Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

Abstract

The equilibrium polymerization of sulfur is investigated by Monte Carlo simulations. The potential energy model is based on density functional results for the cohesive energy, structural, and vibrational properties as well as reactivity of sulfur rings and chains ͓Part I, J. Chem. Phys. 118, 9257 ͑2003͔͒. Liquid samples of 2048 atoms are simulated at temperatures 450рTр850 K and Pϭ0 starting from monodisperse S 8 molecular compositions. Thermally activated bond breaking processes lead to an equilibrium population of unsaturated atoms that can change the local pattern of covalent bonds and allow the system to approach equilibrium. The concentration of unsaturated atoms and the kinetics of bond interchanges is determined by the energy ⌬E b required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15р⌬E b р21 kcal/mol over a wide temperature range (Tу450 K), within which polymerization occurs readily, with entropy from the bond distribution overcompensating the increase in enthalpy. There is a maximum in the polymerized fraction at temperature T max that depends on ⌬E b . This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for T рT max , because entropy is less important than enthalpy. The molecular size distribution is described well by a Zimm-Schulz function, plus an isolated peak for S 8 . Large molecules are almost exclusively open chains. Rings tend to have fewer than 24 atoms, and only S 8 is present in significant concentrations at all T. The T dependence of the density and the dependence of polymerization fraction and degree on ⌬E b give estimates of the polymerization temperature T f ϭ450Ϯ20 K.

Structural transformation between long and short-chain form of liquid sulfur from ab initio molecular dynamics

“…Average length of the polymeric units in l-S was first directly measured by electron spin resonance by Gardner and Fraenkel and it was found to be of order 10 4 at 171 • C [86] and then decreasing with temperature. Theoretical models [75,76] and computer simulations [78,81] also qualitatively reproduce this temperatureinduced chain shortening with longest chains near T λ .…”

Structure and dynamics in amorphous tellurium and Tenclusters: A density functional study

“…40 Fig. 14 for crystalline and amorphous Te at 300 K, and for the liquid at three higher temperatures.…”

“…39) were used to develop a classical force field for sulfur in our study of its ring-opening polymerization. 40 The large number of allotropes and regularity of structural "motifs," such as the patterns of bond lengths and dihedral angles, as well as the interconversion mechanism between rings and chains, make these fascinating elemental clusters. Our recent density functional/molecular dynamics calculations on liquid Te at temperatures from 970 to 560 K (Ref.…”

A reactive force field simulation of liquid–liquid phase transitions in phosphorus

“…P and S are semiconductors under normal conditions, but become metallic at P well within the reach of current experimental methods. 13,14 Our recent computer simulation of polymerization in S was based on a realistic interatomic potential 15,16 and showed that the transition is driven by the entropy associated to the distribution of covalent bonds, i.e., a sulfur sample can be viewed as an assembly of N atoms and M (M рN) bonds. The low T molecular phase comprising mainly S 8 units 17 is one such configuration.…”