The mutual diffusion coefficient of methanol–n‐hexane near the consolute point

Abstract

The composition and temperature dependence of the mutual diffusion coefficient near the liquid-liquid critical point of methanol-n-hexane mixtures has been determined by Gouy interferometry. The critical exponent was found to be 0.685. Constant-temperature extrapolation to zero diff usivity located the spinodal curve. Spinodal loci calculated from the NRTL model are inconsistent with the experimentally determined values. W. M. Clark and R. L. Rowley Department of Chemical EngineeringRice University Houston, TX 7725 1 SCOPEMutual diffusion coefficients can be separated into two parts: a mobility or Onsager term and a thermodynamic factor. The mathematical criterion, which defines the spinodal curve and demarcates the unstable region interior to the equilibrium coexistence curve, can be expressed as the loci of points where the thermodynamic factor is identically zero. Classical and light-scattering experiments have shown that the diffusion coefficient goes to zero as the temperature approaches the liquid-liquid critical point at constant critical composition. Although Skripov et al. (1980) concluded that the diffusion coefficient for the methanoln-hexane system vanished at the same rate as the thermodynamic factor, indicating a finite Onsager term, it has been fairly well established by studies on other systems that the Onsager coefficient actually diverges as the critical point is approached. One purpose of this study was to determine the critical exponent in the methanol-n-hexane system by a series of temperaturejump-initiated diffusion experiments in a Gouy interferometer. The diffusion critical exponent has significant implications in terms of universality and scaling theories.The second purpose was to use diffusion coefficient measurements to determine the spinodal curve. Since the diffusion coefficient must be zero at the spinodal, extrapolation of measured diffusivities to zero could be used to determine its location. No methods have heretofore been able to provide spinodal information in liquid-liquid phase-splitting systems. Classical equilibrium studies provide only coexistence information. Nevertheless, the location of the spinodal curve could be extremely valuable in developing and testing liquid mixture models for the Gibbs free energy since it is related to the second derivative with respect to composition, as shown in Eq. 7. Generally, liquid-mixture model parameters are fitted from the solubility or equilibrium concentration information. No other data have been available to test the model at other compositions at the same temperature. The spinodal criterion on the other hand provides additional restrictions that a satisfactory and consistent liquid-mixture model must satisfy. CONCLUSIONS AND SIGNIFICANCEDiffusion coefficients were measured in methanol-nhexane mixtures as a function of temperature along the critical composition in a temperature-jump cell using a Gouy interferometer. The critical exponent was found to be 0.685, in good agreement with previous studies on other systems, indicating that...

Solubility in binary mixtures at the immiscibility critical point

“…The critical temperature is 34.3 * 0.2OC. This temperature is higher than that reported by Kiser et al ( 1 961), 33.2OC, and by Clark et al (1986). 33.84OC.…”

MD Simulations of Diffusivities in Methanol‐n‐hexane Mixtures Near the Liquid‐liquid Phase Splitting Region

“…The values of the Fick diffusivity obtained from the simulations are in very good agreement with published experimental data of Clark and Rowley [17]. These diffusivities approach zero near composition regions where liquid-liquid phase splitting occurs.…”

“…Consequently, the Fick diffusivity D 12 also tends to approach vanishingly small values. This has been confirmed experimentally by Clark and Rowley [17] for diffusion in methanol-n-hexane mixtures. It has always been claimed in the literature that the M-S diffusivity Ð 12 is well-behaved, displaying no severe composition dependences.…”

“…The thermodynamic factor C approaches zero for temperatures and compositions for which liquid-liquid phase splitting can occur [17,18]. Consequently, the Fick diffusivity D 12 also tends to approach vanishingly small values.…”

Uphill diffusion in multicomponent mixtures

“…At any temperature, T, there is an order of magnitude decrease of G as x 1 approaches the critical composition from either end of the composition range. The severe reduction in the magnitude of G gets reflected in a corresponding decrease in the magnitude of the Fick diffusivity D 12 ; see experimental data 21 in Fig. 10c.…”