Gravitational Effects in X-Ray Studies of Critical Opalescence

Abstract

Because of the high value of the isothermal compressibility of a one‐component fluid when the fluid is near its liquid—vapor critical point, the fluid density can vary appreciably at different heights in a sample cell. A calculation is made of the magnitude of these gravitational effects in small angle x‐ray scattering experiments. First, the scaling‐law equation of state is used to develop a method for computing the density profile in a sample cell. The calculated density profile is then employed to find the scattered intensity expected in a small angle x‐ray scattering apparatus employing slit collimation. The slit arrangement is chosen to be simple enough to permit relatively easy calculation while still providing collimation similar to the collimation used in present‐day equipment. The scattered intensity is assumed to be given by the Ornstein—Zernike scattering relation. After collimation corrections are applied to the computed ``observed'' intensity, the corrected intensity is compared with the intensity expected in the absence of gravitational effects. This comparison indicates that while gravitational effects almost certainly have not appreciably affected the recently published x‐ray studies of critical opalescence, gravitational effects will be significant if experimental techniques are refined to permit measurements at smaller scattering angles and at temperatures closer to the critical point.