Diagrams representing possible states of a polymer solution

9 Diagrams representing possible states of a polymer solution 

In the previous sections, we described various regimes. It is natural to try to represent the state of a polymer solution by a point in a plane, in order to establish a map of the various domains. This has been done by Daoud and Jannink,49 but it is possible to proceed in other ways. 

For instance, we can consider the interaction as fixed and represent a solution by a point in the plane (1/JV,C) where N is the number of links and C the number of monomers per unit volume. In a very analogous way, in the theory of magnetism, the state of a ferromagnetic system is represented by a point in the plane (T, M) where T is the temperature and M the magnetization of the system. Thus the straight line 1 /N = 0 of the plane (1/W,C) just corresponds to the spontaneous magnetization curve (coexistence curve) M =. H(r) of the plane (T, M). In particular, the critical point (1/JV = 0, C = 0) of the plane (1/iV, C) corresponds to the critical point (T = TC,M = 0) of the plane (T, M). 

On the contrary, with Daoud and Jannink,49 we can consider the length of the polymers as fixed and assume that the temperature and consequently the solubility of the solution may vary. In this case, a polymer solution is represented by a point in the (C, T) plane. The good-solubility domain corresponds to temperatures T TF where Tr in the Flory temperature. By definition TrF(N) is the temperature at which the second virial coefficient vanishes and TF = lim Trf (N - qo ). Anyway, if N is large TrF(N) is close to TF. 

The region T TF corresponds to a poor solubility domain, and when T is lowered, the demixtion curve is encountered. However, in this region (even for T Tf), it is impossible to faithfully represent a solution by a point in a plane,51 because then the properties of the solution depend on too many parameters (at least three). In the following, we thus ignore the region T TF, reserving to study it in Chapter 14. 

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