Interpenetration functions

Together with Eq. (24) this gives a relationship for the interpenetration function in terms of this equivalent radius ... 

This equation looks very similar to Eq. (23) for the draining function 0, The meaning, however, is different the function 0 is determined by the resistance of the penetration of small molecules (the solvent molecules) into the clouds of connected segments, while the interpenetration function results from the far more inhibited interpenetration of two connected segment clouds. Figure 8 elucidates the difference. 

Fig. 14. Dependence of the interpenetration function R on the number of arms in star molecules. The full line represents the result of the renormalization group theory [90], the data points refer to measurements [77]. Reprinted with permission from [77]. Copyright [1983] American Society...

At this point two essential remarks have to be added. The first is concerned with the reduced concentration X =A2M c = c 2 hich is a rather universal scaling parameter. It indicates the fact that the same master curve is obtained whether for a special sample the concentration is changed or the molar mass is varied. Even the solvent can be changed as long as the good solvent condition remains fulfilled, i.e., the coil interpenetration function W(z) should have reached its plateau value Finally it may be noticed that at no stage of this outline did the chemical nature of the sample have to be introduced. In fact, measurements... 

For the coil interpenetration function (sec Equation 3.1-159), Oono and Freed (1982) have obtained... 

Reliable experimental data on the behaviour of polymer dimensions with increasing solvent quality is too rare, in fact the classical data of Beny is still widely cited. Neutron scattering does provide a new approach (see Chapter 11), but concomitant light scattering/intrinsic viscosity measurements remain the main probe. A recent paper furnishes a novel approach by using bacterium synthesized poly(D-/S-hydroxy-butyrate), PHB, in trifluorethanol. Values of > 7 may be obtained and aj is found to be asymptotically proportional to z. Further, the interpenetration function T [equation (10)] does not increase to an asymptote as a function of as predicted by all current theories but instead reaches a maximum before falling to an asymptotic limit 2 0.22. 

The second virial coefficients can also be related to the interpenetration functions W defined by ... 

When the polymers are in good solvents and for a symmetrical system Mq = Mb, Ra = Rbt and therefore = b = it has been demonstrated that the difference of the interpenetration functions AV = Wab is related to the molecular weight by the scaling law ... 

In very asymmetric systems where the radius ratio o is either very large or very small, the mutual virial coefficient Gab (o equivalently the mutual interpenetration function Was) is very difficult to measure because it gives only a small contribution to the osmotic pressure or scattering intensity. In the symmetric case where the masses of the two different polymers are equal, Waa Was are of the same order of magnitude and their difference has been measured recently by lightscattering using the so-called optical 0-solvent method which gives direct access to the monomer virial coefficient difference... 

The effect of branching can also be studied by means of the dependence of the interpenetration function on the functionality of the star ... 

Within the framework of the two-parameter theory, the interpenetration function F defined by... 

---