Poisson–Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes

Poisson–Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes

Ubbink, J.
Khokhlov, A.R.

Applied Sciences

Biotechnology

2004-03-15

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson–Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Ångstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson–Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)].

Boltzmann equation
Poisson equation
adsorption
adsorbed layers
polymer electrolytes
osmosis
chemical potential
free energy
finite element analysis

http://resolver.tudelft.nl/uuid:152afe33-fdec-457d-93f7-9a72ea69082e

https://doi.org/10.1063/1.1647048

American Institute of Physics

0021-9606

http://link.aip.org/link/JCPSA6/v120/i11/p5353/s1

Journal of Chemical Physics, 120 (11), 2004

Institutional Repository

journal article

(c) 2004 Ubbink, J.; Khokhlov, A.R.; American Institute of Physics