Computer simulations of colloidal gels: how hindered particle rotation affects structure and rheology.

The effects of particle roughness and short-ranged non-central forces on colloidal gels are studied using computer simulations in which particles experience a sinusoidal variation in energy as they rotate. The number of minima n and energy scale K are the key parameters; for large K and n, particle rotation is strongly hindered, but for small K and n particle rotation is nearly free. A series of systems are simulated and characterized using fractal dimensions, structure factors, coordination number distributions, bond-angle distributions and linear rheology. When particles rotate easily, clusters restructure to favor dense packings. This leads to longer gelation times and gels with strand-like morphology. The elastic moduli of such gels scale as G'∝ω0.5 at high shear frequencies ω. In contrast, hindered particle rotation inhibits restructuring and leads to rapid gelation and diffuse morphology. Such gels are stiffer, with G'∝ω0.35. The viscous moduli G'' in the low-barrier and high-barrier regimes scale according to exponents 0.53 and 0.5, respectively. The crossover frequency between elastic and viscous behaviors generally increases with the barrier to rotation. These findings agree qualitatively with some recent experiments on heterogeneously-surface particles and with studies of DLCA-type gels and gels of smooth spheres.

How Proton Transfer Equilibria Influence Ionic Liquid Properties: Molecular Simulations of Alkylammonium Acetates.

Protic ionic liquids (PILs) form through proton transfer from a Brønsted acid to a Brønsted base. In this work we use molecular dynamics simulation to study how PIL properties vary with χ, the extent of the proton transfer reaction. Three PILs are considered: N-propylammonium acetate, [N3][Ac], N-butylammonium acetate, [N4][Ac], and N, N-dimethylbutylammonium acetate, [N114][Ac]. In all cases density and viscosity increase with increasing χ, while diffusivities of all species decrease with increasing χ. In each PIL the ionic conductivity exhibits a maximum at intermediate χ due to competition between increasing ion concentration and decreasing ion mobility. Ionicity analysis suggests that strongly correlated behavior is present at all χ. Finally, we determine the χ for which the properties of each simulated PIL best agree with experimental data; these are χ = 0.86, 0.80, and 0.18 for [N3][Ac], [N4][Ac], and [N114][Ac], respectively. These results suggest that proton transfer is nearly complete in the primary ammonium PILs but not in the tertiary ammonium PIL, consistent with recent experimental observations. We propose that this difference is due to cooperative production of hydrogen bonds with increasing χ in the primary ammonium PILs, which does not occur in the tertiary ammonium PIL.

Femtosecond laser desorption ionization mass spectrometry imaging and multivariate analysis of lipids in pancreatic tissue.

Femtosecond laser desorption ionization mass spectrometry was used to obtain mass spectrometric (MS) images of lipids in human pancreatic tissue. The resulting MS images were analyzed using multivariate analysis, specifically principal component analysis and maximum a posteriori (MAP) reconstruction. Both analysis methods showed that the MS images can be separated into lipid and non-lipid areas. MAP analysis further indicated that the lipid areas are composed of phosphatidylcholines and fatty acids. However, definitive identification of the lipids cannot be made because none of the intact parent ions of phosphatidylcholine, sphingomyelins, and/or other lipids were observed. The MAP analysis also revealed that the non-lipid areas could be separated into components that are due to the sample chemical treatment and topography.

Structural and Transport Properties of Tertiary Ammonium Triflate Ionic Liquids: A Molecular Dynamics Study.

Ammonium-based protic ionic liquids (PILs) have shown promising physicochemical properties as proton conductors in polymer membrane fuel cells. In this work, molecular dynamics simulations are used to study the structural, dynamic, and transport properties of a series of tertiary ammonium triflate PILs. Nonpolarizable all-atom force fields were used, including two different models for the triflate anion. Previous simulation studies of these PILs have yielded poor results for transport properties due to unrealistically slow dynamics. To improve performance, polarization and charge-transfer effects were approximately accounted for by scaling all atomic partial charges by a uniform factor, γ. The optimum scaling factor γ = 0.69 was determined by comparing simulation results with available experimental data and found to be transferable between different ammonium cations and insensitive to both the temperature and choice of experimental data used for comparison. Simulations performed using optimized charge scaling showed that the transport properties significantly improved over previous studies. Both the self-diffusion coefficients and viscosity were in good agreement with experiment over the whole range of systems and temperatures studied. Simulated PIL densities were also in good agreement with experiment, although the thermal expansivity was underestimated. Structural analysis revealed a strong directionality in interionic interactions. Triflate anions preferentially approach the ammonium cation so as to form strong hydrogen bonds between sulfonate oxygen atoms and the acidic ammonium hydrogen. The ionic conductivity was somewhat underestimated, especially at lower temperatures. Analysis of conductivity data suggests that there is significant correlated motion of oppositely charged ions in these PILs, especially at short times. These results overall indicate that the transport properties of this class of PILs are accurately modeled by these force fields if charge scaling is used and properly calibrated against selected experimental data.

