Thermodynamic perturbation theory for associating fluids confined in a one-dimensional pore

In this paper, a new theory is developed for the self-assembly of associating molecules confined to a single spatial dimension, but allowed to explore all orientation angles. The interplay of the anisotropy of the pair potential and the low dimensional space results in orientationally ordered associated clusters. This local order enhances association due to a decrease in orientational entropy. Unlike bulk 3D fluids which are orientationally homogeneous, association in 1D necessitates the self-consistent calculation of the orientational distribution function. To test the new theory, Monte Carlo simulations are performed and the theory is found to be accurate. It is also shown that the traditional treatment in first order perturbation theory fails to accurately describe this system. The theory developed in this paper may be used as a tool to study hydrogen bonding of molecules in 1D zeolites as well as the hydrogen bonding of molecules in carbon nanotubes.