An improved spectrophotometric method tests the Einstein-Smoluchowski equation: a revisit and update

Theoretical prediction and experimental measurements of light attenuation in chemically pure and optically transparent solvents have attracted continuous attention, due in part to their curious nature, and in part to the increasing requirements of solvent-related applications. Yet hitherto, a majority of accurate spectrophotometric measurements of transparent solvents upon visible light radiation often end up using long-path-length cells, usually over dozens of cm, rendering the measure costly and complex; meanwhile, the guidance for choosing the Einstein-Smoluchowski equation or its variants as the best formula to predict the light scattering in solvents has remained elusive. Here we demonstrate a simple, versatile and cost-effective spectrophotometric method, enabling a sensitivity of 10-4 dB cm-1 over a 0.5 cm differential path length based on using standard double-beam spectrophotometer. We prove that this method reduces the path length by a factor of 100 while still making its closest approach to the record-low measurement of solvent extinction. We also validate that all the present equations used for predicting the light scattering in the solvent possess similar capacities, suggesting that the criterion for the choice of the appropriate formula simply depends on the equation's practicability. Following the elucidation of the wavelength range where the light scattering dominates the extinction, we further identify differences between scattering coefficients via the theoretical predictions and experimental measures, exposing the need for an improved theory to account for the solvent scattering phenomenon.