Abstract:The classical Voorn-Overbeek thermodynamic theory of complexation and phase separation of oppositely charged polyelectrolytes is generalized to account for the charge accessibility and hydrophobicity of polyions, size of salt ions, and pH variations. Theoretical predictions of the effects of pH and salt concentration are compared with published experimental data and experiments we performed, on systems containing poly(acrylic acid) (PAA) as the polyacid and poly(N,N-dimethylaminoethyl methacrylate) (PDMAEMA) or poly(diallyldimethyl ammonium chloride) (PDADMAC) as the polybase. In general, the critical salt concentration below which the mixture phase separates, increases with degree of ionization and with the hydrophobicity of polyelectrolytes. We find experimentally that as the pH is decreased below 7, and PAA monomers are neutralized, the critical salt concentration increases, while the reverse occurs when pH is raised above 7. We predict this asymmetry theoretically by introducing a large positive Flory parameter (= 0.75) for the interaction of neutral PAA monomers with water. This large positive Flory parameter is supported by molecular dynamics simulations, which show much weaker hydrogen bonding between neutral PAA and water than between charged PAA and water, while neutral and charged PDMAEMA show similar numbers of hydrogen bonds. This increased hydrophobicity of neutral PAA at reduced pH increases the tendency towards phase separation despite the reduction in charge interactions between the polyelectrolytes. Water content and volume of coacervate are found to be a strong function of the pH and salt concentration.

We review constitutive modeling of solutions and melts of linear polymers, focusing on changes in rheological behavior in shear and extensional flow as the concentration increases from unentangled dilute, to entangled, to dense melt. The rheological changes are captured by constitutive equations, prototypes of which are the FENE-P model for unentangled solutions and the DEMG model for entangled solutions and melts. From these equations, and supporting experimental data, for dilute solutions, the extensional viscosity increases with the strain rate from the low–strain rate to the high–strain rate asymptote, but in the densely entangled state, the high–strain rate viscosity is lower than the low–shear rate value, especially when orientation-dependent friction is accounted for. In shearing flow, shear thinning increases dramatically as the entanglement density increases, which can eventually lead to a shear-banding inhomogeneity. Recent improvements in constitutive modeling are paving the way for robust and accurate numerical simulations of polymer fluid mechanics and industrial processing of polymers.

The effects of pH and salinity on both the bulk phase behavior and the layer-by-layer (LbL) growth kinetics are investigated for polyanion poly(acrylic acid) or PAA with two polycations, namely poly(N,N-dimethylaminoethyl methacrylate) or PDMAEMA and poly(diallyldimethylammonium chloride) or PDADMAC, with the goal of relating the phase behavior to the LbL growth kinetics. Depending on salinity, pH, and mixing ratio, the complex formed in the bulk is either a powdery precipitate or a gel-like coacervate, and the multilayers grow either linearly or exponentially with deposition time. In addition to primary Coulombic interactions, we observe that polymer-specific interactions have a profound effect on both bulk complexation and LbL growth of the three PE pairs studied here. The overall strength of interaction between polyelectrolytes, as indicated by their phase behavior, has a nonmonotonic effect on LbL growth rate, apparently because stronger interactions not only increase the driving force for diffusion but also reduce the effective diffusion coefficient of a polyelectrolyte molecule through the LbL multilayer. As a result, there is little correspondence between coacervation and exponential growth on one hand and precipitation and linear growth on the other. Salt concentration has a nonmonotonic effect on LbL growth kinetics at pH 7, with exponential growth found over the range 15−60% of the critical salt concentration (C S c ) needed to transition from coacervation to a clear solution in the bulk, regardless of the physical chemistry of polyelectrolytes employed, whereas salt concentrations both below and above this range result in linearly growing films. Finally, for our polyelectrolyte pairs at pH 7, we report a "universal curve" for the dependence of LbL growth rate, normalized by its maximum value, against the salt concentration, normalized by C S c . If it proves to be robust, this correlation could be used to estimate optimal salinity for LbL growth from bulk measurements of the critical salt concentration needed to suppress complexation.

We compare predictions of two of the most advanced versions of the tube model, namely the "Hierarchical model" by Wang et al. [J. Rheol. 2010, 54, 223] and the BoB (branch-on-branch) model by Das et al. [J. Rheol. 2006, 50, 207], against linear viscoelastic G′ and G″ data of binary blends of nearly monodisperse 1,4-polybutadiene 4-arm star polymer of arm molar mass 24 000 g/mol with a monodisperse linear 1,4-polybutadiene of molar mass 58 000 g/mol. The star was carefully synthesized and characterized by temperature gradient interaction chromatography and by linear rheology over a wide frequency region through time−temperature superposition. We found large failures of both the Hierarchical and BoB models to predict the terminal relaxation behavior of the star/linear blends, despite their success in predicting the rheology of the pure star and pure linear polymers. This failure occurred regardless of the choices made concerning constraint release, such as assuming arm retraction in "fat" or "skinny" tubes. Allowing for "disentanglement relaxation" to cut off the constraint release Rouse process at long times does lead to improved predictions for our blends, but leads to much worse predictions for other star/linear blends described in the literature, especially those of Shivokhin et al. [Macromolecules 2014[Macromolecules , 47, 2451. In addition, our blends and those of Shivokhin et al. were also tested against a coarse-grained slip-link model, the "clustered fixed slip-link model (CFSM)" of Schieber and co-workers [J. Rheol. 2014, 58, 723], in which several Kuhn steps are clustered together for computational efficiency. The CFSM with only two molecular-weight-and chain-architecture-independent parameters was able to give very good agreement with all experimental data for both of these sets of blends. In light of its success, the CFSM slip-link model may be used to address the constraint release issue more rigorously and potentially help develop improved tube models.

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