Polydisperse Polymer Brushes Under Compression: Influence of the Polymers’ Persistence Length and of the Substrate’s Stiffness on the Force Required to Compress Them

Polymers of different length attached by one of their ends to a surface form polydisperse brushes. In this chapter we review some results obtained on a system made up of a brush composed of polymers of three lengths compressed by a flat surface with solvent particles, using numerical simulations. Two case studies are presented: in the first we explore the influence of increasing the stiffness of the surface on which the polymers are grafted on the force needed to compress them, while keeping the properties of the polymers fixed. In the second case study the stiffness of the surface is kept fixed while the persistence length of the polymers is increased. It is found that the surface stiffness propagates through the brush, undiminished by it, requiring a larger compression force for larger surface stiffness. By contrast, the effect of increasing the polymers’ persistence length has the opposite effect: increasing it leads to a smaller force required to compress the brush. It is concluded that changing the surface stiffness changes its Young’s modulusYoung’s modulus and that the brush acts as a nonelastic body through which stiffness propagates. Increasing the polymers’ persistence length makes them bundle and buckle, yielding ordering of the polymers, which in turn reduces their entropy. This increases the entropy of the solvent, which reduces the free energy, and the force, required to compress the brush. We argue that these results help explain atomic force microscopy experiments on cancerous cells and in the understanding of stimuli-responsive materialsStimuli-responsive materials.