Isomolar semigrand ensemble molecular dynamics: Development and application to liquid-liquid equilibria

Morrow, Timothy I.; Maginn, Edward J.

doi:10.1063/1.1839172

Cited by 16 publications

(12 citation statements)

References 54 publications

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“…Impressive progress has been made using this isobaric semigrand ensemble in the condensed phases of spherical particles and chain-of-bead molecules. 27,[53][54][55][56] Additional work is needed to extend these approaches to real molecules and explicit solvents, but particle identity changes in the semigrand ensemble should ultimately facilitate atomistic simulations.…”

Section: Methodsmentioning

confidence: 99%

Nucleation in a Potts lattice gas model of crystallization from solution

Duff

Peters

2009

The Journal of Chemical Physics

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Nucleation from solution is important in many pharmaceutical crystallization, biomineralization, material synthesis, and self-assembly processes. Simulation methodology has progressed rapidly for studies of nucleation in pure component and implicit solvent systems; however little progress has been made in the simulation of explicit solvent systems. The impasse stems from the inability of rare events simulation methodology to be combined with simulation techniques which maintain a constant chemical potential driving force (supersaturation) for nucleation. We present a Potts lattice gas (PLG) to aid in the development of new simulation strategies for nucleation from solution. The PLG captures common crystallization phase diagram features such as a eutectic point and solute/solvent melting points. Simulations of the PLG below the bulk solute melting temperature reveal a competition between amorphous and crystalline nuclei. As the temperature is increased toward the bulk melting temperature, the nucleation pathway changes from a one step crystalline nucleation pathway to a two step pathway, where an amorphous nucleus forms and then crystallizes. We explain these results in terms of classical nucleation theory with different size-dependant chemical potentials for the amorphous and crystalline nucleation pathways. The two step pathway may be particularly important when crystallization is favored only at postcritical sizes.

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Section: Methodsmentioning

confidence: 99%

Nucleation in a Potts lattice gas model of crystallization from solution

Duff

Peters

2009

The Journal of Chemical Physics

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“…Using (51) and (56) we write the first two terms of the constant pressure virial series (48) for μ A in terms of the original virial coefficients as…”

Section: Virial Expansion At Constant Pressure For the Solute Chemicamentioning

confidence: 99%

“…A similar semi-grand ensemble but with fixed pressure rather than fixed volume has been introduced for computer simulations of multicomponent solutions. 50,51 In Sec. III, we introduce the solute PMFs, first…”

Section: Introductionmentioning

confidence: 99%

McMillan-Mayer theory of solutions revisited: Simplifications and extensions

Vafaei

Tomberli

Gray

2014

The Journal of Chemical Physics

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McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the solvent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentration, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {N(A), μ(B), V, T}, to those relevant to the experiment, i.e., fixed {N(A), N(B), p, T}, where μ denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature.

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“…As such, μ AB represents a statistical mechanical finite difference version of a "transmutating" or "alchemical" potential, as also used within the isomolar semigrand ensemble theory [25] or its electronic structure analog [26].…”

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confidence: 99%

Molten salt eutectics from atomistic simulations

2011

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Despite their importance for solar thermal power applications, phase-diagrams of molten salt mixture heat transfer fluids (HTFs) are not readily accessible from first principles. We present a molecular dynamics scheme general enough to identify eutectics of any HTF candidate mixture. The eutectic mixture and temperature are located using the liquid mixture free energy and the pure component solid-liquid free energy differences. The liquid mixture free energy is obtained using thermodynamic integration over particle identity transmutations sampled with molecular dynamics at a single temperature. According to Carnot's cycle, the maximum efficiency of solar thermal power facilities increases with the temperature difference between melting and thermal decomposition of employed heat transfer fluids (HTFs). Consequently, new formulations of low melting but temperature resistant molten salt mixtures are actively sought [1]. Competitive formulations currently include eutectics of alkali and alkali-metal earth nitrates and nitrite mixtures. Unfortunately, the dimensionality of the combinatorial multicomponent space of all possible cations and anions prohibits exhaustive scanning using computer simulation. Once an optimal HTF formulation is identified, however, its realization through simple mixing is readily accomplished in experiment. Identifying new HTFs therefore represents a rewarding challenge for atomistic first principles materials design efforts using theory and computation. Ab initio (AI) based design, through an efficient combination of first principles methods and optimization algorithms [2], has already been applied to inverting band structures [3], identifying stable alloys [4], designing heterogeneous catalysts [5,6], or discovering ternary metal oxides for batteries [7]. Identity transformations, also called "alchemical" transmutations [8], have been successfully applied to compute compositions in the earth's core [9], phase stability in solid solutions [10], and a wide variety of biochemical applications [11], among others.The Gibbs criteria for phase equilibrium dictates that temperature, pressure, and chemical potential of individual components must be equal in coexisting phases. Therefore, knowledge not only of average liquid configurations but also of the solid mixture's structure is essential. For phase transitions of mixtures, the problem is hence strongly linked to the challenge of predicting molecular crystals from first principles [12], which has been addressed for co-crystals only recently [7,13] in mapping out entire phase diagrams. For the identification of HTF mixtures with minimal melting points, however, it is sufficient to simply focus on eutectics, rather than having to screen the entire solid-liquid phase diagram. Here, we present a first principles approach for directly estimating eutectic compositions and temperatures for any number of components, relying on a combination of only a couple of molecular dynamics (MD) calculations per mole fraction at a single temperature and knowledge ab...

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Isomolar semigrand ensemble molecular dynamics: Development and application to liquid-liquid equilibria

Cited by 16 publications

References 54 publications

Nucleation in a Potts lattice gas model of crystallization from solution

Nucleation in a Potts lattice gas model of crystallization from solution

McMillan-Mayer theory of solutions revisited: Simplifications and extensions

Molten salt eutectics from atomistic simulations

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