Interaction between two parallel plates covered with a polyelectrolyte brush layer in an electrolyte solution

An approximate analytic expression is derived for the interaction energy between two parallel plates covered with a polyelectrolyte brush layer in an electrolyte solution. The interaction energy has three components: electrostatic interaction energy between two brush layers before and after their contact, steric interaction energy between two brush layers after their contact, and the van der Waals interaction energy between the cores of the plates. It is shown that these three components are of the same order of magnitude and contribute equally to the total interaction energy between two polyelectrolyte-coated plates in an electrolyte solution. On the basis of Derjaguin's approximation, an approximate expression for the interaction energy between two spherical particles covered with polyelectrolyte brush layers is also derived.