J. Phys. Chem. B 2006, 110, 20879-20888
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Solvent Density Effects on the Solvation Behavior and Configurational Structure of Bare and Passivated 38-Atom Gold Nanoparticle in Supercritical Ethane Moti Lal,*,† Martin Plummer,‡ and William Smith‡ Centre for Nanoscale Science, The Donnan and Robert Robinson Laboratories, UniVersity of LiVerpool, LiVerpool L69 7ZD, United Kingdom, and Computational Science and Engineering Department, CCLRC Daresbury Laboratory, Daresbury, Cheshire WA4 4AD, United Kingdom ReceiVed: May 31, 2006; In Final Form: August 16, 2006
In exploring the effects of solvent density on the mode and the degree of solvation of the bare and passivated 38-atom gold particle in supercritical ethane, we have extended the molecular dynamics simulations of the system, reported previously,34 to cover a range of isotherms in the T > Tc regime, where Tc is the critical temperature of the solvent. Consonant with our previous observations, the modes of solvation of the bare and the passivated particle, deduced from the radial distribution of the solvent about the metal core center of mass, are found to be vastly different from each other at all solvent densities: while the molecules solvating the bare particle form a well-defined, two-region layer around it, those solvating the passivated particle are loosely dispersed in the passivating layer. For the bare particle, the degree of solvation (ϑ) as a function of solvent density passes through a maximum occurring in the close vicinity of the critical point, consistent with our previous results and in agreement with Debenedetti’s theoretical analysis,22,23 which predicts a solvation enhancement effect in the critical region for systems where the unlike solvent/solute interaction is much stronger than the solvent/solvent interaction. Taking the degree of solvation (ϑ) as a measure of solvent quality, we have investigated how the solvent quality would vary along the solvent-density isotherms. In the solvent-density regime F > Fc, the solvent quality is found to be a decreasing function of the density as a result of progressive dominance of the excluded volume effect over the attractive particle/solvent interactions. The particle/solvent affinity is greatly reduced in the presence of the passivating layer, resulting in considerable shrinkage of the good-solvent-quality domain in the supercritical regime. The solvent environment and the presence of the passivating chains produce significant disorder in the equilibrium structure assumed by the nanoparticle core.
1. Introduction Although supercritical fluids (SCFs) were found to possess extraordinary solvent properties well over a century ago,1,2 it was not until the late 1970s that their potential as effective media in the processing and extraction technologies was first realized.3 Today, supercritical fluids feature prominently in this role in technologies as diverse as the manufacture of decaffeinated coffee and nicotine-free tobacco,4 catalysis,5 synthesis and purification of polymers,6 extraction of perfumes and flavors,7 recovery of low-boiling-point chemicals from crude oil residue,8 reaction engineering,9 biotechnology,10 and cleaning of electronic components.11 Most recent advances concern nanomaterials where the tunability of solvent characteristics of supercritical fluids has been brought to bear on the development of promising approaches for the production of monodisperse nanoparticles,12-14 nanowires,15 nanotubes,16 nanocomposites,17 mesoporous nanofilms,18 and protein-nanoparticle conjugates.19 The superiority of supercritical fluids over liquids as solvents and suspending media in the above and other applications is attributed to their high compressibility, low surface tension, low viscosity, and perhaps most significantly, to their special mode of solvating the particles and solute molecules immersed in them.20 The focus of our studies in the field resides in this last * Corresponding author. E-mail:
[email protected]. † University of Liverpool. ‡ CCLRC Daresbury Laboratory.
aspect of the behavior of supercritical fluids. The supercritical regime is characterized by appreciable inhomogeneity and fluctuations in their density,21 particularly close to the critical point, which for simple systems have been shown theoretically to lead to the clustering or depletion of the solvent around the solute molecule, depending on the strength of the interaction between a pair of the solvent and the solute molecule relative to that between a pair of the solvent molecules.22 Enrichment or depletion of the solvent in the immediate surroundings of the solute particles would significantly affect the solventmediated interactions between them and hence their propensity to aggregate or remain dispersed in the solvent. Thus solvation has an important part to play in controlling the state of material dissolved/dispersed in supercritical media. This makes the development of molecular-based understanding of particle solvation and solvation forces a highly desirable objective. To date, theoretical attempts to investigate solvation effects in nanoparticles have considered continuum13 or partly continuum models,24 furnishing somewhat limited insights. Treatments assuming more realistic, all-molecular models call for computer simulation approaches to be applied. Molecular dynamics studies of structureless Lennard-Jones (L-J) nanoparticles or nanoparticles constituted of L-J atoms, immersed in either L-J liquids or in soft-sphere fluids, have been reported in the literature.25,26 These studies did not cover the supercritical regime of the suspending media. Moreover, the models assumed
10.1021/jp0633650 CCC: $33.50 © 2006 American Chemical Society Published on Web 09/21/2006
