Ostwald Ripening in Metallic Nanoparticles: Stochastic Kinetics - The

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Ostwald Ripening in Metallic Nanoparticles: Stochastic Kinetics Stuart T. Gentry,* Shane F. Kendra, and Mark W. Bezpalko Department of Chemistry and Biochemistry, La Salle University, 1900 W. Olney Ave., Philadelphia, Pennsylvania 19141, United States

bS Supporting Information ABSTRACT: This paper looks at the factors that control Ostwald ripening in a bimodal silver nanocolloid system containing tabular particles having one dimension equal to or less than 5 nm. The test system was based on a seeded process using the staged addition of sodium borohydride and hydroquinone (HQ) to silver nitrate. The result was a blend of 20 nm spheres and 30 nm/4
5 nm nanodiscs. The mixture of morphologies allows for a greater differentiation in free energy stability between particles and consequently an accelerated rate of ripening. The rate of the ripening process is shown to be heavily dependent on the relative amount of spherical receptor particles as well as on the presence of hydroquinone as a redox catalyst. A stochastic model is proposed for stepwise adatom kinetics.

’ INTRODUCTION Nanocolloids made from noble metals have enjoyed a long history of study. Under the proper conditions, these systems can be synthesized to have well-controlled spherical particle size distributions and exhibit unique electrical, chemical, biological, and optical properties.1 In more recent years there has been a large amount of interest in nonspherical versions of these colloidal systems. A range of morphologies have been reported including rods, wires, stars, flowers, and triangular nanoprisms.2 These anisotropic morphologies are interesting not only in terms of understanding the development of their shapes but also because they offer an array of new opportunities to exploit nanocolloid technology.3 In order to be commercially practical, these nanocolloids must be stable with time. This has always been a consideration with traditional sols and emulsions but is even more of an issue as colloidal dimensions are reduced to the nanometer range. Colloid particles become increasingly unstable with decreasing particle size due to the relative increase in higher energy surface area. The Gibbs
Thomson equation4 expresses this phase instability in terms of the solubility concentration, C(r), of a particle with radius r.   2γVm ð1Þ CðrÞ ¼ C° exp rRT C° is the solubility of an atom taken from an infinite flat surface, Vm is the molar volume of the particle, γ is the surface energy, R is the gas constant, and T is the temperature. This size-dependent instability leads to Ostwald ripening, which is the transfer of atoms over time from smaller, less stable particles to larger ones.5 What has become apparent in recent years is that this influence of size on the free energy instability becomes even more acute when metal particles are reduced to below a critical size. Published r 2011 American Chemical Society

works have shown that the cohesive energy, melting temperature, and surface tension all show a sudden change in their dependence on size below ∼5 nm in dimension.6 Below this critical threshold, the system is no longer adequately described by the Gibbs
Thomson mean-field approach and instead is increasingly sensitive to local effects. In spite of all this work on nanothermodynamics, little experimental work has been published on the effect of Ostwald ripening in this critical regime. Published studies on ripening in nanocolloid systems are either based on theoretical modeling7 or look at experimental systems having particle sizes much larger than the 5 nm critical threshold.8 One of the difficulties inherent in studying particles having dimensions less than the critical threshold is that it is difficult to separate Ostwald ripening from other simultaneously occurring growth and/or destabilization processes. This article takes a new approach to studying Ostwald ripening in the nanoregime. It makes use of a bimodal system where one set of particles are ca. 20 nm spheres while the second set are 30 nm by 4
5 nm flat nanodiscs. This system can be grown to mature size within 30 min. Ripening then occurs as a subsequent process over a time period of 1
24 h. The difference in free energy stability between the two types of particles creates an accelerated driving force for observing Ostwald ripening. This effect can be modulated by adjusting the relative concentrations of the two particles. This article will explore some of the factors that control ripening in this bimodal system. It will also compare the stability of these small nanodiscs to more traditional nanoprisms having edges that are greater than 100 nm in length and plate thicknesses of 8
10 nm or more. The article will use a stochastic growth

Received: January 29, 2011 Revised: May 9, 2011 Published: June 16, 2011 12736

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Figure 1. TEM’s on sample made from seeded system containing AgNO3, HQ, sodium citrate, and 0.002 mole fraction BH4
. The citrate was added before the BH4
. Data taken from ref 12.

model to explain the ripening process in anisotropic systems in terms of individual adatom kinetics.

