Stochastic Control: Transition from Differentiated to ... - ACS Publications

Jun 12, 2009 - Department of Chemistry and Biochemistry, La Salle UniVersity, 1900 West Olney AVenue,. Philadelphia, PennsylVania 19141. ReceiVed: ...
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J. Phys. Chem. C 2009, 113, 12007–12015

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Stochastic Control: Transition from Differentiated to Undifferentiated Kinetic Growth in Ag Nanoprisms Stuart T. Gentry* and Stephen D. Levit Department of Chemistry and Biochemistry, La Salle UniVersity, 1900 West Olney AVenue, Philadelphia, PennsylVania 19141 ReceiVed: February 23, 2009; ReVised Manuscript ReceiVed: May 12, 2009

A seeded process based on the staged addition of sodium borohydride and hydroquinone (HQ) to silver nitrate was used to form aqueous nanocolloids consisting of tabular triangular structures. The unique selectivity of HQ as a reducing agent was used to look at the factors that affect the formation of these triangular nanoprisms, including pH, choice of stabilizer, and addition point for the stabilizer. A critical factor in the formation of these systems was the stabilizer, with sodium citrate being more effective than either poly(vinyl pyrrolidone) or poly(vinyl alcohol) at forming large nanoprisms, and with large differences seen if the stabilizer is added before or after the seed particle was formed. The results are explained used a stochastic model for crystal growth, with a transition from slow, differentiated kinetic growth based on edge-defect termination to rapid, undifferentiated kinetic growth based on 2-dimensional nucleation. Introduction Nanoparticles made from noble metals have intrigued scientists for over 150 years, going back to Michael Faraday’s ground breaking work in 1857.1 These particles were generally thought to be spherical, but in 1954 Turkevich, Garton, and Stevenson reported triangular gold particles in addition to thermodynamically stable spheres.2 These observations were confirmed by Milligan and Morriss in 1964.3 In recent years, nonspherical particles have received a great deal of new interest due the implications that particle morphology has on electric-field enhancement for Raman spectroscopy, chemical sensors, and catalysis. There are a number of approaches that have been used to form nonspherical colloidal nanoparticles. Many of these methodologies rely on external control such as the use of soft templates (micelles),4 hard templates (substrates),5 photoinduced reformation,6 and lithography.7 In addition to these external controls, nonspherical particles can be grown via direct chemical reaction in solution. This latter approach, while simpler in concept, brings the challenge of using chemistry to control particle morphology during the various steps required to grow crystalline sols. This paper looks at the growth of nonspherical nanoparticles prepared via chemical growth. One of the complexities of chemical systems is the competition between the growth of existing particles and the possible ongoing nucleation of new particles. To help control this competition, this paper makes use of hydroquinone (HQ) as a selective reducing agent. HQ has unique properties in that under acidic conditions it is unable to reduce isolated silver ions (hence is unable to initiate new particles from solution) but readily reduces silver ions in the presence of preformed particles.8 This phenomenon forms the foundation of the photographic development process.9 The current work focuses on the factors that control crystal habit or morphology in chemically grown systems. A number of papers refer to a transition between slow, kinetically * Corresponding author. E-mail: [email protected]. Phone: 215-9511259. Fax: 215-951-1772.

controlled growth of triangular nanoprisms versus fast, thermodynamic growth of quasi-spherical particles.10 They base this explanation on the observation that triangular nanoprisms are very different than the near-spherical structures predicted by thermodynamics. This paper will offer an alternative explanation based on stochastic crystal growth. Under the approach first pioneered by Gibbs and extended later by Volmer and Wulff, crystal structures that are at thermodynamic equilibrium are governed by the minimization of the overall free energy. This in turn requires minimizing the sum of the product of area, ai, and surface tension, γi, for each of the outer faces of the crystal. (eq 1) For metallic fcc crystals like silver: γ111 < γ100 < γ110.11

∑ γi ai ) minimum

(1)

i

Based on this approach, the lowest energy habit for large metallic crystals of gold or silver has been calculated to be a truncated octahedral structure, with only slightly higher energy for symmetric twinning defects about {111} reflection planes.12,13 In practice, the formation and growth of nanoparticles is more complicated than the large-scale structures envisioned by Gibbs.14 At the very earliest stages of particle nucleation, cluster structures can be complex. As these atomic structures grow from dimers and tetramers up to close to 100 atoms in size they are dominated by “magic number” considerations for stable clusters.15 In some respects these clusters are better described as molecular compounds than as crystals. As the size grows beyond 100 atoms, the metallic clusters transition to mesoscale systems.16 These demonstrate long-range order but can form crystal structures that are different than full-scale macroscopic systems. For example, the lowest free-energy form for gold particles in the range of 100-200 gold atoms is predicted to be a decahedral structure rather than an fcc crystal.12 It is only when metallic particles grow to a size greater than ca. 2 nm in equivalent diameter (>200 atoms), that they take on their final fcc structure. Even above this transition from decahedral to fcc crystal form,