Nested sampling of isobaric phase space for the direct evaluation of the isothermal-isobaric partition function of atomic systems.

Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions.

Computational Study of Uniaxial Deformations in Silica Aerogel Using a Coarse-Grained Model.

Simulations of a flexible coarse-grained model are used to study silica aerogels. This model, introduced in a previous study (J. Phys. Chem. C 2007, 111, 15792), consists of spherical particles which interact through weak nonbonded forces and strong interparticle bonds that may form and break during the simulations. Small-deformation simulations are used to determine the elastic moduli of a wide range of material models, and large-deformation simulations are used to probe structural evolution and plastic deformation. Uniaxial deformation at constant transverse pressure is simulated using two methods: a hybrid Monte Carlo approach combining molecular dynamics for the motion of individual particles and stochastic moves for transverse stress equilibration, and isothermal molecular dynamics simulations at fixed Poisson ratio. Reasonable agreement on elastic moduli is obtained except at very low densities. The model aerogels exhibit Poisson ratios between 0.17 and 0.24, with higher-density gels clustered around 0.20, and Young's moduli that vary with aerogel density according to a power-law dependence with an exponent near 3.0. These results are in agreement with reported experimental values. The models are shown to satisfy the expected homogeneous isotropic linear-elastic relationship between bulk and Young's moduli at higher densities, but there are systematic deviations at the lowest densities. Simulations of large compressive and tensile strains indicate that these materials display a ductile-to-brittle transition as the density is increased, and that the tensile strength varies with density according to a power law, with an exponent in reasonable agreement with experiment. Auxetic behavior is observed at large tensile strains in some models. Finally, at maximum tensile stress very few broken bonds are found in the materials, in accord with the theory that only a small fraction of the material structure is actually load-bearing.

Investigation of the bulk modulus of silica aerogel using molecular dynamics simulations of a coarse-grained model.

Structural and mechanical properties of silica aerogels are studied using a flexible coarse-grained model and a variety of simulation techniques. The model, introduced in a previous study (J. Phys. Chem. C 2007, 111, 15792-15802), consists of spherical "primary" gel particles that interact through weak nonbonded forces and through microscopically motivated interparticle bonds that may break and form during the simulations. Aerogel models are prepared using a three-stage protocol consisting of separate simulations of gelation, aging, and a final relaxation during which no further bond formation is permitted. Models of varying particle size, density, and size dispersity are considered. These are characterized in terms of fractal dimensions and pore size distributions, and generally good agreement with experimental data is obtained for these metrics. The bulk moduli of these materials are studied in detail. Two different techniques for obtaining the bulk modulus are considered, fluctuation analysis and direct compression/expansion simulations. We find that the fluctuation result can be subject to systematic error due to coupling with the simulation barostat but, if performed carefully, yields results equivalent with those of compression/expansion experiments. The dependence of the bulk modulus on density follows a power law with an exponent between 3.00 and 3.15, in agreement with reported experimental results. The best correlate for the bulk modulus appears to be the volumetric bond density, on which there is also a power law dependence. Polydisperse models exhibit lower bulk moduli than comparable monodisperse models, which is due to lower bond densities in the polydisperse materials.

A Monte Carlo simulation study of methane clathrate hydrates confined in slit-shaped pores.

