Rayleigh instability of charged aggregates: Role of the dimensionality, ionic strength, and dielectric contrast

We extended a previous analysis of the classical Rayleigh instability of spherical charged droplets in the presence of neutralizing monovalent counterions [M. Deserno, Eur. Phys. J. E 6, 163 (2001)], by generalizing the problem for suspensions of aggregates with D-dimensional symmetry, corresponding for D = 2 to infinite (rodlike) cylindrical charged bundles and for D = 3 to spherical charged droplets. In addition, we include the effects of added monovalent salt and of dielectric contrast between the charged aggregate and the surrounding solvent. The electrostatic energy taking the microion screening into account is estimated using uniform profiles within the framework of the cell model. We verify the robustness of these results by also considering Debye-Hückel-type microion profiles that are obtained by the minimization of a linearized Poisson-Boltzmann free-energy functional. In the case when the microions can enter inside the charged aggregates, we confirm the occurrence of a discontinuous phase change between aggregates of finite size and an infinite aggregate, which takes place at a collapse temperature that depends on their volume fraction phi and on the salt content. Decrease of phi shifts the phase-change temperature toward higher values, while salt addition has an opposite effect. We obtain analytical expressions for the phase-separation line in the asymptotic limit of infinite dilution (phi-->0), showing that the collapse temperature depends logarithmically on phi . As an application for D = 3 we discuss the stability of the pearl-necklace structures of flexible polyelectrolytes in poor solvents. The case D = 2 is applied to the problem of finite bundle sizes of stiff polyelectrolytes that attract each other-via, e.g., multivalent counterions-leading to an effective surface tension.