We compute the phase diagram of salt-free polyelectrolyte solutions using a modified Debye-Huckel Approach. We introduce the chain connectivity via the Random Phase Approximation with two important modifications. We modify the electrostatic potential at short distances to include a bound on the electrostatic attractions at the distance of closest approach between charges. This modification is shown to act as a hard core in the phase diagram of electrolyte solutions. We also introduce a cut-off on the integration of the modes of wave length smaller than the size over which the chains are strongly perturbed by the electrostatic interactions. This cut-off is shown to be essential to predict physical phase diagram in long chain solutions

We analyze solutions of strongly charged chains bridged by linkers such as multivalent ions. The gelation induced by the strong short range electrostatic attractions is dramatically suppressed by the long range electrostatic correlations due to the charge along the non-cross-linked monomers and ions. A modified Debye-Hückel approach of cross-linked clusters of charged chains is used to determine the mean field gelation transition self-consistently. Highly dilute polyelectrolyte solutions tend to segregate macroscopically. Semidilute solutions can form gels if the Bjerrum length l(B) and the distance between neighboring charged monomers along the chain b are both greater than the ion size a.

The sol-gel transition (SGT), upon which the infinite cluster (IC) of thermoreversibly bonded particles (gel fraction) appears against a background of a set of finite clusters (sol fraction), is first quantitatively considered with due regard for large and complicated (mesoscopic) cycles inevitably present in the IC. To this end we present a new approach based on a concept of the monomer identity breaking and density functional description. We strictly derive, via a proper choice of basic structural units of the gel fraction, all statements usually supposed to be just Flory (Stockmayer) assumptions. A further analysis of the IC structure reveals some new IC structural units (those involved into mesoscopic cycles) overlooked in both Flory and Stockmayer approaches and to be described by a new order parameter characteristic only of the gel phase. As a result, the SGT is found to transform from a geometric phenomenon to a genuine 1st order phase transition always followed by a phase separation into sol and gel phases. The free energy, total conversion, volume fractions of the gel fraction and dangling monomers as well as other structural quantities are calculated as functions of a reduced monomer density and analyzed for all the existing models. The Flory approach is found to be superior to the Stockmayer-Tanaka one and satisfactorily describe some of the dense weak gel properties but fail (even qualitatively) in a quite extended vicinity of the SGT.

Thermoreversible crosslinking of polyelectrolyte chains via short-range attractions such as hydrogen bonding induced by uncharged or charged particles is studied within the Flory model of ideal association. Electrostatic interactions between the charges at different linking fractions are taken into account by using a generalized random phase approximation approach which includes the network connectivity. We find that at certain concentration of linking agents an infinitely large polymer network is formed. We calculate the structural gelation lines for linkers of different charges and functionalities.

An advanced theoretical model for the structure of the interface between two immiscible homopolymers is presented. The theory is based on a combination of the Flory−Huggins model and the square-gradient approach. We first analyze the effect of molecular weights of the components on the interfacial tension in the limit of high molecular weight (χN ≫ 1). A general approximate expression for the interfacial free energy of the system is derived, the expression being valid for both limits of narrow and broad interfaces. The interfacial tension for a system of two immiscible homopolymers is calculated as a function of the homopolymer molecular weights and the Flory χ-parameter. The results are compared with the predictions of other theories and also with experimental data.