Intersegmented Interactions

In the Flory-Huggins picture, the interchain interaction parameter should be related to the intersegment interaction parameter by... 

As was repeatedly emphasized, away from the phase separation region (i.e. at high temperatures for systems with a UCST), the intersegment interaction in a polymer chain reduces to the existence of segment excluded volume, which manifests itself by swelling (expansion) of polymer coils. These interactions also lead to a correlation of the segment density fluctuations as it occurs in general-type systems near the critical point. 

Since l is proportional to and q is proportional to 1/L, i is proportional to. Substitution of Eq. (67) into Eq.(62) gives the Langevin equation for the Rouse modes of the chain within the approximations of preaveraging for hydrodynamic interactions and mode-mode decoupling for intersegment potential interactions. Equation (62) yields the following results for relaxation times and various dynamical correlation functions. 

Since intersegment hydrodynamic interaction dominates the friction coefficient, we ignore the i = j part that leads to the free-draining contribution. If we define the inverse propagator G according to... 

Another contribution to the steric interaction is the intersegment force. The intersegment force is caused by the direct interaction between segments of polymers with each other. This interaction depends strongly on the solvent. Below T the interaction among the monomers is stronger than the interaction of the monomers with the solvent, which results in an attractive... 

The latter depends on both the temperature and the energy of solvent-segment interaction. Then, v can be zero (see Equation 4.218) for some special temperature, called the theta temperature. The solvent at the theta temperature is known as the theta solvent or ideal solvent. The theta temperature for polymer solutions is a counterpart of the Boil temperature for imperfect gases this is the temperature at which the intermolecular (intersegment) attraction and repulsion are exactly counterbalanced. In a good solvent, however, the repulsion due mainly to the excluded volume effect dominates the attraction and v > 0. In contrast, in a poor solvent the intersegment attraction prevails, so V < 0. 

Claesson et al. [373] studied the effect of temperature on the interaction between monolayers of the nonionic surfactant Ci2 S. These authors observed that the versus h curves exhibit a minimum related to attraction, whose depth increases with the increase of temperature (Fig. 29). Most probably, this is an effect of the intersegment attraction of hydrophobic origin, which cannot be described by the Alexander-de Geimes theory. Theories applicable to this case are reviewed by Russel et al. [284]. 

We shall use these two limits as guides in interpreting the experimental data. For values of KRg intermediate between the limits, the full form of Equation 4.12 is needed. A convenient result of the above argument is that the intersegment electrostatic interaction energy becomes short-ranged as for the... 

If V(Ri - Rj) is the intersegment potential energy due to excluded volume interactions (and electrostatic interactions if charges are present), the force on the ith segment is... 

The above equation is known as the Rouse equation (Rouse 1953), when there are no intersegment potential interactions (Gaussian chain). Now the dynamics is equivalent to that of a vibrating string. By adopting the continuous chain representation, il = s,0 < s < L, whereL = Nl is the contour length of the chain, the Rouse equation for a Gaussian chain becomes... 

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