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Role of Solvent in the Shape-Controlled Synthesis of Anisotropic Colloidal Nanostructures Rajesh Sathiyanarayanan,†,§ Mozhgan Alimohammadi,† Ya Zhou,† and Kristen A. Fichthorn*,‡ †
Department of Chemical Engineering and ‡Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ABSTRACT: We use molecular dynamics simulations to study the role played by solvent in promoting anisotropic growth of colloidal nanostructures. Considering the growth of Ag nanowires and nanoplates in organic solvent, we study how solvent influences the aggregation of a small and relatively isotropic nanocrystal with a larger nanowire or a square nanoplate. We observe that when the two nanocrystals approach one another they almost always adopt a mesocrystal configuration, a freeenergy minimum in which the two particles hover next to each other with their facets parallel and one or two layers of solvent between them—analogous to experimentally observed mesocrystal structures. Nanocrystal aggregation occurs from the mesocrystal state, and the free-energy barrier for aggregation is smallest on the smallest facets, which perpetuates anisotropic growth. By characterizing solvent ordering around the nanocrystal surfaces, as well as aggregation mechanisms, we find that solvent ordering is disrupted at the edges of the crystals, and this is where initial contact between the two nanoparticles is most likely to occur. Because the small nanocrystal is in close proximity to edges of the large nanostructure at its smallest facets, the free-energy barriers for aggregation are smaller there. Our general model contains features that are observed in a wide variety of systems that exhibit mesocrystal states and oscillatory solvation forces. These studies indicate that solvent can play a key role in promoting the anisotropic growth of colloidal nanostructures.
’ INTRODUCTION Achieving the controlled synthesis of colloidal nanomaterials with selected shapes and sizes is an important goal for a variety of applications that can exploit their unique properties (e.g., optical,16 catalytic,711 magnetic,12,13 etc.). In the past decade, a number of promising solution-phase synthesis techniques have been developed to fabricate various nanostructures.1423 A deep, fundamental understanding of the phenomena that promote selective growth and assembly in these syntheses would enable tight control of nanostructure morphologies in next-generation techniques. In this work, we focus on phenomena that underlie the synthesis of one-dimensional or anisotropic nanomaterials,15,16,1821,2325 such as nanowires, nanoribbons, and nanoplates, whose formation requires enhanced growth along certain directions and suppressed growth along others. There are several different phenomena that could facilitate such anisotropic growth. For example, this type of growth might be achieved via the use of polymers, surfactants, or other solution-phase species that selectively adsorb on certain crystal facets and induce shape-selective growth.2,18,2631 Anisotropic growth could also occur due to intrinsic forces between colloidal nanoparticles. For example, it has been postulated that dipoledipole interactions could cause particles with relatively uniform aspect ratios to aggregate into a chain along the direction of their dipoles.3133 Recently, we have shown that local charge nonuniformity can also cause nanocrystals to aggregate along preferred crystal directions.34 Solvent-mediated phenomena could also facilitate anisotropic growth of nanocrystals. For example, solvent most likely plays a r 2011 American Chemical Society
role in the formation of “mesocrystals” or particles comprised of aligned crystallites with solvent and/or other solution-phase species in the space between the crystallites.3538 Mesocrystals have been proposed to be intermediates in the process of oriented attachment,35,39,40 which is prevalent in the growth of anisotropic nanostructures.24,25,28,31,4145 In oriented attachment, nanocrystal aggregation occurs along specific crystal directions, such that the aggregate is a twinned or single-crystal structure.35,46,47 Yuwano et al. recently used cryogenic transmission electron microscopy to observe a correlation between the sizes and shapes of intermediate ferrihydrite mesocrystals and final goethite nanowires grown by oriented attachment.38 Molecular dynamics (MD) simulation studies also suggest that solvent-mediated phenomena could promote the anisotropic growth of nanomaterials by facilitating anisotropic aggregation. These studies show that the interaction between solvophilic (solvent-loving) nanoparticles can oscillate between attraction and repulsion as a function of nanoparticle separation,4853 similar to what is seen experimentally in studies with the surface forces apparatus54,55 and with atomic-force microscopy5557 for a variety of different liquids. The force oscillations can be linked to solvent layering between the two particles, with repulsive maxima corresponding to nanoparticle separations that can accommodate wellordered solvent layers and attractive minima corresponding to Received: May 18, 2011 Revised: August 26, 2011 Published: August 29, 2011 18983
