Measuring packing length in simulations for different polymer architectures

The packing length figures prominently in scaling predictions of the entanglement length and bulk modulus for polymer melts and solutions. has been argued to scale as the ratio of chain displaced volume V and mean square end-to-end distance. This scaling works for several cases; however, it is not obvious how to apply it to chains with side groups, and the scaling must fail for sufficiently thin, stiff chains. In this work, we measure the packing length in simulations, without making any scaling assumptions, 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 local volume fraction. Using our measured packing length, we find good agreement of entanglement properties with Lin-Noolandi scaling for flexible polymers of different architectures.