Interaction between Brush Layers of Bottle-Brush Polyelectrolytes: Molecular Dynamics Simulations

Interactions between tethered layers composed of aggrecan (charged bottle-brush) macromolecules are responsible for the molecular origin of the cartilage biomechanical behavior. To elucidate the role of the electrostatic forces in interaction between bottle-brush layers we have performed molecular dynamics simulations of charged and neutral bottle-brush macromolecules tethered to substrates. In the case of charged bottle-brush layers the disjoining pressure $P$ between two brush layers in salt-free solutions increases with decreasing the distance $D$ between substrates as $P\propto D^{-1.8}$. A stronger dependence of the disjoining pressure $P$ on the surface separation $D$ was observed for neutral bottle-brushes,$ P\propto D^{-4.6}$, in the same interval of the disjoining pressures. These scaling laws for dependence of the disjoining pressure $P$ on the distance $D$ are due to bending energy of the bottle-brush macromolecules within compressed brush layers. The weaker distance dependence observed in polyelectrolyte bottle-brushes is due to interaction between counterion clouds surrounding the bottle-brush macromolecules preventing strong brush overlap.