannel measurement instrument (Keithley 2602 System SourceMeter) served as the current source for the thermoelectric element and as the resistance measurement device for the NTC. With this setup, the substrate temperature was varied from 289 to 316 K. The voltage at the electrodes was provided by a frequency generator (Tektronix AFG320) and observed with an oscilloscope (Tektronix TDS3014). The electrodes were placed in contact with needles from a tip probe station (Karl Suss MicroTech). Before experiments were conducted, needles, chuck, tweezers, and substrates were rinsed with isopropanol to remove contaminants. For each growth experiment, we put a 15 μL drop of solution on the electrodes and applied an ac voltage φext of the form φext = V0 sin(2πft) with frequency f = 100 kHz and amplitude V0 = 4 V if not stated otherwise. As a result, the nanowires grew between the fingers of the interdigitated electrodes. Observation of Nanowire Growth. Growth Morphologies. In our experiments, we observed different types of wire shapes. The majority of the wires grew as in Figure 3a. These show occasional kinks, many branches, and an average width of 100 nm. Few exceptions can be found (e.g., wires with

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EXPERIMENTS Materials and Methods. Potassium tetrachloroplatinate(II) (K2PtCl4, 98%) and NMP (99.5%) for the lift-off were purchased from Sigma-Aldrich, chromium (Cr, 99.9%) was purchased from Goodfellow, gold (Au, 99.99%) was purchased from ESG GmbH, and glass slides were purchased from Menzel. The AR-P5350 photoresist and AR 300-35 developer for lithography were both from Allresist GmbH. Aqueous K2PtCl4 solutions with concentrations of 1, 0.1, and 0.01 mM were prepared with deionized water. The solution was stored in daylight. When K2PtCl4 solutions age, Cl− ligands in the [PtCl4]2− complex are exchanged with water molecules, thereby altering the ionic charge of the complex. The corresponding reaction scheme was extensively investigated by Elding.10,11 By employing the reaction rate constants determined in those papers, we simulated the temporal evolution of the concentration of various chloroplatinates (Supporting Information). According to the example of the simulated concentration evolution in Figure 2, there is a time window with a dominant fraction of the neutral cis[PtCl2(H2O)2] complex, which is denoted as cis-PtCl2 in the following text. For a 10 μM K2PtCl4 solution, the fraction of cis7499


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Temperature Dependence. Our measurements of the nanowire growth velocity as a function of the temperature suggest a change in the rate-limiting process at about 301 K (Figure 4). To explain this temperature behavior, we propose

Figure 3. Different nanowire types grown at V0 = 4 V, f = 100 kHz, and c∞ = 10 μM. Wires like those in part a occur most often. On the right side of the image, a pair of connected nanowires is visible. The scale bars are 1 μm.

extremely high growth velocities (around 3.5 times higher than for the wires in Figure 3a under the same conditions) as well as a tapered shape with high widths of up to 500 nm. Also, nanowires such as those in Figure 3b occurred. They showed a much smaller growth velocity (around 3 times lower than for the wires in Figure 3a under the same conditions), a slightly smaller width (∼80 nm), and a smaller density of branches than did the wires in Figure 3a. Because the named exceptions are very rare events, all of our investigations refer to the type of wire shape in Figure 3a. We measured the resistance of a typical wire that turned out to be 2.4 kΩ. Together with the wire diameter of 100 nm and its length of 4 μm, this yields a conductivity of 212 kS/m, which is roughly 1 order of magnitude lower than the bulk conductivity of pure platinum. We attribute this difference to the polycrystalline structure and crystallographic defects of the wire. Determination of Growth Velocity. The growth of a nanowire from one electrode to the other comprises two stages: (i) random deposition of small metal asperities at the electrodes, which results in a field enhancement and causes a greater dielectrophoretic force4 and (ii) the growth of the wire. The first stage will be briefly denoted as nanowire nucleation characterized by a certain nucleation time tn. The remaining time is called the growth time tg. In our experiments, we measured the time between switching on the voltage and the sudden increase in current when a nanowire reaches the opposite electrode or when two nanowires, growing from opposite electrodes, meet each other. From this assembly time, ta = tn + tg, an apparent nanowire growth velocity of vg = dnw/ta was defined with dnw as the length of the nanowires, measured in the SEM. For kinked wires, we measured the traverse along the nanowire. In the case of microwires, wire growth can be observed by light microscopy. Ranjan et al.4 studied the growth of silver microwires and found that nucleation already occurred within 400 ms. Because nanowires are hard to observe in situ, we interrupted the wire growth after different periods of time in order to obtain an estimate of the nucleation time. For a growth interrupt after 53 s, we measured vg = 12.3 ± 2.8 nm/s, and for 116 s, we measured a similar value, vg = 11.0 ± 6.3 nm/s (temperature 298 K, voltage amplitude V0 = 6 V). Under the assumption of a negligible growth velocity during the nucleation time and a constant growth velocity afterward, the apparent growth velocity is used to calculate the nucleation time. We find that the nucleation time is negligible compared to the growth time, tn ≪ tg. Hence, in our data evaluation we used vg = dnw/ta to determine the wires’ growth velocities.