10.1021/jp9016689 CCC: $40.75  2009 American Chemical Society Published on Web 06/12/2009

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the thermodynamics of nanoparticles continue to deviate from their ultimate large-scale crystal structures. Silver particles below ca. 15 nm in diameter show a contraction in their lattice constants,17 higher surface tensions,18 and significantly lower melting temperatures19 as compared to larger samples. The nucleation and growth of new metallic nanoparticles must go through all of these stages of development. Although the final truncated-octahedral structures that are predicted by thermodynamics are similar to the quasi-spherical structures generated by fast-growth conditions, this does not necessarily mean that the growth is driven by thermodynamics. We define a thermodynamically controlled system as one that is driven by the composite free-energy gradient. This can include both the initial growth of the particle as well as systems held at temperatures sufficient to overcome energy barriers to rearrangement. These factors, however, do not explain the transition seen in particle morphology in the current work. Instead, we will present an alternative model that considers the observed particles as undergoing a transition between differentiated, edge-terminated kinetics and undifferentiated, “2dimensional nucleation” kinetics. This is based on traditional Burton-Cabrere-Frank (BCF) crystal theory.20,21 BCF describe the stochastic competition that can occur when individual metal atoms (or “adatoms”) are able to migrate across a flat surface of a crystal after being added on to the crystal. The critical question is whether those adatoms have enough time to find and become anchored at an edge defect or alternatively whether they prematurely encounter other mobile adatoms and thus begin to rapidly nucleate new growth layers on the otherwise flat faces of the crystal. (This will be discussed in greater detail later.) It should also be noted that the other approach that is often coupled to thermodynamic vs kinetic discussions is the suggestion that stabilizers such as poly(vinyl pyrrolidone) (PVP) play a key role by preferentially blocking the addition of new atoms onto select crystal surfaces.22 This may be true of other systems. However, we will show that for the chemical system used in this current work the general trend for forming triangular plates does not depend on the choice of stabilizer. In fact, sodium citrate proved more effective at generating triangular nanoprisms than did PVP. The observed differences in particle formation that result from various chemical systems point out the challenges that still remain for fully understanding the growth dynamics of spherical and nonspherical nanoparticle systems. It is the breadth of these unanswered questions that has led to the continued publication of theoretical and experimental work on what might naively have been thought to be well-characterized metallic systems. Experimental Section Sample Preparation. All chemicals were reagent grade and used as received from the supplier without additional purification. Glassware was soaked in concentrated HNO3 and rinsed multiple times in water. Unless otherwise stated, the standard formulation was a 15 mL solution containing 0.2 mM silver nitrate (Aldrich, prepared as a 1.0 × 10-3 M stock solution), 0.4 µM NaBH4 (1.0 × 10-4 M solution prepared fresh each day, adjusted to pH 7-7.5, and kept chilled in ice water), 0.2 mM hydroquinone (Aldrich, prepared fresh each day as a 5.0 × 10-2 M solution), 0.2 mM sodium citrate (prepared as a 1.0 × 10-3 M stock solution), and water (Fisher Scientific, HPLC grade). The standard process was to combine the water, AgNO3, and 0.002 mol-fraction NaBH4 and then allow the mixture to sit for 2 min to allow the BH4- to fully react and for the seed system

Gentry and Levit to reach equilibrium. The sodium citrate stabilizer was then added, and the mixture was held for another 4-10 min to allow the stabilizer to partition itself throughout the mixture. It is important that the citrate be added after the NaBH4. Adding it before the BH4- leads to differences in the seed formation and ultimately to very different final particle morphologies (cf. final section of paper). Finally, the hydroquinone was added to complete the reaction. Samples were stored in the dark during particle formation to ensure that there was no UV-induced reaction. The poly(vinyl pyrrolidone) (MP Biomedicals) used in this work had a molecular weight of 40 000. The poly(vinyl alcohol) (Acros) was 88% hydrolyzed with an average molecular weight of 88 000. All reported mole fraction concentrations are relative to the starting concentration of AgNO3. Additional details about the process parameters are presented in the Supporting Information. Instruments. The plasmon extinction spectra were recorded using a Hitachi U-2910 UV/vis spectrometer. An Ocean Optics, Inc. USB4000 CCD linear array spectrometer system with ISSUV/vis light sources was also used for some of the spectra. These instruments were run in absorption mode but were actually measuring the optical extinction since plasmons both absorb and scatter incident light. Transmission electron micrographs were recorded in the bright-field mode using a Phillips CM12 scanning/transmission electron microscope at the USDA’s Eastern Regional Research Center. Samples were evaporated on carbonized copper grids, and the microscope was operated at 80 kV. Particle diameters were determined by analyzing the micrographs using ImageJ, a Java program developed at the National Institute of Mental Health.23 The transverse widths of nanoprisms were determined from micrographs of large aggregates, formed during drying on the TEM grid, measuring the widths of particles situated edge-on to the electron beam. Results Application of HQ Reducing System to Form Nanoprisms. A previous paper demonstrated the unique selective-oxidation properties of hydroquinone when used to reduce silver.8 These properties are well documented when HQ is used for developing photographs.9 In this case the selectivity was exploited for the preparation of nanosols. When AgNO3 and HQ are combined by themselves under acidic conditions without any other active reducing agent, then there is no reaction between the two. On the other hand, if a very small amount of NaBH4 is first added to the system, then the borohydride will generate small seed particles. Once those seeds are present, then the HQ is able to reduce the rest of the unreacted Ag+ that is present in the system. Alternatively, the silver/HQ reaction can be initiated by using UV radiation to excite the hydroquinone to a higher electronic state, or the pH can be raised to increase the reactivity of the HQ. The latter technique is used in the opposite direction for photography, adding acid to drop the pH and terminate (or “fix”) the development reaction. While the previous work focused on forming traditional spherical particles, the system parameters can be modified to form nonspherical morphologies. These are generally flat nanoprisms that form a variety of crystal habits including triangular, truncated-triangular, hexagonal, and quasi-circulardisk tabular particles depending on the conditions. The current work used 0.002 mol-fraction BH4- to form seed particles. Sodium citrate was used as a colloidal stabilizer but it was not added until after the seed particles were formed. (Citrate is unable to reduce silver at room temperature so only acts as a