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The Journal of Physical Chemistry C separations that cannot accommodate an integer number of layers. As a consequence of solvent ordering and force oscillations, we expect that the particles will reside in an attractive freeenergy minimum for some time without aggregating, analogous to experimentally observed mesocrystals, before they surmount a free-energy barrier and aggregate. The possible sensitivity of the solvation free-energy barrier to nanostructure geometry is an interesting prospect to consider in the case of anisotropic nanocrystals that contain various facets of different sizes. Solvent ordering can be sensitive to local crystallographic structure, and we anticipate differences in the local freeenergy barrier for aggregation on different crystal facets or differences between facets and edges. There is evidence that structure-sensitive solvent ordering can affect the alignment of two nanocrystals as they approach one another.52 Similar alignment effects, due to depletion forces, can also occur.58 Here, we investigate the propensity for solvent to align two nanocrystals as they approach one another, to hold the nanocrystals in mesocrystal states, and to promote oriented attachment in a model system designed to mimic the initial stages of anisotropic crystal growth. In this work, we employ MD simulations to simulate the approach and the initial stages of aggregation of a small and relatively isotropic nanocrystal with a larger, anisotropic nanostructure in solution. Considering the wide variety of systems that exhibit mesocrystal states37 and oscillatory solvation forces5457 (e.g., organic and inorganic nanoparticles with a wide range of different solvents), we adopt a simple model that can capture general characteristics that are likely to be present in many different systems. We consider a model system that contains two different types of forces: solventmediated forces and van der Waals interactions. Our solvent consists of Lennard-Jones (LJ) spheres. The LJ potential can capture general attributes of a wide variety of liquids, and atomic-scale simulations of solvation forces indicate that LJ liquids reproduce the oscillatory trends seen experimentally for more complicated and structured molecules.48,49,5970 With regard to van der Waals interactions, we choose to study Ag nanocrystals because Ag has a large Hamaker constant,54 ensuring strong van der Waals attraction between the nanoparticles. If solvent-mediated interactions play a significant role for Ag nanoparticles, then we expect them to also be significant for a variety of solids with smaller Hamaker constants. A variety of different anisotropic Ag nanostructures have been synthesized experimentally via solutionphase methods.71 Moreover, evidence for an aggregative mechanism has been found for the growth of Ag nanowires in N,N-dimethylformamide (DMF),41 and our studies have relevance for understanding oriented attachment in these experimental systems. As we will discuss below, we observe a tendency for solvent to align the two nanocrystals prior to aggregation, as well as to promote anisotropic growth.
’ MODELS AND METHODS The nanocrystals in our study are shown in Figure 1. We consider the initial stages of formation of an anisotropic structure, when the addition of a small and relatively isotropic nanocrystal could either perpetuate anisotropic growth or promote the formation of a more isotropic structure. We consider fcc nanocrystals, to mimic Ag. The small nanocrystal has three (3 3) (100) layers (27 atoms total) stacked in a rectangular cuboid configuration, such that it has four (110) facets and two (100) facets (cf., Figure 1). We consider two different shapes for the
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Figure 1. Snapshots of initial nanocrystal configurations depicting (a) the nanowire and (b) the nanoplate along with the small nanocrystal and solvent molecules. The various possible initial alignments of the two nanocrystals are indicated. For clarity, only half of the solvent molecules are shown, and their size is reduced.
