Experimental method to measure the effect of charge on bimolecular collision rates in electrolyte solutions

A stable, monoprotic nitroxide spin probe is utilized as a model to study molecular collisions in aqueous electrolyte solutions. The rate constants of bimolecular collisions, K(col) for 2,2,5,5-tetramethylpyrrolidin-1-oxyl-3-carboxylic acid (CP) when it is uncharged (at low pH) and K(col)⁻ when it is charged (CP⁻; at high pH), are measured as functions of temperature and ionic strength. The ratio f* ≡ K(col)⁻/K(col) is a direct measure of the effect of charge on the collision rate. Neglecting the small differences in size and diffusion coefficients of CP and CP⁻, f* is the fractional change in collision rate due to Coulomb repulsion which was treated theoretically in Debye's classic paper [Trans. Electr. Chem. Soc. 1942, 82, 265]. K(col) and K(col)⁻ are determined from EPR spectral changes due to spin-spin interactions which are dominated by Heisenberg spin exchange under the conditions of these experiments. Values of f* vary linearly with values of κ · d in the range 0.4 < κ · d < 1.8, where κ and d are the inverse Debye screening length and the distance at closest approach, respectively. Values of d obtained in two independent ways, (1) from rotational correlation times measured by EPR and (2) by insisting that the experimental results be consistent with the Debye theory at infinite dilution, yield similar results. As the ionic strength is increased (κ increased), the screening effect reduces the effect of the Coulomb barrier more slowly than predicted by the Debye theory. While values of K(col) and K(col)⁻ vary substantially with T, approximately following the Stokes-Einstein-Smoluchowski equation, values of f* depend only slightly on temperature at a given value of κ · d, as is predicted by Debye's theory.