Determination of phase diagrams via computer simulation: Methodology and applications to water, electrolytes and proteins

Abstract

In this review we focus on the determination of phase diagrams by computer simulation with particular attention to the fluid-solid and solid-solid equilibria. The calculation of the free energy of solid phases using the Einstein crystal and Einstein molecule methods are described in detail. It is shown that for the hard spheres solid both methods yield the same results and that free energies of solid phases present noticeable finite size effects. Finite size corrections can be introduced, although in an approximate way, to correct for the dependence of the free energy on the size of the system. The computation of free energies of solid phases can be extended to molecular fluids. The procedure to compute free energies of solid phases of water (ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI and XII) using the SPC/E and TIP4P models will be described.Other methods to estimate the melting point of a solid, as the direct fluid-solid coexistence or simulations of the free surface of the solid will be discussed. It will be shown that the melting points of ice Ih for several water models, obtained from these two methods and from free energy calculations agree within statistical uncertainty. Phase diagram calculations can help to improve potential models of molecular fluids; for water, the TIP4P/2005 model can be regarded as an improved version of TIP4P. We will also review some recent work on the phase diagram of the simplest ionic model, the restricted primitive model. Although originally devised to describe ionic liquids, the model is becoming quite popular to describe charged colloids. Besides the possibility of obtaining fluid-solid equilibria for simple protein models will be discussed. In these primitive models, the protein is described by a spherical potential with certain anisotropic bonding sites.

72 pages, 15 figures

References in corpus (25)

• Temperature Dependence of the Hydrophobic Hydration and Interaction of Simple Solutes: An Examination of Five Popular Water Models
• Finite-size corrections to the free energy of crystalline solids
• Reversible self-assembly of patchy particles into monodisperse icosahedral clusters
• Free energies of crystalline solids: a lattice-switch Monte Carlo method
• Controlling crystallization and its absence: Proteins, colloids and patchy models
• Phase behaviour of a simple model of globular proteins
• Three-dimensional Binary Superlattices of Oppositely-charged Colloids
• Liquid-liquid phase transitions in supercooled water studied by computer simulations of various water models
• Melting and nonmelting of solid surfaces and nanosystems
• Freezing by Monte Carlo Phase-Switch
• First principles simulations of direct coexistence of solid and liquid aluminium
• Adjusting the melting point of a model system via Gibbs-Duhem integration: application to a model of Aluminum
• Phase diagram of model anisotropic particles with octahedral symmetry
• Lattice-switch Monte Carlo
• Freezing line of the Lennard-Jones fluid: a Phase Switch Monte Carlo study
• Phase diagram of silica from computer simulation
• Absence of superheating for ice Ih with a free surface : a new method of determining the melting point of different water models
• Phase diagram of silicon from atomistic simulations
• The range of meta stability of ice-water melting for two simple models of water
• Residual Entropy of Ordinary Ice from Multicanonical Simulations
• Physics of Solid and Liquid Alkali Halide Surfaces Near the Melting Point
• Simulations of binary hard-sphere crystal-melt interfaces:Interface between a one- component fcc crystal and a binary fluid mixture
• Phase diagram of Gaussian-core nematics
• Field-theoretic description of ionic crystallization in the restricted primitive model
• Numerical calculation of the combinatorial entropy of partially ordered ice

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• Effects of surface interactions on heterogeneous ice nucleation for a monatomic water model
• Data-Driven Prediction of Complex Crystal Structures of Dense Lithium
• Predicting Patchy Particle Crystals: Variable Box Shape Simulations and Evolutionary Algorithms
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• Free energy calculations for atomic solids through the Einstein crystal/molecule methodology using GROMACS and LAMMPS
• Potential Energy Landscape of TIP4P/2005 water
• Solid-solid phase transition in hard ellipsoids
• Interfacial free energy and Tolman length of curved liquid-solid interfaces from equilibrium studies
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• Self-assembly scenarios of patchy colloidal particles
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• Nucleation barriers in tetrahedral liquids spanning glassy and crystallizing regimes
• Phase diagram of the ST2 model of water
• DNA brick self-assembly with an off-lattice potential
• Self-assembly of two-dimensional binary quasicrystals: A possible route to a DNA quasicrystal
• A study of the influence of isotopic substitution on the melting point and temperature of maximum density of water by means of path integral simulations of rigid models
• A possible four-phase coexistence in a single-component system
• The kinetics of the ice-water interface from ab initio machine learning simulations
• Same and interconvertible high-pressure ice phases
• Fluid-Fluid and Fluid-Solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory
• Modeling the High-Pressure Solid and Liquid Phases of Tin from Deep Potentials with ab initio Accuracy
• Classical nucleation theory of ice nucleation: second-order correction of thermodynamic parameters
• A hard-sphere quasicrystal stabilized by configurational entropy
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• The phase diagram of ice: a quasi-harmonic study based on a flexible water model
• The phase diagram of ice Ih, II, and III: a quasi-harmonic study
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• Inverse melting in a two-dimensional off-lattice model
• Efficient mapping of phase diagrams with conditional Boltzmann Generators
• A streamlined molecular-dynamics workflow for computing solubilities of molecular and ionic crystals
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• Critical surface adsorption of confined binary liquids with locally conserved mass and composition
• Using schematic models to understand the microscopic basis for inverted solubility in $\gamma$D-crystallin
• A patchy-particle 3-dimensional octagonal quasicrystal