Ind. Eng. Chem. Res. 2000, 39, 3059-3068
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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 CO2 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 CO2, 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 processes, 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 unknown but is thought to be crucial. Theoretically, diffusion coefficients are of great importance in providing 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 important bearing on any process operating in this region. The near-critical behavior has been explained by considering the chemical potential gradient as the driving force for diffusional process.4,5,9 According to this development, the determinant of the matrix for the diffusion coefficients in multicomponent systems tends toward zero near the critical point.10 Clifford and
Coleby11 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 LeveltSengers 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 (compressibility 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 including 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 region15-18 based on the mode-coupling theory. Luettmer-Strathman and Sengers15 extended the description of transport properties of binary mixtures into the crossover region. Kiselev and Kulikov16 developed a practical representation of thermodynamic and transport properties in pure and binary mixtures near the vapor-liquid critical line. However, these studies are
10.1021/ie990705d CCC: $19.00 © 2000 American Chemical Society Published on Web 07/13/2000
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mostly focused on the viscosity and thermal conductivity near the critical point. Measurements of diffusion coefficients near the solvent critical point are scarce compared with the other transport properties. In the highly compressible region, especially when working close to the critical point, it is difficult to obtain reliable data. Several workers have reported a large decrease in diffusion coefficient near the pure solvent critical point, but the thermodynamic state at which the decrease is observed is not consistent. The discrepancies are due, in part, to differences in experimental methods. Tshenkaya3 measured diffusivities of naphthalene in supercritical CO2 at 308 K as measured by the weight loss of solid tablets in a highpressure cell. Although experimental details are nonexistent, this method appears to be a so-called “infinite couple,” with a sharp initial concentration gradient at the solid/fluid interface. He reported diffusion coefficients as a function of pure solvent density, spanning the critical density. There was a strong minimum in diffusion coefficient at a CO2 density of 0.460 g/cm3, very near the critical density Fc ) 0.47 g/cm3. Ago et al. used the Taylor dispersion method for diffusivities of acetone4 and benzene5 in CO2 at temperatures about 10 K above the critical point. These solutes exhibit Type I phase behavior. They injected microliter quantities of pure liquid solutes and studied the effect of the injected quantity on D12. They reported a strong decrease in the diffusion coefficient as pressures decreased from 200 to 85 bar (Pc ) 73.8 bar), but only when large volumes of solute were injected. The preferred implementation of the Taylor dispersion method is to inject a solute that is already predissolved in the solvent, which minimizes the initial concentration and density gradients in the system. Thus, it is difficult to interpret the composition of the diffusion coefficients from the experiments of Ago et al. Higashi et al.6 used a capillary evaporation technique for the solids naphthalene, 2,6-dimethylnaphthalene, and 2,7-dimethylnaphthalene in CO2. Measurements were at 308.2 K and pressures from 152 to 72.1 bar. These authors reported a weak minimum in D12 at P ) 81.4 bar (F ) 0.735 g/cm3), but D12 increased with further reduction in pressure and density, even before the critical density region was traversed. The studies cited above reflect a variety of experimental methods; also, the phase behavior of the CO2/ solute systems (continuous or discontinuous binary critical locus) is important. In this work, we determine the diffusion coefficients of five solid solutes in CO2 near the critical temperature of CO2 and for pressures from 75 to 170 bar, using the Taylor-Aris dispersion method. These systems should exhibit a discontinuous critical locus with a lower critical end point near the CO2 critical point. An anomalous decrease in the diffusion coefficients is observed, even at infinite dilution when the critical point is approached. The limitations of the experimental method near the critical point have been investigated. A interpretation based on the density inhomogeneities in SCF19,20 is presented to understand the experimental data. In addition, a crossover theory that considers the singular and background (regular) contributions for transport properties was used to describe semiquantitatively our experimental data. Experimental Section Theoretical Background. Diffusion coefficients were measured by using the Taylor-Aris dispersion
method.21,22 Alizadeh et al.23 rigorously analyzed this technique for measurement of molecular diffusion coefficients in incompressible liquids. Levelt-Sengers et al.12 have discussed some of the limitations of this method when operating near the critical point of a pure solvent. Typical data analysis methods have been described elsewhere.24,25 When a tracer solute is imposed as a pulse at the inlet of a column of radius R and length L, through which a mobile phase is flowing at a laminar flow velocity u, the averaged concentration of the tracer at the column exit is given by23
C(t) )
M2 2πR2xπKt
exp
(
)
-(L - ut)2 4Kt
(1)
In this expression, M2 is the amount of the solute in the injected pulse in excess of that present in the same volume of the carrier stream. The dispersion coefficient K is
K)
R2u2 +D 48D
(2)
where D is the binary molecular diffusion coefficient. In this study, the diffusion coefficients are obtained by fitting the response curve (C(t)) to the theoretical solution with correction for baseline drift and offset.26 Experimental Apparatus. A schematic of the experimental apparatus is shown in Figure 1. Zero dead volume fittings were used throughout the apparatus. A pulseless micropump (ISCO, µLC-500) was used to supply compressed CO2. The use of a pulseless pump eliminates pressure and density gradients in the nearcritical solvent that would otherwise be introduced by the use of a common piston pump. The sample injection valve is a Valco Model A60, equipped with 10-15-µL sample loop and a helium-driven actuator. The fused silica capillary diffusion column has a diameter of 2.556 × 10-4 m and a length of 11.20 m. The detector is a Linear Model 200 variable wavelength UV detector. A Lindberg Model WB1130 constant temperature water bath is used to maintain the system temperature. Capillary tubing is used as both the dispersion tube and the sample cell for the UV detector. This arrangement eliminates any peak broadening due to fittings between the dispersion tube and the detector or that due to the finite volume of the flow cell of the detector. The UV detector signal is captured with a data acquisition system and a computer. The solute cell, which allows the solid solute to be predissolved in CO2, was kept at the same temperature in the water bath and at a pressure smaller than the system, to prevent leakage as pointed out by Levelt Sengers et al.12 Because the experiment was carried out in the critical region, a high degree of accuracy in both temperature and pressure measurement is desirable. The system pressure is set by a back-pressure regulator charged with nitrogen and monitored by using a high-accuracy (0.01%) digital pressure transducer (Paroscientific Digiquartz, Model 740). A manual high-pressure generator (High-Pressure Equipment, Model 62-6-10) was used to compress the nitrogen gas for the back-pressure regulator. The pressure measurement is accurate to within (0.02 bar, and the temperature control is precise to within (0.05 K. Injected Quantity of Solute. The injection valve was actuated by helium supplied at 5.5 bar. The moving
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Figure 1. Schematic of the Taylor-Aris dispersion apparatus: (1) syringe pump; (2) pressure transducer; (3) solute cell; (4) injection valve; (5) dispersion column; (6) constant-temperature enclosure; (7) UV detector; (8) data acquisition system; (9) Gaussian profile; (10) back-pressure regulator; (11) manual pressure generator; (12) restrictor.
sample injection technique ensures that the injection pulse is square.27 The quantity of solute injected was fixed each time, usually with the injection time