Table 1. LJ Parameters for Solvent and Nanocrystal Interactions pair interaction
ε (kcal/mol)
σ (Å)
AgAg
1.39
2.54
SS AgS
0.09 0.35
3.95 3.25
large, anisotropic nanostructures. In the first of these [cf., Figure 1(a)], we consider a growing nanowire, which we model as a rectangular cuboid comprised of six (4 10) (100) layers (240 atoms) with two (100) and two (110) facets on the long dimension and two (110) facets for the “ends”. The second nanostructure [cf., Figure 1(b)] is a square nanoplate consisting of 674 atoms with two large (12 12) (100) facets and alternate stacking of (12 12) and (11 11) (100) layers to produce four similar (110) side facets. We note that, since the large and small nanocrystals possess the same types of facets [i.e., (100) and (110)], they could aggregate in registry, exhibiting oriented attachment. To maintain a general description of an isotropic solvent molecule S, we consider a (truncated) Lennard-Jones (LJ) (12-6) solvent, such that the interaction U between solvent molecules i and j separated by a distance of rij has the form 8 2 ! !6 3 12 > σ σ > < 4ε4 5, if rij e rcut rij rij ð1Þ Uðrij Þ ¼ > > : 0, if rcut < rij The parameters σ(= σSS, where S = solvent) and ε(= εSS) are those for a united atom (CH2) from the TraPPE force field72 and are given in Table 1. Although the embedded-atom method73 and similar potentials74 are often employed to describe metallic bonding in metals such as Ag, these potentials do not explicitly account for long-range van der Waals interactions that are relevant in governing the approach and the formation of mesocrystal states involving colloidal nanoparticles. The long-range van der Waals interaction between Ag atoms in different nanocrystals is given by UvdW ðri, j Þ ¼
C6 ri,6 j
ð2Þ
Equation 2 is the attractive dispersion term in eq 1 with a C6 coefficient given by C6 = 4εσ6. We obtained the value of ε = εAgAg from an experimental estimate of the Hamaker constant for Ag.75 To prevent a singularity as two atoms approach closely, 18984
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The Journal of Physical Chemistry C we also adopt the Pauli repulsion term in eq 1 with a value for σ = σAgAg that was used in previous studies.76 We model the Ag nanocrystals as rigid bodies, and thus, we do not consider interactions between Ag atoms in the same nanocrystal. In this way, we suppress random rearrangement of the nanocrystals as they approach one another, and we ensure that they maintain well-defined shapes. We used LorentzBerthelot mixing rules to compute LJ parameters for the interaction between Ag atoms and solvent particles. The values of these parameters are given in Table 1, where we see that εSAg = 3.89 εSS, indicating a solvophilic system, in which the solvent self-attraction is less than its attraction to the nanocrystals. We used a cutoff of 10 Å (≈ 2.5σSS) for the interaction range. We used DL_POLY,77 version 2.20, to simulate the small nanocrystal and one of the large nanostructures in a solvent-filled box in the canonical ensemble with a constant number of particles N, volume V, and temperature T. The Nose-Hoover thermostat78,79 was used to maintain constant temperature. For simulations involving the nanowire [Figure 1(a)], the simulation box volume was (70 70 100) Å3, and the volume was (85 85 60) Å3 for the nanoplate in Figure 1(b). These boxes were filled with solvent atoms such that the solvent was in the liquid phase with a reduced number density of F*(= Fσ3SS) = 0.7 and a reduced temperature of T*(= kBT/εSS) = 1.0. To assess nanocrystal aggregation mechanisms and kinetics, we directly simulate the approach of two nanocrystals that have different initial positions with respect to each other. From the resulting trajectories, we can visualize various mesocrystal states (free-energy minima) and aggregation mechanisms, and we can directly assess the time scales involved in aggregation. Another way of characterizing aggregation tendencies is to calculate the potential of mean force (PMF) between two nanoparticles as they approach one another.4853,58 In simulations for which aggregation is the thermodynamically favored outcome (as is the case here), the PMF depends on the choice of a reaction coordinate (e.g., the center-of-mass separation of the two particles), and unless the reaction coordinates are chosen to coincide with specific reaction pathways, the free-energy barriers inferred from PMFs do not reflect free-energy barriers