Nonlinear Polymer Diffusion with Interchange Reactions
Polymers in a solvent move by Brownian motion with a diffusion rate D(n) where n is the number of bonds in the polymer. By interchange reactions, polymers may exchange bonds (change length). Under the assumption that the polymer lengths are Flory distributed, we obtain a pair of coupled nonlinear diffusion equations in the particle density and average bond number. We introduce a simulation algorithm, borrowed from rarefied gas dynamics, which is useful for general polymer transport problems. Solutions of the nonlinear diffusion equations are found to be in good agreement with simulation results. An example is presented where the diffusion equations fail while the simulation yields the correct results.
Unable to display preview. Download preview PDF.