Surface Tension and Molecular Correlations near the Critical Point
The van der Waals, Cahn—Hilliard theory of interfacial tension is reformulated for a fluid in the neighborhood of its critical point. The reformulated theory becomes equivalent to the Ornstein&m...
The van der Waals, Cahn—Hilliard theory of interfacial tension is reformulated for a fluid in the neighborhood of its critical point. The reformulated theory becomes equivalent to the Ornstein&m...
Influence of Electric and Magnetic Fields on the Molecular Alignment in the Liquid Crystal Anisal-p-aminoazobenzene
The molecular alignment has been studied for anisal-p-aminoazobenzene in the presence of external magnetic and ac electric fields. Measurements of the dielectric loss at a microwave frequency of 24 kM...
The molecular alignment has been studied for anisal-p-aminoazobenzene in the presence of external magnetic and ac electric fields. Measurements of the dielectric loss at a microwave frequency of 24 kM...
Equation of State in the Neighborhood of the Critical Point
J. Chem. Phys. 43, 3898 (1965); doi:10.1063/1.1696618
Issue Date: 1 December 1965
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A specific form is proposed for the equation of state of a fluid near its critical point. A function 
(x, y) is introduced, with x a measure of the temperature and y of the density. Fluids obeying an equation of state of van der Waals type (``classical'' fluids) are characterized by being a constant. It is suggested that in a real fluid (x, y) is a homogeneous function of x and y, with a positive degree of homogeneity (Sec. 2). This leads to a nonclassical compressibility, the behavior of which is determined by the degree of homogeneity of (Sec. 3). A previously derived relation connecting the degree of the critical isotherm, the degree of the coexistence curve, and the compressibility index, again follows, this time without the restrictive assumption of effective isochore linearity (Sec. 4). The locus in the temperature—density plane of the points of inflection in the pressure—density isotherms, as determined experimentally by Habgood and Schneider, is accounted for (Sec. 5). It is shown that if a certain combination of the compressibility and coexistence curve indices is an integer, then the constant-volume specific heat on the critical isochore has a logarithmic singularity at the critical temperature with, in general, a superimposed finite discontinuity (Sec. 6).
©1965 American Institute of Physics
(x, y) is introduced, with x a measure of the temperature and y of the density. Fluids obeying an equation of state of van der Waals type (``classical'' fluids) are characterized by being a constant. It is suggested that in a real fluid (x, y) is a homogeneous function of x and y, with a positive degree of homogeneity (Sec. 2). This leads to a nonclassical compressibility, the behavior of which is determined by the degree of homogeneity of (Sec. 3). A previously derived relation connecting the degree of the critical isotherm, the degree of the coexistence curve, and the compressibility index, again follows, this time without the restrictive assumption of effective isochore linearity (Sec. 4). The locus in the temperature—density plane of the points of inflection in the pressure—density isotherms, as determined experimentally by Habgood and Schneider, is accounted for (Sec. 5). It is shown that if a certain combination of the compressibility and coexistence curve indices is an integer, then the constant-volume specific heat on the critical isochore has a logarithmic singularity at the critical temperature with, in general, a superimposed finite discontinuity (Sec. 6).
©1965 American Institute of Physics
| History: | Received 15 July 1965 |
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REFERENCES (15)
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- H. W. Habgood and W. G. Schneider,
Can. J. Chem. 32, 98 (1954) . - J. W. Essam and M. E. Fisher, J. Chem. Phys. 38, 802 (1963).
- T. D. Lee and C. N. Yang,
Phys. Rev. 87, 410 (1952) . - After this article was submitted it was called to the author's attention that E. Helfand, in a paper presented at the March, 1965 meeting of the American Physical Society at Kansas City, proposed particular cases of Eq. (6) to account for nonclassical behavior near the critical point; and that R. B. Griffiths subsequently showed that Helfand's equation of state implied a logarithmic specific heat singularity, as is found in Sec. 6 of the present paper.
- This formulation of the behavior of at the critical isochore arose from remarks made by R. B. Griffiths (private communication) and by the referee of this paper, to both of whom the author is indebted.
- D. S. Gaunt, M. E. Fisher, M. F. Sykes, and J. W. Essam, Phys. Rev. Letters 13, 713 (1964).
- In the widely used notation of Fisher, g, f, d are called
, 
![[prime]](http://scitation.aip.org/stockgif3/prime.gif)
, 1/
, respectively. - B. Widom, J. Chem. Phys. 41, 1633 (1964).
- C. N. Yang and C. P. Yang, Phys. Rev. Letters 13, 303 (1964).
- L. Onsager,
Phys. Rev. 65, 117 (1944) . - M. E. Fisher,
Phys. Rev. 136, A1599 (1964) . - B. Widom, J. Chem. Phys. 37, 2703 (1962).
- G. S. Rushbrooke, J. Chem. Phys. 39, 842 (1963).
- W. M. Fairbank, M. J. Buckingham, and C. F. Kellers, Bull. Am. Phys. Soc. (II) 2, 183 (1957).
- R. B. Griffiths, Phys. Rev. Letters 14, 623 (1965).
