Measuring packing length in simulations for different polymer architectures*

The packing length p is the range over which the density near a given monomer is dominated by monomers from the same chain. Bulky, flexible polymers have larger p while thin, stiff polymers have smaller p. The packing length figures prominently in scaling predictions of the entanglement length and bulk modulus for polymer melts and solutions. p has been argued to scale as the ratio V/R^2 of chain displaced volume V and mean-square end-to-end distance R^2. This scaling works for several cases, but it is not obvious how to apply it to chains with side groups, in particular how to estimate the diameter of such a chain.
In this work, we measure the packing length, as the typical distance of closest approach of two polymer strands in a simulated bead-spring melt. We use the intermolecular correlation function to measure the distance up to which a given polymer strand dominates the volume fraction. We compare this measured packing length to our recent measurements of the entanglement length in simulations. Using our measured packing length, we find good agreement of entanglement properties with the Lin-Noolandi ansatz for flexible polymers of different architectures, which we explore by varying chain stiffness and sidegroup lengths.