Statistical mechanics of surface tension. It is shown that we can derive the expression of surface tension in terms of disrtribution functions from purely statistical considerations regarding surface tension as the increase in free energy for an increase of unit area of the interface between the liquid and vapor phases.
The expression obtained is
γ=1/2∫∫…∫dφ
12/dR
12x
212-Z
212/R
12ρ
S(2)(Z, R
12)dZ
1dv
12,
where γ is the surface tension, φ
12 is the intermolecular potential and ρ
S(2) (Z, R
12) is the excess pair density reckoned relative to an arbitrary Gibbs dividing surface. The above expression can be transformed into
γ=∫(p
N-p
T)dZ
1where
p
N(Z)=kTρ
(1)(Z
1)-1/2∫∫…∫dv
12∫Z
1Z
1-Z
12dφ
12/dR
12Z
12/R
12ρ
(2)(ζ, R
12)dζ,
p
T(Z
1)=kTρ
(1)(Z
1)-1/2∫∫…∫dv
12dφ
12/dR
12x
122/R
12ρ
(2)(Z
1, R
12).
The results coincide with those of kirkwood and Buff which were derived by calculating stresses directly.
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