Polymer entanglement

Gandhi,K.S., Williams,M.C. Effect of solvent character on polymer entanglements. 

Here vj vltT) is the viscosity of the solution at a concentration tij and a temperature T, and v is the value of vx chosen as a reference for the comparison of viscosities at different concentrations. In deriving this equation it was assumed that the effect of diluting a polymer with a solvent or a plasticizer, in decreasing the number of effective polymer-polymer entanglements, is negligible if the amount of diluent added is sufficiently small. We define a quantity ac by... 

Polymer entanglement has been an important concept governing the physical properties of polymers. For example, UHMW-PE single-crystalline materials can be super-drawn up to a draw ratio of 300.30 This high drawability is assumed to be due to the existence of entanglement.31 The first evaluation of entanglement was offered by Porter and Johnson for the MW dependence of melt viscosity and the polymer concentration dependence for the solution viscosity.32 33... 

The concept of polymer entanglements represents intermolecular interaction different from that of coil overlap type interaction. However, it is difficult to define the exact topological character of entanglements. The entanglements concept was aimed at understanding the important nonlinear rheological properties, such as the shear rate dependence of viscosity. However, viscoelastic properties could not be defined quantitatively as is possible with the reptation model. Because an entanglement should be... 

P 14. — — Shear viscosities of polyisobutene systems. — A study of polymer entanglement. Polymer 3, 11—16 (1962). 

The Edwards tube model of polymer entanglements was already discussed in Section 7.3.1. The topological constraints imposed by neighbouring chains on a given chain restrict its motion to a tube-like region (see Fig. 7.10) called the confining tube. The motion of the chain along the contour of-... 

Tsukeshiba II. Huang M. Na YH, Kurokawa T, Kuwabara R, Tanaka Y. Furukawa II. Osada Y, Gong JP (2005) Effect of polymer entanglement on the toughening of double network hydrogels. J Phys Chem B 109 16.304-16309... 

Jeyaseelan and Giacomin (1995) examine the use of large-amplitude oscillatory-shear (LAOS) rheology of filled polymer melts (HDPE filled with carbon black) and use transient-network theory (which separates filler and polymer entanglement effects) to describe the non-linear flow behaviour. 

Capillary zone electrophoresis is not only the simplest form of CE, but also the most commonly utilized. Discussion of this mode permits the presentation of a generic design for the instrumentation for CE. The addition of specialized reagents to the separation buffer readily allows the same instrumentation to be used with the other modes mentioned in the previous section addition of surfactants with MEKC, ampholines for CIEF and a sieving matrix (linear polymers, entangled matrices) for CGE. The discussion on CZE in the following subsections allows for analysis of some of the basic principles governing analyte separation by this technique. 

Intermolecular dipolar relaxation. Nearby protons on other molecules, including solvent, will not contribute significantly to the relaxation of protonated carbons, because of the r dependence deduced above. They do have a detectable influence on unprotonated carbons, however, typically contributing 0.1 Hz to 1/Ti. They can also influence the proton resonances, especially if they are held fairly close to the proton in question by, for example, some polymer entanglement. In this case f(t) will include not only any angular... 

Rosa, A. Orlandini, E. Tubiana, L. Micheletti, C., Structure and Dynamics of Ring Polymers Entanglement Effects Because of Solution Density and Ring Topology. Macromolecides 2011,44,8668-8680. 

The problems associated with polymers in bulk or in concentrated solutions form a class unto themselves. - A discussion of such problems immediately raises que.stions about the validity of ordinary statistical mechanics for systems with a large number of internal constraints. " We do not consider the interesting topological problems associated with theories of polymer entanglements. In order to pursue any statistical mechanical theory of polymers in bulk, it is imperative that the question of internal constraints be fully understood. 

Although not true topological knots, the cross-links in polymer entanglements, which behave as gels on sufficiently short timescales, are also topological in nature. 

---