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 poly mer 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 iso tropic state to an oriented state below the critical degree of polymerization occurs through necking at a non zero 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 lay ers. 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.

Higgs Boson Mass and Other Constants Estimated by Polymer Statistics Methods

“…Thus, we can see that friction forces have electroweak nature. Firstly, λ n is expressed by help of the β-exponent and connected with the energy dissipation during drawing [2,3].…”

“…Secondly, the exponent η is dealing with a dynamic exponent [2,3,8] and characterized the viscosity of swelling polymer coil [2,3].…”

“…About the α−relaxation transition the draw ratio at break, λ br , has a maximum [1,2] in copolymers of low pressure ethylene -acrylic acids with the small number of the latter comonomer (~0.1-0.3mol% [1,3]) as well as in linear polyethylene (PE) (see [4] and refs. in it).…”

“…in it). At this point the expression λ n 2 /λ br 2 = P(N) (obtained for room temperature) should be changed as formulated in [2]. Here, λ n is the neck draw ratio, P(N) = l a /l a cr is the probability of collision of chain ends, l a is the mean thickness of amorphous layers in isotropic material, l a cr is the same value at N = N cr , N = M w /µ is the polymerization degree, µ = 14kg/kmol is the molecular mass of repeated CH 2 group, lnN cr ≈ 15.89.…”

“…The theoretical curves in Figure 1 seem to confirm our assumption that near the α -relaxation transition the phase transition from n = 0 to n = 2 occurs. Here, we have used precise value for lnN cr ≈ 15.69 in comparison with [2].…”