A theoretical framework for the experimental determination of host–guest interaction energies in solid inclusion compounds

Abstract

A mathematical model is developed to provide the framework of an experimental approach for determining host–guest interaction energies in solid inclusion compounds with one-dimensional tunnel host structures. The approach considers the competitive inclusion of two different types of potential guest molecules X(S)qX and X(S)rX (q≠r) within the tunnel host structure, where X represents a given type of end group (e.g., CH3, halogen, etc.) and S represents an appropriate spacer unit (e.g., CH2, CH, etc.). Sequential and simultaneous models for the growth of the guest substructure within the host tunnel are considered. The relative proportions (m and 1−m) of the two types of guest molecule included within the host tunnel depend on the relative proportions (γ and 1−γ) of the two types of guest molecule in the external “pool” of potential guest molecules and the relative “affinities” (χ and 1/χ) of the host tunnel structure for including the two different types of guest molecule. Expressions linking χ, m, and γ are developed, and can be applied to determine χ directly from experimental measurements of m for a series of inclusion compounds prepared for different (known) values of γ. Fundamentally, the value of χ depends on the intermolecular interaction energies per unit length of tunnel for the two different types of guest molecule, and χ may be expressed in terms of the host–guest interaction energies for the spacer units S and the end groups X, and the guest–guest (X⋯X) interaction energy. The mathematical model provides a framework for assessing these different energy contributions from experimental measurements of m for sets of inclusion compounds prepared for different values of the parameters q, r, and γ, and with the same host tunnel structure.