End to end loop formation in a single polymer chain with internal friction

We use Rouse and Zimm models with solvent viscosity independent internal friction to study the end to end loop formation of a single polymer chain within the Wilemski–Fixmann theoretical framework. Our calculation shows internal friction makes loop formation between two ends of a polymer chain slower but has a weaker dependence on the chain length as compared to no internal friction. The average looping time shows not linear but fractional dependence on the solvent viscosity. Also the effect of the internal friction to the looping time is neither additive nor multiplicative but always additive to the reconfiguration time. Our numerical results show internal friction can reduce the looping rate by a factor of two to an order of magnitude depending on the time scale associated with it.