20880 J. Phys. Chem. B, Vol. 110, No. 42, 2006 for the nanoparticles correspond poorly to particles of major interest in the field of nanotechnology, such as transition metal atom clusters and semiconductor nanoparticles.27 Force fields for modeling these particles must take adequate account of the many-body nature of the interatomic interactions in the particle.28 Much of the published work on modeling/simulation of nanoparticles with realistic force fields has been directed to the investigation of these objects in the vacuum,29,30 at interfaces,31 and most recently, in water.32,33 Both classical and ab initio approaches have been pursued. We have undertaken a computer simulation program that focuses primarily on the investigation of nanoparticle solvation in supercritical fluids assuming atomistic/molecular models both for the nanoparticle and the solvent. Our objectives are to understand, in molecular terms, how the particle morphology, the thermodynamic state (T, F) of the solvent, and the presence of the passivating layer at the particle surface would determine the degree of solvation, ϑ, and the mode of association of the solvent molecules with the particle. Clearly, the degree of solvation is directly related to the affinity of the particle for the solvent and so would have a strong bearing on the solvent quality. Specific systems considered in our simulations are gold nanoparticles in ethane, which have been the subject of several experimental investigations.12,13 In a previous publication,34 we reported a molecular dynamics simulation study where significant differences in the mode and the degree of solvation of two different size gold nanoparticles were found to occur. Those simulations revealed how the differences in the configurational structure of the passivating layers on the two particles gave rise to the particle-size-dependent solvent quality. Since the earlier computations were limited to just the critical density (Fc),34 it was necessary to extend the simulations to cover a reasonably wide range of densities, below and above Fc, to investigate the solvent density effects on the solvation behavior of the particle. The importance of density-dependent solvation effects in the supercritical regime lies in their immediate relevance to the process of fine-tuning of the solvent quality of SCFs required in many cutting edge applications.12,13 This is achieved in practice by allowing the solvent density to change systematically by progressively changing the pressure at constant temperature. Here we present our simulation study of the density-dependent solvation of the 38-atom particle at a number of isotherms above Tc. 2. A Brief Description of the Model and the Simulation Methodology 2.1. The 38-Atom Gold Nanoparticle. Computational studies directed to the determination of the minimum-energy structure have produced several candidates, both ordered and disordered, for the most stable configurations to be assumed by gold nanoparticles.30,35-37 For the 38-atom particle, the minimumenergy structure is a truncated octahedron30,36 (Figure 1A) for the Sutton-Chen potential,38 which is used here for computing the interactions between the gold atoms. As discussed previously,34 this morphology is composed of two regions, an inner region of six atoms assuming an octahedral geometry (square bipyramid) and an outer, surface region made up of eight (111) and six (100) faces, accommodating the remaining 32 atoms. This configuration with the interatomic distances obtained by Cleveland et al.37 was taken as the initial configuration of the nanoparticle in the simulations, in common with our earlier study.34 The PassiVated Particle. Chemical methods developed in recent years39 yield passivated nanoparticles, i.e., particles
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Figure 1. (A) Minimum-energy structure assumed by the 38-atom gold nanoparticle. The black dots represent the location of the atoms in the particle. (Reprinted with permission from Science 1999, 285, 1368. Copyright 1999 AAAS). (B) Location of the ligand sulfur atoms (yellow dots) at a (111) facet of the particle, assumed in the initial configuration of the passivated system. The locating sites lie close to the (111)/(100) edges
covered with ligands, in particular alkanethiolates terminally attached to the particle surface through the formation of Au-S bond. Energetically favorable locations of the S atom on the surface have been identified by several research groups by means of DFT computations for the adsorbate/adsorbent interaction energy.40,42-44 One may infer from these computations that, for our particle, the most preferred locations for S lie in the close vicinity of the (111)/(100) edges above the (111) faces.41 In constructing the initial configuration of the passivated particle, we selected these sites for the location of the S atoms of the passivating ligands, shown schematically in Figure 1B. With each (111) facet of our particle possessing three bonding sites, the total number of such sites on the particle surface is 24. The ligand passivating the nanoparticle is the same as considered in our previous study,34 namely n-C12H25 thiolate with the S atom bound to the particle surface. As before,34 the interaction between the sulfur and the gold atoms is modeled in terms of the Morse potential, UM(r) ) U0[{1 - exp(- kM(r - r0))}2 1], with the values of the various parameters obtained by Luetdke and Landman.44 This potential allows the chemisorbed S atoms to move on the core surface without having to encounter the incidence of the Au-S bond rupture and consequent desorption. Inclusion of this motion in the model is necessary to take account of the surface diffusion of the passivating chains.54,55 The alkyl part of the passivating molecule is represented by a united-atom model in which the atoms belonging to the methylene (CH2) and the methyl (CH3) groups of the chain are subsumed into single interaction sites. In conformity with the model assumed for the passivating ligand, the molecules of the solvent, ethane, are represented by pairs of methyl united-atom sites joined by covalent bonds. These sites are assumed to be identical to the terminal methyl sites in the passivating chain in respect of their bonded and nonbonded interactions. Details of the force fields assumed for modeling the various interactions in the system may be found in our earlier publication,34 which also includes the values of the corresponding parameters in the tabular form.53 2.2. Simulation Methodology. The simulations were performed using the MD simulation package DL_POLY_2.46 On the basis of data replication strategy for its parallelisation and using second-order Verlet algorithm for velocity integration, the code offers proven capability for simulating large, complex systems such as macromolecules, glasses, and liquid crystals.48
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Figure 2. Liquid/vapor equilibrium phase diagram of ethane drawn from the data (solid points) given in the Supporting Information of ref 45. Dotted horizontal line: critical isotherm; dotted vertical line: critical isochore, which divides the T > Tc phase regime into two density domains, F > Fc and F > Fc. The unfilled symbols represent the (F, T) points selected for the present simulations. 4: Tr ) 1.02; ×: Tr ) 1.12; 0: Tr ) 1.22; O: Tr ) 1.32; /: Tr ) 0.92. (The solid points and the line passing through them are reprinted with permission from J. Phys. Chem. B 1998, 102, 2569. Copyright 1998 American Chemical Society).
