Self-Diffusion of Star and Linear Polyelectrolytes\nin Salt-Free and Salt Solutions

This work explored\nsolution properties of linear and star poly(methacrylic\nacids) with four, six, and eight arms (<i>L</i>PMAA, 4PMAA,\nPMAA, and 8PMAA, respectively) of matched molecular weights in a wide\nrange of pH, salt, and polymer concentrations. Experimental measurements\nof self-diffusion were performed by fluorescence correlation spectroscopy\n(FCS), and the results were interpreted using the scaling theory of\npolyelectrolyte solutions. While all PMAAs were pH sensitive and showed\nan increase in hydrodynamic radius (<i>R</i><sub>h</sub>) with pH in the dilute regime, the <i>R</i><sub>h</sub> of star polymers (measured at basic pH values) was significantly\nsmaller for the star polyacids due to their more compact structure.\nFully ionized star PMAAs were also found to be less sensitive to changes\nin salt concentration and type of the counterion compared to linear\nPMAA. While <i>R</i><sub>h</sub> of fully ionized linear\nPMAA decreased in the series Li<sup>+</sup> > Na<sup>+</sup> >\nK<sup>+</sup> > Cs<sup>+</sup> in agreement with the Hofmeister\nseries, <i>R</i><sub>h</sub> of star PMAAs was virtually\nindependent of\ntype of the counterion for eight-arm PMAA. However, molecular architecture\nstrongly affected interactions of counterions with PMAAs. In particular, <sup>7</sup>Li NMR revealed that the spin–lattice relaxation time <i>T</i><sub>1</sub> of Li<sup>+</sup> ions in low-salt solutions\nof eight-arm PMAA was ∼2-fold smaller than that in the solution\nof linear PMAA, suggesting slower Li<sup>+</sup>-ion dynamics within\nstar polymers. An increase in concentration of monovalent chloride\nsalts, <i>c</i><sub>s</sub>, above that of the PMAA monomer\nunit concentration (<i>c</i><sub>m</sub>) resulted in shrinking\nof both linear and star molecules, with the hydrodynamic size <i>R</i><sub>h</sub> scaling as <i>R</i><sub>h</sub> ∝ <i>c</i><sub>s</sub><sup>–0.11±0.01</sup>. Self-diffusion of linear and star polyelectrolytes was then studied\nin a wide range of polyelectrolyte concentrations (10<sup>–3</sup> mol/L < <i>c</i><sub>m</sub> < 0.5 mol/L) in low-salt\n(<10<sup>–4</sup> mol/L of added salt) and high-salt (1\nmol/L) solutions. In both the low-salt and high-salt regimes, diffusion\ncoefficient <i>D</i> was lower for PMAAs with a larger number\nof arms at a fixed <i>c</i><sub>m</sub>. In addition, in\nboth cases, <i>D</i> plateaued at low polymer concentrations\nand decreased at higher polymer concentrations. However, while in\nthe high-salt conditions, the concentration dependence of <i>D</i> reflected transitions between the dilute to semidilute\nsolution regimes as expected for neutral chains in good and theta\nsolvents, analysis of the diffusion data in the low-salt conditions\nusing the scaling theory revealed a different origin of the concentration\ndependence of <i>D</i>. Specifically, in the low-salt solutions,\nboth linear and star PMAAs exhibited unentangled (Rouse-like) dynamics\nin the entire range of polyelectrolyte concentrations.