Figure 4. Measured nanowire growth velocity as a function of the temperature (10 μM K2PtCl4). The lines are fits according to eqs 3 and 4.

that at high temperatures the diffusion of platinum complexes to the nanowire tip is rate-limiting whereas at low temperatures ( 301 K to the equation vg(T ) = a1D(T )

(3)

where a1 (707 m−1) is the fit parameter. In the low-temperature regime (T < 301 K), the temperature dependence of the growth velocity was fit to the Arrhenius function

⎛ −E ⎞ vg(T ) = a 2 exp⎜ A ⎟ ⎝ kBT ⎠

(4)

where the reaction rate constant a2 (2.68 × 10 m/s) and the activation energy EA are the fit parameters. In the range from 289 to 301 K, we obtain EA = 1.80 eV, which is a reasonable value for an activation energy. The nanowire density along the electrodes decreases dramatically for low temperatures (cf. Figure 5a). Furthermore, the nanowires have a diameter of approximately 60 nm, which is at least 40 nm less than for the standard temperature T = 298 22

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arrive at the nanowire tip, the complexes establish a physisorbed state on the tip surface. Finally, electron transfer takes place and Pt(II) is reduced to Pt(0), which becomes part of the growing wire. Because platinum clusters were detected in the solution, they also might contribute to the wire growth. The wire growth mechanism for the platinum clusters is similar; therefore, the following modeling applies to both particle types: complexes and clusters. The transport of the particles in the solution is described by the continuity equation

Figure 5. Nanowires grown at (a) T = 289 K and (b) T = 316 K. Scale bars are 1 μm. Low temperatures decrease the wire diameter and density.

K. We attribute the low density to a slower nucleation rate at lower temperatures. Figure 5b shows wires grown at T = 316 K, which do not show any changes at T = 298 K concerning the wire density and diameter. Concentration Dependence. Figure 6 shows our measured growth velocities as a function of the platinum

∂c + ∇·j ⃗ = 0 ∂t

(5)

with c as the particle concentration and j ⃗ as the particle flux. The particle flux consists of two contributions: the diffusion flux and a convective flux resulting from an external potential ψ j ⃗ = −D∇c − M ∇ψ

with the diffusion coefficient D and the mobility Dc M= kBT

(6)

(7)

The clusters and complexes are polarizable particles with a dielectrophoretic potential energy17

α(∇φ)2 (8) 2 where φ is the electrical potential. For the clusters, the polarizability α is given by the Clausius− Mosotti relation18 ψDEP = −

Figure 6. Measured nanowire growth velocity as a function of the cisPtCl2 concentration at temperatures of 298 and 316 K. The lines are linear fits through the origin and a fitted constant for 298 K and above 100 μM.

α=

concentration c∞ at temperatures of 298 and 316 K. The fit curves reveal a linear relationship for low concentrations at both temperatures. However, at higher concentration (>88 μM), the curve at 298 K exhibits a clear plateau. Additionally, at 298 K nanowires were grown from a solution with a cis-PtCl2 concentration of 46 μM (which is in the linear region), and more KCl was added to produce an overall K+ concentration of 400 μM. For this case, we found an increase in the growth velocity to the plateau level. At 316 K and for platinum concentrations above 100 μM, the nanowire growth times are in the range of only a few seconds. Kawasaki et al.9 observed a nucleation time of approximately 1 s for nanowires grown from an aqueous H2PtCl6 solution. Because the nucleation time is already on the order of the growth time, a precise measurement of the growth velocity at both high temperatures and high concentrations is impossible in the present geometry of the experiment. Increasing the platinum concentration was found to increase the wire density, which is presumably due to an enhanced wire nucleation rate.