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Figure 1. TEM on samples made from seeded system with 0.2 mM AgNO3 and 0.002 mol fraction NaBH4, followed by second stage of 1.0 mol fractions of sodium citrate and HQ. Sample A shows the seed particles (2.5 nm ave. diameter), whereas sample B shows the final particles.

Figure 3. Time development of nanoprisms using standard seeded formulation. Samples taken at 5 min, 11 min, 20 min, and 1 h following addition of HQ. Samples spun in centrifuge, with sediment subsequently redispersed in water prior to collecting data.

Figure 2. (a) Extinction spectrum for anisotropic particles shown in Figure 1B. (b) Spectrum taken from spherical particles in ref 8 and was obtained using the same level of AgNO3 and citrate as in (a) but with phosphate buffer and the citrate added prior to the addition of 0.05 mol fraction NaBH4 to form the seed.

stabilizer.) The point of addition of the citrate is critical with respect to the resultant characteristics of the seed particles. The typical workflow was that water, AgNO3, and NaBH4 were combined in solution and allowed to react. When the seed formation was complete, sodium citrate was added to the system and held for a short interval. Finally HQ was added to the sol to complete the vast majority (>99%) of the silver reduction. (See the Supporting Information for more details.) Figure 1 shows micrographs that were obtained by using this modified, seeded HQ process. At the end of the BH4- seed stage, the sample was clear and colorless. Figure 1A shows that seed particles were present, just too small in diameter (2.5 nm) and in too low a concentration to affect the visual appearance of the sol. However, once the HQ reducing agent was added to the system along with the citrate stabilizer, the particles developed into large triangular nanoprisms with edge lengths on the order of 80-150 nm. Their transverse widths were roughly 8 nm. The uniform thin width of these nanoprisms is apparent in Figure 1B as seen by the translucency exhibited by overlapping prisms. Spherical nanoparticles, by contrast, are typically opaque in these experiments with crystal faults visible as different domains in the particles. Figure 2 shows the optical extinction spectrum corresponding to the particles in Figure 1. It compares this spectrum to that obtained from traditional spherical particles as discussed in ref 8. The anisotropic signal is consistent with theoretical calculations found in the literature.24 The large peak at 768 nm in Figure 2 is a longitudinal (in-plane) dipole peak while the small peak at 334 nm is a quadrupole signal for the transverse (out-ofplane) polarization. The shoulder peak at ca. 420-440 nm is attributed to being a mixture of nonspherical longitudinalquadrupole, nonspherical transverse-dipole, and spherical dipole

Figure 4. Spectra for samples shown in Figure 3. Figure includes peak positions for each.

signals (from residual small-diameter particles). Visually, the sample in Figure 2 was a turbid blue color as compared to the clear yellow appearance of more traditional spherical silver nanoparticles. To help understand the growth of these particles, we removed samples at various times following the addition of the HQ reducing agent. These samples were spun in a centrifuge (12 000 rpm for 10 min) and the sediment was redispersed in water prior to being transferred to a TEM grid. The centrifugation was done to separate the growing particles from unreacted AgNO3. Figures 3 and 4 present optical and micrograph data on these samples. It can be seen that some triangular nanoprisms had begun to form as early as 5 min into the process. More generally, however, the 5-min colloid was comprised of a number of small irregularly shaped particles. As time proceeded, the particles grew and one began to see the irregular tabular shapes morphing into more defined triangular shapes, although many irregular shapes remained. These particles continued to grow and to develop more defined shapes, with the 1-h sample containing a high proportion of well-controlled triangular nanoprisms, albeit with some variation in edge lengths and truncated corners. These data are important in that they demonstrate that the particles grow into the triangular morphology, rather than immediately forming small triangular nanoprisms which then continue to grow uniformly in size. The data also differ from

