Adsorption of Polyelectrolytes at an Oppositely Charged Surface

TitleAdsorption of Polyelectrolytes at an Oppositely Charged Surface
Publication TypeJournal Article
Year of Publication2000
AuthorsAV Dobrynin, A Deshkovski, and M Rubinstein
Date Published01/2000

We develop a scaling theory of polyelectrolyte adsorption at an oppositely charged surface. At low surface charge densities, the thickness of the adsorbed layer is determined by the balance between electrostatic attraction to the charged surface and chain entropy. At high surface charge densities, it is determined by the balance between electrostatic attraction and short-range monomer-monomer repulsion. These different stabilizing mechanisms result in the nonmonotonic dependence of the layer thickness on the surface charge density. PACS numbers: 61.20.Qg, 61.25.Hq Macromolecules carrying electric charges, called poly-electrolytes [1,2], constitute one of the most interesting and least understood areas of polymer physics. Charged poly-mers are widely used in industry and are present in nature. The long-range Coulomb interactions are responsible for both the rich behavior of these systems and the difficulties in developing theory to describe them. While a coherent picture of polyelectrolyte solutions is beginning to emerge [3–6], the behavior of polyelectrolytes near charged surfaces and interfaces is far from being understood [7]. The progress in this direction will have a significant im-pact on different areas ranging from materials science to biophysics. The significant fraction of theoretical works dealing with polyelectrolyte adsorption on a charged surface has been carried out within the framework of the self-consistent field method [7]. In these theories the polymer density distribution is coupled with the local electrostatic potential through the combination of the Poisson-Boltzmann equa-tion and the diffusive equation describing the polymer conformations in the effective external potential. It was argued recently [8] that the Poisson-Boltzmann description of the electrostatic interactions is inapplicable to a system containing multivalent ions, the best examples of which are polyelectrolyte molecules. The major drawback of this approach is that it fails to capture the correlations between multivalent ions. These correlation effects can become so strong that the multivalent ions form a strongly correlated Wigner liquid [8,9]; the structure is impossible to obtain within the framework of the classical Poisson-Boltzmann approach. Thus, the newly emerging picture of electro-static interactions in multivalent systems requires reinves-tigation of polyelectrolyte adsorption. In this Letter we develop a scaling theory of polyelectrolyte adsorption at an oppositely charged surface from a dilute salt-free solution. In our model we used new ideas of the strong correlations in polyelectrolyte systems at low polymer concentrations and a related description at higher polymer concentrations in the adsorbed layer. Consider a flexible polyelectrolyte chain with degree of polymerization N, fraction of charged monomers f, and bond length a in a solvent with Bjerrum length l B ෇ e