Self-Diffusion of Star and Linear Polyelectrolytes in Salt-Free and Salt Solutions

Abstract

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 (R_h) with pH in the dilute regime, the R_h 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 R_h of fully ionized linear PMAA decreased in the series Li⁺ > Na⁺ > K⁺ > Cs⁺ in agreement with the Hofmeister series, R_h 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, c_s, above that of the PMAA monomer unit concentration (c_m) resulted in shrinking of both linear and star molecules, with the hydrodynamic size R_h scaling as R_h ∝ c_s^{–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 < c_m < 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 c_m. 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.