  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 study
systematically 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.
Further, we fit the characteristic memory modes of the tracers with damped
harmonic oscillations and identify LJ contributions, bond vibrations, and slow
network relaxations, which enter the kernel with an almost linear scaling with
the LJ attractions. This procedure proposes a reduced functional form for the
tracer memory, allowing for a convenient inter- and extrapolation of the memory
kernels. This leads eventually to highly efficient simulations utilizing the
generalized Langevin equation (GLE), in which the polymer network acts as an
additional thermal bath with tuneable intensity.
