Measuring the packing length in polymer simulations

Predicting the entanglement length in melts and solutions from single-chain properties has been a longstanding challenge in polymer physics. It has been understood for some time that bulky, flexible chains entangle differently than skinny, stiff chains. For bulky flexible chains, other chain segments are prevented from approaching more closely than the packing length, and entanglement properties are described by Lin-Noolandi scaling. For skinny stiff chains, other segments can approach within a chain diameter, and entanglement is described by Morse scaling. Recent progress has unified these regimes, and focused attention on measuring the packing length, defined by the typical distance of close approaches, rather than by a scaling estimate of limited applicability. By measuring entanglement properties and the packing length for a family of bead-spring chains of different bulkiness and flexibility, we observe Lin-Noolandi scaling where it should be valid. More recently, we have applied the technique of measuring the packing length to all-atom simulations of real polymer melts, and compared our values to those inferred from experimental data and Lin-Noolandi scaling, with promising results.