Transition from two-to three-dimensional behavior in anisotropic polymer layers

Abstract

Two types of anisotropic polymer systems were studied in the spherical approximation used in the classical theory of ferromagnetism. These were a three-dimensional system composed of weakly interacting layers with isotropic interactions between chain segments in the layer planes and thin quasi-two-dimensional polymer films possessing intra-and interchain interaction anisotropy, whose behavior is close to that of two-dimensional systems. Laws that govern a change in the temperature T _cr of phase transition from the long-range order state to a disordered state depending on the magnitude of anisotropy and the size of the layers were established. For systems of the former type in which interlayer interactions is weakened, T _cr tends to zero, being inversely proportional to lng, where g is the ratio of the interaction constant between the layers to that of inplane interaction in a layer. For systems of the latter type, the transition temperature T _cr → 0 according to the T _cr ∼ √ɛ law, where ɛ is the parameter that characterizes the anisotropy of intra-and interchain interactions. The number of layers required for the systems to be considered three-dimensional was estimated. Regardless of the type of boundary conditions for finite systems, the number of layers increases with enhancement of interaction anisotropy (a decrease in g and ɛ) and an increase in the number of chains in the layers, especially for systems of the former type. Transverse orientational correlations of chain segments with respect to the arrangement of the layers decrease according to a power law, as in the case of infinite two-dimensional systems. There are fluctuations of three-dimensional long-range orientation order in the plane of the layers, the fluctuations are enhanced with an increase in the anisotropy of interactions in the system.