Mathematical analysis of the alignment of guest molecules in solid one-dimensional inclusion compounds: the design of materials for applications in non-linear optics

A mathematical model of solid one-dimensional inclusion compounds is developed to assess the factors controlling the alignment of unsymmetrical guest molecules of the type XY within a tunnel host structure. Two models (uni-directional and bi-directional sequential models) are considered for the growth of the guest substructure within the host tunnel, and in these models the orientational characteristics of the guest molecules are considered to be functions of the energies of the X … X, X … Y and Y … Y guest-guest interactions and the host … XY and host YX interactions. The conditions, defined in terms of the relationships between these energies, that give rise to a parallel alignment of guest molecules within the host tunnel structure are derived. The fundamental understanding of the factors controlling the extent of parallel alignment of guest molecules within tunnel host structures developed in this paper is discussed in the context of the design of such inclusion compounds for applications in second harmonic generation and other second-order non-linear optical properties.