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photoinduced triangular nanoprisms reported elsewhere, where the extinction peak grows at a fixed wavelength.6 Figure 4 also shows a small amount of additional modification in the optical signal after the sample reaches full size at 1 h. There is a small shift in the peak back to lower wavelength as seen in the 4-h sample. We interpret this result as being due to final equilibration of the system, with small levels of Ostwald ripening or surface rearrangement occurring with local defects. Once this equilibration occurs, the systems were stable without additional change. In some cases we have held on to samples for more than 3 months with little subsequent change seen in the particle distribution or morphology after the first week. (cf. the Supporting Information) It is also important to note that all of the tabular particles seen from 11 min through 1 h had constant transverse thicknesses of 8-10 nm even though the particles more than doubled in edge length in the longitudinal direction. Once the particles began to develop flat surfaces, the thickness of those surfaces ceased to grow and all of the remaining accretion of new silver atoms occurred along the edge surfaces of the nanoplates. As we consider the explanation of these results, one should keep in mind that the initial seeds contained less than 1% of the silver atoms present in the formulation. At the end of the initial seeding stage the remaining 99% of the silver was still in its oxidized ionic form. It was only after the hydroquinone was added to the system that the remainder of the silver was able to react. This second-stage growth was limited to the existing, growing particles; HQ is unable to create new particles on its own when the reaction is carried out under slightly acidic conditions.8 Role of Stabilizing Agent. It is known that stabilizers play a critical role in the formation of nanoprisms. It has been proposed by others that stabilizers control the morphology by either acting as a micellar templating agent4 or as a surfacespecific capping agent.22 In the latter case, it has been proposed that PVP preferentially binds to flat {111} Ag crystal surfaces. This preferential binding is said to block additional silver from bonding to the {111} surfaces, leaving only the {100} or {110} surfaces along the edges available to new growth. A related explanation is that preferential capping of the {111} surfaces leads to differentiated surface energies at the various faces25 rather than steric blocking. The results in the current work, while not totally conclusive, do not appear to support any of these models even when using PVP as the stabilizer. Use of Citrate as Stabilizer. Figure 5 compares the results obtained when adding different amounts of sodium citrate to the system. The citrate was varied from 0.02 to 2.0 mol fraction relative to AgNO3. As can be seen, there is very little difference in the final extinction spectra. Indeed, the only significant difference in final results is the case where the stabilizer was totally eliminated from the formulation, in which case one sees the characteristic optical spectrum of a destabilized colloid made up of large aggregates. There is some shifting back and forth in the location of the peak maxima in Figure 5, but there is no clear trend in this shift and is likely more dependent on subtle variations in the sample preparation. If the morphology of the tabular triangular prisms was controlled by citrate acting as a face-specific capping agent as has been suggested for PVP, then changing the concentration of stabilizer should have had a large impact on the final shape of the particles. This was not observed in Figure 5 even though the citrate concentration was varied over a 2-orders-ofmagnitude range. It has been suggested that even at citrate levels as low as 0.02 mol fraction the surfaces of the particles may

Gentry and Levit

Figure 5. Effect of citrate level on nanoprisms development. Citrate level varied from 0 to 2.0 mol fraction. Remainder of formulation was standard seed process. The figure shows spectra obtained after 1 h (the lower extinction spectrum in each of the plots) and after 6 h.

have been saturated with stabilizer and that is why no changes are seen at higher citrate levels. We think it unlikely that this is the case. Not only is the citrate level very low (4 × 10-6M), but the long-term (1-30 days) stability of the particles depends on the citrate level. (cf. the Supporting Information) This would not be the case if the particle surfaces were already saturated with citrate at the lowest levels of stabilizer, such that all of the systems had the same amount of bound citrate, with the excess remaining in solution. A face-specific capping mechanism would also fail to explain the transition to more spherical particles when the pH or the HQ concentration were varied to increase the system reactivity. While there is no significant difference in the final peaks when varying the citrate level, it is interesting to note the difference in the time necessary to reach those final particles. Figure 5 shows the final spectra seen after six hours and the in-process spectra obtained after the first hour of growth. The 1-h spectra show that as the citrate level was decreased, the system was slower to generate nanoprisms, not faster. The 2.0 mol fraction sample was able to reach its final peak height within 1 h while the 0.02 mol fraction sample only reached 21% of its ultimate peak height within the first hour of reaction. In all cases, the systems had reached their final equilibrium states by the time the 6-h spectra were obtained. The prediction from traditional colloid chemistry is that adding stabilizer to a colloid typically slows the growth of the particle by reducing the surface-energy mismatch with the liquid media and by physically blocking the surface of the entire particle. These phenomena for the entire crystal are similar in principle to those suggested for the face-specific interactions proposed for PVP. In Figure 5, however, one sees that stabilizer actually speeds up or enhances the growth process, albeit still generating the same final nanoparticles at the completion of the reduction process. These results are not due to citrate by itself reacting with the Ag+ since citrate is nonreactive as a sole reducing agent under the conditions used in this experiment. One explanation may be that the citrate is able to help stabilize and facilitate the HQ/Ag+ electrochemical reaction at the particle/water interface in a manner similar to the“superadditivity” of bicomponent developer systems in photography.26 Effect of Other Stabilizers. The previous section looked at how the level of sodium citrate used in the standard process affects the crystal habit. Another approach is to look at the effect