⎛π ⎞ 3 ⎜ ⎟R e[K (f )]d ε p ⎝2⎠

(9)

with dp as the cluster diameter and ε = εrε0 as the dielectric constant of water. For metals, the Clausius−Mosotti factor is K = 1 in the considered frequency range. The polarizability α of cis-PtCl2 is due to the induction of transient dipoles and the alignment of remanent intrinsic molecular dipoles μ19 α = α0 +

μ2 3kBT

(10)

Because of a lack of literature data for the dipole moment of cis[PtCl2(H2O)2], here we use data reported for the similar complex cis-[PtCl2(NH3)2] as an order of magnitude estimate. According to ab initio calculations for cis-[PtCl2(NH3)2],20 a rough estimate of the dipole moment of cis-[PtCl2(H2O)2] is μ ≈ 10 D. Typical values of the electronic polarizability α0 of less than 1 × 10−38 C m2 /V21 are small compared to the orientation polarizability. Thus, we estimate the total polarizability by α ≈ μ2/3kBT ≈ 1 × 10−37 C m2/V. In addition to the clusters and complexes, there are remaining K+ and Cl− ions from the original K2PtCl4 solution. The flux of ions follows eq 6 as well, however with a different potential ψion = zeφ (11)

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THEORY Model. Generally, we consider the nanowire growth to happen in a sequence of the following steps. cis-PtCl 2 complexes are convectively transported to the nanowire tip by the dielectrophoretic force7,16 and diffusion along the resulting concentration gradient. From a microscopic perspective, this corresponds to the Brownian motion and the directed movement through a viscous medium, respectively. Once they

with z as the charge number and e as the elementary charge. The applied voltage at the electrodes and the inhomogeneously distributed ions affect the electric potential φ that is governed by the Poisson equation 7501


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∇2 φ = −∑i

Dc∞exp[ψ̃ (r2)]

(12)

jr (r ) =

where the index i numbers the ionic species and F is the Faraday constant. Along the two electrode surfaces, the boundary condition for φ is given by φ = V0 sin(2πf t) and 0. For numerical calculations, we further require the vanishing normal derivative of the electric potential on the remaining boundaries. In the limit of small ion concentrations and large voltage, the influence of the charge density of the ions on the electric field is negligible. This is demonstrated for typical process parameters by a numerical calculation in the Supporting Information. Calculation of the Growth Velocity. To determine the velocity of nanowire growth from either neutral complex molecules or metallic clusters, we consider a static electrode geometry and calculate the stationary concentration profile of the wire-forming particles. The neglect of the movement of the nanowire tip relative to the solution is justified because our calculations show that the nanowire growth velocity is much slower than the particle velocities in the solution. During the entire nanowire growth process, only a tiny fraction of the particles in the solution are consumed. Therefore, we assume a constant concentration c = c∞ within an undepleted region far from the electrode, referred to as the particle reservoir. To estimate the upper bound of the wire growth velocity, we assume that the particle attachment time is much shorter than the transport time of the particles from the reservoir to the electrode. Consequently, a particle concentration at the electrode surface of c(r1) = 0 arises. On the remaining boundaries, the normal component of the particle flux is zero. In a first step, we consider a simplified spherically symmetric electrode geometry (Figure 7a), which allows an analytical

1

symbol f V0 r1 r2 S T εr η dp D Ω c α dp D Ω c α

1

r ′2

r exp[ψ̃ (r ′) − ψ̃ (r2)]

∫r 2 1

r ′2

(13)

dr ′ dr ′

value

description

100 kHz ac frequency 4V voltage amplitude 50 nm cf. Figure 7 1.1 μm cf. Figure 7 0.4 μm cf. Figure 7b 301 K temperature 81 rel. dielectric const. 0.75 mPa s eq 1 cis-PtCl2(H2O)2 Specific Parameters ∼1 nm molecule diameter22 −10 2 5.9 × 10 m /s diff. coeff.: eq 2 1.51 × 10−29 m3 Ω = mPt/ρPt 10 μM concentration 1 × 10−37 C m2/V polarizability Pt Cluster-Specific Parameters 23 nm cluster diameter 2.56 × 10−11 m2/s diff. coeff.: eq 2 6.37 × 10−24 m3 Ω = πdp3/6 1.43 × 1016 m−3 c = cPtΩPt/Ω 1.37 × 10−32 C m2/V eq 9

numerically evaluating eq 16 using Maxima software. In the case in which only complexes are present in the solution, we obtain vg = 1.1 nm/s, whereas the opposite case of only clusters in the solution yields vg = 0.64 nm/s. Obviously, our model predicts that any intermediate case should yield a growth velocity in this narrow growth velocity window. Moreover, our analytical result for the wire growth velocity (eqs 15 and 16) reveals that the growth velocity is proportional to the particle concentration c∞ and to the diffusion coefficient of the particles. For a more accurate estimation of the wire growth velocity, we considered a 3D electrode geometry where the nanowire was approximated by a cylinder-symmetric model consisting of a semisphere with radius r1 and a cylinder of length S (cf. Figure 7b, r2 is the distance from tip center to the counter electrode). The numerical calculation of the stationary solution of eqs 5 and 6 together with the resulting nanowire growth velocity on the nanowire surface is shown in Figure 8. With the parameters in Table 1, the tip-growth velocity for this setup and Pt complexes is obtained as 0.88 nm/s, which supports the estimation within our spherical model. However, the theoretically calculated growth velocity is slower than the measured data by a factor of about 20. To provide additional context, we analyzed the experimental data from Bhatt et al.,7 who did similar experiments with gold clusters at a much higher concentration. The extracted growth velocities of his microwires are in the range of 0.7 to 7.7 μm/s

