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

A mathematical model is developed to provide the framework of an experiment al approach for determining host-guest interaction energies in solid inclus ion compounds with one-dimensional tunnel host structures. The approach con siders the competitive inclusion of two different types of potential guest molecules X(S)(q)X and X(S)(r)X (q not equal r) within the tunnel host stru cture, where X represents a given type of end group (e.g., CH3, halogen, et c.) and S represents an appropriate spacer unit (e.g., CH2, CH, etc.). Sequ ential and simultaneous models for the growth of the guest substructure wit hin 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 (gamma and 1-gamma) of the two types of guest mole cule in the external "pool" of potential guest molecules and the relative " affinities" (chi and 1/chi) of the host tunnel structure for including the two different types of guest molecule. Expressions linking chi, m, and gamm a are developed, and can be applied to determine chi directly from experime ntal measurements of m for a series of inclusion compounds prepared for dif ferent (known) values of gamma. Fundamentally, the value of chi depends on the intermolecular interaction energies per unit length of tunnel for the t wo different types of guest molecule, and chi may be expressed in terms of the host-guest interaction energies for the spacer units S and the end grou ps X, and the guest-guest (X...X) interaction energy. The mathematical mode l provides a framework for assessing these different energy contributions f rom experimental measurements of m for sets of inclusion compounds prepared for different values of the parameters q, r, and gamma, and with the same host tunnel structure. (C) 1999 American Institute of Physics. [S0021-9606( 99)71145-1].