The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the θ state, independent of polymer-solvent chemistry, in the crossover regime between θ 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" ϕ, 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, ϕ = 1), we find a standard second-order θ 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 θ 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 θ conditions is found to be the same for chains with and without stickers. arXiv:1903.07356v2 [cond-mat.soft]
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.
Dense suspensions of particles in viscous liquid often demonstrate the striking phenomenon of abrupt shear thickening, where their viscosity increases strongly with increase of the imposed stress or shear rate. In this work, discrete-particle simulations accounting for short-range hydrodynamic, repulsive, and contact forces are performed to simulate flow of shear thickening bidisperse suspensions, with the packing parameters of large-to-small particle radius ratio δ = 3 and large particle fraction ζ = 0.15, 0.50, and 0.85. The simulations are carried out for volume fractions 0.54 ≤ ϕ ≤ 0.60 and a wide range of shear stresses. The repulsive forces, of magnitude FR, model the effects of surface charge and electric double-layer overlap, and result in shear thinning at small stress, with shear thickening beginning at stresses σ ∼ FRa−2. A crossover scaling analysis used to describe systems with more than one thermodynamic critical point has recently been shown to successfully describe the experimentally-observed shear thickening behavior in suspensions. The scaling theory is tested here on simulated shear thickening data of the bidisperse mixtures, and also on nearly monodisperse suspensions with δ = 1.4 and ζ = 0.50. Presenting the viscosity in terms of a universal crossover scaling function between the frictionless and frictional maximum packing fractions collapses the viscosity for most of the suspensions studied. Two scaling regimes having different exponents are observed. The scaling analysis shows that the second normal stress difference N2 and the particle pressure Π also collapse on their respective curves, with the latter featuring a different exponent from the viscosity and normal stress difference. The influence of the fraction of frictional contacts, one of the parameters of the scaling analysis, and its dependence on the packing parameters are also presented.
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