Interaction between polymer-grafted particles

Previous self-consistent field theory (SCFT) calculations have predicted that the steric interaction between two polymer-grafted particles in good solvent can become attractive, but this conclusion has since been questioned. Here we reexamine the problem with a new numerical scheme using multiple coordinate systems, and find that the interaction remains repulsive regardless of the particle size, brush thickness, or particle separation. The erroneous attraction in the earlier calculations can be attributed to numerical inaccuracy and a subtle issue with how the chains were grafted to the particles. Using our corrected SCFT solution, we also investigate the accuracy of a previous calculation based on strong-stretching theory (SST) and the applicability of the Derjaguin approximation, where the interaction between large particles is estimated from the one-dimensional uniform compression of polymer brushes.