A study of critical phenomena and dissipative nanostructures in self-organizing polymer systems

Abstract

A research methodology based on scaling concepts is developed in detail for nonequilibrium polymer systems. Melt-crystallized linear high-density polyethylene is chosen as an example. In flexible-chain semicrystalline polymers, the transition from a solid isotropic or oriented state to a melt or from a solid isotropic state to an oriented state below the critical degree of polymerization occurs through necking at a nonzero external field on the combined line of first- and second-order phase transitions. A melt is a symmetric phase with a zero order parameter. Lamellar and fibrillar semicrystalline phases are phases with inherent order parameters that are periodic functions of one coordinate, and the neck draw ratio is another order parameter. At the critical degree of polymerization, all the phases are identical. In terms of the fluctuation theory of phase transitions and critical phenomena, the quantitative dependence of macroscopic properties on nanostructure parameters in this polymer material is revealed. The neck draw ratio and the draw ratio at break are macroscopic properties. The structure is characterized by the average thickness of amorphous layers. The square of the neck draw ratio is equal to the product of the square of the draw ratio at break and the probability of collision of chain ends. In turn, this probability is proportional to the average thickness of amorphous layers in an isotropic sample. The problems of dynamic scaling and entanglements are discussed.