Conformations of weakly charged quenched polyelectrolyte chains tethered to a similarly charged planar surface are analyzed on the basis of a combination of scaling, analytical, and numerical self-consistent field (SCF) approaches. Scaling theory predicts universal power law dependences of the large-scale conformational properties (like the end-to-end distance) of grafted chains on the overall surface charge per unit area. The SCF approach allows analysis of the detailed conformational structure of grafted polyions as a function of the distribution of immobilized charges between the surface and grafted chains. The analytical solution is only available in the limiting cases of sparse grafting of polyions to the charged plane and sufficiently dense grafting of polyions to a neutral surface. In the intermediate case when both interchain interactions and interaction of grafted chains with the surface are important, only numerical solutions can be obtained. We consider various ways to distribute the charges between the surface and the brush chains while keeping the sum of the two contributions constant. Upon increasing the charge on the surface, by concomitant reduction of the grafting density of the tethered chains we found: (i) an increase in height of the polymer layer; (ii) the development of a depletion zone of end points near the surface; and (iii) a sharpening of the end-point distribution with the peak shifting away from the surface. In the appropriate limiting cases excellent agreement of analytical SCF predictions is obtained with the numerical results
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