Self-organising Dissipative Polymer Structures
  In frameworks of the scaling theory of phase transitions and critical phenomena the quantitative dependence of macroscopic properties on nanostructural parameters in a polymeric material is revealed. The draw ratios at neck and at break are referred to the macroscopic properties. The structure is characterized by an average thickness of amorphous layers in isotropic melt-crystallized linear high density polyethylene which is chosen as an example. The square of the neck draw ratio is equal to the product of the square of the draw ratio at break and the chain ends collision probability. This probability in its turn is proportional to the average thickness of amorphous layers in the isotropic material. The neck draw ratio is a parameter of order. Polymers with flexible chains are solutions in solid state as well as in melt, the interacting ends of a marked chain serving as a solvent. At critical polymerization degree all the phases are identical. This research is an important contribution to the molecular theory of polymer liquids. It has been found that the melt viscosity vs the molecular weight of linear flexible-chain polymer follows the power law with the 3.4-exponent within the reptation model near the critical point. This is different from the value 3 expected for the melt of ring macromolecules. The rotation vibration precession motion of chain ends about the polymer melt flow direction were taken into account to find better agreement with the experiment. 
Andrei N. Yakunin
cond-mat.soft cond-mat.stat-mech