Universal scaling and characterization of gelation in associative polymer solutions

A multiparticle Brownian dynamics simulation algorithm with a Soddemann-Dünweg-Kremer potential that accounts for pairwise excluded volume interactions between both backbone monomers and associating groups (stickers) on a chain is used to describe the static behavior of associative polymer solutions, across a range of concentrations into the semidilute unentangled regime. Predictions for the fractions of stickers bound by intrachain and interchain associations, as a function of system parameters such as the number of stickers on a chain, the number of backbone monomers between stickers, the solvent quality, and monomer concentration, are obtained. A systematic comparison between simulation results and scaling relations predicted by the mean-field theory of Dobrynin [Macromolecules 37, 3881-3893 (2004)] is carried out. Different regimes of scaling behavior are identified by the theory depending on the monomer concentration, the density of stickers on a chain, and whether the solvent quality for the backbone monomers corresponds to θ or good solvent conditions. Simulation results validate the predictions of the mean-field theory across a wide range of parameter values in all the scaling regimes. The value of the des Cloizeaux exponent, θ 2 = 1 / 3, proposed by Dobrynin for sticky polymer solutions, is shown to lead to a collapse of simulation data for all the scaling relations considered here. Three different signatures for the characterization of gelation are identified, with each leading to a different value of the concentration at the solgel transition. The Flory-Stockmayer expression relating the degree of interchain conversion at the solgel transition to the number of stickers on a chain, modified by Dobrynin to account for the presence of intrachain associations, is found to be validated by simulations for all three gelation signatures. Simulation results confirm the prediction of scaling theory for the gelation line that separates sol and gel phases, when the modified Flory-Stockmayer expression is used. Phase separation is found to occur with increasing concentration for systems in which the backbone monomers are under θ-solvent conditions and is shown to coincide with a breakdown in the predictions of scaling theory.