Scaling Laws of Polyelectrolyte Adsorption

TL;DR

This paper develops simple scaling laws describing how charged polymers adsorb onto surfaces, depending on their charge fraction and salt concentration, with results validated by experiments and numerical solutions.

Contribution

It introduces new scaling laws for polyelectrolyte adsorption parameters as functions of charge fraction and salt concentration, extending understanding of adsorption behavior.

Findings

Gamma and D scale as p^{-1/2} for strongly charged polyelectrolytes in low salt.

D scales as c_b^{1/2}/p in salt-rich solutions.

Gamma scales as p/c_b^{1/2} for weak and c_b^{1/2}/p for strong polyelectrolytes.

Abstract

Adsorption of charged polymers (polyelectrolytes) from a semi-dilute solution to a charged surface is investigated theoretically. We obtain simple scaling laws for (i) the amount of polymer adsorbed to the surface, Gamma, and (ii) the width of the adsorbed layer D, as function of the fractional charge per monomer p and the salt concentration c_b. For strongly charged polyelectrolytes (p<1) in a low-salt solution, both Gamma and D scale as p^{-1/2}. In salt-rich solutions D~c_b^{1/2}/p whereas the scaling behavior of Gamma depends on the strength of the polymer charge. For weak polyelectrolytes (p<<1) we find that Gamma~p/c_b^{1/2} while for strong polyelectrolytes Gamma~c_b^{1/2}/p. Our results are in good agreement with adsorption experiments and with numerical solutions of mean-field equations.