for transformations. For this system, the reaction coordinates are not known, and direct MD simulations of aggregation are helpful for elucidating aggregation pathways. We initially considered three sets of initial positions for the nanowire, as can be seen in Figure 1(a). In position 1, the small particle is initially closest to one of the two large (100) “side” facets of the nanowire; in position 2, the small particle is initially close to a large (110) side facet; and in position 3, the small particle is closest to a small (110) “end” facet of the nanowire. As shown in Figure 1(b), there are two different initial positions for the small crystal with respect to the nanoplate. In position 1, the small particle is closest to a large (12 12) (100) facet, and in position 2, the small particle begins near a thin (110) side facet. In each of these initial positions, the small crystal was initially placed in a randomly chosen orientation such that its center of mass was 10 Å from the centroid of the closest plane of atoms on the large nanostructure. With an initial separation of 10 Å, the two nanocrystals are far enough apart so the small crystal can rotate freely and adjust its position with respect to the large one, and there is a minimum of one solvent layer between the closest atoms in the small and large crystals. In addition, many of the Ag atoms fall within the cutoff of the AgAg interaction, so that the two crystals experience van der Waals attraction and we minimize
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Table 2. Number of Observed Simulation Outcomes for Each Initial Orientation Shown in Figure 1a
position 1
2
3
outcome
number of
number of
observations
observations
rectangular particle
square plate
aggregation (PA)
8 (0.32)
1 (0.04)
Mesocrystal State 1
15
14
Mesocrystal State 2
—
5
Mesocrystal State 3
2
4
dissociation
—
1
aggregation (PA)
8 (0.32)
9 (0.36)
Mesocrystal State 1
16
14
Mesocrystal State 2 Mesocrystal State 3
— —
1 —
dissociation
1
1
aggregation (PA)
18 (0.72)
Mesocrystal State 1
5
Mesocrystal State 2
—
Mesocrystal State 3
—
dissociation
2
—
a
In Mesocrystal States 1 and 2, the nanocrystals align with their facets parallel, and they have one and two solvent layers between them, respectively. In Mesocrystal State 3, the nanocrystals assume various nonparallel alignments. In the case of aggregation, we include the aggregation probability PA.
long trajectories in which the small crystal wanders away from the large one. For each initial configuration, we conducted a 2 ns equilibration run, in which both the large and small nanocrystals were fixed and solvent molecules were allowed to move and equilibrate around them. In subsequent 2 ns production runs, we simulated the motion of both the small crystal and the solvent, while the large nanostructure remained fixed. We ran 25 simulations for each of the initial positions shown in Figure 1.
’ RESULTS AND DISCUSSION Table 2 summarizes the various outcomes that we observed at the end of the production runs. During the course of a run, we typically found that the small crystal rapidly reorients itself (usually within less than 40 ps) so that one of its facets is parallel to the facet of a large nanostructure and the two particles have one layer (Mesocrystal State 1 in Table 2) or two layers (Mesocrystal State 2 in Table 2) of solvent molecules between them. Snapshots of these states are shown in Figure 2(a) and (b). Subsequently, two main types of outcomes were observed at the end of the 2 ns runs: either the two nanocrystals aggregated or the small crystal “hovered” in Mesocrystal State 1 or 2 without aggregating. Less common outcomes are that the small crystal drifted away from the large one (dissociation) or that it hovered in a nonparallel orientation (Mesocrystal State 3). A snapshot of Mesocrystal State 3 is shown in Figure 2(c). The rapid reorientation and subsequent hovering of the small crystal in the mesocrystal states are indicative that theses states are free-energy minima. We note that these loosely associated states closely resemble experimentally observed mesocrystals.3540 To characterize aggregation kinetics, we note that the escape of the small crystal from the free-energy minimum of a mesocrystal state to a neighboring free-energy minimum of the 18985
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Figure 3. Residence probability P(t) given by eq 4 for the small nanocrystal at position 3 for the nanowire.
