Entangled polymer systems

Graessley,W.W. Linear viscoelasticity in entangling polymer systems. J. Chem. Phys. 54, 5143-5157 (1971). 

In this situation, which is also discussed in Section 7.5, we refer to experimental evidence according to which components of the relative permittivity tensor are strongly related to components of the stress tensor. It is usually stated (Doi and Edwards 1986) that the stress-optical law, that is proportionality between the tensor of relative permittivity and the stress tensor, is valid for an entangled polymer system, though one can see (for example, in some plots of the paper by Kannon and Kornfield (1994)) deviations from the stress-optical law in the region of very low frequencies for some samples. In linear approximation for the region of low frequencies, one can write the following relation... 

The mesoscopic approach gives an amazingly consistent picture of the different relaxation phenomena in very concentrated solutions and melts of linear polymers. It is not surprising the developed theory is a sort of phenomenological (mesoscopic) description, which allows one to get a consistent interpretation of experimental data connected with dynamic behaviour of linear macromolecules in both weakly and strongly entangled polymer systems in terms of a few phenomenological (or better, mesoscopic) parameters it does not require any specific hypotheses. 

Kremer K, Crest GS (1990) Dynamics of entangled linear polymer melts A molecular-dynamics simulation. J Chem Phys 92(8) 5057-5086 Kremer K, Sukumaran SK, Everaers R, Grest GS (2005) Entangled polymer systems. Corn-put Phys Commun 169(1—3) 75-81... 

In the present paper, after a rapid presentation of the reptation model in its simplest version, in order to pinpoint the underlying hypothesis, we discuss the interest of complementary self diffusion and viscoelastic measurements, and present the currently available methods for measuring diffusion in entangled polymer systems. Then, results obtained on polydimethylsiloxane (PDMS), a model liquid polymer well above its glass temperature at room temperature will be described, and the consequences on the limits of the entangled regime as seen from diffusion measurements, compared to what is observed in rheometry, will be discussed. 

Part I summarizes the main ideas of de Gennes, Doi and Edwards about tube models and reptation in entangled polymer systems. Attention has been limited to properties for which predictions can be made without invoking the independent alignment approximation macromolecular diffusion, linear viscoelasticity in the plateau and terminal regions, stress relaxation following a step strain from rest of arbitrary magnitude, and equilibrium elasticity in networks. 

Topological invariants offer in principle a rigorous approach to the statistical mechanics of entangled polymer systems, but this approach suffers from a number of disadvantages. First of all, the invariants are so complex that the use of topological invariants for more than two chains is hardly possible jjjjg restriction would... 

We ask what relation exists between and td. Assuming that long-timescale motions of a chain occur dominantly in the reptation mode, Dol and Edwards [65] formulated an elegant theory of viscoelasticity of entangled polymer systems and showed that is related to td by... 

Approximately, ° in entangled polymer systems is given by the product of the longest relaxation time t and elastic modulus G[l,17]. 

Hoei, Y. Ikeda, Y. Sasaki, M., A Erozen Tube Model of Melting Point Depression of Solvents in Entangled Polymer Systems. J. Phys. Chem. B 2003,107,1483-1490. 

K. Osaki, K. Nishizawa, and M. Kurata, Material Time Constant Characterizing the Nonlinear Viscoelasticity o Entangled Polymer Systems Macromolecules 15, 1068-1071 1982,... 

Of course, parameter x should not be considered as a free parameter. It can be estimated for a given polymer system. We shall consider an entangled polymer system, for which... 

In this work, we discuss briefly some aspects of the molecular theory for diffusion in entangled polymer systems proposed by de Gennes, and we review the studies on diffusion of PDMS chains in melts and in networks, not only considering the influence of free volume or polydispersity effects but also focusing attention on data analysis procedures. Since most of the data available for self-diffusion of PDMS has been obtained using NMR techniques, some considerations of the NMR methods and models used for analysis of the experimental results are included as well. 

Padding, J.T. and Briels, W.J. (2007) Ab-initio coarse-graining of entangled polymer systems, in Nanostructured Soft Matter, NanoScience and Technology, Springer, Netherlands, pp. 437 60. 

Noolandi et al established the theory of intrachain reaction rates in entangled polymer systems. Raap and Grollmann established theoretical relations relative to the reactions of linear macromolecules in solution possessing initially several reactive sites per macromolecule. Both intra- and inter-molecular reactions take place and the theoretical relations allow the determination of their respective contributions. 

Numerous computer simulations have been carried out in order to examine the transition from Rouse to reptation dynamics [70, 78-88]. Entanglement effects on chain dynamics clearly showed up. However, the discussion as to what extent the characteristic featmes of the reptation model for concentrated polymer liquids are verified by these simulations still remains controversial. It also should be mentioned that a series of phenomenological nonreptative models were published recently [89-94]. They mainly focus on viscoelastic properties of entangled polymer systems. 

The illustrative and intuitive nature of the tube/reptation model is juxtaposed by its partly phenomenological character that makes it impossible to trace the formalism back to elementary principles on a molecular level. The strategic idea to project the whole multiparticle complexity of an entangled polymer system to the assumption of a fictitious tube, so to speak, is the beginning and the end of our thinking in the frame of this model. 

---