  The selective solute partitioning within a polymeric network is of key
importance to applications in which controlled release or uptake of solutes in
a responsive hydrogel is required. In this work we investigate the impact of
cross-links on solute adsorption in a swollen polymer network by means of
all-atom, explicit-water molecular dynamics simulations. We focus on a
representative network subunit consisting of poly($N$-isopropylacrylamide)
(PNIPAM) and $N$,$N'$-methylenebisacrylamide (BIS/MBA) cross-linker types. Our
studied system consists of one BIS-linker with four atactic PNIPAM chains
attached in a tetrahedral geometry. The adsorption of several representative
solutes of different polarity in the low concentration limit at the linker
region is examined. We subdivide the solute adsorption regions and distinguish
between contributions stemming from polymer chains and cross-link parts. In
comparison to a single polymer chain, we observe that the adsorption of the
solutes to the cross-link region can significantly differ, with details
depending on the specific compounds' size and polarity. In particular, for
solutes that have already a relatively large affinity to PNIPAM chains the
dense cross-link region (where many-body attractions are at play) amplifies the
local adsorption by an order of magnitude. We also find that the cross-link
region can serve as a seed for the aggregation of mutually attractive solutes
at higher solute concentrations. Utilizing the microscopic adsorption
coefficients in a mean-field model of an idealized macroscopic polymer network,
we extrapolate these results to the global solute partitioning in a swollen
hydrogel and predict that these adsorption features may lead to non-monotonic
partition ratios as a function of the cross-link density.
