Molecular origin of the heterogeneity in the nematic and smectic liquid crystals: Elastic constants, gradients of order parameters, and visualization of small objects

The formation of heterogeneous nematic and smectic liquid crystals in the general case of an arbitrary geometry is investigated in the framework of molecular-statistical approach [Emelyanenko and Khokhlov, J. Chem. Phys. 142, 204905 (2015)]. The molecular aspects of the orientational and translational orderings at the curved surfaces of small solid objects dispersed in liquid crystal are considered, and the differential equations for gradients of the order parameters in vicinities of the small objects are presented in the general form. The five elastic constants are obtained within the same approach, from which we were able to predict that a significant space variations of the order parameters can be observed within the $0.5--0.8\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\text{m}$ area around any small object, almost independently of its own dimension. Therefore, the liquid crystals can be a simple tool for the optical visualization of nano-objects. It is also demonstrated that the kind of molecular self-organization (smectic, nematic or conventionally isotropic) at the surfaces of small solid objects can be different from that in the bulk of mesogenic material. Totally we predict eight various combinations of simple states at the surfaces and in the bulk depending on the solid objects' size and temperature. It is also shown that the surfaces of $10\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\text{m}$-size solid objects and larger act almost as flat surfaces, while the surfaces of $1\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\text{m}$-size solid objects and smaller act almost as point defects.