’ 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 seeded formulation was a 15 mL aqueous 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), 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 ultrapure water (Millipore Direct QUV). The standard process was to initially form particle seeds by combining the water, AgNO3, citrate, and NaBH4 in that order under mild agitation. With only 0.002 mole fraction borohydride relative to AgNO3, more than 99% of the silver ions were left unreacted at the completion of the seed formation step. The seed particles were given 2 min to equilibrate, and then the bulk of the silver reduction was carried out by the subsequent addition of the hydroquinone (HQ) as the primary reducing agent. Under slightly acidic conditions HQ is too weak a reducing agent to reduce silver unless nascent seed particles are already present.9 Sodium citrate acts as a colloidal stabilizer for the system. Depending on the point of addition of the citrate, the pH of the system, and the concentration of seed particles, one can obtain a variety of morphologies including spheres, small nanodiscs, and/ or large triangular nanoprisms.10 The pH of the system was generally left unadjusted unless otherwise noted, but was slightly on the acidic side (6
6.5 pH). Samples were stored in the dark during particle formation to ensure that there was no UV-induced reaction. All reported mole fractions are relative to the initial concentration of silver ions in the AgNO3. An alternative process to the seeded process described above is to use UV radiation to initiate particle formation.9 In the presence of UV light, HQ is able to initiate new particles without the need to

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Figure 2. UV/vis spectra on a sample similar to that shown in Figure 1. The optical data show an overlay of spectra taken at different times during the initial growth stage and then during subsequent aging of the fully formed colloid.

rely on preformed particles. The result is that one can grow spherical colloids using a single-stage process of only AgNO3, citrate, HQ, and UV light. Instrumentation. The plasmon extinction spectra were recorded using a Hitachi U-2910 UV/vis spectrometer. Transmission electron micrographs were recorded in the bright-field mode using a Phillips CM12 scanning/transmission electron microscope at the U.S. Department of Agriculture’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.11 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 edgeon to the electron beam.

’ RESULTS Particle Morphology and Stability. Figures 1 and 2 show representative data for Ag particles made with hydroquinone (HQ) as the reducing agent and with the sodium citrate added prior to seed formation. This system will be the principal test vehicle for this paper. The micrographs in Figure 1 show a system that is composed of a bimodal ensemble of small particles. One mode consists of quasi-spherical solids with diameters of 15
25 nm. These are manifest in the TEM as opaque shapes with multiple crystalline domains. The second mode, seen as translucent uniformly shaded solids in the micrographs, is flat particles. These particles have ca. 4
5 nm plate thicknesses as seen for example in the inset micrograph. The tabular faces have a variety of geometries ranging from circular to triangular, but all of which have longitudinal dimensions on the order of 25
35 nm. [All dimensions were based on an analysis of a broader selection of particles from multiple micrographs.] Figure 2 shows the optical extinction spectrum for the bimodal sample. The figure shows the development of the spectrum during particle growth and then shows the continued evolution of the optical signal once growth was complete and the particles had begun to undergo a process of reformation. The spectra show a 12737

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Figure 3. TEM and UV/vis spectra for system made of large triangular nanoprisms. Sample was made with same composition as Figure 1, but with citrate added after the initial borohydride-generated seeds were formed.

Figure 5. Particle-size histograms collected on the same systems as shown in Figure 4. Data are for the (a) nanodiscs and (b) quasi-spheres that form the mixed system. Histograms are based on ca. 200 measurements for each colloid.

Figure 4. TEM’s for blended system with colloid transferred to TEM grid 3 h and 1 day after initial colloid formation. Dark images are multidomain quasi-spheres. Uniformly colored lighter images are nanodiscs. The sample was prepared with additional HNO3 added to the formulation. Optical spectra and additional TEM’s are in the Supporting Information.