Details of the underlying methodology and implementation of the code are well documented.47 The simulations were carried out in a 100 × 100 × 100 Å3 cubic cell subjected to standard periodic boundary conditions. Initially, the nanoparticle, in the minimum configurational energy state, was placed at the center of cell. The number of ethane molecules introduced in the cell ranged from 1000 to 12 000, depending on the desired solvent density. In the initial configuration of the passivated particle, all the alkyl chains of the ligands assumed the fully extended, all-trans conformational state. Our protocol for constructing the initial configuration of the system in the cell has been described previously.34 The simulations were performed in the (NVT) canonical ensemble with the application of the Hoover thermostat for maintaining the constant-temperature condition. The magnitude of the time steps assumed in the simulations was 1 fs. A typical simulation run composed of four million steps, found to be sufficiently long for the system to converge to the equilibrium state and yield results with acceptable accuracy. The equilibration phase of the runs (the early stage where the system gradually relaxes to the equilibrium state from its initial configuration) was found to be of the order of a nanosecond. After the system had attained equilibrium, data on the position coordinates of the atoms in the cell were stored at suitable intervals of time in the run, to be used in the computation of the configurational and the solvation properties of the system. 3. Results and Discussion In pursuing our objective, we performed several series of simulations covering the solvent density regions both below and above the critical density, Fc. The (F, T) points in the phase diagram of the solvent, at which the present simulations were performed, are shown in Figure 2. Simulations along the isotherms crossing the critical isochore are designed to investigate the solvation behavior as the system moves from the F < Fc to the F > Fc region in the supercritical regime 3.1. Solvation of the Bare Particle. The Mode of SolVation. The mode of solvation refers to the manner in which the solvent molecules associated with the particle are distributed around it. This feature of solvation is therefore depicted simply by the radial distribution of the solvent about the particle center of
Figure 3. Radial distribution of the solvent methyl groups about the nanoparticle center of mass at solvent densities below the critical density. (s, black): Fr ) 0.242; (- - -, magenta): Fr ) 0.484; (‚‚‚, blue): Fr ) 0.969. (A) Tr ) 1.02; (B) Tr ) 1.32. Fr and Tr are the solvent density and temperature, respectively, reduced by the corresponding critical values.
mass. Typical distributions computed from the present simulations are shown in Figures 3 and 4. A main feature of the distributions presented in Figure 3 (F < Fc) is the presence of a sharp peak accompanied by a minor, secondary peak in its immediate vicinity. Thus, in common with our earlier study (F ) Fc), the distributions reveal the occurrence of a two-region solvation layer around the bare particle, a highdensity inner region, represented by the sharp peak, and a lowdensity outer region manifest in the secondary peak. At the
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Figure 4. Radial distribution of the solvent methyl groups about the nanoparticle center of mass at solvent densities (F) greater than the critical density (Fc). (s, blue): Fr ) 1.94; (- - -, magenta): Fr ) 2.91. (A) Tr ) 1.02; (B) Tr ) 1.32.
lowest bulk solvent density considered, Fr equal to 0.242, the maximum density in the inner region is about 12.5 times the corresponding bulk density at the reduced temperature (Tr) equal to 1.02, the mean density being about five times the bulk density. The increase in the bulk solvent density at constant temperature leads to the reduction of the relative magnitudes of both the maximum and the mean density of the inner region of the solvation layer, shown in Figure 5A,B. The effect of temperature on the structure of the solvation layer may be examined simply by comparing the distributions presented in Figure 3A with those in B. It is found that, as Tr is increased from 1.02 to 1.32, both the maximum and the mean relative densities of the inner region are reduced by almost a factor of 2 at Fr ) 0.242, the effect becoming progressively smaller with the increase in Fr. A further notable effect is that the secondary peak in the distribution tends to diminish with the increase in T, meaning that, at higher temperatures, the distinction between the two regions of the solvation layer is blurred. It may be observed that the secondary peak in the distribution corresponding to Fr ) 0.242 at Tr ) 1.02 transforms into a tail of the primary peak at Tr ) 1.32. At higher solvent densities, although the secondary peaks retain their entity at this temperature, they are considerably suppressed. At the bulk solvent densities >Fc, the radial distributions of the solvent around the nanoparticle (Figure 4A,B) point to the solvating layer, assuming a structure that is more complex than that observed in the density regime F < Fc. The outer region is now characterized by spatial oscillations in the solvent density, reminiscent of the liquid structure. The oscillations become more pronounced with the increase in the solvent density, their amplitude progressively decaying to zero as the bulk solvent is reached. In this density domain of the supercritical region,
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Figure 5. Relative maximum and mean densities of the inner region of the solvation layer as functions of the reduced bulk density (F/Fc). (A) relative maximum density (Fmax/F); (B) relative mean density (Fmean/ F), where F is the bulk density. (-b-, black): Tr ) 1.02; (-2-, magenta): Tr ) 1.12; (-9-, blue): Tr ) 1.32. The vertical red dotted line is the dividing line between the F < Fc and the F > Fc density domains.
