Onset of entanglement and reptation in melts of linear homopolymers: consistent rheological simulations of experiments from oligomers to high polymers

Abstract

The shear rheological behavior is investigated in this work for a series of poly(ethyl acrylate) samples, whose molar mass ranges from oligomers to high polymers. The focus was on studying the onset of entanglement effects over selected reptation models in order to ascertain their ability to reproduce the complex shear modulus of the polymers and to provide consistent values of the microscopic parameters driving the structural relaxation of the polymer system.Among ordinary reptation topological models, we found that, the Doi-Edward model, implemented with contour length fluctuation and constraint release mechanism for the tube relaxation, better reproduced the rheological response of the materials. Most importantly, we were able to simulate material functions to obtain consistent microscopic information on the materials, such as Rouse time and entanglement molar mass, over the whole range of investigated molar masses, therefore overcoming the discrepancy usually found, mostly in the mass region of partial entanglement. Finally, descriptions of the polymer entanglement features, in agreement with the experimental and microscopic model findings, are provided in the framework of the packing-length phenomenological model, and by means of analytical calculations of the polymer viscosity according to the Milner-McLeish-Likhtman model.

The Entanglements of Macromolecules and Their Influence on the Properties of Polymers

“…The tube model describes the motion of the entangled polymer in the melt or in a concentrated solution . According to the reptation concept, formulated by de Gennes, a polymer chain moves inside a virtual tube, with the diameter depending on the restrictions made by other macromolecules.…”

“…In a more advanced approach three characteristic types of chain motion can be defined: a) fast chain movements perpendicular to the tube axis, b) longitudinal fluctuation of the segment density, c) evolution of the axis of the tube, leading to disentangling of the chain. The relaxation time of the last motion, τ d , is long and is described by the equation: τ d ~ τ s M 3 /〈 M e 〉, where τ s is the relaxation time in the monomeric scale (≈10 −11 s) dependent on the reciprocal of temperature and M is a molecular mass . Many experimental results can be satisfactorily described by tube models, especially when additional relaxation mechanisms are included, such as contour length fluctuations of the reptating chain and constraint release from the motion of neighboring chains …”

“…The tube model describes the motion of the entangled polymer in the melt or in a concentrated solution. [10,11,[13][14][15] According to the reptation concept, formulated by de Gennes, [13] a polymer chain moves inside a virtual tube, with the diameter depending on the restrictions made by other macromolecules. In the simplest version of this model the motion of the macromolecule perpendicular to the tube is restricted by the tube wall, but its motion along the tube is free.…”

“…The relaxation time of the last motion, τ d , is long and is described by the equation: τ d ~ τ s M 3 /〈M e 〉, where τ s is the relaxation time in the monomeric scale (≈10 −11 s) [11] dependent on the reciprocal of temperature [17] and M is a molecular mass. [11] Many experimental results can be satisfactorily described by tube models, especially when additional relaxation mechanisms are included, such as contour length fluctuations of the reptating chain and constraint release from the motion of neighboring chains. [11,15,18,19] The shear modulus accordingly to the original tube model is described by equation: [11]…”

“…[11] Many experimental results can be satisfactorily described by tube models, especially when additional relaxation mechanisms are included, such as contour length fluctuations of the reptating chain and constraint release from the motion of neighboring chains. [11,15,18,19] The shear modulus accordingly to the original tube model is described by equation: [11]…”