Heat Capacities and Asymmetric Criticality of Coexistence Curves for Benzonitrile + Alkanes and Dimethyl Carbonate + Alkanes

Abstract

The critical behavior of isobaric heat capacities per unit volume for a series of critical binary solutions {benzonitrile + octane, or dodecane, or hexadecane} and {dimethyl carbonate + nonane, or decane, or dodecane} were studied. The corresponding exponent was obtained to be in consistent with the 3D-Ising value. The amplitudes in one-phase and two-phase regions were deduced, which were used to test some critical amplitude ratios. Analysis of the dependence of the effective critical exponent of the heat capacity on the temperature indicated a critical crossover from the 3D-Ising to the mean-field for all the studied systems. It was found that the heat capacity does play an important role for describing the asymmetric criticality of coexistence curves by the complete scaling theory.

The liquid–liquid coexistence curves of {benzonitrile+n-pentadecane} and {benzonitrile+n-heptadecane} in the critical region

“…The obtained values of these parameters for {x benzontrile + (1 À x) n-pentadecane} and {x benzontrile + (1 À x) n-heptadecane} are listed in table 8. Figure 3 shows the results of the fits for the order parameter x of these systems, and the agreements between the calculated values of Dx by equation (9) and the experimental ones, which indicates that the crossover theory can well describe the coexistence curves in a wide temperature range.…”

“…If the volume change upon mixing is negligible, V c may be calculated with the assumption of ''ideal mixing'' (V c ¼ ð1 À x 2;c ÞV 0 1;c þ x 2;c V 0 2;c ), where V 0 1 and V 0 2 are molar volumes of benzonitrile and n-alkane, Pérez-Sánchez et al [8] neglected the termD x 2 1 ð À 0 jsj 1Àa =ð1 À aÞ þB cr jsjÞ for mole fraction x 2 in equation (16) because of the absence of heat capacity data and the opposite contributions of terms of |s| 1Àa and |s|. As it was pointed [9,17,[22][23] that in equation (17), the contribution of |s| b term was dominant, and the assumption ofB x 2 1 ¼B x 2 2 ¼ 0 only caused little change ofB x 2 0 and a 1 . Therefore, equations (16) and (17) could be simplified as:…”

“…This concept has been applied to explain the singularity of the diameter of the coexistence curves for one-component fluids [6] and for both incompressible and weakly compressible binary fluid systems [7,8]. Moreover, as we indicated [9], the contribution of the heat capacity plays an important role in describing the asymmetric criticality within the frame of the complete scaling theory.…”

“…a equations (20) and (21) as indicated in table 10. It is possibly resulted from the neglect of the termD x 2 1 ð À 0 jsj 1Àa =ð1 À aÞ þB cr jsjÞ, which has been shown to be important in describing the asymmetry criticality of the coexistence curve [9]. Thus, precise experimental data of the heat capacities for these systems both in the critical and the non-critical regions are expected.…”

Critical asymmetry of liquid–liquid coexistence curve of binary mixture nitromethane+3-pentanol

“…43 In recent years, the "complete scaling theory" was developed to rep- showed that the complete scaling theory can well represent the 53 experimental asymmetric behaviors of the coexistence curves and the 54 osmotic compressibilities in two-phase region [9][10][11]. It was found 55 that the asymmetric coefficient a 3 related to the compressibility Yang-Yang anomaly [12][13][14][15].…”