  Simulating soft matter systems such as the cytoskeleton can enable deep
understanding of experimentally observed phenomena. One challenge of modeling
such systems is realistic description of the steric repulsion between nearby
polymers. Previous models of the polymeric excluded volume interaction have the
deficit of being non-analytic, being computationally expensive, or allowing
polymers to erroneously cross each other. A recent solution to these issues,
implemented in the MEDYAN simulation platform, uses analytical expressions
obtained from integrating an interaction kernel along the lengths of two
polymer segments to describe their repulsion. Here, we extend this model by
re-deriving it for lower-dimensional geometrical configurations, deriving
similar expressions using a steeper interaction kernel, comparing it to other
commonly used potentials, and showing how to parameterize these models. We also
generalize this new integrated style of potential by introducing a segmental
Lennard-Jones potential, which enables modelling both attractive and repulsive
interactions in semi-flexible polymer networks. These results can be further
generalized to facilitate the development of effective interaction potentials
for other finite elements in simulations of soft-matter systems.