Monte Carlo simulations are used to study the structure, stability, and dissociation mechanisms of methane hydrate crystals inside carbon-like slit-shaped pores. The simulation conditions used mimic experimental studies of the dissociation of methane and propane hydrates in mesoporous silica gels (Handa, Y. P.; Stupin, D. J. Phys. Chem. 1992, 96, 8599). Simulations are performed under conditions of fixed methane pressure and fixed water loading, with the temperature increased in steps, with long equilibrations at each temperature. The initial structures of the confined hydrates are taken to be bulk-like, and pore widths chosen to accommodate integer or half-integer numbers of hydrate unit cells. Density profiles and orientational order parameter profiles are obtained and used to understand the structural changes associated with hydrate dissociation. Three different common water models, SPC/E, TIP4P, and TIP4P/2005, are used and the results compared. For water modeled using either the TIP4P or TIP4P/2005 potentials, dissociation temperatures are depressed proportionally to the inverse pore width, as predicted by the macroscopic Gibbs-Thomson equation. This behavior is observed for pores small enough that only half-cages of the clathrate structure are present. Experimental work has verified Gibbs-Thomson behavior for pores as small as 2 nm (Seshadri, K.; Wilder, J. W.; Smith, D. H. J. Phys. Chem. B 2001, 105, 2627); micropores of the size studied here have not yet been studied by experiment. Interestingly, the dissociation of hydrates modeled using the SPC/E water potential does not display the predicted pore-size dependence, and the dissociation mechanisms in this model seem to be quite different than those in the TIP4P-type models. In the SPC/E hydrates, with increasing temperature, cage dissocation occurs before methane desorption. In TIP4P-type hydrates, these processes occur either at the same temperature (to within the resolution of this study) or with dissociation occurring at higher temperatures than desorption. These simulations show that a variety of interesting clathrate structures and phase behaviors may be accessed in suitably designed microporous materials, with potentially useful applications in gas storage or separations.

Boiling point determination using adiabatic Gibbs ensemble Monte Carlo simulations: application to metals described by embedded-atom potentials.

The normal boiling points are obtained for a series of metals as described by the "quantum-corrected Sutton Chen" (qSC) potentials [S.-N. Luo, T. J. Ahrens, T. Çagin, A. Strachan, W. A. Goddard III, and D. C. Swift, Phys. Rev. B 68, 134206 (2003)]. Instead of conventional Monte Carlo simulations in an isothermal or expanded ensemble, simulations were done in the constant-NPH adabatic variant of the Gibbs ensemble technique as proposed by Kristóf and Liszi [Chem. Phys. Lett. 261, 620 (1996)]. This simulation technique is shown to be a precise tool for direct calculation of boiling temperatures in high-boiling fluids, with results that are almost completely insensitive to system size or other arbitrary parameters as long as the potential truncation is handled correctly. Results obtained were validated using conventional NVT-Gibbs ensemble Monte Carlo simulations. The qSC predictions for boiling temperatures are found to be reasonably accurate, but substantially underestimate the enthalpies of vaporization in all cases. This appears to be largely due to the systematic overestimation of dimer binding energies by this family of potentials, which leads to an unsatisfactory description of the vapor phase.

Extension of the Steele 10-4-3 potential for adsorption calculations in cylindrical, spherical, and other pore geometries.

Simplified fluid-substrate interaction models derived from the Lennard-Jones potential are widely used in the simulation of gas physisorption phenomena. In this paper, we reinterpret the well known Steele 10-4-3 potential for a gas molecule interacting with a planar surface, and use the resultant scheme to derive new potentials for cylindrical and spherical pore geometries. These new potentials correctly recover the Steele result in the limit of infinite pore radius, a useful improvement over existing models. We demonstrate the new cylindrical Steele 10-4-3 potential in calculations of argon adsorption via fluid density functional theory. This potential yields markedly different adsorption behavior than existing cylindrical potentials, which follow from small but significant differences in both the strength and the shape of the fluid-surface interaction. These differences cannot be fully reconciled simply by reparameterizing (scaling) the existing models; the new potential is more realistic in design, and is especially to be preferred in studies where comparison with planar substrates is made. Finally, we discuss extensions of this approach to more complicated pore geometries, yielding a family of Steele-like potentials that all satisfy the correct planar limit.

Thermodynamic and structural properties of finely discretized on-lattice hard-sphere fluids: Virial coefficients, free energies, and direct correlation functions.