Kinetic Growth in Ag Nanoprisms

J. Phys. Chem. C, Vol. 113, No. 28, 2009 12011 tight curvature of the early stage particles make this polymeric alignment difficult. The small-molecule nature of the citrate ions may make it much easier for citrate functional groups to arrange themselves along the particle surfaces as the particles grow in size and shape. Discussion of Growth Mechanism

Figure 6. Samples made using PVOH or PVA to replace sodium citrate in the standard formulation. These samples were prepared with 0.05% or 0.20% (by weight) PVP or with 0.01% or 0.20% PVA.

Figure 7. TEMs for 0.20% systems shown in Figure 6.

of using alternative stabilizers as replacements to the citrate. Figures 6 and 7 show data on systems made by replacing the citrate with either poly(vinyl pyrrolidone) (PVP) or poly(vinyl alcohol) (PVA). As can be seen, one sees the same general trend of forming tabular, roughly triangular prisms irrespective of the choice of stabilizer, although the specific characteristics do change when switching from one capping agent to another. If the nanoprisms in this work were due to the stabilizers acting as face-selective capping agents on the {111} faces then one would expect that switching from nonselective citrate to selective PVP would enhance the formation of nanoprisms. However, we see the opposite effect in the current work. The PVP and PVA systems both formed nanoprisms, but these systems were less controlled than the citrate systems. The polymeric stabilizers gave a mixture of particles of differing morphologies and smaller dimensions. In addition, the PVP and PVA systems required a full 6-8 h to reach their final particle size (or maximum peak heights) as compared to citrate at 2-3 h. These longer development times were presumably due to steric hindrance from the polymer chains slowing down the HQ/ Ag+/particle kinetics as well as differences in the surface energies due to the changes in colloidal stabilizer. In spite of the strong chemical interaction that has been reported for pyrrolidone units with metallic silver surfaces, we speculate that PVP is actually a less efficient stabilizer than citrate at the critical early stages of particle formation. The polymeric nature of PVP requires that the chain undergo reptilian rotation along the polymer backbone if the sequential monomer units are going to align and interact with nascent particles. The

It is well documented that the flat longitudinal surfaces of silver triangular nanoprisms are made up of {111} planes of silver’s fcc lattice, while the transverse edges are {100} or {110} surfaces.27 However, if this morphology is not being controlled by the stabilizer selectively blocking growth along one set of crystal faces then it leaves the question of what is controlling the crystal habit. We will show that morphology can be controlled by the stochastic nature of the growth process. Kinetic Control of Crystal Habit. As discussed in the introduction section of this paper, thermodynamics are an important component of crystal growth. A number of researchers have described the transition from quasi-spherical structures formed under fast-growth conditions to tabular triangular prisms formed under slow conditions as being due to a transition from thermodynamic to kinetic control.10 However, this can be misleading. Just because final quasi-spherical particles resemble the expected thermodynamic structures does not mean that the process is thermodynamically controlled, at least in the classical sense of being driven by the free-energy gradient or surfaceenergy minimization. A better description of this transition between fast, spherical versus slow, nonspherical growth in metallic systems may be to describe it as the transition between nondifferentiated kinetics and differentiated kinetic control. These are different stochastic regimes that can be explained using traditional BCF crystal theory and two-dimensional crystal nucleation.20,21 The addition of an atom (or “adatom”) to a growing crystal can be broken into 3 individual processes. The first is the addition step. This is the transfer of the metal atoms from solution to the crystal surface. This is controlled by the phase transition at the solid/liquid interface and by the diffusion in solution. The second step is the migration step. This is the process of random 2-dimensional migration (surface diffusion) of the adatom across low-binding-energy surfaces. This can be modeled as a random-walk process. The final step is the termination step. According to BCF theory an adatom will eventually be lost back to solution unless its surface migration brings it to a defect site such as a kink or step that has a high enough binding energy to permanently anchor the adatom to the crystal. A key element of BCF theory is the distinction between surface sites on flat crystal faces where adatoms will have low coordination to other lattice sites versus sites on rough surfaces where a new adatom can coordinate to a much higher number of neighboring atoms. The low coordination number for a single adatom on a flat surface and the accompanying loss of entropy for an atom on the solid rather than in solution combine to create a relatively unstable state for adatoms on flat surfaces. The result is a low activation-energy barrier for adatoms being able to migrate across the surface by hopping to neighboring sites (Figure 8) as well as for being lost back to solution. One outcome of BCF theory is the prediction that in the absence of defect sites, a perfect 2-dimensional crystal face will be unable to sustain new growth. By contrast, a migrating adatom that finds a defect site such as a kink, a step, or a 2-dimensional cluster on the crystal face will be able to interact with a larger number of neighboring