Figure 2. Snapshots from MD simulations of the small crystal and (a) the nanowire in Mesocrystal State 1, (b) the nanoplate in Mesocrystal State 2, and (c) the nanoplate in Mesocrystal State 3, in which the (100) facet of the small crystal is tilted away from the (100) facet of the nanoplate. To clearly depict solvent ordering, we show a slice of the simulation box containing the small crystal and the solvent around it.
aggregated state, another mesocrystal state, or the dissociated state can be described as a Poisson process.80 In a Poisson process, the distribution f(t) of escape times t is exponential and given by f ðtÞ ¼ ReRt
ð3Þ
Here, the escape rate R reflects the free-energy barrier ΔG as R ∼ exp(ΔG/kBT). From eq 3, we find that the average residence time in state A before an observed transition to state B (e.g., Mesocrystal State 1 f Aggregation) is 1/R. We can use this knowledge to obtain the transition rates between pairs of states from average residence times in MD simulations.81,82 Such information for specific crystal systems could be useful in rateequation approaches for describing crystal growth in the presence of anisotropic aggregation or oriented attachment.8385 To demonstrate this approach, we use eq 3 to calculate the residence probability P(t) that a particle in a mesocrystal state at time 0 will still be there at time t. From eq 3, this is given by PðtÞ ¼ eRt
ð4Þ
Following the procedure described in ref 81, we obtained the residence probability for aggregation events at position 3 for the nanowire—the position for which we observed the largest number of aggregations. The resulting probability is shown as a moving average in Figure 3. At long times (t > 1000 ps), we do not have sufficient statistics to adequately characterize P(t) (the longest aggregation time we observed is 1524 ps), and we observe a sharp drop-off as a result of this. At short times, it is likely that an equilibration time is needed after we initiate the trajectory of the small nanocrystal, and short-time aggregations result from particles that have not fully equilibrated in Mesocrystal State 1. For example, we observed several direct aggregations without prior hovering at short times. Over intermediate times, the small nanocrystal has clearly equilibrated in Mesocrystal State 1 and
subsequently aggregated. From an average of five different linear regressions of the data with initial times between 180 and 200 ps and ending times between 800 and 1000 ps, we find a rate of R = 0.64((0.03)/ns. To generally characterize the aggregation rates on different nanocrystal facets, we can define an aggregation probability PA using eq 3. If the system resides in a free-energy minimum (e.g., Mesocrystal State 1) prior to aggregation, then from eq 3 we have PA ðτÞ ¼ 1 eRτ
ð5Þ
PA gives the probability that the nanocrystals will aggregate within a time interval of τ. Provided that τ is not too long or too short, PA will reflect differences in the rates and free-energy barriers for aggregation on the different facets. We calculate PA as the fraction of aggregations observed for a given initial configuration at the end of all 25 production runs, each of length τ = 2 ns. Aggregation probabilities for the various initial conditions in Figure 1 are shown in Table 2. A survey of the aggregation probabilities in Table 2 indicates that the likelihood of the two nanocrystals to aggregate is sensitive to their initial alignment. In simulations involving the nanowire, the aggregation probability when the small particle approaches an end [position 3 in Figure 1(a)] is more than twice the values for when the small particle approaches a side [positions 1 and 2 in Figure 1(a)]. The surface area of a side facet of the nanowire (334.56 and 354.86 Å2 for positions 1 and 2, respectively) is ∼2.42.5 times the surface area of an end (141.94 Å2) so that a small crystal randomly approaching a nanowire will be about five times as likely to encounter a side facet as an end facet. Nevertheless, the probability that the small crystal will actually attach to a side is significantly less than at an end. The dependence of PA on the initial alignment is especially prominent for the nanoplate. In position 1 [cf., Figure 1(b)], we see only a single instance of aggregation in 25 runs. However, the aggregation probability for position 2 at the side of the nanoplate is similar to those for the sides of the nanowire. In this case, the surface area of the large facet for position 1 is 1204.4 Å2, while that of side facet 2 is 384.25 Å2. If we compare the aggregation probabilities for all cases in Table 2, we see that PA for a given facet is roughly inversely proportional to the surface area of the facet. To illustrate typical aggregation mechanisms, we show two sequences of snapshots from MD simulations where aggregation occurred in Figure 4. In the majority of the trajectories where aggregation occurs, the small crystal tends to orient itself so that it makes initial contact with the large one via an edge or a 18986
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Figure 4. Sequences of snapshots illustrating the first contact in typical aggregation events. In (a), (b), and (c), we show initial contact at the (110) edge of the nanoplate, and in (d), (e), and (f), we show initial contact on the (100) face of the nanoplate. A slice of solvent with a thickness of two layers is shown in the area of first contact and aggregation, so the mechanisms can be clearly seen.
