Entangled polymers

Figure C2.1.13. (a) Schematic representation of an entangled polymer melt, (b) Restriction of tire lateral motion of a particular chain by tire otlier chains. The entanglement points tliat restrict tire motion of a chain define a temporary tube along which tire chain reptates.

The molecular aspects of. interdiffusion of linear entangled polymers M > Mc cmi fng elcffft g (S pofymer interfaces are summarized in Table 1 [1]. The regJt tion( i qraiq piS 1the interface structure relations in Table 1 hav gbp p... 

M. Cates. Reptation of living polymers Dynamics of entangled polymers in the presence of reversible chain-scission reactions. Macromolecules 20 2289-2296, 1987. 

The diffusion coefficients of entangled polymers in solution will most certainly depend on the viscosity of the medium and vice versa. It is reasonable therefore to expect that the diffusion coefficient would correlate well with the weight average molecular weight of the polymer. M is therefore used with equation (lO) giving... 

Restricted diffusion, correlated motion of spins, or any deviation from a free behavior of the molecules will result in a propagator shape different from a Gaussian one. A wide range of studies have dealt with such problems during the last two decades and NMR has turned out to be the method of choice for quantifying restricted diffusion phenomena such as for liquids in porous materials or dynamics of entangled polymer molecules. 

Deformation of Entangled Polymer Molecules Under Shear... 

Grossmann, P. D. and Soane, D. S., Experimental and theoretical studies of DNA separations by capillaryelectrophoresis in entangled polymer solutions, Biopolymers, 31, 1221, 1991. 

Cottet, H. and Gareil, R, Electrophoretic behavior of fully sulfonated polystyrenes in capillaries filled with entangled polymer solutions,. Chromatogr. A, 772, 369, 1997. 

NSE Studies on Entangled Polymer Melts Poly(tetrahydrofurane) (PTHF)... 

One tool for working toward this objective is molecular mechanics. In this approach, the bonds in a molecule are treated as classical objects, with continuous interaction potentials (sometimes called force fields) that can be developed empirically or calculated by quantum theory. This is a powerful method that allows the application of predictive theory to much larger systems if sufficiently accurate and robust force fields can be developed. Predicting the structures of proteins and polymers is an important objective, but at present this often requires prohibitively large calculations. Molecular mechanics with classical interaction potentials has been the principal tool in the development of molecular models of polymer dynamics. The ability to model isolated polymer molecules (in dilute solution) is well developed, but fundamental molecular mechanics models of dense systems of entangled polymers remains an important goal. 

Entangled Polymer Liquids. Do Linear Chains Reptate ... 

Several research groups used another interesting column technology as an alternative to the modification of the capillary surface. This method is inherited from the field of electrophoresis of nucleic acids and involves capillaries filled with solutions of linear polymers. In contrast to the monolithic columns that will be discussed later in this review, the preparation of these pseudostationary phases need not be performed within the confines of the capillary. These materials, typically specifically designed copolymers [85-88] and modified den-drimers [89], exist as physically entangled polymer chains that effectively resemble highly swollen, chemically crosslinked gels. 

Because of the high viscosity of the entangled-polymer solutions, the buffer can be retained on the outer surfaces of the capillary and electrodes after the... 

The viscosity scales, from Eq. (1), as Tj-GoTi-gp since and are the characteristic modus and relaxation times appearing respectively in the integral. The plateau modulus is independent of molecular weight for highly entangled polymers [1] but inversely proportional to so... 

As we conjectured in the introduction, the fundamental role of topology in this approach to entangled polymer dynamics would indicate that changes to the topology of the molecules themselves would radically affect the dynamic response of the melts. In fact rheological data on monodisperse star-branched polymers, in which a number of anionically-polymerised arms are coupled by a multifunctional core molecule, pre-dated the first application of tube theory in the presence of branching [22]. Just the addition of one branch point per molecule has a remarkable effect, as may be seen by comparing the dissipative moduli of comparable linear and star polymer melts in Fig. 5. 

The recognition of the two fundamental mechanisms of reptation and arm fluctuation for linear and branched entangled polymers respectively allows theoretical treatment of the hnear rheology and dynamics of more complex polymers. The essential tool is the renormahsation of the dynamics on a hierarchy of timescales, as for the case of star polymers. It is important to stress that experimental checks on well-controlled architectures of higher complexity are still very few due to the difficulty of synthesis, but the case of comb-polymers is an example where good data exists [7]. 

It became clear in the early development of the tube model that it provided a means of calculating the response of entangled polymers to large deformations as well as small ones [2]. Some predictions, especially in steady shear flow, lead to strange anomaUes as we shall see, but others met with surprising success. In particular the same step-strain experiment used to determine G(t) directly in shear is straightforward to extend to large shear strains y. In many cases of such experiments on polymer melts both Hnear and branched, monodisperse and polydisperse,the experimental strain-dependent relaxation function G(t,Y) may be written... 

The process of chain retraction can be applied to more complex topologies of entangled polymers under the same assumptions discussed for linear polymers... 

If the ideas of Marrucci [69] are correct and the non-monotonic predictions of the simple Doi-Edwards theory need to be modified in the case of polymer melts (for a recent development see [78]), then an explanation will be required for the apparent difference at high shear rates between melts and wormlike micelle solutions. There is also evidence that ordinary entangled polymer solutions do exhibit non-monotonic shear-stress behaviour [79]. As in the field of linear deformations, it may be that a study of the apparently more complex branched polymers in strong flows may shed light on their deceptively simple linear cous-... 

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