A two-dimensional polymer growth model

Abstract

A polymer growth Hamiltonian with an accompanying novel lattice has been constructed to model reaction dynamics of polydisperse polymer systems that have kinetics affected by an environment which is altered over time by the polymerization process itself. Monte Carlo dynamics are used to simulate the polymerization process with bond breaking/formation moves analogous to a correlated percolation model. Lattice events thus occur on the time scale of reactivity rather than the much shorter time scales of either monomer motion or conformational dynamics, though an effort is made to include the latter as well. The equilibrium behavior of the system has been well mapped out and is complex enough to model a variety of real polymer systems such as solid state polymerization, living polymers and thermosetting polymers. Detailed equilibrium structural information such as molecular weight distributions and extent of cross polymerization have been obtained. Pseudodynamic information such as the time-dependence in the polymer weight distribution and more detailed quantities may also be obtained with respect to Monte Carlo time scales.

Wormlike Micelles as Templates for Rod-Shaped Nanoparticles: Experiments and Simulations

“…Due to their transient nature, they exhibit novel static and dynamic properties on time scales both long and short compared to their finite lifetime. Theoretical treatments of wormlike micelles include grand canonical Monte Carlo simulations on 2D and 3D lattices in which the breaking and reformation of micelles is implemented via individual monomer states [23] or by polymer growth Hamiltonian [24,25] or by defining probabilities of bond breaking and forming and slithering snake dynamics with or without inclusions of chain stiffness in the models [23,[26][27][28][29][30][31][32][33].…”

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

“…16 Lattice models 17 beyond MF have been studied, 18,19 and there are recent studies incorporating temperature effects. 20,21 Nevertheless, MF ap-proaches, with some use of Monte Carlo ͑MC͒ to incorporate geometrical factors, are widely used to investigate branching and gelation in long-chain polymers, 22 and similar methods have been used to study related highly cross-linked systems. 23 The absence of potential energy models in most studies rules out discussions of temperature effects and thermal equilibration, and this work is among the first to include branching in the simulation of equilibrium polymerization based on a continuum model of particle interactions.…”