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The Aggregation Kinetics of a Simulated Telechelic Polymer

We investigate the aggregation kinetics of a simulated telechelic polymer gel. In the hybrid Molecular Dynamics (MD) / Monte Carlo (MC) algorithm, aggregates of associating end groups form and break according to MC rules, while the position of the polymers in space is dictated by MD. As a result, the aggregate sizes change every time step. In order to describe this aggregation process, we employ master equations. They define changes in the number of aggregates of a certain size in terms of reaction rates. These reaction rates indicate the likelihood that two aggregates combine to form a large one, or that a large aggregate splits into two smaller parts. The reaction rates are obtained from the simulations for a range of temperatures. Our results indicate that the rates are not only temperature dependent, but also a function of the sizes of the aggregates involved in the reaction. Using the measured rates, solutions to the master equations are shown to be stable and in agreement with the aggregate size distribution, as obtained directly from simulation data. Furthermore, we show how temperature induced variations in these rates give rise to the observed changes in the aggregate distribution that characterizes the sol-gel transition.