Solvation in a One-Dimensional System

The concept of solvation is important in the study of solvent effects on any process taking place in solution. We define solvation as the process of transferring a single particle from a fixed point in the vacuum to a fixed point in the solution. The process is carried out at given thermodynamic variables, say T, P constants, T, V constants, etc. 

Since our particles are structureless, in the sense that they do not have any internal partition function, it is sufficient to study the pseudochemical potential of the species of which the solvation thermodynamics is under study. 

We have already obtained the pseudochemical potentials of a species in a mixture of hard rods, in section 4.5.3. We generalize here the expression for mixtures of interacting particles. 

First we note that the chemical potential for a one-component system (4.5.16) may be written as 

Since in the ideal gas limit, we have from (4.5.18) and (4.5.19) that 

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