We report experimental results and a theoretical analysis of the Debye length in aqueous solutions of nonadsorbing polyelectrolytes. The measurements were done using a surface forces apparatus, in which the normal forces between smooth mica surfaces in aqueous hyaluronic acid (HA) solutions were measured as a function of surface separation (to (1 Å). HA is negatively charged and does not adsorb to the negatively charged surface of mica, as was established by optical and viscosity measurements and in agreement with the measured force-distance curves. From these measurements it appears that the multivalent polyelectrolyte is "depleted" from the gap between the surfaces. We use the mean-field Poisson-Boltzmann theory to theoretically predict the effective Debye length and double-layer force under such conditions and compare the predictions with the experimental results. The comparison gives excellent agreement and shows that the effective Debye length is determined solely by the monovalent ions in the solution. Specifically, the effective Debye length κ eff -1 for the double-layer interaction is determined by an effective ionic concentration given by n s n c , where ns and nc are the bulk negative and positive monovalent ion concentrations, respectively.
We obtained mean-field expressions for the compression normal forces between two identical opposing quenched polyelectrolyte brushes in the presence of monovalent salt. The brush elasticity is modeled using the entropy of ideal Gaussian chains, while the entropy of the microions and the electrostatic contribution to the grand potential is obtained by solving the nonlinear Poisson–Boltzmann equation for the system in contact with a salt reservoir. The interplay between these distinct contributions upon variations of the ionic strength determines the brush thickness. For the polyelectrolyte brush we considered both an isotropic charged slab as well as a longitudinally heterogeneous charge profile obtained using a self-consistent field theory. Using the Derjaguin approximation, we related the planar-geometry results to the realistic two-crossed cylinders experimental setup. Theoretical predictions are compared to experimental measurements of the salt dependence of the compression normal forces between two quenched polyelectrolyte brushes formed by the adsorption of diblock copolymers poly(tert-butyl styrene)-sodium poly(styrene sulfonate) onto an octadecyltriethoxysilane hydrophobically modified mica surface.
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