Figure 5. Solvent density F relative to the bulk liquid density Fb in a slice of the simulation box surrounding (a) a side view of the nanowire, (b) an endon view of the nanowire, and (c) a side view of the nanoplate. The insets depict the orientation of the large nanostructure for each density map.
vertex—perhaps because it is easier to disrupt solvent ordering around the large crystal in this way. For aggregation of the nanoparticle with the nanowire and when the initial position of the nanoparticle is near the edge of the nanoplate, first contact most often occurs at the edge of the large particle. As we see in Figure 4(a)(c), the nanoparticle and the nanoplate initially contact each other edge to edge. Similarly, in Figure 4(d)(f), when the small nanoparticle approaches the large, square facet of the nanoplate, initial contact occurs via its vertex.
Solvent ordering at the nanocrystal surfaces influences the type and frequency of aggregation events. We observe solvent ordering around the surfaces of both large nanostructures in this study, which is evident in Figure 2. Plots of the solvent density in slices of the simulation box surrounding the large nanostructures (in the absence of the small crystal) are shown in Figure 5. Here, we see that the solvent density is the highest in the first solvent layer next to the nanocrystal surfaces. In this layer, localized regions of high solvent density occur and reflect ordering of 18987
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The Journal of Physical Chemistry C solvent on the nanocrystal surfaces. All of the nanostructures exhibit a second solvent layer, where lateral ordering is not as pronounced as in the first layer. A weakly defined third layer can be seen next to some of the facets. Between the high-density solvent layers, we observe low-density regions—two to three are visible in Figure 5. Extensive layering occurs for the large facet of the nanoplate [Figure 5(c)], as well as along the long facets of the nanowire [Figure 5(a)] and along the side facets of the nanoplate (not shown). There are disruptions to layering at the edges of these facets [Figure 5(b) and (c)], and layering disruptions are especially prominent along the edges of the end facets of the nanowire [Figure 5(a) and (b)]. Considering the observed aggregation mechanisms in Figure 4 and the solvent density profiles in Figure 5, we can conclude that the disruption of solvent ordering at the nanocrystal edges plays a key role in facilitating aggregation. The free-energy barrier for aggregation is the lowest (highest PA) on the end facets of the nanowire because these facets are the smallest, and solvent layering and ordering within the first layer are disrupted at all four edges. If the small nanocrystal is close to the end of the nanowire, it is also in close proximity to an edge, where it can easily join the nanowire. In contrast, extensive lateral ordering of first-layer solvent molecules can be achieved on the large (100) facets of the nanoplate, where the trajectory begins far from an edge and the free-energy barrier for aggregation is the highest. The sides of the nanowire and the nanoplate are intermediate between these two extremes because solvent ordering and layering can be achieved along the long dimension but is disrupted at the edges on the thin dimension.
Figure 6. Initial conditions for the small nanocrystal with respect to the nanoplate for simulations probing aggregation near the edge of the plate. In (a) we show the initial angles of the small particle with respect to the (100) facet of the nanoplate, and in (b) we indicate different initial positions along the edge of the plate.