although the temperature variations do produce quantitative changes in the mode of solvation, the effect is less marked than that found in the regime F < Fc. Figure 5 brings out the striking difference that exists between the F < Fc and F > Fc domains in respect of the effects of the bulk solvent density changes at different temperature on the accumulation of the solvent molecules in the inner region of the solvation layer. As the solvent density exceeds Fc, these effects become quite small and are negligible for the reduced densities >2. Thickness of the inner region of the solvation layer, identified with the base length of the primary peak of the radial distribution, varies between 3.7 and 5.3 Å, depending on the temperature and the solvent density. Despite considerable scatter ((0.3 Å) in the computed data, presented in Figure 6, the trend in the variation of the thickness with solvent density (represented by solid lines) is discernible. The thickness decreases appreciably with the increase in the solvent density in the F < Fc regime, the variation slowing down in the F > Fc regime. As one would expect, the temperature increase has a broadening effect on the inner region. The magnitudes of the thickness of the inner region of the system are comparable to the value of the L-J length parameter, σ, assumed for the methyl/Au interaction, which implies that the inner region is composed of a monomolecular layer of the solvent molecules with most of the methyl groups located close to the position of the minimum of the nanoparticle/methyl interaction potential. One may visualize two extreme orientations to be assumed by the solvent molecules with respect to the nanoparticle surface: parallel (0°) and perpendicular (90°). For
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Figure 6. Thickness of the inner region of the solvation layer as a function of reduced bulk solvent density, F/Fc. (-b-, black): Tr ) 1.02; (-2-, blue): Tr ) 1.32.
Figure 7. Relative mean density (equal to Fjo/F) of the outer region of the solvation layer as a function of reduced bulk density (F/Fc). (-b-, black): Tr ) 1.02; (-2-, blue): Tr ) 1.32.
Figure 8. Thickness of the outer region as a function of reduced solvent density, F/Fc. (-b-, black): Tr ) 1.02; (-2-, blue): Tr ) 1.32.
a monomolecular layer of the solvent molecules in the former orientation, the radial distribution would produce a sharp, single peak. The latter orientation would give rise to two peaks with their maxima separated by a distance equal to the length of the bond, 1.5 Å, connecting the two methyl groups of the solvent molecule. A uniform population of the orientations between 0° and 90° would yield a distribution with a broad or a flat top. Distributions with a single sharp maximum, presented in Figures 3 and 4, thus point to an essentially parallel orientation with respect to the particle surface assumed by the solvating molecules in the inner region. The properties of the outer region of the solvation layer, the mean density, and the thickness, are presented in Figures 7 and 8. A decreasing function of both bulk solvent density and temperature, the mean density of the outer region, Fjo, is
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Figure 9. Degree of solvation (ϑ) versus reduced bulk solvent density (Fr) for the bare nanoparticle. (-b-, black): Tr ) 1.02; (-9-, blue): Tr ) 1.22; (-2-, orange): Tr ) 1.32.
measurably greater than the bulk density in the regime F < Fc. In the regime F > Fc, on the other hand, Fjo is, within statistical uncertainty, virtually indistinct from F, particularly at the higher temperature. In this regime, therefore, the distinction between the outer region of the solvation layer and the bulk solvent resides essentially in the difference in the structure of the two regions as “seen” by the particle in the form of the variation of g(r) with distance, i.e., oscillating g(r) in the outer region and uniform g(r) (equal to unity) in the bulk region. The thickness of the outer region is ∼4 Å in the regime F < Fc, suggesting that in this regime the outer region of the solvation layer is composed of one monomolecular layer. As the system enters the F > Fc regime, the thickness increases sharply, due essentially to the development of a more complex structure represented by a sequence of more than one oscillation in g(r). Because one oscillation would correspond to one molecular layer, the number of oscillations would represent the number of molecular layers constituting the outer region. Thus it may be inferred from the distributions given in Figure 4 that, in the regime F > Fc, the outer region of the solvation layer consisted of at least two molecular layers about 4-4.5 Å apart. Degree of SolVation. A quantitative measure of the affinity of the solvent for the solute, the degree of solvation, ϑ, is directly related to the excess number of solvating molecules, i.e., the number of solvent molecules in the solvation layer in excess of the number required to fill the volume occupied by both the solute molecule and the solvation layer at the prevailing bulk solvent density. The excess number, nEsolv, is expressible in terms of the Kirkwood-Buff integral:49
nEsolv ) 4πF
∫0∞ (g(r) - 1)r2 dr
(1)
In our system, g(r) is the particle center-of-mass/solvent radial distribution function and F is the number density of the solvent molecules in the bulk limit, which is reached when g(r) assumes a constant value of unity. Obviously, the contribution of the bulk regime to the Kirkwood-Buff integral is zero, which means that the upper limit of the integral can be set equal to the distance, rb, which defines the boundary between the solvation layer and the bulk regime. In common with our previous study,34 the degree of solvation is defined as the excess number per metal atom: ϑ ) nEsolv/N, where N is the number of gold atoms constituting the nanoparticle. It is straightforward to compute ϑ from the g(r) data generated in our simulation runs. Figure 9 presents some of our computed results showing the variation of ϑ with the bulk solvent density, F at Tr ) 1.02, 1.22, and 1.32. We observe that, at the
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Figure 10. Excess number as a function of distance from the particle center of mass. (A) Fr ) 0.727, Tr ) 1.02. r < 6 Å corresponds with the space occupied by the nanoparticle, which makes a negative contribution to the excess number. 6 Å e r e 10 Å spans the inner region of the solvation layer and 10 e r e 16 Å covers the outer region. r > 16 Å is the bulk solvent region. (B) Fr ) 2.91, Tr ) 1.22. The first negative region (r < 6 Å) is due to the particle excluded volume effect. The solvation layer lies between r ) 6 and 20 Å.
