Universal scaling and characterization of gelation in associative polymer solutions

Abstract

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, θ2=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.

Influence of Network Topology on the Viscoelastic Properties of Double Dynamics Hydrogels

“…We attribute this reduction of effective crosslink density to a screening effect present in the IPN-derived single networks that is induced by the presence of the noncross-linked copolymer. 15 The presence of free (non-crosslinked) polymer chains could reduce the probability of the terpyridine groups to find a partner to create an interchain junction and/or could reduce the solvent quality 44 (because of the higher total polymer concentration), which would also favor intrachain bond formation by decreasing the random coil size of the copolymer. The influence of the surrounding chains is probably enhanced by the fact that the concentration of the cross-linked copolymer is low.…”

“…This large difference cannot be explained only by the screening effect and shows that, to obtain a larger elastic modulus, it is more favorable to have a large number of chains with few stickers than having a lower number of chains with more stickers. This result is in good agreement with ref , in which the authors show, based on simulations, that, in the semi-diluted regime, reducing the distance between stickers in a polymer chain favors the formation of intrachain associations. As already pointed out above, the polymer concentration is thus a key parameter for these systems.…”

“…Second, the copolymer used for preparing the DCN sample has a larger average molar mass between stickers of the same nature, M xx , than the copolymers used for IPN2 (Tables and ). A larger M xx value decreases the probability to form intramolecular bonds, which are elastically inactive, and thus favors higher G ′ values . Of course, this only applies if the concentration of cross-linkers is large enough to ensure that the chains contain several stickers.…”

“…A larger M xx value decreases the probability to form intramolecular bonds, which are elastically inactive, and thus favors higher G′ values. 44 Of course, this only applies if the concentration of cross-linkers is large enough to ensure that the chains contain several stickers.…”

Universal scaling of the diffusivity of dendrimers in a semidilute solution of linear polymers

“…It has been modified recently to study the dynamics of associative polymer solutions 46 along the lines of an earlier inhouse BD code based on the Molecular Modelling ToolKit. [47][48][49] The decomposition of the diffusion tensor, which is computationally demanding, has been efficiently implemented recently using the Positive Split Ewald algorithm (PSE). 50 This is available as a plugin to HOOMD-Blue.…”