Entanglements, mesh size

This equation may be recast into a form which reveals the dependence on entanglement mesh size d... 

Most of the available CR-DTD models assume that the relaxed portions of the chains behave as a simple solvent (diluent) for the unrelaxed portions having the fraction (p (f), and a bulk system having this fraction is equivalent to a polymer solution of the concentration If this assumption is valid, the entanglement mesh (tube) in the bulk system is fully dilated to that in the solution. This argument leads to the replacement of a t) by the entanglement mesh size in the solution, so, = a/

molecular picture. Equation (3.38) is simplified as... 

A semi-dilute solution has an entangled aspect similar to a network. An individual chain can be envisioned as constituted by a series of blobs of size equal to the transient network mesh size [16], which obviously decreases with increasing concentration. For c=c , is similar to the chain mean size. For c c, however, the mesh size is independent on the chain length. In a good solvent, according to Eqs. (5) and (6), these conditions are satisfied by ... 

An entangled solution can be characterized as a network vdth an average mesh size, f, similar to the pore size of the gel. Mesh sizes for various polymers are expressed as a function of the polymer concentration ... 

Here, is a measure of the average mesh size of the entangled network. Understanding of these molecular parameters, for example, the concentration dependence of the diffusion coefficient is well developed for neutral polymer solutions (25) and polyelectrolytes with a large amount of simple salts. However, for salt-free polyelectrolytes, reliable data are lacking and understanding is rather poor. 

FIG. 2.7 Relevant length scales for the colloidal structure of worm-like micelles contour length, Lc, entanglement length, /e, mesh size, m, persistence length, Zp and cross-sectional radius, rcs. Values shown are those measured for a solution with 1.5% total surfactant at a cetyltrimethylammonium tosylate (CTAT)/sodium dodecylbenzenesulfonate (SDBS) ratio of 97/3 with 0.10% added sodium tosylate. (Reproduced from Schubert, B.A., Kaler, E.W., and Wagner, N.J., Langmuir, 19, 4079 -089, 2003. With permission.)... 

In atomic force microscopy (AFM) indentation measurements, thin films of Ca " -PA gels displayed an apparent elastic modulus of 200 MPa, whereas HCl-PA gels had an elastic modulus of 100 MPa (Fig. 5d) [168]. The mesh size of Ca " -PA gels was calculated according to the MacKintosh model for sterically entangled semiflexible networks. The persistence length and the mesh size were estimated to be 102 and 20 nm, respectively [182]. 

Entanglements are characterized by the tube diameter a (the mesh size of the temporary entanglement network see Figure 40). The polymer strand between entanglements is a random walk of Ne/g( (a/f correlation blobs, where iVe is... 

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