Reptation and Linear Viscoelasticity

If we knew how a physical property changed as we altered we could deduce how this property depended upon b and N. several statistical measures of length of the chain, for example of gyration  

We could say quite generally that the average dimension of a chain is linear in the link length but is some function of N, f(TV)  

This transformation applies equally well to a non-Gaussian chain, for example in a good solvent where v = 0.5  

The constant in Equation (5.112) cannot be readily evaluated using scaling theory. Our transformation applies equally well to the radius of gyration or the root mean square end-to-end length, only the numerical constant changes. We would like to be able to apply this idea to the role of concentration in semi-dilute and concentrated polymer regimes. In order to do this we need to define a new parameter s, the number of links or segments per unit volume  

We can define a critical segment concentration s equivalent to pc provided we allow for the total number of links. If we ignore the constants in the expression we obtain  

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