Supercooling computer simulations

W. Kob,/. Phys. Cond. Matt., 11, R85 (1999). Computer Simulations of Supercooled Liquids... 

In the previous section we have discussed the relation between the time- and frequency-dependent friction and viscosity in the normal liquid regime. The study in this section is motivated by the recent experimental (see Refs. 80-87) and computer simulation studies [13,14, 88] of diffusion of a tagged particle in the supercooled liquid where the tagged particle has nearly the same size as the solvent molecules. These studies often find that although the fric-... 

Lennard-Jones binary mixture of particles is a prototypical model that describes glass-forming liquids [52,53,158,162-165]. The temperature and the density dependence of diffusivity D(T, p) have been obtained by computer simulations for the Lennard-Jones binary mixture in the supercooled state. To relate fragility of binary Lennard-Jones mixture to thermodynamic properties necessitates determination of the configurational entropy SC(T, p) as well as the vibration entropy Sv,h(T, p) at a given temperature and density. 

Water is well known for its unusual properties, which are the so-called "anomalies" of the pure liquid, as well as for its special behavior as solvent, such as the hydrophobic hydration effects. During the past few years, a wealth of new insights into the origin of these features has been obtained by various experimental approaches and from computer simulation studies. In this review, we discuss points of special interest in the current water research. These points comprise the unusual properties of supercooled water, including the occurrence of liquid-liquid phase transitions, the related structural changes, and the onset of the unusual temperature dependence of the dynamics of the water molecules. The problem of the hydrogen-bond network in the pure liquid, in aqueous mixtures and in solutions, can be approached by percolation theory. The properties of ionic and hydrophobic solvation are discussed in detail. 

It is known that the density autocorrelation function or the intermediate scattering function F(q, ai) in the supercooled fluid phase can well be described by a stretched exponential function of the form F q,u>) A exp[—(t/computer simulations. This particular relaxation is called a relaxation, and such a characteristic decay manifests itself in a slower decay of the dynamical structure factor S q,u>) and of the a peak of the general... 

Most of the structural and dynamic studies in solutions have been carried out at ambient temperature and atmospheric pressure or not far from it. An increasing number of papers is devoted to supercooled [16-19] and glassy [18,20,21] water and solutions as well as to studies of water [22] and of aqueous solutions [23,24] at high temperature and/or pressure. Computer simulation methods are very flexible and are suitable for various studies at almost any thermodynamic conditions, and therefore a new strategy of the research can be established easily simulations may predict some properties of the solutions at conditions which can be later verified when the appropriate experimental conditions become available. 

An appealing approach to the study of nucleation is to observe it directly in a computer simulation using the method of molecular dynamics. It is evident that one cannot closely mimic experimental conditions, since computer time scales extend only over tens to hundreds of picoseconds. Thus deep quenches carried out at high quench rates are necessary to form supercooled liquids that have some reasonable chance of nucleating. Under such conditions glass formation is also observed, and in fact the first observation of nucleation was a chance event, although since that time more systematic studies have been carried out. 

Given that the supercooling of a liquid can lead to structurally distinct possibilities (the stable crystal or a glass), structural order parameters are especially valuable in understanding low-temperature metastabiUty. In particular, it has been demonstrated (van Duijneveldt and Frenkel, 1992) that the bond-orientational order parameters introduced by Steinhardt et al (1983) are well suited for detecting crystalline order in computer simulations of simple supercooled liquids. The bond-orientational order parameters are so named because they focus on the spatial orientation of imaginary bonds" that connect molecules to their nearest neighbors defined as above with... 

This chapter reviews recent applications of computer simulation techniques, in particular the method of molecular dynamics (MD) by us and others to supercooled liquids, glass transition phenomena, and amorphous solids. 

It is assumed at the outset that the reader is familiar with the basic Monte Carlo (MC) and molecular dynamics (MD) methods of computer simulation of liquids. This area is now the subject of a large body of literature, as well as review articles and lecture series. In recent years, a number of authors have taken advantage of the ability of the simulation methods to obtain detailed information on the properties of supercooled simple liquids in internal equilibrium. This is possible because the measurements are made on a time scale that is short with respect to the time scale on which the crystallization event occurs. These time-scale differences lead directly to the existence of the type of study on which this chapter focuses. 

Inset (a.l). Relations between the continuous cooling at rate —5 deg/min of the laboratory experiment, and the equivalent quench-hold sequence used in MD experiments for evaluating supercooled liquid properties and illustrated in Fig. S. For the equivalent computer simulation experiment, each minute time interval would represent 10 psec. Inset (a.2). Relation between percentage of instantaneous perturbation relaxed and number of relaxation times elapsed, at constant t (isothermal relaxation). 

It is of interest to inquire further into the structure of the metastable state, and particularly its relationship with the stable crystal into which it will eventually transform. It has been suggested that the temporaiy stability of supercooled states of spherical particles is related to the predominance of structures with fivefold symmetry, such as the icosohedron. Such structures cannot fill space uniformly nevertheless, quite large units of this kind (Fig. 19) have been identified in recent computer simulation experiments. ... 

Fig. 21. Entropy versus log-temperature diagram for the hard-sphere model. The solid curves give the computer simulation values for the supercooled fluid, glass, and crystal. The dashed curves have the following bases (a) a calculation from the virial equation using the known first seven coefficients and higher coefficients obtained from the conjectured closure (the plot corresponds quite closely with that calculated from the Camahan-Starling equation ) and (i>) an extrapolation of higher temperature behavior such as that used by Gordon et al., which implies a maximum in the series of virial coefficients. The entropy is defined in excess of that for the ideal gas at the same temperature and pressure. Some characteristic temperatures are identified 7, fusion point 7 , upper glass transition temperature T/, Kauzmann isoentropic point according to closure virial equation.

Computer simulations reveal another interesting aspect of supercooled water, which is the limited propagation of the coordination number [7]. As discussed earlier, bulk water consists of species with different coordination numbers. Supercooled water mostly consists of 4-cordinated species along with a small percentage of 5- and 3-coordinated species. As the tetrahedral network structure is the stable configuration of the system, 5- and 3-coordinate species are defects in the system. These defects are of course not static, they propagate in the system. 

Malenkov GG (2006) Structure and dynamics of liquid water. J Struct Chem 47 S1-S31 Malenkov GG, Tytik DL, Zheligovskaya EA (2003) Structural and dynamic heterogeneity of computer simulated water ordinary, supercooled, stretched and compressed. J Mol Liq 106 179-198... 

In addition to new insights gained from computer simulation, new experimental techniques have led to some reassessments of previously accepted wisdom. The suggestion that spinodal decomposition of the melt could exist as a precursor to polymer nucleation has already been mentioned. Several groups have suggested that crystallization occurs through a series of intermediate stages and that the final crystal structure is not a refiection of the structure that initially formed from the supercooled melt (137-141). 

I. Brovchenko, A. Geiger, and A. Oleinikova, Liquid-liquid phase transitions in supercooled water studied by computer simulations of various water models, J. Chem. Phys. 123(4), 044515 (2005). 

---