Determination of phase diagrams via computer simulation: methodology and applicationsto 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 methodology tocompute the free energy of solid phases will be discussed. In particular, the Einstein crystaland Einstein molecule methodologies are described in a comprehensive way. It is shownthat both methodologies yield the same free energies and that free energies ofsolid phases present noticeable finite size effects. In fact, this is the case for hardspheres in the solid phase. Finite size corrections can be introduced, although in anapproximate way, to correct for the dependence of the free energy on the size ofthe system. The computation of free energies of solid phases can be extendedto molecular fluids. The procedure to compute free energies of solid phases ofwater (ices) will be described in detail. The free energies of ices Ih, II, III, IV,V, VI, VII, VIII, IX, XI and XII will be presented for the SPC/E and TIP4Pmodels of water. Initial coexistence points leading to the determination of thephase diagram of water for these two models will be provided. Other methods toestimate the melting point of a solid, such as the direct fluid–solid coexistence orsimulations of the free surface of the solid, will be discussed. It will be shownthat the melting points of ice Ih for several water models, obtained from freeenergy calculations, direct coexistence simulations and free surface simulationsagree within their statistical uncertainty. Phase diagram calculations can indeedhelp to improve potential models of molecular fluids. For instance, for water, thepotential model TIP4P/2005 can be regarded as an improved version of TIP4P.Here we will review some recent work on the phase diagram of the simplest ionicmodel, the restricted primitive model. Although originally devised to describe ionicliquids, the model is becoming quite popular to describe the behavior of chargedcolloids. Moreover, the possibility of obtaining fluid–solid equilibria for simpleprotein models will be discussed. In these primitive models, the protein is describedby a spherical potential with certain anisotropic bonding sites (patchy sites).