Reptation in swollen systems

Our discussion of reptation has been limited to completely dense systems—e.g., a dry network with closely spaced entanglement points or a polymer melt of very long chains, incorporating one extra test chain. To 

Thus the equivalence between blobs and monomers is imperfect and scaling laws for entanglements may be absent, or may be confmed to unphysically high values of N. 

In the following lines, we shall, however, describe the scaling laws which would occur in a melt of blobs, if the entanglement abilities of the blobs were identical to those of monomers. We know that this is too crude, but it may be a useful reference for comparison. 

for simplification, we shall not include explicitly the number Ng in our discussion, but assume that Ng is constant and ignore al powers of Ng. This is criminal, since Ng 200, but it simplifies the pesentation (An improved discussion for melts, incorporating Ng, is summarized at the end of Section VIII.3.1.) 

We discuss first the case where the network is replaced by a semi-dilute solution of concentration c, composed of chains with a large degree of polymerization N. In this solution we add one test chain (N) and ask for the reptation time of the test chain T( (c). For simplicity we choose an ather-mal solvent (a = u, or x = 0). 

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