Statistical thermodynamics of hard-rod fluids

However, we shf)uld also emphasize at the outset of this chapter that the confined fluid is not suitable for the study of yet another feature of central importance to us, namely confinement-induced phase transitions. This is because one can rigorously prove that, in general, one-dimensional systems cannot undergo discontinuous jihase cliaiig( s [16]. However, this apparent lack of realism is outweighed by the analyticity of the current model system and its capability to reproduce other important features of more sophisticated models or even experimental systems sufficiently reali.stically as we pointed out above. Our analysis in this chapter is based upon the original work by Vanderlick et al. [25] and has in ] art been adopted from the book of Davis [26]. 

Let us begin by introducing a system of one-dimeusional rods of length d where the interaction between a pair of rods is described the intcrmoleadar potential 

That is to say the potential just prevents any pair of rods from interpenetrating. For convenience, we treat the fluid as a thermodynamically open system such that its equilibrium properties are determined by the grand potential [rf., Ef s. (1.32) and (1-51)] 

The connection to the microscopic level of description is then provided by the standard relation [cf., Elq. (2.81)] 

it is apparent from Ekj. (3.5) that U depends on the hard-rod configuration only through intermolecular distances zij. Thus, we can apply the 

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