Repulsive chains at.finite concentrations

The error arises from the fact that in reality the distribution probability of the end-to-end vector is not Gaussian but is given by a law of the form 

In brief, the Gaussian approximation does not take into account the existence of the exponent y (and of similar exponents see Chapter 12) and this is why it is unrealistic. 

In reality, all the older theories have the same defect and, consequently, if some of them lead to more exact values of v, this is only the result of an accumulation of errors which cancel partially. 

As will be seen later on, the renormalization theory provides a solution to these difficulties but unfortunately at the cost of complications which, until now, explicitly prevented the construction of a reasonably realistic model of a chain in a good solvent. 

As we saw in the preceding sections, the theory of isolated chains in a good solvent faced many difficulties and it is clear that, in principle, it is even more difficult to work out a theory of polymer solutions at finite concentrations. 

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