temperature closest to the critical point (Tr ) 1.02), the degree of solvation as a function of the solvent density passes through a well-defined maximum occurring just below the critical density. This furnishes clear evidence of the enhancement effect in the tendency of the solvent molecules to cluster around the solute as the critical point is approached, the effect predicted theoretically for systems where the ratio of the magnitudes of the solute-solvent and the solvent-solvent attraction is much greater than one,22,23 which indeed is the case for the present system.34 This effect has been established experimentally for molecular solutes.50 At the higher temperatures, the presence of the maximum is uncertain within the estimated statistical error ((0.03) in ϑ, indicating the disappearance of the enhancement effect as the system moves away from the near-critical regime. The occurrence of the maximum in the ϑ versus T plot at F ) Fc, reported previously,34 was also interpreted in terms of the same enhancement effect. The present simulations reveal that it is only in the regime 1 e Tr e 1.2, Fr < 2, that the degree of solvation is noticeably sensitive to the changes in temperature. As Figure 9 shows, close to the critical temperature (Tr ) 1.02), ϑ is an increasing function of the solvent density in the regime Fr < 1; the effect is reversed as the system enters the Fr > 1 regime. Theoretically, the reversal should commence as soon as the critical density is exceeded. Our simulation results, however, show the occurrence of the maximum quite close but not exactly at the critical density. Possible influence of the presence of the nanoparticle on the critical properties of the solvent combined with a lack of absolute precision in the computed values of ϑ may have contributed to this shift in the position of the maximum. At T > 1.2Tc, ϑ appears to be quite insensitive to changes in the solvent density in the regime F < Fc. Because ϑ provides a quantitative indication of the preference of the solvent molecules for remaining in the close vicinity of the solute, it may be taken as a reasonable measure of the solvent quality in the dilute limit where the solute-solute interactions are too weak to influence the solvent quality. Positive values of ϑ may thus be identified with the solute being subjected to the “good” solvent condition and the negative values with the “bad” solvent condition. ϑ ) 0 would signify the “neutral” solvent condition. Applying this yardstick to measure the solvent quality, we conclude immediately that, for the bare nanoparticle, good solvent conditions prevail in the density regime Fr < 1.7, the region of the highest solvent quality being around the critical point. The solvent quality deteriorates with increasing density in the regime Fr > 1, becoming poor (negative ϑ) at all temperatures as the density approaches twice its critical value. We see from the distributions given in Figures 3 and 4 that the space around the particle center of mass contains regions
of both positive (g(r) > 1) and negative (g(r) < 1) contributions to the Kirkwood-Buff integral. The most dominant region of negative contribution is invariably the space occupied by the particle where no solvent molecules were found. In the solvent density regime F < Fc, both the inner and the outer regions of the solvation layer are the positive contributors to the excess number. This is brought out more transparently by the excess number versus distance-from-the-center-of-mass plots; typical plots are presented in Figure 10A and B, corresponding respectively to the F < Fc and F > Fc regimes. As one would expect, the negative contribution of the particleoccupied space to the degree of solvation increases with F. As stated above, the contribution of the inner region of the solvation layer is always positive. In the regime F e Fc, this contribution exceeds 85% and is as high as 125% in the vicinity of Fc. The contribution of the outer region (the secondary peak in Figure 10A) is also found to be an increasing function of the solvent density and a decreasing function of temperature, In this density regime, the combined contribution of the inner and outer regions of the solvation layer far outweighs the negative contribution due the particle excluded-volume effect (i.e., exclusion of the solvent molecules from the space occupied by the particle), resulting in the prevalence of the good solvent condition for the nanoparticle. As Figure 10B shows, in the solvent density domain F > Fc, the negative contribution to the excess number, hence to the degree of solvation, derives not only from the particle-excluded volume effect but from the oscillatory nature of the distribution of the excess number. The first peak, which represents the inner region of the solvation layer, contains both positive and negative areas of similar magnitudes, so the net contribution from the inner region, although positive, is greatly reduced. In the succeeding three peaks, belonging to the outer region of the solvation layer, the positive and negative contributions almost cancel each other, thus making negligible contribution to the excess number at all the three solvent densities considered in this domain. So, what essentially determines the degree of solvation, hence the solvent quality, is the balance between the excess accumulation of the solvent molecules in the inner region, a result of the attractive particle/solvent interaction, and the negative contribution due to the particle-excluded volume effect. ϑ ) 0 marks the exact balance between these two effects, which occurs at Fr = 1.7 for the present system. Thus in the density regime Fr < 1.7, the particle/solvent interactions appear to win over the particle-excluded volume effect, leading to good solvent conditions for the particle, while reverse is true in the regime F > 1.7, which gives rise to poor solvent conditions. 3.2. The Passivated Particle. In our previous study, the presence of the passivating layer around the particle was found
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Figure 12. Degree of solvation (ϑ) vs reduced solvent density (Fr) for the passivated particle. (b, black): Tr ) 1.02; (9, magenta): Tr ) 1.12; (9, orange): Tr ) 1.22; (2, green): Tr ) 1.32. The solid line corresponds to the points at Tr ) 1.02. The vertical dotted red line is the dividing line between the F < Fc and F > Fc density domains.
