Percolation of Trace Amounts of Linear Polymers in Melts of Cyclic Polymers

Melts of CPs, intentionally contaminated with small fractions of LPs, are studied using the bond fluctuation model to probe the extreme sensitivity of the rheology to trace amounts of linear chains. Using primitive path analysis to compute the number of entanglements on the molecules, the threshold concentration at which LPs percolate through the system is calculated using a mean-field theory. It is found that the percolation threshold decreases with the molecular weight, and is approximately 25-30 times smaller than the overlap concentration of the linear chains for the longest polymers studied. These simulations help to understand and justify the approximations made in earlier theoretical investigations.