  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.