Figure 11. Radial distribution of the solvent methyl groups about the core center of mass of the passivated particle. (s, blue): Fr ) 0.727; (s, magenta): Fr ) 0.969; (s, orange): Fr ) 1.939. (A) Tr ) 1.02; (B) Tr ) 1.32.
to greatly affect both the mode and the degree of solvation, attributed in large part to the steric hindrance produced by the anchored chains, which severely limited the access of the solvating molecules to the close vicinity of the metal core surface.34 It is of interest to see if the solvent density variations introduce any new features in the solvation of these particles not brought out by the earlier computations, which focused only on the temperature effects. We have, therefore, also extended our simulations of the passivated particle to the solvent density range spanning both the F < Fc and F > Fc domains of the supercritical regime. Parts A and B of Figure 11 show selected distributions at two temperatures. It may be noted that the g(r) versus r plots, presented above at different densities, display broadly similar qualitative features, but the quantitative differences occurring in them are quite substantial, implying significant dependence of the extent of solvation of the passivating layer on the solvent density. Absence of well-defined peaks in the distributions suggests that the solvating molecules are loosely dispersed in the passivating layer, which represents the main qualitative feature of the mode of solvation. Two key factors controlling the propensity of the solvent molecules to reside in the passivating layer are the available volume in the layer (i.e., the volume of the layer minus the volume occupied by the chains) and the strength of the interactions between the solvent and the various interaction sites that constitute the passivating chains. In the present case where the chains are anchored at the core surface at full coverage, the available volume of the layer is rather low, leading to a severe spatial constraint on the accommodation of the solvent in the layer. The presence of the solvent molecules in the layer can, however, be energetically favorable if the number of chain segments lying within the range of interaction with the solvent methyl significantly exceeds the solvent coordination number,
i.e., the mean number of neighboring molecules within the sphere of effective interaction in the bulk phase. At low solvent densities, where the bulk coordination number is low, the solvent molecules are likely to gain the energy advantage by migrating to the passivating layer in substantial quantity, leading to a higher number density of the solvent in the layer than in the bulk. This is borne out by the distributions at the lowest solvent density presented in Figure 11, where we find that, at both temperatures, g(r) is mostly greater than 1 in the region occupied by the passivating layer (10 Å e r e 25 Å). Thus at this solvent density, the passivation layer makes a positive contribution to the excess number and hence to the solvent quality. The energy advantage accrued to the solvating molecules is progressively reduced with the increase in the solvent density because, at higher densities, the mean number of neighboring molecules in the bulk phase lying in the sphere of effective interaction would be higher, and so lowering the energy difference between a molecule solvating the passivating layer and a molecule in the bulk solvent. This would inevitably diminish the propensity of the solvent molecules to migrate to the passivating layer, which is manifested in the reduction of g(r) with the increase in F. As F exceeds the critical density, the reduction in g(r) occurs so much that it lies below the g(r) ) 1 line in the whole r region of the passivating layer, which directly points to the prevalence of very poor solvent conditions for the passivated particle in this solvent density regime. The effect of temperature on the mode of solvation may be seen by comparing the distributions presented in Figure 11A (Tr ) 1.02) and B (Tr ) 1.32). The main effect is the reduction of g(r) with the increase in T. Because the ratio of the probabilities of a solvent molecule being found in the bulk phase and the passivation layer is proportional to exp(-∆U/kT) (ignoring entropic effects), where ∆U is the energy difference for the solvent molecule in the two phases, the increase in T would lead to a reduction in the probabilities ratio and hence in g(r). It is readily seen that the greater the magnitude of the energy difference, the greater is the temperature effect. The temperature effect found at the lowest F is quite large but is substantially reduced at the higher densities, a consequence of the reduction in the value of ∆U with the increase in the solvent density discussed above. The degree of solvation, ϑ, of the passivated particle, calculated by numerically integrating the Kirkwood-Buff integral, is presented in Figure 12 as a function of the solventreduced density at various temperatures. The region of the good solvent condition (ϑ > 1) is limited to Fr < 0.9, the solvent quality rapidly deteriorating with the
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Figure 13. Distribution of the Au atoms about the core center of mass. (A) the minimum-energy configuration depicted in Figure 1; (B) bare particle in ethane at Fr ) 0.727; (C) passivated particle in ethane at Fr ) 0.727. (-[-, blue): Tr ) 1.02; (-2-, magenta) Tr ) 1.32.
