Normal force and interpenetration between polyelectrolyte brushes

We examine the normal force between two opposing polyelectrolyte brushes and the interpenetration of their chains that is responsible for sliding friction. We focus on the special case of semi-dilute brushes in a theta solvent, for which the classical strong-stretching theory (SST) can be solved analytically. Interestingly, SST predicts that the brushes contract as they are compressed together maintaining a polymer-free gap, which provides an explanation for the ultra-low frictional forces observed in experiment. We examine the degree to which the SST predictions are affected by chain fluctuations by employing self-consistent field theory (SCFT). While the normal force is relatively unaffected, fluctuations are found to have a strong impact on brush interpenetration. Even still, the contraction of the brushes does significantly prolong the onset of interpenetration, implying that a sizeable normal force can be achieved before the sliding friction becomes significant.