Semi-dilute solutions mesh size

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 ... 

Fig. 5 Schematic representation of the aggregate domains (shaded area) tying the PF8 chains to form a cluster. The overlap of the unassociated chains in the cluster as well as in the bulk of the semi-dilute solution generates a dynamic network with the characteristic mesh size of Reprinted with permission from [31]. (2007) by the American Chemical Society...

In a semi-dilute solution, each macromolecule can be described by a series of unperturbed sections, separated by regions tangled with other chains. This has been schematised in Fig. 3.10, in which the chains mark out a 3-dimensional lattice the nodes of the lattice represent points where the chains tangle. The lattice fluctuates in space and time and the mean mesh size clearly depends on the polymer concentration Cp. In fact. 

The above presentation of scaling for thermodynamic properties is direct but not illuminating. A much better picture of what happens in semi-dilute solutions can be obtained if we investigate spatial properties. Consider the solution shown in Fig. III.4. When photographed at a certain time, this looks very much like a network with a certain average mesh size... 

We now focus on one particular chain in the semi-dilute solution this could be, for example, one chain labeled by deuteration with all the other chains being normal. We may visualize it as a succession of units or blobs of size (Fig. ni.5). Inside one blob, (from the defmition of the mesh size) the chain does not interact with other chains. Thus, inside one blob we must still have correlations of the excluded volume type. This implies that the nimber of monomers per blob (g) is related to by the law of swollen coils ... 

For the q range studied, the values for the bimodal networks are found to be similar to unimodal networks. The fact that the correlation size in a swollen network is much lager than in the corresponding semi-dilute solution is usually taken to be an indication of inhomogeneities in the network structure. However, the similarity of the results from the unimodal and bimodal networks seems to suggest that in the absence of non-random crosslinking, the distribution of crosslink densities is not the dominant factor in determining spatial correlations in a swollen network at the level of the network mesh size. 

This result, however, cannot be obtained directly by a scaling argument. In a semi-dilute 6 solution, there are two characteristic lengths the correlation length I/c (which represents the distance between three-body contacts and has been chosen here as the tube diameter) and the distance between entanglements 2 (distance between two body contacts) which is the mesh size of the transient network. These two lengths play a role in the viscoelastic properties of semi-dilute 6 solutions. Their relative importance is still a matter of controversy. 

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