The distance fluctuation criterion for melting: Comparison of square-well and Morse potential models for clusters and homopolymers

Abstract

We explore the distance fluctuation criterion ͑''Lindemann criterion''͒ for melting transitions. Distances from average positions in accord with Lindemann, or interparticle distances, in accord with Jellinek and Berry or Etters and Kaelberer, are examined. The primary goal is to determine which of these offers the more useful criterion. The choice of origin can sometimes effect the significance of the index. We study three systems with two kinds of potentials. They are all composed of 64 particles: ͑a͒ and ͑b͒, a homopolymer and a cluster that consist of beads interacting pairwise through square-well potentials, and ͑c͒ a cluster of particles interacting pairwise through Morse potentials. For each of the noncrystalline structures, in contrast to the crystals originally studied by Lindemann, the fluctuation parameter based on interparticle distances gives a clearer separability of liquid and solid phases than that based on fluctuations from average positions. The solid-like forms of the Morse cluster, the square-well cluster, and the square-well homopolymer have similar behavior, indicating that a broad class of systems can be evaluated with this index. In these systems, relative fluctuation parameters provide a suitable criterion for the melting transition. The critical values for the interparticle distance criterion, which are in the range of 0.03-0.05, are smaller than those for the Lindemann criterion ͑0.1-0.15͒.

Soft matrix and fixed point of Lennard-Jones potentials for different hard-clusters in size at glass transition

“…41 and 0.1-0.15 in Ref. 40. This also validates the theory of fixed point for self-similar L-J potentials and the Eqs (6)- (18).…”

“…Lindemann criterion has been applied to study solid-versusliquid behavior: distance-fluctuations cannot increase without destroying the lattice structure. 40 Here it has been found that the Lindemann ratio, contained in Eq. (18), is equivalent to the stability condition of recursion equation (6), which also indicates the inverse cascade at the GT is only determined by the intrinsic and instantaneous geometric structure, without any presupposition and relevant parameter.…”

Vapor-liquid critical and interfacial properties of square-well fluids in slit pores

“…SW model was introduced originally to understand simple liquid; 34 however, due to its analytic tractability it has become even more useful for colloidal system, [35][36][37] heterochain molecules, [38][39][40] and complex system, [41][42][43] among others.…”

Multiscale analytic continuation approach to nanosystem simulation: Applications to virus electrostatics

“…This phenomenology describes a smooth transition in ion accessibility from 0 to 1 is suggested in other studies, [44][45][46][47][48] the basis of which is fluctuating positions of the fixed and mobile ions, as well as the continuous profile of electron density around a given ion. The mean displacement of an ion from an equilibrium position was considered to be Ͼ0.1͑a i + b l ͒ Å.…”