Measurement of enthalpies and entropies of activation as a function of pairwise distance for the pairwise relative diffusion of SrI2 in water over lengthscales from 6 Å to 40 Å

Abstract

Quasi-elastic neutron scattering (QENS) has been used to provide insight into the motions within solutions for many decades. Coherent QENS (CQENS) determines the motions of one ion relative to another, it is unique among all diffusion measurement methods, and the quantity measured can be called the pairwise relative diffusion coefficient D_p. It is an effective value for the experimental conditions. Here, we report the results of CQENS measurements of D_p for a 0.8 M solution of SrI₂ in D₂O at temperatures 10, 30, 50, 70, and 90 °C to observe the effect of temperature and to calculate the thermochemical activation values of E_a, Δ^‡S, and Δ^‡G for diffusion kinetics at 19 pairwise distances over the experimental q-range. For all five temperatures, the value of D_p tends to decrease with distance from 6 Å up to 11 Å (10 Å = 1 nm), although not monotonically. From the minimum at 11 Å, D_p tends to increase up to the longest measured distance of 38 Å. From the temperature dependencies at the various distances, the values of activation energies, activation enthalpies, and activation free energies (E_a, Δ^‡S, and Δ^‡G) for D_p can be calculated. For E_a, a modest peak appears in the 9 Å to 10 Å range, a shallow minimum near 18 Å and possibly a broad peak centered at 30 Å. Perhaps more interestingly, for distances in the 6 Å to 7 Å range there are two different activation energies for the ranges above and below 50 °C. The molecular mechanism responsible for this break cannot be ascertained from this data, but the dividing temperature appears where the difference between the macroscopic thermal expansion coefficients of the SrI₂ solution and pure D₂O changes from negative to positive. Finally, values of Δ^‡G are calculated from the E_a (as Δ^‡H) and the Δ^‡S values at each of the set of distances.