Using both molecular simulation and theory, we examine fluid-phase thermodynamic and structural properties of on-lattice hard-sphere fluids. Our purpose in this work is to provide reference data for on-lattice density functional theories [D. W. Siderius and L. D. Gelb, Langmuir 25, 1296 (2009)] and related perturbation theories. In this model, hard spheres are located at sites on a finely discretized cubic lattice where the spacing between lattice sites is between one-tenth and one-third the hard-sphere diameter. We calculate exactly the second, third, and fourth virial coefficients as functions of the lattice spacing. Via Monte Carlo simulation, we measure the excess chemical potential as a function of density for several lattice spacings. These results are then parametrized with a convenient functional form and can immediately be used in on-lattice density functional theories. Of particular interest is to identify those lattice spacings that yield properties similar to those of the off-lattice fluid. We find that the properties of the on-lattice fluid are strongly dependent on lattice spacing, generally approaching those of the off-lattice fluid with increasing lattice resolution, but not smoothly. These observations are consistent with results for larger lattice spacings [A. Z. Panagiotopoulos, J. Chem. Phys. 123, 104504 (2005)]. Certain lattice spacings are found to yield fluid properties in particularly good agreement with the off-lattice fluid. We also find that the agreement of many different on- and off-lattice hard-sphere fluid properties is predicted quite well by that of the virial coefficients, suggesting that they may be used to identify favorable lattice spacings. The direct correlation function at a few lattice spacings and a single density is obtained from simulation. The on-lattice fluid is structurally anisotropic, exhibiting spherical asymmetry in correlation functions. Interestingly, the anisotropies are properly captured in the Percus-Yevick-based calculation of the direct correlation function. Lastly, we speculate on the possibility of obtaining a theoretical equation of state of the on-lattice hard-sphere fluid computed in the Percus-Yevick approximation.

Structure, thermodynamics, and solubility in tetromino fluids.

To better understand the self-assembly of small molecules and nanoparticles adsorbed at interfaces, we have performed extensive Monte Carlo simulations of a simple lattice model based on the seven hard "tetrominoes", connected shapes that occupy four lattice sites. The equations of state of the pure fluids and all of the binary mixtures are determined over a wide range of density, and a large selection of multicomponent mixtures are also studied at selected conditions. Calculations are performed in the grand canonical ensemble and are analogous to real systems in which molecules or nanoparticles reversibly adsorb to a surface or interface from a bulk reservoir. The model studied is athermal; objects in these simulations avoid overlap but otherwise do not interact. As a result, all of the behavior observed is entropically driven. The one-component fluids all exhibit marked self-ordering tendencies at higher densities, with quite complex structures formed in some cases. Significant clustering of objects with the same rotational state (orientation) is also observed in some of the pure fluids. In all of the binary mixtures, the two species are fully miscible at large scales, but exhibit strong species-specific clustering (segregation) at small scales. This behavior persists in multicomponent mixtures; even in seven-component mixtures of all the shapes there is significant association between objects of the same shape. To better understand these phenomena, we calculate the second virial coefficients of the tetrominoes and related quantities, extract thermodynamic volume of mixing data from the simulations of binary mixtures, and determine Henry's law solubilities for each shape in a variety of solvents. The overall picture obtained is one in which complementarity of both the shapes of individual objects and the characteristic structures of different fluids are important in determining the overall behavior of a fluid of a given composition, with sometimes counterintuitive results. Finally, we note that no sharp phase transitions are observed but that this appears to be due to the small size of the objects considered. It is likely that complex phase behavior may be found in systems of larger polyominoes.

Predicting gas adsorption in complex microporous and mesoporous materials using a new density functional theory of finely discretized lattice fluids.

We introduce a nonlocal on-lattice version of density functional theory (DFT) that allows for efficient modeling of fluids in complex inhomogeneous materials. In its previous implementations, classical DFT has required fine discretization of the fluid density. As a result, in studies of gas adsorption it has been used only in idealized pore models with high symmetry. Our new lattice DFT dramatically reduces the computational demand required to model simple fluids and hence can be efficiently applied to complex materials with multiple directions of asymmetry. We apply our new lattice DFT to study nitrogen adsorption in a slit pore with open ends and directly obtain the correct desorption hysteresis. We also apply our DFT to predict hydrogen adsorption accurately in an atomistic model of a metal-organic framework.

