Kirkwood-Muller equation

Table II shows clearly the large differences between various theories for many-electron systems. The Kirkwood-Muller equation always yields somewhat too large coefficients for the atoms which are the only spherical systems but the London equation deviates by a greater amount on the low side. The Slater-Kirkwood equation gives a high value for He but yields coefficients smaller than the empirical ones for all other cases.

The constant, C, can also be calculated with the help of the Kirkwood-Muller equation, as later explained, or with the Slater-Kirkwood expression. 

By making use of the Kirkwood-Muller equation and substituting the available experimental data for the physical properties of nitrogen and carbon, Horvath and Kawazoe (1983) arrived at the following equation for the adsorption of nitrogen by molecular sieve carbons at 77 K ... 

In equation (4), A is the number density of atoms per unit surface area A is the dispersion constant the subscripts 5 and / refer to the adsorbent and adsorbate, respectively and do = 0.S5 asf is the z-coordinate at which the 10-4 potential for a single planar surface passes through its zero-point value. The 10-4 potential is obtained by integration of the Lennard-Jones 12-6 potential over an infinite planar surface. The dispersion constants A and Aff represent the adsorbate-adsorbent and adsorbate-adsorbate interactions, respectively these coefficients are calculated from the Kirkwood-Muller equations in the original HK paper [6], Combining equations (2-4) yields an equation that relates filling pressure to pore width ... 

In Eq. (33), N is the molecular density (i.e., molecules per unit surface area) A is the dispersion coefficient the subscripts s and f refer to the adsorbent and adsorbate, respectively and d = (2/5) The 10-4 potential is obtained by integrating the I.ennard-Jones potential over an unbounded planar surface [105], The dispersion coefficients are calculated using the Kirkwood-Muller equations (as reported in Ref. 19)... 

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