Tracer dynamics in polymer networks: Generalized Langevin description

Tracer diffusion in polymer networks and hydrogels is relevant in biology and technology, while it also constitutes an interesting model process for the dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we systematically study the time-dependent dynamics and (non-Markovian) memory effects of tracers in polymer networks based on (Markovian) implicit-solvent Langevin simulations. In particular, we consider spherical tracer solutes at high dilution in regular, tetrafunctional bead-spring polymer networks and control the tracer-network Lennard-Jones (LJ) interactions and the polymer density. Based on the analysis of the memory (friction) kernels, we recover the expected long-time transport coefficients and demonstrate how the short-time tracer dynamics, polymer fluctuations, and the viscoelastic response are interlinked. Furthermore, we fit the characteristic memory modes of the tracers with damped harmonic oscillations and identify LJ contributions, bond vibrations, and slow network relaxations. Tuned by the LJ interaction parameter, these modes enter the kernel with an approximately linear to quadratic scaling, which we incorporate into a reduced functional form for convenient tracer memory interpolation and extrapolation. This eventually leads to highly efficient simulations utilizing the generalized Langevin equation, in which the polymer network acts as an additional thermal bath with a tunable intensity.