Universality of the collapse transition of sticky polymers

The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the $\theta$ state, independent of polymer-solvent chemistry, in the crossover regime between $\theta$ and athermal solvent conditions, is well known. Here we study, by Brownian dynamics, a polymer model where a subset of monomers is labelled as "stickers". The mutual interaction of the stickers is more attractive than those of the other ("backbone") monomers, and has the additional important characteristic of "functionality" $\varphi$, i.e., the maximum number of stickers that can locally bind to a given sticker. A saturated bond formed in this manner remains bound until it breaks due to thermal fluctuations, a requirement which can be viewed as an additional Boolean degree of freedom that describes the bonding. This, in turn, makes the question of the order of the collapse transition a non-trivial one. Nevertheless, for the parameters that we have studied (in particular, $\varphi=1$), we find a standard second-order $\theta$ collapse, using a renormalised solvent quality parameter that takes into account the increased average attraction due to the presence of stickers. We examine the swelling of the radius of gyration of such a sticky polymer relative to its value in the altered $\theta$ state, using a novel potential to model the various excluded volume interactions that occur between the monomers on the chain. We find that the swelling of such sticky polymers is identical to the universal swelling of homopolymers in the thermal crossover regime. Additionally, for our model, the Kuhn segment length under $\theta$ conditions is found to be the same for chains with and without stickers.Comment: 13 pages, 10 figures, supplementary material (see ancillary directory), to appear in Soft Matte

Universal scaling and characterisation of gelation in associative polymer solutions

A Brownian dynamics algorithm is used to describe the static behaviour of associative polymer solutions. Predictions for the fractions of stickers bound by intra-chain and inter-chain association, as a function of system parameters, such as the number of stickers, the number of monomers between stickers, the solvent quality, and concentration are obtained. A systematic comparison with the scaling relations predicted by the mean-field theory of Dobrynin (Macromolecules, 37, 3881, 2004) is carried out. Different regimes of scaling behaviour are identified depending on the monomer concentration, the density of stickers on a chain, and the solvent quality for backbone monomers. 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 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 characterisation of gelation are identified, with each leading to a different value of the concentration at the sol-gel transition. The modified Flory-Stockmayer expression 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 theta-solvent conditions, and is shown to coincide with a breakdown in the predictions of scaling theory.Comment: 34 pages, 22 figures, includes Supplemental Material, accepted versio