Confined Three-Aggregate Systems and Their Thermodynamics

A class of small systems is considered that includes spatial regions occupied by atoms and molecules in three-aggregate states, with a total volume that is not macroscopic. This does not allow use of the concept of phase for each region with a different aggregate states, as is done in Gibbs thermodynamics. They occur in a large number of systems, starting from well-known porous materials with different specific surface areas (including adsorbents, catalysts, and membranes) to ensembles of colloidal particles with diverse structures and nature, which are in non- or quasi-equilibrium states of the entire system. Specific thermodynamics of three-aggregate volume-limited systems formed by solid surfaces that contain a mobile layering fluid is discussed: the limited system volume V ( H ) is interpreted as quasi-homogeneous in analogy with the minimum unit volume dV macro of a macrosystem (where H is the characteristic size of a small system, and V ( H ) < dV macro ). Thermodynamics of the full system is analyzed by means of statistical thermodynamics based on the so-called lattice gas model. Two-level models reflecting their local heterogeneities at molecular and supramolecular levels are introduced to describe the structures of real materials and systems. Two levels of describing the energy of interaction between components of the system are also introduced: the short-range interaction potential at the molecular level between the fluid components and between solid atoms and components of the molecular mixture and the long-range potential between solid particles. It is shown that the size dependences of thermodynamic properties of confined systems have an effective character reflecting the weighted average effect of contributions from heterogeneous regions near confining surfaces of solids. It is found that apart from the traditional consideration of overlapping of potential fields from opposite solid surfaces, the limitation of the system requires allowance for the implicit interaction between confining walls through fluid molecules. Possible definitions of the concept of phase are considered for small three-aggregate systems. These definitions are consistent with the Gibbs concept of phase equilibrium, along with ways of calculating three types of surface tension in these systems. A thermodynamic analysis is performed of the concept of disjoining pressure.