Bottom-up self-organizing dissipative polymer nanostructures

Abstract

Based on scaling concepts a methodology of research of non-equilibrium polymer systems has been elaborated. Polymers with flexible chains (melt-crystallized linear high density polyethylene is chosen as an example) are solutions in melt as well as in solid state, the ends of a chain serving as a solvent for it. At critical polymerization degree all phases (melt, solid isotropic or oriented state) are identical. 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. Depending on the type of polymer statistics (Gauss or Lévy–Khinchin) and the number of components of an ordering field for the second case, the melt viscosity and the self-diffusion coefficient vs. the molecular weight of linear flexible-chain polymer follow the power laws with the 3.50, 3.41 or 3.33 and −2.50, −2.05 or −1.65 exponents, respectively, within the reptation model near the critical point. Vibrational–rotational Brownian motions of chain ends about the polymer melt flow direction were taken into account to find better agreement with the experiment. The recent experimental results of dynamic mechanic and dielectric spectroscopy show the value 3.5±0.1 for the viscosity exponent of long chains, while NMR data result in −2.3±0.1 for the self-diffusion coefficient exponent of short chains. Possible reasons are discussed.