RESUMO
We consider planar brushes formed by end-grafted polymers with moderate to strong excluded-volume interactions. We first rederive the mean-field theory and solve the resulting self-consistent equations numerically. In the continuum limit, the results depend sensitively on a single parameter, beta, whose square is the ratio of the scaling prediction for the brush height to the unperturbed polymer radius of gyration, and which measures therefore the degree to which the polymers are stretched. For large values of beta, the density profile is close to parabolic, as predicted by the infinite-stretching theory of Zhulina et al. and of Milner et al. As beta decreases, the profile deviates strongly from a parabolic one. By calculating the most probable paths and comparing their contribution to various properties with those obtained from the full self-consistent theory, we determine the effect of the fluctuations about such paths. At large values of beta, these effects are very small everywhere. As beta decreases, fluctuation effects on the density profile become increasingly important near the grafting surface, but remain small far from it. For all values of beta, we find that polymer paths which begin far from the grafting surface are strongly, and almost uniformly, stretched throughout their length, including their free end points. Paths which begin close to the grafting surface are also stretched, but they initially move away from the grafting surface before reaching a maximum height and then returning to it. The classical theory is then derived from the self-consistent field equations by retaining, for each end point location, only that single trajectory which minimizes the free energy of the system. This free energy contains an entropy, of relative weight beta-1, which arises from the distribution of end points. Even for brushes which are only moderately stretched, the results of the classical theory for the brush profile and polymer end point distribution agree well with those of the full self-consistent theory except near the grafting surface itself. There the density profile as calculated in the self-consistent theory shows a characteristic decrease which is not captured by the classical theory. However it does capture the fact that the individual polymer paths are stretched in general throughout their length, including the end points, and yields nonmonotonic paths for polymers whose end points are close to the grafting surface. In addition, it reproduces extremely well the form of the density distribution far from the grafting surface, which is essentially Gaussian. This results from the fact that the stretching energy dominates the interaction energy of those polymers which extend far from the grafting surface, so that their behavior is nearly ideal. In the limit of infinite stretching, beta --> infinity, the theory reduces to that of Zhulina et al. and of Milner et al.
RESUMO
We study theoretically the interaction of a polyampholyte chain with charged planes, cylinders, and spheres. Due to the random character of the charge distribution along the chain, a polyampholyte possesses a spontaneous dipole moment, which can interact favorably with charged objects. Depending on the charge strength of the object and the polyampholyte length and fraction of charged monomers, this attractive interaction can be strong enough to induce adsorption. The addition of salt weakens the trend to adsorption, but proves necessary to adsorb polyampholytes of the same net charge as the charged object in the case of planes and cylinders. Long polyampholytes form globules, for which the number of uncompensated charges and thus the spontaneous dipole moment is reduced. Nevertheless, globules can adsorb on charged objects via two pathways: they either adsorb as a whole, (intact globule), or they are dissolved into a coil state prior to adsorption. Applications to the complexation behavior of polyampholytes with stiff, rodlike polyelectrolytes and with charged microspheres or charged spherical micelles are given.
