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Virial coefficients of Lennard-Jones mixtures
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10.1063/1.3148379
/content/aip/journal/jcp/130/22/10.1063/1.3148379
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/22/10.1063/1.3148379

Figures

Image of FIG. 1.
FIG. 1.

Virial coefficients for mixture I for . Values are made dimensionless by the critical density of the pure LJ fluid (Ref. 23) . Mixture I is symmetric with respect to exchange of the species, so some of the coefficients are identical, as indicated in the legends. Data are presented on a scale. Calculated coefficients are plotted with their 67% confidence limits (which are often smaller than the line thickness) and lines are drawn to join them using an interpolation scheme presented elsewhere (Ref. 29).

Image of FIG. 2.
FIG. 2.

Mixture I spinodals in the composition-density plane. Dotted lines are calculated from VEOS4, solid lines from VEOS5, and dot-dashed lines from VEOS6. Each group of lines from left to right in the figure corresponds to the indicated temperature (in units of ). Spinodal lines terminate where the critical criterion [Eq. (7)] is satisfied (even though spinodal condition continues to be met at higher density). Black dot-dashed line traversing figure from to 1 at the far right is the line of critical points according to VEOS6.

Image of FIG. 3.
FIG. 3.

Critical line for mixture I in the pressure-temperature plane. Dotted line (circles) is computed from VEOS4, solid line (squares) VEOS5, and dot-dashed line (triangles) VEOS6. Open symbols at left correspond to equimolar mixture and critical lines for each pure substance begin at the right and trace identical curves (owing to the symmetry of the mixture).

Image of FIG. 4.
FIG. 4.

Comparison of mixture I spinodal at to established binodals (Ref. 22) at the same temperature. Dotted and solid lines are computed from VEOS4 and VEOS5, respectively, and end where the VEOS indicates a critical point; the dot-dashed line is computed from VEOS6 and does not exhibit a critical point.

Image of FIG. 5.
FIG. 5.

Same as Fig. 2, but for mixture II.

Image of FIG. 6.
FIG. 6.

Critical line for mixture II in the pressure-temperature plane. Dotted line (circles) is computed from VEOS4, solid line (squares) VEOS5, and dot-dashed line, VEOS6.

Image of FIG. 7.
FIG. 7.

Critical line for mixture II in pressure-composition (top) and temperature-composition (bottom) planes. Dotted line (circles) is computed from VEOS4, solid line (squares) VEOS5, and dot-dashed line VEOS6.

Image of FIG. 8.
FIG. 8.

Schematic of behavior exhibited by critical-point indicators in mixtures III and IV. Lines are the indicated second derivatives (in arbitrary units) evaluated along the spinodals. The abscissa is a coordinate such as density or mole fraction that measures movement along the spinodal line. Along the spinodal, the two second derivatives are necessarily of opposite sign. The “near-miss” condition occurs when lines turn away from zero before crossing it. Two critical points emerge as temperature is varied. Further changes in temperature may move the second critical point to very high density or see it eliminated entirely.

Image of FIG. 9.
FIG. 9.

Mixture III spinodals in the composition-density plane. Dotted lines are calculated from VEOS4, solid lines from VEOS5, and dot-dashed lines from VEOS6. Each group of lines in the figure corresponds to the indicated temperature (in units of ). Spinodal lines terminate where the critical criterion [Eq. (7)] is satisfied (even though spinodal condition continues to be met at higher density). The × symbol indicates the location of a near-miss critical point for VEOS4 and VEOS5, and spinodal lines are drawn past them. Black dot-dashed line at far right is the line of critical points according to VEOS6; the line is drawn thicker at conditions where critical point is given by near-miss criterion (roughly between and 0.6).

Image of FIG. 10.
FIG. 10.

Spinodals for mixture III in the pressure-composition plane. Top: dotted lines are calculated from VEOS4, solid lines from VEOS5, and dot-dashed lines from VEOS6. Each group of lines in the figure corresponds to the indicated temperature (in units of ). Termination of lines and use of × symbol is as in Fig. 9. Bottom: comparison of mixture III spinodal at to established binodals (Ref. 22) at the same temperature, with × symbol indicating the near-miss critical point. Line types are as in top figure.

Image of FIG. 11.
FIG. 11.

Critical line for mixture IV in the pressure-composition plane. Dotted line (circles) is computed from VEOS4; solid line (squares), VEOS5; dot-dashed line (triangles), VEOS6. Line is made thicker and open symbols are used where classical criterion [Eq. (7)] is not satisfied, and critical line is instead eliminated using near-miss critical condition. Symbols indicate temperatures where the virial coefficients were given directly by the Mayer-sampling calculations, and lines connecting them were computed using virial coefficients given by interpolation of the measured coefficients (Ref. 29). In addition, the × symbols indicate MC simulation data (Ref. 23).

Tables

Generic image for table
Table I.

Parameters for the LJ mixtures examined in this work. For all mixtures, the species-1 size and energy parameters and are unity and provide the length and energy scales for the system. The table lists the unlike and species-2 size and energy parameters for the four mixtures in units of the species-1 parameters.

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/content/aip/journal/jcp/130/22/10.1063/1.3148379
2009-06-10
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Virial coefficients of Lennard-Jones mixtures
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/22/10.1063/1.3148379
10.1063/1.3148379
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