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Gentry and Levit

Figure 10. 2-Dimensional nucleation. Figure 8. Surface migration. Figure 11. Simplified hydroquinone oxidation scheme. Figure 9. Twinned crystal reentrant groove.

sites. The intermolecular attractive forces between the adatom and these neighboring sites are roughly additive. Thus, the higher coordination at defect sites leads to higher binding energies, and the adatom can become permanently bound to the lattice, allowing the crystal to sustain growth. Differentiated Kinetics. This model of adatoms migrating across a flat surface until they encounter a higher-coordination defect site can be applied to the differentiated growth of silver nanoprisms. When the electrochemical reactivity is slow, there will be a low flux of Ag° adatoms onto the crystal. Under these dilute conditions, individual migrating adatoms on a flat {111} surface have the time to randomly diffuse across the flat face until they encounter a defect site. Of particular note in metallic fcc crystals are the defect sites at the edges caused by twinned structures. The defect boundary between a pair of twinned fcc {111} planes with hexagonal coordination creates a trigonal set of concave edges. (Figure 9) These reentrant grooves have been used by others to explain the formation of trigonal crystal structures.28 The grooves have enhanced surface energies for anchoring adatoms due to the higher coordination to other atoms that is possible within these grooves. The opposing sides of the crystal have convex structures that inhibit adatom addition. Therefore the hexagonal 2-dimensional coordination of a single pair of twinned planes will have a set of three favored reentrant grooves and an alternating set of three disfavored convex regions, thus leading to triangular growth structures. On the other hand, multipletwinned crystals with more than two twinned regions can generate hexagonal crystals as the various layers alternate between one direction and the other. Undifferentiated Kinetics. The question remains as to how to explain the quasi-spherical structures that are seen with Ag systems under faster-growth conditions. Rather than being under thermodynamic control (driven by the composite free-energy gradient), a more likely explanation is that the higher concentration of adatoms in a highly reactive system causes the crystal growth to transition to a state of enhanced two-dimensional nucleation. As discussed by BCF, adatom migration can be terminated by either anchoring the adatom at a defect or alternatively by losing the atom back to solution. They also describe a third mechanism, however, that comes into play at high adatom concentrations. If the number density of migrating adatoms is high enough, then there is a likelihood that two or more migrating adatoms will collide with one another before they reach an existing defect. If this occurs, they can in essence create their own new defect on the otherwise flat surface, introducing pairwise interactions between each other to stabilize the cluster. If a critical number of adatoms come together, then they can form the stable nucleus for a new layer of growth on the surface. (Figure 10) Depending on the concentration of mobile adatoms on the surface (or the flux of new atoms from solution), the surface roughening can increase at a fast rate thus destroying

any tabular morphology that was present and allowing the crystal to grow in all three dimensions. At the very highest concentrations, this surface roughening can lead to continuous, dendritic growth.29 In the case of silver nanoprisms versus nanospheres, the critical question is whether the flux of new Ag° atoms onto flat crystal surfaces is fast enough that migrating adatoms will collide with each other and undergo 2-dimensional nucleation and surface roughening. Conversely, is the flux slow enough that mobile adatoms are more likely to find an edge defect before colliding with another mobile atom? It is this transition that we refer to as the difference between fast, undifferentiated and slow, differentiated kinetics and that others previously attributed to kinetics vs thermodynamics. It should be note that the above model is for the initial formation of the particle. Crystals can undergo subsequent annealing and/or Ostwald ripening30 to modify the habit to the favored thermodynamic shape. This reformation is difficult when the crystal habit is dominated by large flat surfaces since atoms are most likely to return to lower-energy edge defects, but is more readily allowed in already surface-roughened structures. Applying Stochastic Growth Model to Results pH Response. One way to probe this transition between the two growth regimes is to control the kinetics of the reaction via pH. Figure 11 shows a simplified oxidation scheme for HQ, although the actual chemistry goes through semiquinone intermediates. The oxidation of hydroquinone generates hydrogen ions as part of its half-cell reaction. One consequence of this equation is that the HQ redox potential shows a strong dependence on pH (or H+ concentration) according to the Nernst equation, and thus affects the HQ/Ag reactivity of the system. Sodium hydroxide and nitric acid were added to the system to probe the particle dependence on pH. Strong base or acid was added at increasing levels from 0 to 1.3 × 10-4 M just prior to the addition of the HQ reducing agent, i.e., after the seed was formed and was protected by the citrate stabilizer. It is difficult to measure accurate pH values in very-dilute electrochemically active systems, but the pH values ranged from 6.3 for the highest level of HNO3 addition to 7.0 for the highest level of NaOH addition. [The reported pH’s were those obtained after allowing the pH meter to semistabilize for ca. 15 s., with initial pH’s being higher in value.] Even though the changes in measured pH were relatively small, very large differences in extinction spectra and morphology were observed. (Figures 12 and 13) The standard formulation (without pH adjustment) had a solution pH of 6.8. The resultant particles were triangular nanoprisms and the system took 1 h to reach its peak wavelength of 690 nm. One gets very different results if the pH is raised with strong base. When 1.3 × 10-4 M NaOH was added to the formulation, the new sample had a measured pH of 7.0 and gave quasispherical particles at a peak wavelength of 422 nm. The heightened reactivity of the higher pH samples was readily