strong signal at ∼400 nm. This peak is attributed to the growth of the quasi-spherical particles. Its fixed wavelength is consistent with traditional Mie theory for spherical particles less than 40 nm in size.13 The second, red-shifted peak in the spectra is consistent with flat, tabular particles. This peak is attributed to a dipolar longitudinal (in-plane) plasmon mode generated within the flat nanodiscs.12,14 Unlike spherical particles whose plasmon peaks keep a constant wavelength position for sizes below the critical Mie diameter, the longitudinal signals from the nanoplate particles continuously shift to longer wavelengths as the particles grow in longitudinal face dimension. The nanodisc signals reached a maximum peak wavelength of 625 nm at the end of the growth process in Figure 2a. In Figure 2b, however, the nanodisc signal quickly began to degrade—losing intensity and blue-shifting back toward the spherical signal. After 1 day the second peak had disappeared, and only the quasispherical peak at 400 nm was present, albeit with that peak larger in magnitude. It is this degradation in the nanodisc signal that allows us to monitor Ostwald ripening in this system. This rapid rate of reformation is unique to the small nanodiscs. Figure 3 shows data on large triangular nanoprisms having the same composition as the nanodisc system, but with the citrate stabilizer having been added after rather than before seed formation. The large triangular nanoprisms (>100 nm edge length, 8
10 nm thickness) demonstrate weeks-long stability in the optical signal compared to the hours-long instability of the nanodisc system (30 nm diameter, 4
5 nm thickness). None

of the factors discussed later in this paper were able to cause the large nanoprisms to degrade at a significantly faster rate. This included adding spherical particles to the otherwise unimodal distribution of large nanoprisms and/or adding various reducing agents or stabilizing agents. The critical difference in the two systems is the size of the small nanodiscs relative to the size of the large nanoprisms. The difference of face dimensions of 30 nm vs 100þ nm is what appears most striking to the eye. From theoretical considerations, however, what is probably much more significant for the Ostwald ripening is the difference in plate thicknesses that are linked to those face dimensions. Mode of Particle Reformation. While there are several possible mechanisms for particle reformation (particle aggregation, ripening, and internal reorganization), the degradation in optical signal in Figure 2 is most likely due to Ostwald ripening. Figure 4 shows representative micrographs for samples of the nanodisc system collected 3 h and 1 day after particle formation. The darker particles are the opaque quasi-spherical modes. The lighter particles are the translucent tabular plates. As can be seen, the sample that had been aged for 3 h shows a blend of spheres and plates with the plates having face dimensions larger than the spherical particles. By contrast, the 1 day sample shows that the nanodiscs range in size but are all now smaller in face dimension than the neighboring spherical particles, with some becoming quite small. Figure 5 provides particle-size histograms for the spheres and nanodiscs in Figure 4. The data in Figures 4 and 5 are consistent with Ostwald ripening. The data show that there was a significant decrease in the face diameter of the nanodiscs with time while at the same time there was a simultaneous coarsening of the spherical particles. This is a classical Ostwald ripening response. [Additional data are provided in the Supporting Information related to the alternative modes of instability and evidence for why they were found to be insignificant in these experiments.] Effect of Bimodal Distribution. As will be discussed later in this paper, the kinetics of Ostwald ripening depend in part on two separate factors. The first is the free energy instability of the 12738

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Figure 6. Extinction spectra and time response of peak wavelength location for nanodisc bimodal system centrifuged for 15 min at 12 000 rpm and a spinning diameter of 5 in. Data are for the full sample and for the supernatant fraction.

Figure 7. Time response of peak wavelength location for centrifuged supernatant sample. Supernatant subsequently blended with spherical particles made with UV process. Figure shows time response for different volume ratios: 0:1 (control), 0.2:0.8, and 0.33:0.66 colloidal volumes of spheres:supernatant. Actual molar concentrations of the supernatant colloid are not known due to the centrifugation separation process.

small-size donor particles as compared to the larger-size particles that act as ripening receptors (cf. eq 1). What is also critical, however, is the relative concentrations of donor and receptor particles. This dependence on the concentration of receptors can be seen in Figure 6. These data look at the time stability of the standard bimodal system as compared to that of a sample that had been prepared by centrifuging the system and analyzing the supernatant. On centrifugation, the system separates into a pellet phase that is rich in the larger spherical particles while the supernatant becomes rich in nanodiscs.12 Micrographs show that the change in relative peak heights is not due to a change in individual particle morphologies. Instead, the change in the spectroscopic data in Figure 6a is due to changes in the relative amounts of the two type of particles present in the system. Figure 6b shows the shift in peak location as a function of time.

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Figure 8. Time response of peak location for the standard bimodal system with the postaddition of (a) 1.0 and 3.0 mole fraction hydroquinone and (b) 1.0 and 3.0 mole fraction sodium borohydride relative to AgNO3. The BH4
samples were prepared by adding a series of smaller borohydride additions with a 2 min time delay in between to avoid destabilizing the system.

