Measurement of mass diffusion coefficients using nonexponential forced Rayleigh scattering signals

Abstract

Recent reports on mass-diffusion forced Rayleigh scattering (FRS) experiments have emphasized that the detected signal arises as a difference between two exponentially decaying fields diffracted from “complementary” ground-state and photoproduct population gratings. A mass-diffusion coefficient has nevertheless often been extracted by forcing a single-exponential fit to the data, especially in cases where the decay appears to be monotonic. In this paper, we use simulations and experiments to evaluate the accuracy of single-exponential fits for FRS profiles, and we propose a useful alternative method for obtaining a meaningful rate constant in cases in which the error in the single-exponential analysis is large. We begin by noting from the complementary grating model that (1) severe deviations from single-exponential decay can occur for an arbitrarily small (but nonzero) difference in the ground-state/photoproduct rate constants, and (2) the first cumulant of a FRS decay—in contrast to that of a dynamic light scattering profile—does not (in general) represent a physically useful decay rate. These statements apply to both monotonic and nonmonotonic decays. We then show that a combination of the first two FRS cumulants provides a physically useful mean rate constant. Finally, to address these issues experimentally, we have reexamined the diffusion of methyl red (MR) through 2-propanol at room temperature, a system previously analyzed using single-exponential fits. The new experiments, carried out at higher sensitivity than the previous studies, show that the MR/2-propanol signal is nonmonotonic. The geometric-mean diffusion coefficient obtained from the curvature of the local maximum is compared to the diffusion coefficient inferred from single-exponential fits, and it is found that the latter is larger by nearly a factor of 2. The results reported here should prove important in improving the accuracy of the FRS technique.