Use of polydispersity index as control parameter to study melting/freezing of Lennard-Jones system: Comparison among predictions of bifurcation theory with Lindemann criterion, inherent structure analysis and Hansen-Verlet rule

Abstract

Using polydispersity index as an additional order parameter we investigate freezing/melting transition of Lennard-Jones polydisperse systems (with Gaussian polydispersity in size), especially to gain insight into the origin of the terminal polydispersity. The average inherent structure (IS) energy and root mean square displacement (RMSD) of the solid before melting both exhibit quite similar polydispersity dependence including a discontinuity at solid-liquid transition point. Lindemann ratio, obtained from RMSD, is found to be dependent on temperature. At a given number density, there exists a value of polydispersity index (δ P) above which no crystalline solid is stable. This transition value of polydispersity (termed as transition polydispersity, δ P) is found to depend strongly on temperature, a feature missed in hard sphere model systems. Additionally, for a particular temperature when number density is increased, δ P shifts to higher values. This temperature and number density dependent value of δ P saturates surprisingly to a value which is found to be nearly the same for all temperatures, known as terminal polydispersity (δ TP). This value (δ TP ∼ 0.11) is in excellent agreement with the experimental value of 0.12, but differs from hard sphere transition where this limiting value is only 0.048. Terminal polydispersity (δ TP) thus has a quasiuniversal character. Interestingly, the bifurcation diagram obtained from non-linear integral equation theories of freezing seems to provide an explanation of the existence of unique terminal polydispersity in polydisperse systems. Global bond orientational order parameter is calculated to obtain further insights into mechanism for melting.

Breakdown of universal Lindemann criterion in the melting of Lennard-Jones polydisperse solids

“…The result has been shown to be consistent with one another, both qualitatively and quantitatively, in predicting the existence of terminal 3 polydispersity, beyond which freezing is not possible [9]. The Lindemann ratio, obtained from RMSD, has been shown to be intensely dependent on temperature [8].…”

“…In a recent study [8], in order to investigate the effect of polydispersity on the solid-liquid transition of the Lennard-Jones system [9], we have analyzed the model system using numerical simulations in three distinct ways, namely, by applying the empirical Lindemann criterion of melting, the inherent structure analysis [10][11][12] and the empirical Hansen-Verlet criterion of freezing [13,14]. The result has been shown to be consistent with one another, both qualitatively and quantitatively, in predicting the existence of terminal 3 polydispersity, beyond which freezing is not possible [9].…”

Size-Polydisperse Model Ionic Liquid in Bulk

“…Furthermore, we can also see from Figure that for δ = 7% and 12%, the system is unable to form crystalline structure and instead forms frozen structure. This is consistent with previous studies on polydispersity, which found that if δ of the system exceeds the terminal polydispersity, then it is unable to crystallize and instead forms glass …”

“…This is consistent with previous studies on polydispersity, which found that if δ of the system exceeds the terminal polydispersity, then it is unable to crystallize and instead forms glass. 50 Since our aim is to investigate various properties of the ionic system in liquid phase, we relax the samples at temperature 5% above their respective T h * so that the systems are indeed in the liquid state and at same distance from the respective T h *. This choice of temperatures allows us a better comparison of the systems in their liquid state as fixing the same temperature for all is not ideal due the varying hysteresis loop area as well as thermodynamic melting temperature.…”

Glass transition in monatomic systems: smearing of the same structure vs two structure competition

“…Another class of systems, which demonstrate glass transition, is systems with size polydispersity of particles (see, for instance, Refs [33][34][35]). It was shown in numerous articles that polydisperse hard spheres [33] or Lennard-Jones (LJ) particles [34,35] could demonstrate glass transition if the degree of polydispersity was sufficiently large. At the same time, a polydisperse LJ system looks very different from core-softened systems and one can expect that it should vitrify via some other mechanisms.…”