The data show that the rate of reformation is significantly slowed down by reducing the relative amount of spherical receptors in the supernatant. Figure 7 shows a related study wherein the sample was centrifuged and the supernatant was extracted, but then spherical receptor particles were subsequently added back into the system. In this case the spherical particles were obtained by using a UVinitiated growth process. This UV process has been shown to generate a range of quasi-spherical particles that are 20
50 nm in diameter. The figure shows that the addition of spherical particles caused a resumption in the reformation (or ripening) process. We interpret Figures 6 and 7 as being consistent with a model where supernatant adatoms are continuously desorbed and resorbed. In the relative absence of spherical receptor particles, however, there can be no ripening since the solubilized adatoms are most likely to return to their original nanodiscs. Desorption Process. The previous sections examined some of the thermodynamic and kinetic parameters that control the Ostwald ripening process in our experimental system. We also looked at chemical factors that might affect the resolubilization of silver atoms back into solution. We found that neither the presence nor absence of oxygen had a significant effect on stability, nor did the presence of postformation optical radiation. [See the Supporting Information for more information on these factors.] The one chemical factor that proved to be important was the presence of excess hydroquinone. Figure 8 shows that adding additional HQ beyond the stoichiometric amount needed for the initial silver reduction influenced the reformation process. This excess HQ had no effect on the magnitude of the plasmon signal, only on the rate of signal degradation after the initial particle formation was complete. By contrast, adding a strong reducing agent like NaBH4 was found to slow, rather than speed, the reformation process. While not shown, we also tried replacing the 12739

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Figure 10. Resorption processes. Figure 9. Time response of peak location for the standard (full) colloid as compared to centrifuged pellet. The sample was centrifuged for 15 min at 12 000 rpm.

weak HQ with another weak reducing agent, sodium ascorbate (NaAs). The NaAs gave results similar to that of HQ (cf. Supporting Information). The necessity for HQ to be present was also demonstrated by using centrifugation to separate the nanoparticles from the watersoluble moieties present in the system. The centrifugation pellet containing the particles was separated from the supernatant’s aqueous phase and then redispersed in pure water. Figure 9 shows that this separation process halted the reformation process. We then separately added back to the pellet each of the original water-soluble components that were present in the initial colloid. Hydroquinone was the only water-soluble material that restored the previously observed Ostwald ripening. We interpret the results in Figures 8 and 9 within the context of the redox equilibrium reaction that occurs as metallic silver is oxidized and transferred into the aqueous solution and then rereduced and resorbed back onto the particle. Weak reducing agents like HQ and NaAs are able to facilitate this equilibrium conversion, while strong reducing agents like NaBH4 inhibit the conversion process by pushing the redox equilibrium heavily toward the metallic state. We have also shown that this equilibrium conversion can be diverted by scavenging oxidized silver ions with a precipitate former such as chloride ion.

’ MECHANISM UNDERLYING OSTWALD RIPENING Ostwald ripening can be modeled as a three-step process: (1) desorption of an atom back into solution, (2) probability of collision of the dissolved adatom with a new particle, and (3) resorption onto the new particle. The desorption and resorption processes depend on the thermodynamics of adatoms at the surface of the particles. The collision probability, on the other hand, depends on kinetic parameters such as the rate of diffusive transport, particle concentrations, and collisional cross sections. We can define a ripening parameter, θR, as the fraction of adatom collisions that result in a solubilized adatom adsorbing onto a new particle of different morphology. θR ¼

collisions with different morphology total collisions

ð2Þ

After an adatom has been desorbed from an unstable nanodisc particle, the question is whether it finds a larger, more-stable spherical particle. Contrast this with an atom that leaves a nanodisc and returns to the same nanodisc or alternatively one that collides with another nanodisc. In either of the latter cases the result is that the there is no net change in the number of silver atoms in the overall ensemble of nanodiscs. Ripening will only

occur if the dissolved silver atom leaves a nanodisc and finds a spherical particle. It is generally assumed that the rate-limiting step for Ostwald ripening in dilute liquid suspensions is the diffusive transfer step.15 This implies that θR , 1, i.e., that the vast majority of solubilized atoms are resorbed back onto their original particle. This describes a relatively rapid equilibrium off and back onto the original particles, with only a small fraction of atoms escaping the capture zone of the original particle. Our data on the concentration dependence of receptor particles supports this premise. kdesorb

