Interactions between nodes in a physical gel network of telechelic polymers; self-consistent field calculations beyond the cell model.

Triblock copolymers, with associative end-groups and a soluble middle block, form flower-like micelles in dilute solutions and a physical gel at higher concentrations. In a gel the middle blocks form bridges between domains/nodes that contain the ends. We combine the self-consistent field theory with a simple molecular model to evaluate the pair potential between the nodes. In this model the end-groups are forced to remain in nodes and the soluble middle blocks are in solution. When the distance between the centres of the nodes is approximately the corona diameter, loops can transform into bridges, and the pair potential is attractive. Due to steric hindrance, the interaction is repulsive at smaller distances. Till now a cell-model has been used wherein a central node interacts through reflecting boundary conditions with its images in a spherical geometry. This artificial approach to estimate pair potentials is here complemented by more realistic three-gradient SCF models. We consider the pair interactions for (i) two isolated nodes, (ii) nodes positioned on a line (iii) a central node surrounded by its neighbours in simple cubic ordering, and (iv) a central node in a face centred cubic configuration of its neighbours. Qualitatively, the cell model is in line with the more refined models, but quantitative differences are significant. We also notice qualitative differences for the pair potentials in the specified geometries, which we interpret as a breakdown of the pairwise additivity of the pair potential. This implies that for course grained Monte Carlo or molecular dynamics simulations the best choice for the pair potentials depends on the expected node density.