A computational study of the reconstruction of amorphous mesoporous materials from gas adsorption isotherms and structure factors via evolutionary optimization.

A general method for the three-dimensional reconstruction of mesoporous materials by evolutionary optimization against target data is developed. The method is applied specifically in reconstruction of amorphous material models using gas adsorption data, structure factor data, or a combination of both. A recently introduced lattice-gas approach is used to model adsorption in these calculations, and a high-pass limited Fourier representation is used to facilitate evolution of large-scale structures during the optimization. Reconstructions are made of several material models which mimic real materials obtained either by phase separation and etching or by sol-gel processing. Analysis of the reconstructions provides considerable insight into the type and quantity of structural information probed by gas adsorption and small-angle scattering experiments. We find that reconstructions based only on structure factors tend to underestimate the mean pore size. We also find that in many cases excellent reconstructions can be obtained using only adsorption-branch data, and that in all cases reconstructions based jointly on both types of data are superior to those based only on one, suggesting that these measures contain "complementary" information. It is also found that in most cases the use of desorption data is not warranted, and that the use of adsorption data taken at many temperatures will not improve reconstructions. The reproducibility of the method is shown to be satisfactory. The method can be computationally expensive if gas adsorption data are used, but it is easily parallelized, and therefore results can still be obtained in reasonable time. Finally, the possible application of this approach to real systems, including templated porous materials, is discussed.

Meta-Optimization of Evolutionary Strategies for Empirical Potential Development: Application to Aqueous Silicate Systems.

The use of evolutionary strategy optimizations in fitting empirical potentials against first-principles data is considered. Empirical potentials can involve a large number of interdependent quantities, the number varying with the complexity of the potential, and the optimization of these presents a challenging numerical problem. Evolutionary strategies are a general class of optimization methods that mimic natural selection by stochastically evolving a population of trial solutions according to rules that select for high values of some fitness function. In this work we apply a variety of evolutionary optimization methods to a representative "parametrization problem" in order to determine which such methods are well-suited to such applications. Prior work on the design of evolutionary strategies has generally focused on finding the extrema of relatively simple mathematical functions, and the findings of such studies may not be transferable to chemical applications of very high dimensionality. The test problem consists of parametrization of the Feuston-Garofalini all-atom potential developed for simulation of silicic acid oligomerization in aqueous solution (Feuston, B. P.; Garofalini, S. H. J. Phys. Chem. 1990, 94, 5351). "Meta-optimization" of the evolutionary method is first considered by fitting this potential against itself, using a wide variety of population sizes, recombination algorithms, mutation-size control methods, and selection methods. Simulated annealing is also considered as an alternative approach. Optimal choices of population size, recombination operator, mutation size control approach, and selection method are discussed, as well as the quantity of data required for the parametrization. It is clear from comparisons of multiple independent optimizations that, even when fitting this potential against itself, there are a considerable number of local extrema in the fitness function. Evolutionary methods are found to be competitive with simulated annealing and are more easily parallelized. Finally, the potential is reparametrized against reference data taken from a Car-Parrinello Molecular Dynamics trajectory of several relevant silicate species in aqueous solution, again using several variant algorithms.

Application of the Bethe-Peierls approximation to a lattice-gas model of adsorption on mesoporous materials.

We calculate adsorption and desorption isotherms in models of several classes of porous materials using a lattice-gas model solved in the Bethe-Peierls (quasichemical) approximation. Isotherms and fluid density profiles from the Bethe-Peierls and Bragg-Williams approximations are compared with grand-canonical Monte Carlo simulation results. The Bethe-Peierls approximation produces both more accurate adsorption and desorption isotherms and more realistic fluid density profiles than the Bragg-Williams approximation. Details of the application of the Bethe-Peierls approximation applied to a three-dimensionally inhomogeneous system are given. We show that the numerical solution of this theory can be accomplished using a self-consistent iterator very similar to that currently used in studies employing the Bragg-Williams approximation. This iterative scheme is substantially more efficient than the numerical optimization method used in many previous studies of lattice-gas models in the quasichemical approximation. We find that use of the Bethe-Peierls approximation is only slightly more computationally demanding than the Bragg-Williams approximation, and thus recommend it for use in future work on this class of models.