A method for determining the density fluctuations of supercritical fluids absolutely based on small-angle scattering experiments and application to supercritical methanol

Density fluctuation is a vital concept for understanding disordered systems. A supercritical fluid is a typical disordered system having extremely large inhomogeneity. To determine the density fluctuations using a scattering method, the key physical quantities are the fluid density and the normalized scattering intensity, as well as the small-angle scattering signals. Here, we propose a methodology to obtain all of these quantities absolutely from a scattering experiment. Normalization of scattering intensity relating to the number of molecules per unit volume was performed using fluid density evaluated directly from in situ measurements of the X-ray absorption coefficients. Conversion of scattering intensity to absolute value concerning scattering volume was achieved utilizing the value of the density fluctuation in the ideal state. An analysis of supercritical carbon dioxide confirmed the validity of the present method. By applying this method, the density fluctuations of supercritical methanol were quantitatively determined for the first time. (author)