Molecular correlations in Cell Theories of liquids and solutions

1954 ◽  
Vol 7 (1) ◽  
pp. 28 ◽  
Author(s):  
JA Barker
Keyword(s):  
Cell Theory ◽  
Lennard Jones ◽  
Theory Of Liquids ◽  
Thermodynamic Effects

The thermodynamic effects of correlations between the motions of molecules in neighbouring cells in the Lennard-Jones and Devonshire cell theory of liquids and solutions are calculated approximately, and found to be sufficiently small to be negligible for many purposes.

KIHARA POTENTIAL AND LENNARD-JONES AND DEVONSHIRE EQUATION OF STATE OF LIQUIDS AND DENSE GASES

1966 ◽  
Vol 44 (22) ◽  
pp. 2651-2656 ◽  
Author(s):  
Isamu Nagata
Keyword(s):  
Experimental Data ◽  
Heat Capacity ◽  
Present Theory ◽  
Cell Theory ◽  
Lennard Jones Potential ◽  
Perfect Gas ◽  
Jones Potential ◽  
Dense Gases ◽  
Lennard Jones ◽  
Kihara Potential

The Kihara potential has been applied to the Lennard-Jones and Devonshire cell theory in place of the Lennard-Jones potential. The expressions for the internal energy, heat capacity, and entropy, as well as the compressibility, are given in excess over those of a perfect gas. A comparison between experimental data and the present theory is made.

Corrigenda

1957 ◽  
Vol 240 (1221) ◽  
pp. 273-273
Keyword(s):  
Cell Theory ◽  
Theory Of Liquids

The author regrets the following errors which occurred in ‘The cell theory of liquids. II’ (Barker, J. A. 1956 Proc. Roy. Soc . A, 237, 63): (i) In (3.2), I nm in first summation should be I nm . (ii) On p. 65, line 22, kT /σ should be kT /∊. (iii) In (3.6), ∫ 1 1 G ( r 1 , θ 2 ) should be ∫ -1 1 G ( r 2 , θ 2 ). (iv) In (3.8), r. h. s. should be √( a 2 + r 2 2 – 2 ar 2 cos θ 2 ). (v) On p. 66, line 5, u 2 should be u 1 2 . (vi) In (4.2), r. h. s. should be λ k μ k ω k * . (vii) In (4.12), 1. h. s. should be v f 3 ω 2 * f ". (viii) In (5.6), second = should be –. (ix) In table 8, last column heading should be N̄ 2 /½ cNw 2 .

Theories of the liquid state

1952 ◽  
Vol 215 (1120) ◽  
pp. 4-29 ◽  
Keyword(s):  
Liquid State ◽  
Intermolecular Forces ◽  
Critical Discussion ◽  
Additive Constant ◽  
Pressure Curve ◽  
Lennard Jones ◽  
Theory Of Liquids ◽  
Vapour Pressure Curve ◽  
Theory Of Melting ◽  
Molecular Distribution Function

A critical discussion is given of the various theories of the liquid state, which give an explanation of the liquid properties in terms of the intermolecular forces. In § 2 the general properties of the equation of state of monatomic liquids and the melting and vapourpressure curve are given using the principle of corresponding states with molecular units. In § 3 these experimental data are compared with the theory of Lennard-Jones and Devonshire. The influence of a smaller co-ordination number is investigated in § 4, and in § 5 the difficulties in explaining the additive constant in the vapour pressure curve is discussed. The generalizations of the theory of Lennard-Jones and Devonshire, discussed recently also by Rowlinson and Curtiss, are given in a somewhat simplified representation, showing that the decrease of the co-ordination number can be obtained as a straightforward result of the application of statistical mechanics to the ‘lattice model’ of the liquid state. The transition of the solid to the liquid phase is discussed in § 7, starting with Lennard-Jones and Devonshire’s theory of melting. It is shown that the disordered ‘liquid’ state corresponds to a liquid with a co-ordination number 9, and that an explanation can be given of the melting-point formula of Simon. Finally, in § 8 attempts are discussed to base a theory of liquids on a calculation of the molecular distribution function.

The cell theory of liquids. II

1956 ◽  
Vol 237 (1208) ◽  
pp. 63-74 ◽  
Keyword(s):  
Free Energy ◽  
Critical Region ◽  
Major Part ◽  
Inert Gases ◽  
Simple Cell ◽  
Cell Theory ◽  
Correlation Effects ◽  
Theory Of Liquids

Numerical values of some integrals required in the refined cell theory of liquids are presented for the 12-6 potential in the critical region of density and temperature. The results show the importance of multiple occupation and correlation effects, and of the ‘smearing’ approxiation. Comparison of free energy curves derived from the theory with those for inert gases shows that consideration of binary correlations and multiple occupation of cells corrects the major part of the error of the simple cell theory. It is necessary to take correlations into account in determining multiple occupation factors. The theories of Barker and de Boer are compared; although they are both formally convergent, the theory of Barker appears to give better results in practice.

Variable‐structure cell theory of liquids and glasses

1994 ◽  
Vol 101 (7) ◽  
pp. 6216-6221 ◽  
Author(s):  
Frank L. Somer ◽  
Jeffrey Kovac
Keyword(s):  
Variable Structure ◽  
Cell Theory ◽  
Theory Of Liquids

The cell theory of liquids

1955 ◽  
Vol 230 (1182) ◽  
pp. 390-398 ◽  
Keyword(s):  
Numerical Results ◽  
Cell Theory ◽  
Exact Theory ◽  
Current Cell ◽  
Theory Of Liquids

The cell concept is used as basis for a formally exact theory of liquids. Methods for evaluating the integrals required are indicated, and sufficient numerical results are obtained to discuss the importance of (i) multiple occupation of cells, (ii) correlation or coupling of motion of molecules in different cells, (iii) ‘smearing’ of the potential due to neighbours. Current cell theories are examined in the light of the results.

Molecular association in liquids. III. A theory of cohesion of polar liquids

1952 ◽  
Vol 215 (1120) ◽  
pp. 67-83 ◽  
Keyword(s):  
Free Energy ◽  
Dipole Interaction ◽  
Liquid Structure ◽  
Intermolecular Forces ◽  
Cell Theory ◽  
Electrical Field ◽  
Polar Liquids ◽  
Lennard Jones ◽  
First Approximation ◽  
The Difference

This paper is an extension to polar liquids of the cell theory of liquid structure originally developed by Lennard-Jones & Devonshire. The free energy due to dipole interaction is evaluated using a model consisting of point dipoles fixed on the sites of a lattice but free to rotate in the electrical field of all the others. It is shown that, to a first approximation, the total free energy can be expressed as the sum of the free energy of this model and the free energy of a similar liquid without the dipole-dipole forces. The latter can be evaluated by the method of Lennard-Jones & Devonshire. The theory is applied to the polar liquids HCl, H 2 S and PH 3 . It is found that dipole interaction by itself is not sufficient to explain the difference between the cohesion of these liquids and similar non-polar liquids. The importance of other intermolecular forces between polar molecules is discussed.

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