Growth of equilibrium polymers under non-equilibrium conditions

We investigate the kinetics of self-assembly by means of Brownian dynamics simulation based on a idealized fluid model ( two 'sticky' spots on a sphere) in which the particles are known to form into dynamic polymer chains at equilibrium. To illustrate the slow evolution of the properties of these self-assembling fluids to their equilibrium assembled state values at long times, we perform Brownian dynamics simulations over a range of quench depths from the high temperature unassembled state to the low temperature assembled state. We investigate the time dependence of the average chain length ( cluster mass), the order parameter for the assembly transition ( fraction of particles in the chain state) and the potential energy of the fluid. The rate constant governing the self-assembly ordering process depends both on kinetic-related factors ( the particle hydrodynamic radius and the fluid viscosity) and on thermodynamic energetic variables governing the self-assembly transition (i.e., the entropy and enthalpy of assembly). We provide evidence that an essentially parameter-free description of the polymerization kinetics can be formulated for this model.