A justification of the reptation-tube dynamics of a linear macromolecule in the mesoscopic approach

The paper contributes to the problem of description of relaxation behaviour of entangled linear polymers in terms of dynamics of a single macromolecule. The approach systematically studies deviations from the Rouse dynamics when adding non-Markovian and anisotropic noise. The introduction of these terms decreases in mobility and increases in relaxation times of the macromolecule in comparison with the Rouse case. An intermediate length, which has the meaning of a tube radius and/or the length of a macromolecule between adjacent entanglements, is calculated through parameters of the model. It is shown that introduction of local anisotropy of mobility of particles in the mesoscopic dynamics of generalised Cerf-Rouse modes allows one to get the effects, which used to be associated with reptation motion of the macromolecule. The devised model can be considered as a possible expansion of the conventional reptation-tube model and can be useful, for example, for formulating a consequent theory of viscoelasticity of linear polymers in entangled states.