GENERAL RESEARCH Near-Critical Behavior of Mutual Diffusion Coefficients for Five Solutes in Supercritical Carbon Dioxide Xiao-ning Yang, Luiz A. F. Coelho, and Michael A. Matthews Department of Chemical Engineering, University of South Carolina, Columbia, South Carolina 29208 The Taylor-Aris dispersion technique was employed to measure the binary diffusion coefficients of five solid solutes (phenanthrene, biphenyl, benzoic acid, 1,4-dichlorobenzene, and phenol) in supercritical carbon dioxide within the pressure range from 75 to 170 bar at 308.2 K. Measurements were made at very dilute concentrations, in the vicinity of the pure CO 2 critical point and also near the solid/supercritical fluid lower critical end point. At 308.2 K (4 K above the critical temperature of the solvent), decreasing the pressure (density) of the fluid causes the binary diffusion coefficients to increase until a certain pressure is reached. With further decreases in pressure, approaching the critical pressure of CO 2 , the diffusion coefficients decrease sharply. The decrease in diffusion coefficient near the solvent critical point is discussed using the concept of the solvent density inhomogeneities in supercritical fluids. A crossover theory that considers both the critical singular contribution and background contribution of transport properties is used to describe semiquantitatively the observed decrease in the diffusion coefficient. Introduction Carbon dioxide is a preferred supercritical fluid (SCF) solvent due to its low cost, easily accessible critical point, and environmentally benign nature. The design of SCF processes involving interfacial mass transfer requires knowledge of the binary diffusion coefficients. Behavior of the diffusion coefficient near the solvent critical point or near a binary mixture critical point may greatly influence dynamic processes. For example, in particle formation by rapid expansion or gas antisolvent pro- cesses, the particle size and morphology are a function of mass transfer characteristics as well as the specific process path into the two-phase region. The specific effect of diffusion coefficient on such processes is un- known but is thought to be crucial. Theoretically, diffusion coefficients are of great importance in provid- ing information regarding specific interactions between unlike molecules. Measurement and analysis of diffusion coefficients very near the solvent critical point is challenging. 1,2 In general, diffusion coefficients are expected to increase as the pressure of a fluid is decreased (or equivalently, as density is decreased). However, near the solvent critical point the mutual diffusion coefficients decrease with decreasing pressure. 3-6 Also, for incompressible mixtures near a liquid-liquid critical (or consulate) point the mutual diffusion coefficients have been found to fall toward zero. 7,8 This phenomenon has an impor- tant bearing on any process operating in this region. The near-critical behavior has been explained by con- sidering the chemical potential gradient as the driving force for diffusional process. 4,5,9 According to this de- velopment, the determinant of the matrix for the diffusion coefficients in multicomponent systems tends toward zero near the critical point. 10 Clifford and Coleby 11 discussed the decrease in the mutual diffusion coefficients in the region near the pure solvent critical point and suggested that the decrease in diffusivity may not happen at infinite dilution. According to Levelt- Sengers et al., 12 it is difficult to see experimentally the decrease in diffusion coefficients at infinite dilution near the solvent critical point. One characteristic of critical behavior is the strong divergence of the susceptibility for mixtures (compress- ibility for pure fluids) and the related growth of the correlation length, 2,9,12 which can be described by means of scaling laws. 13 However, it should be pointed out that the validity of the scaling laws is restricted to the region extremely close to the critical point. In this region very close to the critical point, the anomalous asymptotic behavior of transport properties dominates to the extent that the normal background can be neglected. But it has become evident that critical fluctuations are actually present in fluids over a very large range of temperature and pressure. 14 To account for the effects of critical fluctuations on transport properties, it is necessary to consider the nonasymptotic behavior of transport properties includ- ing the crossover to background (regular) classical behavior far away from the critical point. Recently, an advanced treatment of critical phenomena has been developed for studying transport properties in the critical region 15-18 based on the mode-coupling theory. Luettmer-Strathman and Sengers 15 extended the de- scription of transport properties of binary mixtures into the crossover region. Kiselev and Kulikov 16 developed a practical representation of thermodynamic and trans- port properties in pure and binary mixtures near the vapor-liquid critical line. However, these studies are 3059 Ind. Eng. Chem. Res. 2000, 39, 3059-3068 10.1021/ie990705d CCC: $19.00 © 2000 American Chemical Society Published on Web 07/13/2000