Nuclear magnetic relaxation of 23Na in polyelectrolyte solutions

Using the cylindrical solution of the Poisson-Boltzmann equation, an expression is obtained for the nuclear spin-lattice relaxation of counterion nuclei in polyelectrolyte solutions, if these nuclei possess a quadrupole moment. The expression shows that, from a certain degree of neutralization α, the relaxation rate should be a quadratic function of α; while, in the concentration range of 0.05–1N, the concentration dependence is only slight. Experimental results for the nuclear magnetic relaxation rate of 23Na as a function of α in poly(acrylic acid) solutions of ≈0.3N concentration are shown to be in reasonable agreement with the theory. The effect of added NaCl upon the observed relaxation rate is discussed and shown to be describable by an ``additivity rule.''