particle1 3 Ag h particle1 þ AgðaqÞ kresorb

k2

AgðaqÞ þ particle2 f particle2 3 Ag

ðfastÞ ðslowÞ

There is also the question of what happens to the solubilized silver atoms that return to a nanodisc particle: does the off and on transfer of adatoms cause the nanoplates to change morphology and take on more spherical characteristics? Under the theory of stochastic crystal growth,10 at low concentrations of incoming adatoms (such as would be the case in the presence of desorption/resorption), atoms that land on the flat tabular face of a nanodisc are most likely to migrate to a thermodynamically preferred edge defect site in a twinned Ag crystal rather than staying on the face. This is the same stochastic process that controls the formation of tabular morphologies in the first place. It is only under rapid growth conditions that there is sufficient concentration of adatoms to undergo 2-dimensional island nucleation with other adatoms on the flat face. This 2-dimensional island nucleation is required if the particle is going to take on more of a 3-dimensional spherical morphology. The conclusion from this discussion is that the particle morphology will be governed by the same factors that led to their initial shape, and thus desorption/ resorption should have no subsequent effect on their morphology. This conclusion is supported by the previous centrifugation data in Figure 6 where the supernatant retained the same plasmon signal over time. Centrifugation reduced the amount of spherical receptor particles needed for ripening but would not have affected the amount of silver per particle that was desorbed and then resorbed back onto the nanodisc particles. Despite the continued exchange of atoms between nanodiscs and solution, there was no change in the observed optical extinction response of the system.

’ SUMMARY Colloid stability is an issue that must be considered whenever working in the nanotechnology regime. This is particularly true when working with particles whose morphologies are something 12740

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The Journal of Physical Chemistry C other than the most thermodynamically preferred particle shape. In the current work, the blend of 20 nm nanospheres and 30 nm/ 5 nm nanodiscs (diameter/thickness) has been shown to be particularly susceptible to Ostwald ripening. In the course of several hours one can monitor the optical extinction signal and see the nanodisc plasmon peak transition from red-shifted wavelengths to blue as the discs lose atoms to neighboring nanospheres. It has been shown that factors such as the concentration of receptor spheres and weak redox catalysts can either enhance or inhibit the ripening process. What should not be lost while focusing on the details of the one system, however, is the increased susceptibility that this blended nanodisc experimental system shows to Ostwald ripening compared to other nanocolloids systems. Spherical systems and large triangular nanoprism systems all made with the same raw ingredients as the current blended system show much better stability. In the case of large nanoprisms, Figure 3 shows that while there might be a small change in the initial optical signal over the first week, the large plates retained their same basic response over the span of months. This was true even when spherical particles were postadded to the system to act as receptor sites for the Ostwald process. (cf. Supporting Information) The visually most striking difference between the small nanodiscs in this paper and the large nanoprisms is the face dimensions: 25
35 nm diameters for the nanodiscs versus 100þ nm edge lengths for triangular nanoprisms. But this reduction to 25
35 nm is not enough by itself to push the surface energetics into the critical regime where nanodimensionality becomes acutely important. Spheres of this same 25
35 nm dimension do not show the same level of hyperinstability. What is probably much more significant is the plate thicknesses that are linked to those face dimensions. The large stable nanoprisms that have been looked at in the authors’ lab are typically on the order of 8
10 nm thick. The small nanodiscs, on the other hand, have plate thicknesses less than 5 nm. This is within the range reported by others where thermodynamics show a sudden heightened dependence on size. This field of nanothermodynamics is one that continues to receive a great deal of study by both experimentalists and theoreticians. It is another example of why the broad arena of nanotechnology has created such a stir of excitement both in the lab and in the marketplace.

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’ ASSOCIATED CONTENT

bS

Supporting Information. Additional experimental data. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; Ph: 215.951.1259; Fax: 215.951.1772.

’ 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. ’ REFERENCES (1) (a) Park, J.; Joo, J.; Kwon, S. G.; Jang, Y.; Hyeon, T. Angew. Chem., Int. Ed. 2007, 46, 2. (b) Bonnemann, H.; Richard, R. M. Eur. 12741

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