Stochastic models for guest-guest interactions in one-dimensional inclusion compounds

The intrinsic relative preferences of X ... X, X ... Y and Y ... Y interactions between functional groups X and Y can be obtained by considering a set of one-dimensional inclusion compounds containing guest molecules of two (or more) of the types X (sic) X, X (sic) Y and Y (sic) Y, with the molar ratios of these types of guest molecule differing between the members of the set. Limited information on the relative preferences of these interactions can also be obtained by considering a one-dimensional inclusion compound containing only guest molecules of the type X (sic) Y. Two probabilistic models are presented for the sequence of oriented guest molecules in a tunnel. of a one-dimensional inclusion compound containing these different types of guest molecule. One model is specified by a Markov chain and is appropriate when the guest molecules are introduced sequentially into the tunnel. The other model is specified by interaction between a guest molecule and both of its neighbours, and is appropriate when the guest molecules are introduced simultaneously into the tunnel. For both models, functional relationships are obtained between the molar ratios of the different types of guest molecule and the ratios of the numbers of X ... X, X ... Y and Y ... Y interactions, all of which can, in principle, be determined experimentally. The intrinsic parameters, which represent the relative energies of these interactions, can be estimated using the corresponding regression equations.