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

Abstract

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).

Achiral Organic, Inorganic, and Metal Crystals as Auxiliaries for Asymmetric Transformations

“…The reduction in symmetry in some of the sectors of this centrosymmetric crystal has been determined also by the display of pyroelectric effect in certain directions of the sector. The reduction of symmetry and the formation of the polar mixed crystals have been treated theoretically by applying Markov mechanisms and Monte Carlo simulations 17…”

Universality behaviour for polarity formation in channel-type inclusion compounds

“…Taking advantage of fundamental knowledge on growth induced polarity formation [9][10][11] we can assume a time-homogeneous Markov chain description [12] being particularly valid in the case of lateral guest-guest interactions in the order of a small perturbation [13]. In case lateral interactions between channels become more significant, probabilities describing the step-by-step growth of polarity (X net ) become themselves dependent on the local level of polarity as growth goes on.…”

Influence of Solid Solution Formation on Polarity: Molecular Modeling Investigation of the System 4-Chloro-4‘-nitrostilbene/4,4‘-Dinitrostilbene

“…Application of a Generalized Markov Mean-Field Model. Polarity formation and miscibility arising during the growth of a face ( hkl ) are described by means of a generalized Markov mean-field model; see refs and . In this model, the crystal is assumed to grow layer-by-layer; that is, a new layer starts to grow only when the previous layer is completed.…”

“…Further on, it is assumed that crystal growth occurs near thermal equilibrium; that is, the time needed for the attachment of a new layer is much larger than the surface relaxation time. The molar fractions , , and (with g = I, II) in the asymptotic state are obtained by the following equations of consistency which have to be solved numerically; see ref . is the attachment probability that a molecule in state s = u , d , or n (up, down, or nonpolar, respectively) will be attached to a surface site g = I, II. On the basis of the assumption of thermal equilibrium formation of an adlayer, the probabilities are given by normalized Boltzmann factors with and x s = 1 − X gas if s ∈{ u , d }; otherwise, x s = X gas if s = n .…”

“…The term x s originates from the chemical potentials of the two different components. Note that the chemical potentials in the gas and the solid are assumed to be the same; see ref . denotes the mean-field estimate of all the first nearest neighbor interactions involved between an attaching molecule in state s on surface site g = I, II…”