Theories of excluded volume

We must note also a second important restriction of the continuous chain model. As we will see. by construction it deals with infinitely long chains n — oo. infinitesimally close to the -point , 5C — 0. Thus naive two parameter theory is valid only very close to the -temperature. In later chapters we will see how further renormalization leads to a theory of excluded volume effects valid for all /%, > 0. 

The second virial coefficient of polyelectrolytes is treated theoretically either by applying the theory for charged spherical colloids with a correction for the chain character of the polyion or as an extension of the theory of the second virial coefficient for nonionic linear polymers. An example of an extension of the theory of the second virial coefficient for nonionic linear polymers to polyelectrolytes is the above-mentioned Yamakawa approach of using perturbation theory of excluded volume to calculate A2 [42],... 

Ry virtue of the equivalence between the polymer theory of excluded volume and the one-con I ponent tp field theory (except the numerical feictor), the arguments of reiiormal-izability in field theory (Aniit, 1978) are used in (k,a) space of the polymer problem. 

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