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 450less than or equal toTless than or equal to850 K and P=0 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 DeltaE(b) required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15less than or equal toDeltaE(b)less than or equal to21 kcal/mol over a wide temperature range (Tgreater than or equal to450 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 DeltaE(b). This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for Tless than or equal toT(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 DeltaE(b) give estimates of the polymerization temperature T-f=450+/-20 K. (C) 2003 American Institute of Physics.

Equilibrium polymerization of cyclic carbonate oligomers. III. Chain branching and the gel transition

Ring-opening polymerization of cyclic polycarbonate oligomers, where monofunctional active sites act on difunctional monomers to produce an equilibrium distribution of rings and chains, leads to a "living polymer." Monte Carlo simulations [two-dimensional (2D) and three-dimensional (3D)] of the effects of single [J. Chem. Phys. 115, 3895 (2001)] and multiple active sites [J. Chem. Phys. 116, 7724 (2002)] are extended here to trifunctional active sites that lead to branching. Low concentrations of trifunctional particles c(3) reduce the degree of polymerization significantly in 2D, and higher concentrations (up to 32%) lead to further large changes in the phase diagram. Gel formation is observed at high total density and sizable c(3) as a continuous transition similar to percolation. Polymer and gel are much more stable in 3D than in 2D, and both the total density and the value of c(3) required to produce high molecular weight aggregates are reduced significantly. The degree of polymerization in high-density 3D systems is increased by the addition of trifunctional monomers and reduced slightly at low densities and low c(3). The presence of branching makes equilibrium states more sensitive (in 2D and 3D) to changes in temperature T. The stabilities of polymer and gel are enhanced by increasing T, and-for sufficiently high values of c(3)-there is a reversible polymer-gel transformation at a density-dependent floor temperature. (C) 2002 American Institute of Physics.

Equilibrium structure of erbium-oxygen complexes in crystalline silicon

The equilibrium structure of ErOn (nless than or equal to6) complexes in crystalline silicon has been investigated by density-functional computations. Two different geometries have been considered, corresponding to the substitutional and tetrahedral interstitial site for erbium. All atomic coordinates have been optimized by Car-Parrinello molecular dynamics. The resulting structures have low symmetry, with E-O distances of similar to2.35 Angstrom. The substitutional site is the most stable one for nless than or equal to2, while the tetrahedral interstitial is favored for n>2.

Equilibrium polymerization of cyclic carbonate oligomers. II. Role of multiple active sites

Ring opening polymerization of bisphenol A polycarbonate is studied by Monte Carlo simulations of a model comprising a fixed number of Lennard-Jones particles and harmonic bonds [J. Chem. Phys. 115, 3895 (2001)]. Bond interchanges produced by a low concentration (0.10%less than or equal toc(a)less than or equal to0.36%) of chemically active particles lead to equilibrium polymerization. There is a continuous transition in both 2D and 3D from unpolymerized cyclic oligomers at low density to a system of linear chains at high density, and the polymeric phase is much more stable in three dimensions than in two. The steepness of the polymerization transition increases rapidly as c(a) decreases, suggesting that it is discontinuous in the limit c(a)-->0. The transition is entropy driven, since the average potential energy increases systematically upon polymerization, and there is a steady decline in the degree of polymerization as the temperature is lowered. The mass distribution functions for open chains and for rings are unimodal, with exponentially decaying tails that can be fitted by Zimm-Schulz functions and simpler exponential forms. (C) 2002 American Institute of Physics.

Equilibrium polymerization of cyclic carbonate oligomers

A model of the polymerization of ring oligomers of bisphenol A polycarbonate (BPA-PC) is used to investigate the influence of dimensionality (2D or 3D), density and temperature on the size distribution of the polymer chains. The polymerization step is catalyzed by a single active particle, conserves the number and type of the chemical bonds, and occurs without a significant gain in either potential energy or configurational entropy. Monte Carlo and molecular dynamics simulations show that polymerization of cyclic oligomers occurs readily at high density and is driven by the entropy associated with the distribution of interparticle bonds. Polymerization competes at lower densities with long range diffusion, which favors small molecular species, and is prevented if the system is sufficiently dilute. Polymerization occurs in 2D via a weakly first order transition as a function of density and is characterized by low hysteresis and large fluctuations in the size of polymer chains. Polymerization occurs more readily in 3D than in 2D, and is favored by increasing temperature, as expected for an entropy-driven process. (C) 2001 American Institute of Physics.

Competitive adsorption of reactive dyes from solution: equilibrium isotherm studies in single and multisolute systems

Experimental data of the adsorption of reactive dyestuffs onto Filtrasorb 400 activated carbon (FS400) were determined in an equilibrium isotherm study. As most industrial wastewater contains more than one pollutant, an investigation into the effect of multisolute systems (using the unhydrolysed form of the reactive dyes) on the adsorption capacity was undertaken. Equilibrium isotherm models were employed to describe the adsorption capacities of single, binary and ternary dye solutions. The results of these analyses showed that adsorption of reactive dyes from single and multisolute systems can be successfully described by Langmuir, and Redlich–Peterson equilibrium isotherm models. Experimental data indicated that competitive adsorption for active sites on the carbon surface results in a reduction in the overall uptake capacity of the reactive dyes investigated.

Neutral and Charged 1-Butyl-3-methylimidazolium Triflate Clusters: Equilibrium Concentration in the Vapor Phase and Thermal Properties of Nanometric Droplets

Ground state energy, structure, and harmonic vibrational modes of 1-butyl-3-methylimidazolium triflate ([bmim][Tf]) clusters have been computed using an all-atom empirical potential model. Neutral and charged species have been considered up to a size (30 [bmim][Tf] pairs) well into the nanometric range. Free energy computations and thermodynamic modeling have been used to predict the equilibrium composition of the vapor phase as a function of temperature and density. The results point to a nonnegligible concentration of very small charged species at pressures (P ~ 0.01 Pa) and temperatures (T 600 K) at the boundary of the stability range of [bmim][Tf]. Thermal properties of nanometric neutral droplets have been investigated in the 0 T 700 K range. A near-continuous transition between a liquidlike phase at high T and a solidlike phase at low T takes place at T ~ 190 K in close correspondence with the bulk glass point Tg ~ 200 K. Solidification is accompanied by a transition in the dielectric properties of the droplet, giving rise to a small permanent dipole embedded into the solid cluster. The simulation results highlight the molecular precursors of several macroscopic properties and phenomena and point to the close competition of Coulomb and dispersion forces as their common origin.

Adsorption of Zn(ii), Pb(ii), and Co(ii) using natural sorbents: equilibrium and kinetic studies.

Water Research, 40 14 (2006) 2645.

Adsorption of methylene blue onto activated carbon produced from steam activated bituminous coal: A study of equilibrium adsorption isotherm.

Chemical Engineering Journal, 124 (2006) 103.