Determination of liquid-liquid critical point composition using ${90}^{\circ }$ laser light scattering

Despite over a century of characterization efforts, liquid-liquid critical point compositions are difficult to identify with good accuracy. Reported values vary up to 10% for even well-studied systems. Here, a technique is presented for high-precision determination of the critical composition of a partially miscible binary liquid system. Ninety-degree laser light-scattering intensities from single-phase samples are analyzed using an equation derived from nonclassical power laws and the pseudospinodal approximation. Results are reported for four liquid-liquid systems (aniline + hexane, isobutyric acid + water, methanol + cyclohexane, and methanol + carbon disulfide). Compared to other methods, the ${90}^{\circ }$ light-scattering approach has a strong dependence on composition near the critical point, is less affected by temperature fluctuations, and is insensitive to the presence of trace impurities in the samples. Critical compositions found with ${90}^{\circ }$ light scattering are precise to the parts-per-thousand level and show long-term reproducibility.

Figure 1

(a) Aniline + hexane coexistence curve data from Ref. [14]. The data are fit with simple scaling [Eq. (1); dotted line] and truncated complete scaling [Eq. (3); dashed line]. (b) Sample removal test of the simple scaling fit. Error bars are 2 standard deviations as reported by the fitting software.

Figure 2

Aniline + hexane critical composition determined using mole, mass, and volume fraction for the composition coordinate and using all 14 data points, 10 points, or 7 points. Horizontal bars indicate fitting uncertainty at 2 standard deviations. (a) Coexistence curve fit using simple scaling, Eq. (1). (b) Coexistence curve fit using complete scaling truncated at the $D_2$ term, Eq. (3). (c) ${90}^{\circ }$ light-scattering fit using Eq. (20).

Figure 3

Representative coexistence curve and pseudospinodal curve for a liquid-liquid system of components A and B.

Figure 4

Three-dimensional plot of $I_{90}$ data for the aniline + hexane system with an overlay of the corresponding surface fit to Eq. (20). The $I_{90}$ data were collected 6 years after the samples were prepared.

Figure 5

(a) Initial coexistence curve data for the aniline + hexane system (light blue diamonds) compared against the corresponding $I_{90}$ data for $\mathrm{\Delta }{T}_1=0.05\mathrm{K}$ (dark red circles). The $I_{90}$ data were collected 6 years after sample preparation. The red dashed line is from the surface fit of the $I_{90}$ data to Eq. (20). (b) Sample removal test of the $I_{90}$ data fit. Error bars, barely visible, are 2 standard deviations as reported by the fitting software. (c) Comparison between literature values of the aniline + hexane critical composition (dark blue lines) with the measurement reported here. The light blue line is from a truncated complete scaling fit of the initial coexistence curve (CC); the red line is from analysis of $I_{90}$ data collected 6 years later. Literature references are found in Appendix pp2.

Figure 6

Aniline + hexane $I_{90}$ data versus $\mathrm{\Delta }{T}_1$ for a sample with an aniline mole fraction of 0.5728. The red dashed line is from the surface fit of the $I_{90}$ data to Eq. (20). The $I_{90}$ data were collected 6 years after sample preparation.

Figure 7

(a) Initial coexistence curve data for Set A of the isobutyric acid + water system (light blue diamonds) compared against the corresponding $I_{90}$ data for $\mathrm{\Delta }{T}_1=0.05\mathrm{K}$ (dark red circles). The $I_{90}$ data were collected 2 years after sample preparation. The red dashed line is from the surface fit of the $I_{90}$ data to Eq. (20). (b) Sample removal test of the $I_{90}$ data fit. Error bars, barely visible, are two standard deviations as reported by the fitting software. (c) Comparison between literature values of the isobutyric acid + water critical composition (blue lines) with the two sets of measurements reported here using $I_{90}$ data (red lines). The samples in Set B were incubated after initial measurements were made, leading to long-term changes in $T_{\mathrm{cx}}$ values—see the text. Literature references are found in Appendix pp3.

Figure 8

(a) Initial coexistence curve data for the methanol + cyclohexane system (light blue diamonds) compared against the corresponding $I_{90}$ data for $\mathrm{\Delta }{T}_1=0.05\mathrm{K}$ (dark red circles). The $I_{90}$ data were collected 5 years later. The red dashed line is from the surface fit of the $I_{90}$ data to Eq. (20). (b) Sample removal test of the $I_{90}$ data fit. Error bars, just visible, are 2 standard deviations as reported by the fitting software. (c) Comparison between literature values of the methanol + cyclohexane critical composition (blue lines) with the measurements reported here using $I_{90}$ data (red lines). Literature references are found in Appendix pp1.

Figure 9

(a) Initial coexistence curve data for the methanol + carbon disulfide system (light blue diamonds) compared against the corresponding $I_{90}$ data for $\mathrm{\Delta }{T}_1=0.05\mathrm{K}$ (dark red circles). The $I_{90}$ data were collected 7 years after sample preparation. The red dashed line is from the surface fit of the $I_{90}$ data to Eq. (20). (b) Sample removal test of the $I_{90}$ data fit. Error bars, just visible, are 2 standard deviations as reported by the fitting software. (c) Comparison between literature values of the methanol + carbon disulfide critical composition (blue lines) with the measurement reported here using $I_{90}$ data (red line). Literature references are found in Appendix pp4.

Figure 10

(a) Initial coexistence curve data for Set B of the isobutyric acid + water system immediately after sample preparation (light blue diamonds) and 8 years later (dark blue circles). The Set B samples were incubated for 2 months at $35{}^{\circ }\mathrm{C}$ shortly after the initial measurements. (b) Three-dimensional plot of $I_{90}$ data at 8 years, and the corresponding surface fit to Eq. (20).

Figure 11

Aniline + hexane $I_{90}$ data fitting residuals for the $\mathrm{\Delta }{T}_1=0.05\mathrm{K}$ cross section collected 6 years after sample preparation. (a) Residuals when $x_{\mathrm{C}}$ is fixed at 0.5368, the optimum $x_{\mathrm{C}}$ value from $I_{90}$ data analysis. (b) Residuals when $x_{\mathrm{C}}$ is fixed at 0.5318, the optimum $x_{\mathrm{C}}$ value from coexistence curve analysis.

Figure 12

Initial aniline + hexane coexistence curve fitting residuals using the complete scaling equation truncated at the $D_2$ term [Eq. (3)]. (a) Residuals when $x_{\mathrm{C}}$ is fixed at 0.5318, with the optimum $x_{\mathrm{C}}$ value from coexistence curve analysis. (b) Residuals when $x_{\mathrm{C}}$ is fixed at 0.5368, with the optimum $x_{\mathrm{C}}$ value from $I_{90}$ data analysis. (c) Residuals when $x_{\mathrm{C}}$ is fixed at 0.5368 and a simple linear impurity correction is included in the complete scaling equation.