increase in the solvent density. The effect of temperature, which is appreciable at Fr ) 0.73, is to reduce the solvent quality. The effect becomes progressively smaller with increasing density, and it almost disappears as the density increases to three times its critical value. Comparison of the results presented in Figure 12 with those for the bare particle, shown in Figure 9, reveals the extent of the changes in the solvation behavior of the particle resulting from passivation. The good-solvent-quality regime is now shrunk by a factor of 2, with a very substantial reduction in the degree of solvation in the whole solvent density range. At Tr equal to 1.22, for example, the degree of solvation is reduced as a result of passivation from a value of +0.2 to a value of -0.1 at Fr equal to 0.73, while at Fr equal to 2.9, the reduction occurs by a factor of 16.5! Such dramatic changes in ϑ are predominantly a consequence of the steric shielding of the metal core by the passivating ligands, whereby the approach of the solvent molecules to the close proximity of the core is precluded. In this way, the solvent/core interactions, which constitute the most significant force driving the solvation process, are greatly reduced in the presence of passivating layer. The result is drastic deterioration in the solvent quality for the passivated particle. 3.3. Configuration of the Passivating Layer. The values of the configurational properties of the passivating chains, in particular the mean square distance between the anchor (S) and the terminal methyl group, 〈R2S-CH3〉, and the mean values of nearest-neighbor distance between the anchors and between the terminal methyl groups, computed at various state points (F, T) of the solvent, have shown that the structure of the layer, established previously,34 in which passivating chains exist in a highly extended (nearly all-trans) state in parallel orientation with respect to each other, remains essentially unaffected by the changes in the solvent density. The temperature changes, however, do bring about measurable, albeit small, changes in the chain configuration: the increase in the reduced temperature (Tr) from 1.02 to 1.32 resulted in a reduction of approximately 5% in the 〈R2S-CH3〉 value. The small magnitude of the temperature-induced reduction in the end-to-end distance indicates that it is only the terminal bond of the chain which is able to undergo trans f gauche( transition, the spatial constraint on the other bonds in the chain being too severe to allow such bond conformational transitions to occur. The insensitivity of the configurational structure to the solvent conditions is a consequence of the fact that a terminally anchored assembly of highly extended, parallel chains at full coverage would exist in such a deep energy minimum that any entropy gain to be had from the chain configurational changes would be insufficient to perturb the structure. It is quite possible that rather than causing disruption, the solvating molecules embedded in the layer in an orientation parallel to the long axes of
the chains may enhance its structural stability by further lowering the interaction energy of the system; the energy will be lowered if upon entering the layer, the solvent molecule replaces a pair of interacting methylene groups between the chains by two CH3/CH2 interacting pairs. 3.4. Configuration of the Metal Core. In the previous paper, we presented a brief, qualitatiVe account of the changes in the structure of the metal core resulting from its interactions with the solvent and the passivating layer.34 It is desirable to have some quantitative idea of the extent of such changes occurring in a range of solvent conditions. To this end, we have evaluated the core structure in terms of the radial distribution of the core atoms about the core center of mass at different solvent densities and temperatures. Typical results are displayed in Figure 13. In the initial, minimum-energy configuration of the core (Figure 13A), the gold atoms divide into three groups in respect of their distance from the core center: the group of six atoms, constituting the inner octahedral region, located at r ) 2.01 Å; eight atoms at r ) 3.33 Å, located at the centers of the eight (111) facets of the core surface; and 24 atoms at r ) 4.32 Å, occupying the corners of the truncated octahedron. The last two groups constitute the surface atoms. Parts B and C of Figure 13 show the distributions for the bare and the passivated cores respectively at two temperatures, Tr ) 1.02 and 1.32. Comparing these distributions with that for the minimum-energy configuration, it is immediately clear that both the inner and the outer regions of the core undergo large distortions in the solvent environment. For the bare particle, the six atoms of the inner region are no longer equidistant from the core center. At Tr ) 1.02, they are split into two peaks, the first peak corresponding to the four atoms initially at the corners of the square bipyramid and the second peak to the two atoms at its apexes. From this we infer that the base of the bipyramid is shrunk and the height of the two apexes is increased. The shape of third peak in the distribution at Tr equal to 1.02 is a consequence of the fact that the lines located at r ) 3.33 and 4.32 Å in Figure 13A broaden to give rise to partially overlapping distributions. As Tr is increased to 1.32, the two peaks representing the inner region distribution merge into a single broad peak, indicating the disappearance of the original, well-defined structure of this core region. The distribution of the surface atoms is also given by a single, featureless peak (the second peak), allowing little distinction to be made between the two surface atom groups. The deformation of the structure of the passivated core is even more drastic (Figure 13C), which we believe is a result of the occurrence of the Au-S anchoring bonds. The S/S and Au/S interactions appear to be the driving force that leads to a highly distorted core structure, with the distribution characterized by a succession of many peaks. At Tr ) 1.02, the highest peak is located r ) 4.45 Å with about 40% of the core atoms populated
Bare and Passivated 38-Atom Gold Nanoparticle in the distance range 4-5 Å from the core center. The core is expanded so that maximum distance of the surface atoms from the core center is increased from its initial value of 4.32 Å to about 7 Å. The distribution is broadened with the increase in temperature with a shift of about +0.5 Å in the position of the highest peak. It may be noted that the bare particle also undergoes expansion, albeit to a lesser extent. The changes in the solvent density did not give rise to any significant modification of the salient features of the distributions presented in Figure 13B,C; only minor, quantitative differences were observed. Thus it appears that the primary causes underlying the distortion of the core structure are the thermal effects and the additional interactions arising from the sulfur atoms bound to core surface, the effect of the solvent being of secondary importance. 4. Concluding Remarks In this study, we have succeeded in elucidating the effects of the changes in the density of the solvent on the solvation behavior of the bare and passivated gold particle in the supercritical regime. The solvating molecules are strongly bound to the bare particle, forming a well-defined solvation layer that is composed of two distinct regions, an inner region and an outer region. Although the dominant contribution to the degree of solvation derives from the inner region, the contribution of the outer region is appreciable in the density regime F e Fc. At the temperature closest to critical value (Tr ) 1.02), the degree of solvation as a function of the solvent density passes through a maximum, an effect closely similar to the one established previously in the study of the variation of the degree of solvation with temperature at the critical density.34 In both cases, the occurrence of the maximum is attributed to the enhancement effect produced close to the critical point in systems where the solute/solvent interactions are much stronger than the solvent/ solvent interactions. As for the passivated particle, because the solute/solvent interactions are dominated by the weak ethane/ chain-segment forces, the solvating molecules are loosely dispersed in the passivating layer at all solvent densities. Using the degree of solvation as a quantitative indicator of the solvent quality in the dilute limit, we have been able to delineate the good and the poor solvent-quality regimes in the supercritical solvent. For the bare particle, the good-solventquality regime covers the density range F < 1.7Fc, with the highest solvent quality found close to the critical point. In the solvent density regime F > Fc, the solvent quality is a decreasing function of the solvent density, becoming negative as F approaches twice its critical value. This is explained in terms of the shift of balance with changing solvent density between the two opposing contributions to the solvent quality, namely the excluded-volume effect and the particle-solvent interactions. The presence of the passivating layer dramatically diminishes the solvent quality for the particle: the good-solvent-quality regime is shrunk by a factor of 2, and at the highest solvent density considered, the solvent quality is reduced by more than an order of magnitude. The highly extended configurational state of the passivating chains, established in our previous study, remains almost unperturbed by the changes in the solvent density. The temperature has a small but measurable effect on the chain configuration, due essentially to an increase in the trans f gauche transition probability of the terminal bonds of the chain resulting in the reduction of the mean square end-to-end distance. The interaction of the metal core with the passivating chains and the solvent produces significant disorder in its structure, with the passivating chains having much greater effect on the core structure than the solvent density changes.