The analytical solution of eq 13 with respect to the boundary conditions is given by c(r ) = c∞

(16)

Table 1. Simulation Parameters

α(V0r1)2

r exp[ψ̃ (r ′) − ψ̃ (r )]

(15)

The simulation parameters for complexes and clusters are given in Table 1. The nanowire growth velocity is obtained from

∂ψ̃ ⎞⎤ ∂ ⎡ 2 ⎛ ∂c ⎢r D⎜⎝ − − c ⎟⎠⎥ = 0 ∂r ⎣ ∂r ∂r ⎦

∫r

dr ′

vg = Ωjr (r1)

solution. Because the transition time to steady state is large compared to f−1, we use the time average of the potential energy (eq 8) and insert it into eq 6. The stationary limit of eq 5 for r2 ≫ r1 then leads to

4kBTr 4

r ′2

Balancing the volume of deposited particles with the increased wire volume finally gives an estimate of the nanowire growth velocity on the nanowire tip

Figure 7. Electrode geometries considered as a nanowire approximation in our models: (a) spherical and (b) cylinder-symmetric setups.

ψ ̃ (r ) = −

∫r

r2 r2 exp[ψ̃ (r ′)]

(14)

and from eq 6 we obtain for the magnitude of the radial flux density of particles 7502


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considerably fewer nanowires per substrate area at lower temperatures indicates that the initial nanowire formation depends strongly on temperature. Thus, the corresponding activation energies are comparatively high. If Cl adsorption affects the initial wire formation, then the reported desorption energy of Edes = 2.4 V23 for Cl desorption from Pt(111) in vacuum supports this suggestion. The corresponding Arrhenius factor exp(−Edes/kBT) changes by more than 3000 from 289 to 303 K. However, in aqueous environments some modifications should apply. Furthermore, we found a tendency that at lower temperatures slightly thinner nanowires grow. This could be related to the higher electric field at smaller wire tips, which is needed to compensate for the smaller thermal activation. Catalytic Effect of Potassium Ions. At first glance, it seems that the linear part of the curve at 298 K in Figure 6 corresponds to the diffusion-limited region and the following plateau to the reaction-limited region. However, Figure 4 suggests that T = 298 K and c = 10 μM correspond to the reaction-limited region. Additionally, we analyzed the slopes of the velocity curves vg(T) in Figure 6 for low concentrations. In the diffusion-limited regime, the slope depends only on the diffusion coefficient D(T) (eq 15). For the ratio of the diffusion coefficients, we obtained D(316 K)/D(298 K) = 1.5, whereas the observed slopes differ by a factor of 4. This means that the growth velocity at 298 K is slower than it would be in a diffusion-limited case. Hence, the reaction must be the slowest step in the process chain (i.e., the process is reaction-limited). When the concentration of K2PtCl4 increases, the concentrations of cis-PtCl2 and K+ increase. The rate constant of electron transfer between redox couples in solution depends strongly on the addition of electrolytes,24,25 which was also shown for reactions at electrodes.26 Peter et al.27 observed that for certain cations there is a saturation concentration above which the reaction rate constant a2 in eq 4 does not increase anymore with the concentration of the electrolyte. To find out whether catalysis by K+ is relevant in our case, we conducted an additional experiment with extra KCl as described in the Experiments section. The resulting nanowire growth velocity of 43 ± 8 nm/s is on the plateau level and clearly shows the catalytic influence of K+ on the reduction rate. When a certain KCl concentration is exceeded, the K+ effect saturates and the deposition rate and thus the nanowire growth velocity do not increase any further.

Figure 8. Particle concentration near the nanowire tip and wire growth velocity along the wire surface (arrows) with a maximum of 0.75 nm/s.

for various voltages and ac frequencies. The theoretically predicted growth velocity according to our model for a cluster diameter of 13.5 nm and a concentration of 2.23 × 1019 m−3 is 2.1 nm/s and thereby a factor of 1000 slower than the experimental values.

