Calculation of activity coefficients from a novel numerical solution of the Poisson–Boltzmann equation and application to 23Na NMR of sodium polystyrene sulfonate

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Abstract
Interaction of sodium cations with polystyrene sulfonate (PSS) is studied. The Poisson–Boltzmann equation, modified in order to incorporate ion–ion correlation, is solved numerically using a cell model. Outstanding agreement is found between the calculated and measured activity coefficients γ± for systems consisting of NaPSS+NaCl, KPSS+KCl, CaPSS+CaCl2, and the more complex system, the quarternary mixture NaPSS+CaPSS+NaCl+CaCl2. A complementary study by sodium‐23 NMR provides a reliable estimate of the fractions of bound, atmospherically condensed, and free sodium ions for NaPSS in the presence of added NaCl, HCl, MgCl2, and MnCl2. We find a nice correlation (ρ = 0.93, N = 16) between the observed 23Na line broadenings and the calculated electrostatic field gradients for these various cases.