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This work explored solution properties of linear and star poly(methacrylic acids) with four, six, and eight arms (LPMAA, 4PMAA, PMAA, and 8PMAA, respectively) of matched molecular weights in a wide range of pH, salt, and polymer concentrations. Experimental measurements of self-diffusion were performed by fluorescence correlation spectroscopy (FCS), and the results were interpreted using the scaling theory of polyelectrolyte solutions. While all PMAAs were pH sensitive and showed an increase in hydrodynamic radius (Rh) with pH in the dilute regime, the Rh of star polymers (measured at basic pH values) was significantly smaller for the star polyacids due to their more compact structure. Fully ionized star PMAAs were also found to be less sensitive to changes in salt concentration and type of the counterion compared to linear PMAA. While Rh of fully ionized linear PMAA decreased in the series Li+ > Na+ > K+ > Cs+ in agreement with the Hofmeister series, Rh of star PMAAs was virtually independent of type of the counterion for eight-arm PMAA. However, molecular architecture strongly affected interactions of counterions with PMAAs. In particular, 7Li NMR revealed that the spin−lattice relaxation time T1 of Li+ ions in low-salt solutions of eight-arm PMAA was ∼2-fold smaller than that in the solution of linear PMAA, suggesting slower Li+-ion dynamics within star polymers. An increase in concentration of monovalent chloride salts, cs, above that of the PMAA monomer unit concentration (cm) resulted in shrinking of both linear and star molecules, with the hydrodynamic size Rh scaling as Rh ∝ cs −0.11±0.01. Self-diffusion of linear and star polyelectrolytes was then studied in a wide range of polyelectrolyte concentrations (10−3 mol/L < cm < 0.5 mol/L) in low-salt (<10−4 mol/L of added salt) and high-salt (1 mol/L) solutions. In both the low-salt and high-salt regimes, diffusion coefficient D was lower for PMAAs with a larger number of arms at a fixed cm. In addition, in both cases, D plateaued at low polymer concentrations and decreased at higher polymer concentrations. However, while in the high-salt conditions, the concentration dependence of D reflected transitions between the dilute to semidilute solution regimes as expected for neutral chains in good and theta solvents, analysis of the diffusion data in the low-salt conditions using the scaling theory revealed a different origin of the concentration dependence of D. Specifically, in the low-salt solutions, both linear and star PMAAs exhibited unentangled (Rouse-like) dynamics in the entire range of polyelectrolyte concentrations. 

We use coarse-grained molecular dynamics simulations to study deformation of networks and gels of linear and brush strands in both linear and nonlinear deformation regimes under constant pressure conditions. The simulations show that the Poisson ratio of networks and gels could exceed 0.5 in the nonlinear deformation regime. This behavior is due to the ability of the network and gel strands to sustain large reversible deformation, which, in combination with the finite strand extensibility results in strand alignment and monomer density, increases with increasing strand elongation. We developed a nonlinear network and gel deformation model which defines conditions for the Poisson ratio to exceed 0.5. The model predictions are in good agreement with the simulation results. 

We develop a forensic-like framework for network structural characterization based on an analysis of their nonlinear response to mechanical deformation. For model networks, this methodology provides information about the strand degree of polymerization between cross-links, the effective cross-link functionality, the contribution of loops and entanglements to network elasticity, as well as the fraction of stress-supporting strands. For networks with trapped entanglements, we identify a transition from cross-link-controlled to entanglement-controlled network elasticity with increasing degree of polymerization of network strands between cross-links and show how specific features of this transition are manifested in changes of entanglement and structural shear moduli characterizing different modes of network deformation. In particular, this cross-link-to-entanglement transition results in saturation of the network shear modulus at small deformations and renormalization of the degree of polymerization of the effective network strands determining nonlinear elastic response in the strongly entangled networks. The developed approach enables the classification of networks according to their topology and effectiveness of stress distribution between network strands.