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

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 (2003)]. Liquid samples of 2048 atoms are simulated at temperatures 450⩽T⩽850 K and P=0 starting from monodisperse S8 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 ΔEb required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15⩽ΔEb⩽21 kcal/mol over a wide temperature range (T⩾450 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 Tmax that depends on ΔEb. This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for T⩽Tmax, because entropy is less important than enthalpy. The molecular size distribution is described well by a Zimm–Schulz function, plus an isolated peak for S8. Large molecules are almost exclusively open chains. Rings tend to have fewer than 24 atoms, and only S8 is present in significant concentrations at all T. The T dependence of the density and the dependence of polymerization fraction and degree on ΔEb give estimates of the polymerization temperature Tf=450±20 K.