Polyelectrolyte manifolds

We present the first scaling theory describing the equilibrium conformations of polyelectrolyte manifolds with arbitrary connectivity. Randomly branched polyelectrolytes and charged polymerized membranes are considered as particular cases. The most important result of the analysis is the dependence of the fractal dimension of charged manifolds on the mass of the clusters: the fractal dimension of large clusters is equal to their spectral dimension whereas for small clusters it appears to be smaller. This type of behaviour is related to the effect of charge renormalization and is unknown for ordinary neutral fractal objects. Thus the interplay between the counterions distribution and the connectivity is demonstrated.