J. Phys. Chem. B, Vol. 110, No. 42, 2006 20887 An experimental quantity related to the solvation of dissolved molecules in the dilute limit is the limiting partial molar volume. Although the computation of this quantity through computer simulation of molecular solutes in supercritical media has been reported in the literature,51 to our knowledge, no such studies for nanoparticles have been published. One of the objectives of our ongoing work in this area is to explore the viability for accurate computation of the partial molar volumes of nanoparticle solutes by the MD approach. Given that the approach proves promising, we plan to perform the desired computations for the bare and passivated particle solutions and seek a quantitative interpretation of this quantity in terms of the mode and the degree of solvation of the nanoparticles. A further direction of major importance for our work concerns the determination of the solvent-mediated interactions between the nanoparticles and evaluation of the role of these interactions in the size-selective dispersion and aggregation of the particles in supercritical media. The reliability of the computed interactions can be checked against relevant experimentally measurable properties of the system, such as osmotic second virial coefficients. Acknowledgment. Computer resources on the HPCx were provided via our membership of the HPC Materials Chemistry Consortium and funded by EPSRC (portfolio grant EP/ D504872). References and Notes (1) Hannay, J. B.; Hogarth, J. Proc. R. Soc. 1879, 29, 324; Proc. R. Soc. 1880, 30, 178. (2) Villard, P. J. Phys. 1894, 3, 441. (3) Taylor, L. T. Supercritical Fluid Extraction; Wiley: New York, 1996. (4) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Principles and Practice; Butterworth: Boston, 1994. (5) Baiker, A. Chem. ReV. 1999, 99, 453. Jessop, P. G.; Ikariya, T.; Noyori, R. Chem. ReV. 1999, 99, 475. Mesiano, A. J.; Beckman, E. J.; Russell, A. J. Chem. ReV. 1999, 99, 623. (6) Kendall, J. L.; Canelas, D. A.; Young, J. L.; DeSimone, J. M. Chem. ReV. 1999, 99, 543. DeSimone, J. M.; Maury, E. E.; Menceloglu, Y. Z.; McClain, J. B.; Romak, T. R.; Combes, J. R. Science 1994, 265, 356. (7) Ambrogi, A.; Cardarelli, D. A.; Eggers, R. J. Food Sci. 2002, 67, 3236. (8) Brunner, G. Gas Extraction; Steinkoff: Darmstadt, 1994. (9) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.; Brock, E. AIChE J. 1995, 41, 1723. (10) Williams, J. R.; Clifford, A. A.; Al-Saidi, S. H. R. Mol. Biotechnol. 2002, 22, 263. (11) Mount, D. J.; Rothman, L. B.; Robey, R. J. Solid State Technol. 2002, 45, 103. (12) Clark, N. Z.; Waters, C.; Johnson, K. A.; Satherley, J.; Schiffrin, D. J. Langmuir 2001, 17, 6048. (13) Shah, P. S.; Holmes, J. D.; Johnson, K. P.; Korgel, B. A. J. Phys. Chem. B 2002, 106, 2545. (14) Esumi, K.; Sarashina, S.; Yoshimura, T. Langmuir 2004, 20, 5189. (15) Holmes, J. D.; Johnson, K. P.; Doty, R. C.; Korgel, B. A. Science 2000, 287, 1471. (16) Lee, D. C.; Mikulec, F. V.; Korgel, B. A. J. Am. Chem. Soc. 2004, 126, 4951. (17) Saquing, C. D.; Cheng, T.-T.; Aindow, M.; Erkey, C. J. Phys. Chem. B 2004, 108, 7716. (18) Pai, R. A.; Humayun, R.; Schulberg, M. T.; Sengupta, A.; Sun, J.-N.; Watkins, J. J. Science 2004, 303, 507. (19) Meziani, M. J.; Pathak, P.; Harruff, B. A.; Hurezeanu, R.; Sun, Y.-P. Langmuir 2005, 21, 2008. (20) Kajimoto, O. Chem. ReV. 1999, 99, 355. (21) Martinez, H. L.; Ravi, R.; Tucker, S. C. J. Chem. Phys. 1996, 104, 1067. Tucker, S. C. Chem. ReV. 1999, 99, 391. (22) Debenedetti, P. G.; Mohamed, R. S. J. Chem. Phys. 1989, 90, 4528. (23) Petsche, I. B.; Debenedetti, P. G. J. Chem. Phys. 1989, 91, 7075. (24) Rabani, E.; Egorov, S. A. J. Phys. Chem. B 2002, 106, 6771. (25) Shinto, H.; Miyahara, M.; Higashitani, K. J. Colloid Interface Sci. 1999, 209, 79. (26) Qin, Y.; Fichthorn, J. Chem. Phys. 2003, 119, 9745.
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