The growth of polar molecular crystals (near thermodynamic equilibrium) is investigated by a stochastic growth model. Two types of growth are considered: (i) layer by layer growth and (ii) a kink attachment model within a square lattice. An analytical treatment is in qualitative agreement with Monte Carlo simulations. Essentially, a polar seed progresses along the unique axis to form a minor number of orientational defects in one direction, whereas in the opposite direction a "global" reversal of dipolar building blocks is predicted. Polarity reversal can start from a single orientational defect, undergoing continuation and growth in consecutive layers/attachments (kink), leading finally to complete reversal of all molecular dipoles. Eventually, this behavior results in crystals featuring two sectors of opposite average polarity. The number of growth steps upon dipole reversal depends on the intermolecular interactions. It is shown that for lateral coupling close to or smaller than estimated by the Onsager theory of a ferromagnetic transition in 2D (external field H = 0), there is only a small number of attachments needed to obtain reversal, whereas for strong parallel couplings, the number of grown layers before dipole reversal increases exponentially. Our analysis shows that molecular crystals (made of dipolar building blocks) nucleating into a polar seed are subject to a fundamental growth instability which is adverse to the formation of mono domain polar crystals in general.

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This topical review summarizes the theoretical and experimental findings obtained over the last 20 years on the subject of growth-induced polarity formation driven by a Markov chain process. When entering the growing surface of a molecular crystal, an inorganic-organic composite or a natural tissue, the building blocks may undergo 180 orientational disorder. Driven by configurational entropy, faulted orientations can promote the conversion of a growing non-polar seed into an object showing polar domains. Similarly, orientational disorder at the interface may change a polar seed into a two-domain state. Analytical theory and Monte Carlo simulations were used to model polarity formation. Scanning pyroelectric, piezoresponse force and phase-sensitive second-harmonic microscopies are methods for investigating the spatial distribution of polarity. Summarizing results from different types of materials, a general principle is provided for obtaining growth-induced polar domains: a non-zero difference in the probabilities for 180 orientational misalignments of building blocks, together with uni-directional growth, along with Markov chain theory, can produce objects showing polar domains.

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