Srongly Charged Polymer Brushes

– Charged polymer brushes are layers of surface-tethered chains. Experimental systems are frequently strongly charged. Here we calculate phase diagrams for such brushes in terms of salt concentration ns, grafting density and polymer backbone charge density. Electrostatic stiffening and counterion condensation effects arise which are absent from weakly charged brushes. In various phases chains are locally or globally fully stretched and brush height H has unique scaling forms; at higher salt concentrations we find H ∼ n −1/3 s , in good agreement with experiment. Introduction. – Charged polymer layers are a major concern of polymer science, featuring in numerous applications such as colloid stabilization, surface modification technologies, membrane preparation [1] and emerging biotechnologies [2]. A much-studied class of layer is the polymer brush, an assembly of chains end-tethered to a substrate (see fig. 3). Charged brushes are important in biosensor technologies such as DNA microarrays [2] and have provided model systems to study collective physics of charged polymers at interfaces [3–9]. Properties such as brush height have been measured by the surface force apparatus, neutron scattering and other techniques [3–5]. The principal theoretical frameworks have been self consistent field theory and scaling theory [6]. Scaling theories identified distinct brush “phases” [7,8] and later a full “phase” diagram of brush types [9]. Most of this theoretical work has addressed weakly charged brushes where local Gaussian chain statistics are only weakly perturbed by electrical forces. Real polymers, however, are frequently strongly charged. The natural measure of this is the reduced backbone density (“Manning parameter”) q0 = lB/l where l is the (monovalent) charge spacing and the Bjerrum length lB = e /ǫwkT = 7 Å in water. Strongly charged polymers include single-stranded DNA (q0 ≈ 1.6 [10]) and the widely studied polystyrensulfonate, PSS (e.g. q0 ≈ 2.8 at 80% sulfonation [4]). When q0 is not small, two qualitatively new effects arise. (i) Strong repulsive forces may stretch chains beyond the linear Gaussian regime into rodlike configurations with end-to-end size of order the chain contour length itself: the polymer size saturates. (ii) Manning condensation [11]. When q0 > 1, a rodlike polymer attracts its own counterions so strongly that a fraction condenses into a region close to the polymer, renormalizing the