Mean-field solution for random mixtures AxB1-x of an Ising site model

Growth-induced polarity formation in solid solutions of organic molecules: Markov mean-field model and Monte Carlo simulations

A layer-by-layer growth model is presented for the theoretical investigation of growth-induced polarity formation in solid solutions H(1-X)G(X) of polar (H) and nonpolar (G) molecules (X: molar fraction of G molecules in the solid, 0<X<1). The model is characterized by the assumption of thermal equilibrium formation of adlayers, with respect to the up and down orientation of the dipoles of H molecules and to an exchange of H and G molecules, while previously attached layers are kept frozen. The model is analyzed by means of a Markov mean-field description and Monte Carlo simulations. In solid solutions, polarity results from a combined effect of orientational selectivity by H and G molecules with respect to the alignment of the dipoles of H molecules and miscibility between the two components. Even though both native structures (H,G) may be centrosymmetric, polarity can arise just from the admixture of G molecules in the H crystal upon growth. An overview of possible phenomena is given by random selection of molecular interaction energies within an assumed but realistic energy range. The analytical approach describes sufficiently basic phenomena and is in good agreement with simulations. High probabilities for significant vectorial alignment of H molecules are found for low (X< or =0.2) and high (X> or =0.8) fractions of G molecules, respectively, as well as for ordered HG compounds (X=0.5).