Simulating Thermodynamics and Kinetics of Living Polymerization
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The generalized Langevin equation (GLE) has been used to describe the dynamics of particles in a stationary environment. To better understand the dynamics of polymerization, the GLE has been generalized to the irreversible generalized Langevin equation (iGLE) so as to incorporate the non-stationary response of the solvent. This non-stationary response is manifested in the friction kernel and the behavior of the projected (stochastic) force. A particular polymerizing system, such as living polymerization, is specified both through the parameters of the friction kernel and the potential of mean force (PMF). Equilibrium properties such as extent of polymerization have been obtained and are consistent with Flory-Huggin¡¯s theory. In addition, time-dependent non-equilibrium observables such as polymer length, the polymer length distribution, and polydispersity index (PDI) of living polymerization have been obtained. These have been compared to several experiments so as to validate the models, and to provide additional insight into the thermodynamic and kinetic properties of these systems. In addition to the iGLE, a stochastic model has been used to study the effect of nonequilibrium reactivity on living polymerization. This model can be used to determine whether the reaction is controlled by kinetics or diffusion. A combination of the iGLE and stochastic models may help us obtain more information about living polymerization.