STATISTICAL THERMODYNAMICS OF CONFINED THIN-FILMS

This article is devoted to systematic thermodynamic and statistical-ph ysical descriptions of thin films confined by plane-parallel solid sur faces (i. e. walls). Two perspectives are adopted according to how the system is defined in the strict thermodynamic sense. In one view the system is taken to be the composite of the film and the bulk fluid wit h which it is assumed to be in thermodynamic equilibrium. The extensiv e mechanical variables in terms of which the state of the system is de scribed are the volume V and the separation s(z) between the walls. Th e intensive variables conjugate to these are, the pressure p of the bu lk phase and the normal stress T-zz (i. e. the negative pressure) appl ied to the walls. In this view the area A of the interface between the wall and the film is fixed and therefore no mechanical-work term invo lving variations in A can appear in Gibbs' fundamental relation govern ing transformations in the system. In the usual situation, T, p and T- zz are maintained constant. It is demonstrated that when the system ac hieves a state of equilibrium under these conditions, the Gibbs potent ial is minimum. The Gibbs potential is defined here similarly to the o ne normally used to characterize bulk homogeneous phases in terms of t he independent variables T, N and p, except for the presence of an add itional term AszTzz. Earlier thermodynamic analyses of the system as d efined in the first view are reviewed and found to be flawed in that t hey presume a mechanical work term of the form gamma dA, (gamma interf acial tension) although A cannot appear as an extensive variable in th e fundamental relation, for the reasons mentioned above. However, in t he second view presented the system is assumed to consist of a finite lamella of the confined film, the surroundings comprising the remainde r of the film along with the walls. The interfacial area now becomes a proper extensive variable and the transverse contribution gamma dA to the mechanical work appears in the fundamental relation. The conditio ns of fixed T, p and T-zz in the first perspective are shown to be equ ivalent to fixed T, chemical potential mu and T-zz in the second. The criterion for equilibrium of the lamellar system under the latter cons traints is derived and shown to be equivalent to that derived in the f irst perspective under the corresponding constraints. A statistical-ph ysical treatment of the lamella confined by smooth walls is presented in the canonical ensemble and the resulting formulae are explicitly ap plied to two models of low-pressure gas films. The dependence of the i nterfacial tension is rationalized in terms of film-wall intermolecula r potentials.