The analysis of the phase behavior at and a high density. (a) The raw result showing a vdW loop. (b) The free energy along the loop showing its multivalued nature. (c) The density profile with the Maxwell construction. (d) The derivative that is used in locating the Maxwell construction. The integral over in (c) yields an of 3.37.
(a) Surface coverage, , as a function of chemical for . (b) Surface pressure, , as a function of surface coverage for . (c) Phase diagram for the vertical phase separation, line has a slope of . (d) Isotherms for in steps of 0.1. The critical temperature is 8/27 in reduced units.
(a) Thickness vs surface coverage. Upper curve is twice and the lower is the . (b) Swelling ratio, vs temperature where . ’s of 2–5 are dashed and of increasing magnitude at . ’s of 6–10 are solid and of decreasing magnitude at . has the largest swelling ratio ( at ). The symbols indicate the phase transition for , 6, and 10. (c) Inverse Poisson ratio vs log surface coverage. (d) Double log plot of vs . The slope of the line is 1.25. in (a), (c), and (d).
(a) between system at and and . From low to high values of the left minimum, are 0.50, 0.55, 0.60, and 0.65. (b) The minimum value of from curves such as in plot (a) as a function of the reference density, with . Coexistence requires . (c) The density at the minimum vs at . The dashed lines indicate coexistence ( and two solutions). The coexisting densities are indicated by the arrows (0.10 and 0.64). (d) The coexisting densities are plotted against temperature to give the liquid-vapor phase diagram for the vdW fluid. is in units of . is in units of . is in units of .
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