The domain structure in thin ferroelectric films was investigated in the framework of the modified Ising model with short-range exchange and long-range dipole-dipole interactions. The depolarizing field was also taken into account for the study of size effects in thin films. This field is the dominant factor influencing on the existence of phase transitions in the films. We used Monte Carlo method with the standard Metropolis algorithm to generate configurations on three-dimensional cubic lattices. The domains sizes were calculated in the longitudinal and transverse directions relatively to the spontaneous polarization direction. Temperature dependences of the domain sizes are obtained for different values of interaction constants. It was proved that the introduction of the depolarizing field leads to the appearance of a dead layer on the film boundaries. The dead layer thickness increases with increasing temperature. At a certain temperature (not equal to the Curie temperature), the dead layer is destroyed. The temperature dependences of the dielectric susceptibility at different film thicknesses have been calculated. It was shown that these dependencies have two maxima. The first maximum corresponds to a phase transition, the second one exists only for only thin films and corresponds to the destruction of the dead layer.
We developed a mean-field model describing a system of interacting polymer chains in the contact with a spherical granule surface. It is shown that the size of supramolecular structures formed by macromolecules near the granules does not depend on the size of these granules but depends on the temperature and properties of polymer chains. We revealed that the size dependence of supramolecular formations on the mean molecular field changes sharply at the certain critical field value which depends on the temperature.
To study dynamic properties of a polymer coating, we consider a polymer chain with finite length. We take into account a chain bending rigidity and assume that the chain is located near an adsorbing flat surface of a solid. One part of the chain is fixed on the surface, and the second one remains free. It is supposed that the cause of chain stretching is the internal effective mean (molecular) field formed as a result of intermolecular interactions with free ends of other chains. Kinetic equations based on the Kubo method are obtained to calculate the relaxation time of the segments. The dependences of the long-range orientational order parameter and relaxation time on the adsorption parameter, the mean field coefficient and chain bending rigidity parameters are calculated. It is shown that a first-order phase transition occurs at the critical point, which is associated with a drastic change in the degree of the chain elongation. We discovered the “critical deceleration” effect, which consists in a sharp increase in the relaxation time near the critical point during the formation of surface polymer layers on the surface of a solid.
To describe a surface morphology of textured polymer coatings, the model of polymer chains attached to spherical granules was developed. By means of the model, we revealed the influence of coating density on its surface morphology. Diffuse reflection coefficient was calculated for polymer coatings with different morphologies.
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