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DISCUSSION OF THE NANOWIRE GROWTH VELOCITY Diffusion Limitation. At high temperature, we observe the qualitative agreement of experimentally measured nanowire growth velocities with theoretical calculations (cf. eqs 15 and 16). According to the model, only a marginal voltage dependence of the growth velocity exists. Thus, we conclude that diffusion is limiting the transport. Also, the linear concentration dependence in Figure 6 at T = 316 K is in agreement with theory. The experimental data and calculated growth velocities differ by a concentration-independent factor. We suggest that accounting for electrokinetic fluid motion as described by Gierhart et al.6 could solve this contradiction. The fluid motion in question is driven by the transfer of momentum from the dielectrophoretically accelerated particles to the surrounding solution as well as ac electroosmosis, especially at the tip. Both processes increase the number of particles transported to the wire tip. Reaction Limitation. As a striking feature, when traversing to lower temperatures, the growth velocity curve in Figure 4 shows an abrupt change in behavior at approximately 301 K. We suggest that at a low temperature the deposition process of cis-PtCl2 is not fast enough to deposit all arriving particles immediately. Hence, below 301 K the growth process becomes reaction-limited. We propose in the following text several possible mechanisms that control the deposition rate. Finite Tip Surface Coverage. Each adsorbed cis-PtCl2 covers a certain area of the nanowire tip, limiting the total number of complexes reduced per time. At low temperature, the cis-PtCl2 reduction rate is smaller, lowering the growth velocity. The hydration shell of the complexes additionally increases the space consumption. Therefore, the temperature-dependent hydration shell thickness also has an influence on the deposition rate, as was already proposed by Ozturk.8 Adsorption Layer. Adsorption layers on the Pt surface presumably hinder the deposition of Pt; for example, consider the Cl surface coverage.23 Cl desorption, supported by high electric fields, is probably a precondition for further Pt deposition. This could also be one reason that Pt is deposited only at the wire tip but not along the long wire cylinder surface, contrary to the theoretical prediction in Figure 8. Seemingly, there is a certain threshold of the electric field, below which Pt deposition practically does not occur. Our observation of

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CONCLUSIONS Our investigation of platinum nanowires grown by dielectrophoresis from an aqueous K2PtCl4 solution hints at neutral cis-PtCl2 complexes as the major contribution to wire growth. The temperature and concentration dependence of the growth velocity revealed two different regions. (i) In the high-temperature, low-concentration region, we propose the diffusion of cis-PtCl2 to the nanowire tip as the growth-rate-limiting process. A corresponding theoretical model confirmed that the wire growth velocity is proportional to the cis-PtCl2 concentration and its diffusion constant in water, whereas the voltage amplitude has only a minor effect. The estimated growth velocities are about an order of magnitude smaller than the measured ones. This difference is possibly due to the neglect of fluid flow near the nanowire tip, which is driven by the momentum transfer of Pt complexes to the water molecules and by ac electroosmosis because of the 7503


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presence of K+ and Cl− ions. A consideration of these phenomena will be the subject of a forthcoming paper. (ii) In the low-temperature, high-concentration region, the growth velocity is independent of the concentration. An Arrhenius-like dependence of the growth velocity on the temperature suggests the wire growth to be limited by the deposition reaction of platinum on the wire tip. This is due to the limited area on the tip surface over which cis-PtCl2 complexes can adsorb. Cl coverage on the Pt surface and the hydrate shell around cis-PtCl2 could inhibit the reaction further. In particular, the catalytic effect of K+ ions is proposed to be responsible for the observed linear velocity increase with concentration, although the temperature dependence hints at a reaction limitation at those concentrations. However, the atomistic details of platinum deposition are poorly known, and our suggestions need further substantiation.

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ASSOCIATED CONTENT

S Supporting Information *

Modeling of the hydrolysis of a K2PtCl4 solution. TEM and cyclic voltammetry characterization of the prepared solutions. Schematic electrode setup and fabrication instruction. Estimation of the influence of the ion presence on the electric field. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions §

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the European Union (European Social Fund and European Regional Development Fund) and the Free State of Saxony (Sächsische Aufbaubank) in the young researcher group InnovaSens (SAB no. 080942409), by the European Centre for Emerging Materials and Processes Dresden (SAB no. A2-13996/2379), and by the WCU (World Class University) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (project no. R31-2008000-10100-0). We thank Larysa Baraban for many useful discussions, Walter Weber (NamLab) for support with respect to lithography, Arezoo Dianat and Lucio Colombi Ciacchi for DFT calculations, and René Beutner for help with cyclic voltammetry.

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REFERENCES

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Dielectrophoretic Growth of Platinum Nanowires: Concentration and

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