The author investigates the equilibrium behaviour of charged polymers of finite length in a Debye-screened potential between two parallel charged walls. For the polymer he takes the continuum approximation to calculate the spectrum of eigenfunctions for the partition function. For finite but long polymers only the lowest two terms in this expansion contribute to first order to the configurational sum, corresponding to a symmetrical and an antisymmetrical solution. Within this formalism he calculates the monomer density distribution for finite strands of polymer attached to one or both surfaces (tails, loops and bridges) as well as for polymers free in solution. For the free polymer he also finds the free energy as a function of the distance between the plates for several values of the interaction parameters, as well as the effective interaction between the plates due to the polyions. This shows that there can exist an equilibrium separation distance between colloidal particles due to the interactions with charged polymers in solution. This mechanism may also explain the formation of rouleaux for red blood cells.
van Opheusden, J. H. J. (1988). Polyelectrolytes between two membranes or colloidal particles. Journal of physics A: mathematical and general, 21(12), 2739-2751. https://doi.org/10.1088/0305-4470/21/12/017