Stochastic polarity formation in molecular crystals, composite materials and natural tissues

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.