Molecular thermodynamics of solid‐fluid and solid‐solid equilibria

Monson, P. A.

doi:10.1002/aic.11471

Cited by 14 publications

(14 citation statements)

References 36 publications

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“…0 is trivially related to the excess chemical potential and c (2) 0 may be obtained with high accuracy from Ornstein-Zernike (OZ) liquid-state theory or simulation. However, the rest of the terms involve threebody and higher correlations that are much more challenging to obtain.…”

Section: Theorymentioning

confidence: 99%

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Universal features of the free-energy functional at the freezing transition for repulsive potentials

Verma

Ford²

2011

Phys. Rev. E

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The free energy difference between coexisting solid and liquid phases is studied in the context of classical density functional theory (DFT). A bridge function is used to represent the higher-order (n > 2) terms in the perturbative expansion of the excess Helmholtz free energy, and the values of this bridge function within the solid lattice are determined by inversion using literature Monte Carlo simulation results. Four potential models, specifically hard-sphere and inverse 12th-, 6th-, and 4th-power repulsive, are studied. The face-centered cubic (fcc) solid is considered for the hard-sphere and inverse 12th-and 6th-power potentials, while the body-centered cubic (bcc) solid is considered for the inverse 6th-and 4th-power potentials. For a given solid structure there is a remarkable similarity among the bridge functions for different potentials that is analogous to the universality in the sum of elementary diagrams, or bridge functions, of liquid-state theory as originally observed by Rosenfeld and Ashcroft [Physical Review A 20, 1208-1235]. In further analogy with liquid-state theory, the bridge functions in the present problem are plotted as functionals of the second-order convolution term in the perturbative expansion. In each case, the plot indicates a unique functionality in the dense regions of the solid near the lattice sites but a scattered and nonunique behavior in the void regions. Interestingly, knowledge of the functional relationship in the unique region near the lattice sites seems to be sufficient to quantitatively model the solid-fluid phase transition. These qualitative observations are true for both fcc and bcc solid phases, although there are some quantitative differences between them. The findings suggest that pursuit of a closure-based DFT of solid-fluid transitions may be profitable.

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Section: Theorymentioning

confidence: 99%

“…The prediction of solid-fluid phase equilibrium from an interparticle potential model is an important problem in condensed matter theory [1,2]. Classical density functional theory (DFT) [3] is a useful tool in this regard because of its low computational cost as compared to particle-based simulation.…”

Section: Introductionmentioning

confidence: 99%

Universal features of the free-energy functional at the freezing transition for repulsive potentials

Verma

Ford²

2011

Phys. Rev. E

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“…Consequently, its density and other properties vary with position, and key behaviors such as phase transitions can be significantly affected. 1 Moreover, the homogeneity may break spontaneously, without the influence of an external field, such as when the fluid separates into phases of different density, 2 freezes to form a crystal, 3,4 or self-assembles into a mesoscopic structure. 5 In the introduction of their 1962 paper, Stillinger and Buff 6 outlined many compelling reasons for the study of the statistical mechanics of inhomogeneous fluids, and they all remain relevant today.…”

Section: Introductionmentioning

confidence: 99%

Calculation of inhomogeneous-fluid cluster expansions with application to the hard-sphere/hard-wall system

Yang

Schultz

Errington

et al. 2013

The Journal of Chemical Physics

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We examine the suitability of cluster expansion methods for the description of inhomogeneous fluids. In particular, we apply these methods to characterize the density profile, surface tension, and excess adsorption for a hard-sphere fluid near a hard wall. Coefficients for these series up to seventh order are evaluated by the Mayer-sampling Monte Carlo method. Comparison of the series to Monte Carlo simulations of these systems finds very good agreement up to bulk densities approaching the freezing point. This work indicates that knowledge of surface cluster integrals of inhomogeneous systems can be at least as useful as the bulk-phase virial expansions.

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“…Thirty years ago, molecular modeling and simulation was practically unknown within the chemical engineering community. The field has grown since that time such that now nearly every academic department has one or more faculty members who carry out some sort of molecular‐based modeling activity, AIChE meetings host topical conferences and dozens of sessions focused on molecular modeling and simulation, and various aspects of the field have been the subject of past Perspectives articles 1–4. Molecular modeling and simulation is pervasive, but has it become a mainstream chemical engineering tool in the way that process simulations or finite element modeling are?…”

Section: Introductionmentioning

confidence: 99%

From discovery to data: What must happen for molecular simulation to become a mainstream chemical engineering tool

Maginn

2009

AIChE Journal

106

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Molecular thermodynamics of solid‐fluid and solid‐solid equilibria

Cited by 14 publications

References 36 publications

Universal features of the free-energy functional at the freezing transition for repulsive potentials

Universal features of the free-energy functional at the freezing transition for repulsive potentials

Calculation of inhomogeneous-fluid cluster expansions with application to the hard-sphere/hard-wall system

From discovery to data: What must happen for molecular simulation to become a mainstream chemical engineering tool

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