Phase-like Forms Research Articles

Phase change of Lennard-Jones nano clusters containing non magic numbers

Phase changes of Lennard-Jones clusters containing 4N 3 (N= 1−20) identical atoms in terms of solid and liquid phase-like forms have been studied by performing molecular dynamics (MD) simulation at sharply-bounded range of temperatures between freezing temperature (T f) and melting temperature (T m) and at constant pressure. The small differences between the free energies of clusters in different phase-like forms and also the non-rigidity of the cluster (0 ≤ γ ≤ 1) as an order-parameter, which characterizes the phase transition, have been calculated. Plots of the free energy of phase change versus the non-rigidity indicate that the free energy is a continuous function of the non-rigidity and also different crystalline-like cores with different free energies correspond to the same non-rigidity factor at any given temperature.

Formation of single-phase oxide nanoclusters: Cu2O on SrTiO3(100)

Selective formation of the single-phase nanoclusters of Cu2O on SrTiO3(100) substrates in the size range of 10–50 nm is found to occur only in a very narrow oxygen plasma-assisted molecular-beam epitaxy growth parameter window, in comparison with the bulk phase diagram (for oxygen pressure versus temperature). There are distinctive parameter regions, where multiple phaselike forms coexist (CuO/Cu2O and Cu2O/Cu), in agreement with theoretical prediction for small systems, and as opposite to the sharp phase boundaries for the bulk. Observed changes in the nanocluster composition are found to correlate with differences in cluster morphologies.

Structural transitions in small molecular clusters

Clusters of octahedral molecules mimicking TeF6 afford a vehicle to investigate the analog in small clusters of structural phase transitions through molecular dynamics simulations. Three phaselike forms occur for the solid clusters, both closed-shell structures of 51, 89, and 137 molecules, and open-shell structures of 50, 81, and 129 molecules. The indications are that the free energy has at least two minima as a function of the order parameter. However, whether these converge to a single minimum as N, the number of molecules in the cluster, grows large, leading to a second-order transition in the bulk, or remain apart, implying at least a weak first-order transition in the bulk limit, cannot be determined from the simulations.

Modeling self-assembling of proteins: Assembled structures, relaxation dynamics, and phase coexistence

A string-of-beads model used previously to describe folding of a polypeptide into a β-barrel is transformed into four-strand model of a self-assembling system, which also produces a β-barrel. In molecular dynamics (MD) simulations, both isothermal and variable-temperature (annealing), the system behaves much like a typical small cluster, insofar as it exhibits the dynamic coexistence of several phase-like forms over ranges of temperature. A three-state analytic model, then a four-state model, supplemented by degeneracies inferred from the MD simulations, yield partition functions and phase diagrams that reproduce the simulations rather well.

Phase coexistence in clusters: An “experimental” isobar and an elementary model

This work examines the temperature dependence of the coexistence ratios of phaselike forms of atomic clusters of two kinds, a homogeneous cluster bound by pairwise Lennard–Jones forces that simulates Ar55, and a binary, ionic cluster simulating (KCl)32. Two methods have been used: isothermal molecular dynamics and a simple analytical model based on highly simplified densities of states. The phase behavior of the alkali halide cluster is well represented by a two-level density of states, a nondegenerate lower level, and a highly degenerate upper level. The phase behavior of the argon cluster needs an intermediate level of moderate degeneracy to reproduce the three-phase behavior of the simulations.

MELTING AND FREEZING PHENOMENA

Clusters of atoms and molecules lend themselves to the study of phase changes because they are susceptible to the analytic and computational methods appropriate for small systems, yet allow the study of size dependence, e ven approaching the bulk limit. Clusters not only gi ve insights into the nature of bulk phase transitions; they ha ve many properties unique to small systems, such as bands of temperature and pressure within which phaselike forms may coexist - not just curves of coexistence. Moreo ver, more than two phaselike forms may coexist in such bands; in fact, clusters may exhibit phaselike forms that do not exist for bulk matter. These properties of coexistence are the consequence of the small differences between the free energies of the clusters in different, phaselike forms, yet theory predicts that these bands of coexistence ha ve sharp boundaries, due to the disappearance of local stability of each phaselike form. In contrast also to bulk phase equilibrium, coexistence of phaselike forms of clusters and nanoscale particles is a dynamic equilibrium, like that of chemical isomers. Hence, for clusters to exhibit a particular phase, they must dwell in the region of configuration and phase space appropriate to that phase long enough to establish equilibriumlike properties associated with that phase, and not with the entire configuration or phase space. These phenomena come at the cost of loss of the sharp distinction between ''phase'' and ''component,'' and the inapplicability of the Gibbs phase rule.

Multiple phase coexistence in finite systems.

Dynamic coexistence of several phaselike forms, a solid, microcrystalline phase, a homogeneously melted phase, and phases exhibiting a solid core and a melted surface, is found in isothermal molecular-dynamics simulations of magic-number rare-gas clusters. We present a theoretical model for the equilibrium and dynamics of phases of small systems that incorporates homogeneous and heterogeneous phases and gives necessary conditions for the material parameters if a cluster is to exhibit the observed multiple-phase behavior.

Coexistence of multiple phases in finite systems.

Dynamic coexistence of several phaselike forms, a solid, microcrytalline phase, a homogeneously melted phase, and phases exhibiting a solid core and a melted surface, is found in isothermal molecular dynamics simulations of magic-number rare gas clusters. We present a mean-field model showing that the observed behavior is possible if (a) the core and surface both undergo finite-system analogs of first-order transitions with overlapping coexistence regions and (b) the mode-softening defects of the core exhibit an attractive interaction with the vacancy-floater pairs on the surface.