Kinetic Growth in Ag Nanoprisms

Figure 12. pH effect. Various amounts of NaOH or HNO3 added just prior to the HQ addition (after the seed was formed and after the citrate was added). Sample (a) 1.3 × 10-4 M NaOH, pH 7.0, (b) 7 × 10-5 M NaOH, pH 7.0, (c) 3.5 × 10-5 M NaOH, pH 6.9, (d) no pH adjustment (standard formulation), pH 6.8; (e) 7 × 10-5 M HNO3, pH 6.6; (f) 1.3 × 10-4 M HNO3, pH 6.3.

Figure 13. Micrographs for the different pH formulations shown in Figure 12. The particles were formed by adding (a) 1.3 × 10-4 M NaOH, (b) 0.7 × 10-4 M NaOH, (d) no pH adjustment, and (f) 1.3 × 10-4 M HNO3. The flat platelets had edge thicknesses of (b) 20-24 nm, (d) 14-15 nm, and (f) 8-10 nm. The quasi-spherical particles in (a) had average diameters of 55 nm.

apparent in that the samples turned yellow in less than 1 min rather than the 1-3 h seen with more acidic samples. At the other end of the pH spectrum, adding 1.3 × 10-4 M HNO3 to the system gave a pH of 6.3 and particles with an extinction peak at 832 nm. This sample took more than 3 h to reach its maximum optical extinction value. Representative micrographs for these samples are shown in Figure 13. The difference in the observed morphologies are consistent with the differences in optical spectra, with the higherpH, faster-reactivity system giving more spherical particles. The micrograph data indicate that the volume of the particles remained constant; only the shape and aspect ratio changed. This is consistent with the assumption that the BH4 is used to create seed particles, and any subsequent silver that is reduced by the HQ goes to growing the seed particles. [Unfortunately there is a high level in the statistical uncertainty in these volume measurements due to the limited number of particles that were positioned edge-on in the micrographs, with this orientation

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Figure 14. Excess concentration of HQ. Samples were prepared using the standard process with the only variation being the level of HQ that was used: (a) 3.0, (b) 2.0, and (c) 1.0 mol fraction HQ (relative to moles AgNO3).

being necessary to measure edge thicknesses. See the Supporting Information for more detail.] A couple of caveats are worth noting with respect to the above data. Raising the pH with NaOH increased the reactivity of HQ to a high enough level that it was able to react with silver even in the absence of pre-existing clusters. It is still presumed, however, that even if individual silver atoms are reduced in the water phase the majority will add on to existing particles before they reach a high enough level to aggregate and form new particles. This is borne out by the constant volume observation seen with the TEM data in Figure 13. It should also be noted that the pH controls a number of factors in colloidal systems in addition to the electrochemistry. These factors include the zeta potential of the bare metallic particles (with ionic silver and oxides also incorporated into the surface of the metallic particles) and the neutralization of the citrate (with aqueous citrate having pKa’s of 3.14, 4.77, and 6.39).31 All of these factors contribute to a more complex dependence on pH than being exclusively due to simple hydroquinone kinetics. With all of the aforementioned caveats in mind, the data in Figures 12 and 13 are consistent with a transition from differentiated to undifferentiated growth. At a pH below 6.9, the reactivity rate of the silver and HQ was slow (measured in hours) and hence the concentration of new Ag° adatoms on the crystal at any one point in time was low. These conditions favored a migrating adatom being able to find an reentrant groove on an edge rather than undergoing 2-dimensional nucleation with other adatoms on a flat {111} surface. Raising the pH to 7.0 significantly increased the reaction rate (measured in minutes) and concentration of new adatoms on to the crystal. Under these conditions, 2-dimensional nucleation began to dominate over edge-defect termination, leading to high levels of surface roughening and ultimately to 3-dimensional growth of the crystal. Hydroquinone Concentration. The effect of kinetics on particle formation can also be demonstrated by changing the concentration of excess reducing agent. Figure 14 shows that raising the amount of HQ from a mole ratio of 1.0 to 3.0 (relative to moles of initial AgNO3) causes the extinction peak to shift to lower wavelengths (819 vs 651 nm respectively), consistent with less tabular particles. These spectra were collected on systems where the seed formulation and the pH of the system were kept constant, and only the amount of HQ was varied. Since a single molecule of HQ can theoretically reduce two atoms of silver, all of the data represent an excess of reducing agent. Under standard kinetic theory, higher concentrations of HQ translates to a higher reaction rate with silver. The effect of added HQ is not as dramatic as adding NaOH to raise the

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Figure 15. Standard seeded process except the sodium citrate was added before the NaBH4 was introduced to the AgNO3 rather than the standard addition point after the seed formation had reached completion. Figure shows TEM data for (A) the seed particles (6.5-7.0 nm diameter) and (B) the final particles.

