Robert L. Scott

Tricritical phenomena in ‘‘quasibinary’’ mixtures of hydrocarbons. I. Methane systems

Temperature, pressure, and composition measurements are reported for the three coexisting phases in the region of the tricritical points of two ternary mixtures of hydrocarbons: methane+n‐pentane+2,3‐dimethylbutane (I) and methane+2,2‐dimethylbutane+2,3‐dimethylbutane (II). These systems satisfy a ’’quasibinary’’ approximation in which the proportions of the two higher hydrocarbons [expressed as Z = xC/(xB+xC)] are the same in each of the three phases, so that the phase equilibrium is equivalent to that in a binary system with a solute of average properties. Least‐squares analysis does not locate the tricritical point with high precision, but all the measurements are consistent with the predictions of the phenomenological theory that the exponents governing the approach to the tricritical point are the ’’classical’’ mean‐field values. If, in accord with this view, we write the difference between the upper and lower critical‐end‐point temperatures (i.e., extent of the three‐phase region) as Tu−Tl = B(Z−Zt)...

Tricritical phenomena in quasi‐binary mixtures. IV. Ternary ethane systems

Phase equilibria have been studied in binary and quasi‐binary mixtures of ethane with higher alkanes (n‐hexadecane to n‐eicosane) near the tricritical temperature. We report the temperatures and pressures corresponding to the lower and upper critical end points of various mixtures. The compositions of the coexisting phases in the three‐phase region of six mixtures were also studied. The shrinkage of the width of the three‐phase region is consistent with the asymptotic classical theory of tricritical points, while an extended classical theory is necessary to account for the details of the coexistence curves. An examination of the deviations from the quasi‐binary approximation shows that it is a very good approximation for the ethane+(n‐heptadecane+n‐octadecane) system.

Sedimentation and density gradients near the liquid–liquid critical solution point in high gravitational fields

Experiments in the ultracentrifuge and theoretical analysis both strongly suggest that, in a binary liquid mixture near its liquid–liquid critical solution point, the sedimentation rate diverges approximately as (T−Tc)−0.6. As a result of the divergence of the sedimentation rate, a density inversion (a negative value of dρ/dh) can occur at temperaures substantially above the equilibrium critical solution temperature. The turbulence resulting from the instability can give the appearance of phase separation.

Volume changes in the critical solution region

Recent theoretical and experimental studies suggest that (∂2V/∂x2)T, p and (∂2H/∂x2T, p vanish at the critical solution point. We report dilatometric measurements of volume changes in the system n-C6H14 + n-C6F14 at 21 compositions and eight temperatures in the region of its critical solution point at t0 = 22.71°C and xc = 0.35. By mixing two standard mixtures of mole fractions which bracket xc, the magnitude of the volume change is reduced by a factor of ten, permitting the use of a finer capillary. Qualitatively the curves of VEm against x become nearly flat as one approaches the critical point; associated with this is a large increase in the coefficient of thermal expansion. Curve fitting in the critical region is difficult, but analytical and graphical treatments give similar results. At the critical composition (∂2Vm/∂x2)T, p = − 16 cm3 mol−1 at 24.000°C and decreases in magnitude to about − 4 cm3 mol−1 at 22.715°C, about 0.01 K above the critical temperature. This latter value is closer to zero by a factor of about four than any value reported previously and lends further support to the view that the limiting value is in fact zero.

Mixtures of substituted hydrocarbons with hexane isomers: excess volumes and excess enthalpies

Abstract Measurements are reported of the molar excess volumes of: nitroethane + 2-methylpentane (298, 303, and 313 K); +2,3-dimethylbutane and +2,2-dimethybutane (298 and 313 K); 1-chloropentane + n -hexane, +2-methylpentane, and +2,2-dimethylbutane (298 K). Also reported are molar excess enthalpies of: nitroethane + cyclohexane (313 K), + n -hexane (303 K), +2-methylpentane (303 K), +3-methylpentane (303 and 313 K), +2,3-dimethylbutane (303 K), +2,2-dimethylbutane (303 and 313 K), and +1,4-dioxane (303 K) and 1,4-dioxane + 2,2-dimethylbutane (303 K). The excess volumes vary strikingly with the degree of branching of the hexane. The excess enthalpies show much smaller influences of branching.