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It seems possible that a small particle initially in a mesocrystal state on a large facet of the nanoplate could migrate to the edge, where solvent ordering is disrupted, and aggregate there. Such events would also perpetuate anisotropic growth. Presumably, we did not observe these events because of the limited time scales in our MD simulations. To test this hypothesis, we performed another set of MD trajectories in which we began with the small nanocrystal close to the edge of the nanoplate. As shown in Figure 6, we ran 20 trajectories beginning at five different angles along a cylindrical surface with its origin at the edge of the (100) surface and a radius of 10 Å [cf. Figure 6(a)]. For each angle, we probed four different positions along the edge, as shown in Figure 6(b). In these trajectories, we observed 17 instances of aggregation and three instances of hovering, where the small particle moved either to the (100) facet (two instances) or to the (110) side facet (one instance). Contrasting this result to those for the small particle beginning near the centers of the large and side facets of the nanoplate (cf. Table 2), we see that the freeenergy barrier for aggregation is significantly smaller near the edge of the plate, where solvent is more easily disrupted. We also investigated the relative orientations of the two nanocrystals immediately after aggregation, in an attempt to observe instances of oriented attachment. We observed four instances of oriented attachment at the end of the nanowire and two in our auxiliary simulations beginning at the edge of the nanoplate. While the number is small, it is still significant that oriented attachment most likely occurs at locations where the free-energy barrier for aggregation is the lowest—at locations where anisotropic growth is most likely to be perpetuated. A time sequence of snapshots from a trajectory in which oriented attachment occurred at the edge of the nanoplate is shown in Figure 7. Here, we see that the crystals do not aggregate in an aligned fashion and that alignment occurs after initial contact is made. It is important to emphasize that we model the nanocrystals as rigid, so we do not (for example) allow atoms of the small crystal to rearrange to accommodate to the lattice of the large one. Recent MD simulations by Schapotschnikow et al.86 indicate that such rearrangement (or recrystallization) is important in achieving the fusion of two initially misaligned nanocrystals. Thus, we would expect to observe more instances of oriented attachment if we allowed for motion of the crystal atoms.
Figure 7. Time sequence of nanoparticle configurations when the small nanocrystal approaches the edge of the nanoplate and the resulting aggregate is a monocrystal; i.e., oriented attachment occurred. A slice of solvent with a thickness of two layers is shown in the area of first contact and aggregation, so the mechanisms can be clearly seen. 18988
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’ CONCLUSIONS In summary, we find that solvent can play an important role in promoting the anisotropic growth of colloidal nanostructures. Solvent can align a large, anisotropic nanostructure and a small, isotropic nanocrystal along their facets, with one or two layers of solvent between them. The nanocrystals hover in these loosely associated states, which are analogous to experimentally observed mesocrystals.3540 Nanocrystal aggregation occurs from the mesocrystal state, and by probing different initial conditions we find that for a given nanocrystal it occurs the most rapidly on the smallest facets—at the ends of the nanowire or on the thin sides of the nanoplate. In this way, aggregation tends to perpetuate anisotropic crystal growth. Through characterization of solvent ordering around the nanocrystal surfaces, as well as aggregation mechanisms, we find that solvent ordering is disrupted at the edges of the crystals, and this is where initial contact between the two nanoparticles is most likely to occur. Because the small nanoparticle is in close proximity to edges of the large nanoparticle at its smallest facets, the free-energy barriers for aggregation are smaller there. We adopted a simple model for our study, in an effort to capture trends that are observed experimentally for a wide variety of different nanoparticle (surface)/solvent systems that exhibit mesocrystal states37 and oscillatory solvation forces.5457 Because of the generality of the experimental observations, we expect the trends observed here to apply to a range of different solvophilic systems—although specifics of the mesocrystal states and aggregation times will vary. Knowledge from these studies can be used to optimize solution-phase synthesis techniques to produce anisotropic nanostructures with high selectivity. ’ AUTHOR INFORMATION Corresponding Author
*E-mail: fi
[email protected]. Present Addresses §
IBM Semiconductor Research and Development Center, Bangalore 560045, India
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