reaction rate of the system, but the trend of the data are consistent with the proposed model of transition from edge growth to increasing amounts of 2-dimensional nucleation on the faces of the particles. Influence of Seed Creation on Final Particle Morphology The focus of this paper to this point has been on the growth phase of forming nonspherical particles. The most critical stage for setting the morphology, however, is the nucleation phase. Unfortunately, in many respects it is the nucleation phase that is the most difficult to control. For the BH4-seed and HQ-growth process described herein, the reaction of the borohydride occurs over a matter of seconds and only involves less than 1% of the silver. Yet if the resulting seed has the wrong characteristics then one will not obtain the desired triangular nanoprisms. Figure 15 shows micrographs for a system where the only difference from the standard process is that the sodium citrate stabilizer was added before the BH4- was introduced to the AgNO3 rather than after the seed particles were formed. The figure shows the original seed particles as well as the resultant final particles. The micrographs can be compared to those in Figure 1, where the only difference was the later point of addition of citrate for Figure 1. The result of adding the citrate before the BH4- in Figure 15 was that one sees traditional quasispherical particles with diameters of ca. 20 nm rather than large nonspherical prisms. Some of the particles do exhibit tabular morphology with a thickness of ca. 4 nm, but none of the particles show the 100 nm triangular structures seen when the stabilizer is withheld until after the seed is formed. The difference in these morphologies can be attributed to the influence that the citrate stabilizer has on the nucleation and growth of the seed particle. Unfortunately the resolution of the micrographs was not sufficient to characterize the specific morphologies of the small seed particles. Similar results were seen when pre-adding versus post-adding PVP as a stabilizer, albeit with PVP giving less reproducible results than sodium citrate. No matter what the choice of stabilizer, the data demonstrate the critical influence of the early nucleation process on the final particle morphology. Conclusions The unique reaction selectivity of hydroquinone was used to explore the formation of nonspherical nanosols. Borohydride was used to form silver seed particles, with the ratio of NaBH4 to AgNO3 being 0.002:1 mol ratio. Once the seed particles were formed, the remaining unreacted silver was combined with the HQ to add Ag° to the growing particles. Sodium citrate was

Gentry and Levit normally present as a stabilizer to keep the particles from undergoing aggregation, but was only added after the seed particles were first formed. Based on this chemistry and depending on the specific choice of conditions, one can transition from traditional quasi-spherical particles to nonspherical triangular nanoprisms. A key variable is the choice and timing of the stabilizer that is used. Unlike other papers that propose that PVP controls such structures by acting as a selective capping agent on the {111} crystal faces of silver, the work in this paper found that sodium citrate was more effective for this chemical system than either poly(vinyl pyrrolidone) or poly(vinyl alcohol) at generating controlled nanoprisms. The work showed that varying the level of citrate had little effect on the final particle morphology, but did affect the time necessary to develop those particles. Of much larger impact was the pH of the formulation. Small changes in pH from 6.7 to 7.0 had a very large effect on the rate of reaction and on the final habit, with the HQ in slightly acidic reactions being very slow to reduce silver but creating large nanoprisms. On the other hand, if the reaction was carried out under neutral or slightly alkaline conditions then the reaction was very fast and generated spherical particles. The reactivity rate was attributed to the HQ chemistry, while the resultant flux of new Ag° atoms was found to subsequently control the morphology of the particles. These results can be explained using a model based on stochastic crystal growth. As others have suggested,28 slow reactivity favors controlled growth at the {100} or {110} crystal edges of twinned fcc crystals. The question remains as to how to explain the quasi-spherical particle formation under fastgrowth conditions. The model proposed in this paper does not resort to some sort of thermodynamically driven process, but instead explains the results as moving from controlled defectterminated migration of adatoms to rapid, multiadatom collisions leading to 2-dimensional nucleation of new growth layers on otherwise flat surfaces. As the flux of new metallic atoms increases, this 2-dimensional nucleation begins to dominate and leads to high levels of surface roughening. The resultant crystal morphologies are similar to those expected if the system was truly thermodynamically driven, but the dynamics are due to competitive kinetics rather than the composite free-energy gradient. Once the particles are formed, the 3-dimensional roughened crystals are able to undergo reformation via either surface migration or Ostwald migration to refine the crystal habit and continue to reduce the surface energy of the system. But this happens subsequent to the growth process - it does not drive the growth process and is inhibited by structures that are dominated by large flat surfaces. Particle nucleation and growth remain an incredibly complex topics. The interwoven interactions that are present touch on bulk mechanics, interfacial dynamics, molecular vs cluster vs crystalline energy minimization, with all of these caught within the broader umbrella of understanding what is unique within the nanoscale regime. It is because of this complexity that we still search for answers 150 years after Michael Faraday’s work with gold nanosols. Acknowledgment. The authors acknowledge the guidance and open access to instrumentation offered by Dr. Peter Cooke at the USDA Eastern Regional Research Center in Philadelphia, PA. Supporting Information Available: Additional experimental data, including specific information on the formulation parameters for making the particles described in the paper. This

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