Excess volumes of n-hexadecane + the isomers of hexane☆

Abstract Excess volumes have been measured at 293.15 K for n-hexadecane + n-hexane, + 2-methylpentane, + 3-methylpentane, + 2,3-dimethylbutane, and + 2,2-dimethylbutane. In addition, excess volumes were measured at 313.15 K for n-hexadecane + n-hexane, and at 301.15 and 308.15 K for n-hexadecane + 2,2-dimethylbutane. The minimum of the molar excess volume curves occurs uniformly in the region of x(C6) = 0.65, and all the results can be fitted well by the equation V m E cm 3 mol −1 = x(1−x){v 0 + v 1 (1−2x) + v 2 (1−2x) 2 } {1 − B(1 − 2x)} , where the skewing parameter B = −0.55 is the same for all the mixtures.

Tricritical phenomena in quasi‐binary mixtures. III. An extended classical treatment

The phenomenological (classical) treatment of tricritical points is extended by adding higher‐order terms to the sixth‐order free‐energy polynomial of the Griffiths asymptotic theory. The free energy is expanded in powers of the experimental (laboratory) densities of a quasi‐binary mixture, e.g., the mole fraction x or the molar volume Vm. The higher‐order corrections introduce asymmetry into the temperature‐composition coexistence curve and yield an approximately parabolic relation between the two densities. This extended classical theory yields, for experimental susceptibilities (i.e., those defined in terms of one of the laboratory densities) of the three coexisting phases, a Griffiths first sum χ1/2α +χ1/2γ −χ1/2β whose limiting value (as the tricritical point is approached) is not zero, as the asymptotic theory predicts, but rather a nonzero constant. The square‐gradient one‐density approximation is applied to give an extended mean‐field treatment of interfacial tensions in the tricritical region.

A grease-free continuous dilution dilatometer; excess volumes for benzene + carbon tetrachloride

Abstract A new tilting version of the Stokes-Levien-Marsh continuous-dilution dilatometer eliminates systematic errors due to the extrusion of minute amounts of grease from taps. With this improvement small excess volumes can be measured to a precision of 0.00015 cm3 mol−1. Excess volumes for benzene + carbon tetrachloride have been measured at 279.15, 291.15, 295.065, and 298.150 K and (on the benzene-rich side) at 295.565 and 296.065 K. Below about 288 K VmE is negative at all compositions. Above this temperature a positive maximum develops at the carbon tetrachloride-rich end. A second maximum appears at the benzene-rich end around 295 K, and the “double maximum” effect persists to about 296 K. Above about 295.8 K VmE is positive at all compositions. In this temperature region the excess volumes are all very small; between 291 and 296 K, the magnitude of VmE is always less than 0.01 cm3 mol−1.

Tricritical phenomena in quasi‐binary mixtures. V. New measurements on ternary methane systems

Phase equilibria have been studied in ternary mixtures of methane with 2,2‐ and 2,3‐dimethylbutane near the tricritical point. The quasi‐binary approximation allows the path to the tricritical point to be defined experimentally, making it possible to study the details of the phase behavior as the tricritical point is approached. The decrease in the differences in temperature and pressure between the upper and lower critical end points is consistent with the asymptotic classical theory of tricritical phenomena; an extended classical theory is necessary to account for the shape of the coexistence curves.

Indirect determination of concentrations in coexisting phases

A general method is reported for the determination of the compositions of existing phases in multicomponent mixtures. A previous study of tricritical phenoena in ternary mixtures of hydrocarbons is used to demonstrate the method of analysis.