Relaxation of the Segment Orientation

To calculate the quantity ufk in steady state as an expansion in powers of velocity gradients, one can use the relation that is following from equation (7.40) 

one has to rely on the reptation mechanism of changing conformation and use equations (7.32) to find the expansion of the quantity ufk. In the first-order approximation, one can obtain 

We believe that for sufficiently long macromolecules, we can neglect the second term 7r2/x as compared with B, so that from equations (7.32) and (7.41) one has 

One can see that dependence of the steady-state values of the moments on the anisotropy coefficients appears in terms of the second order, as was assumed previously. 

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The relaxation of the segmental orientation and the chain extension in polycarbonate (Makrolon 1143 from Bayer AG) were studied by IR dichroism and heat shrinkage after a step strain deformation to a draw ratio of 1.75. This makes it possible to distinguish between local relaxation mechanisms (Rouse) and large-scale relaxation... 

Abstract Macromolecular coils are deformed in flow, while optically anisotropic parts (and segments) of the macromolecules are oriented by flow, so that polymers and their solutions become optically anisotropic. This is true for a macromolecule whether it is in a viscous liquid or is surrounded by other chains. The optical anisotropy of a system appears to be directly connected with the mean orientation of segments and, thus, it provides the most direct observation of the relaxation of the segments, both in dilute and in concentrated solutions of polymers. The results of the theory for dilute solutions provide an instrument for the investigation of the structure and properties of a macromolecule. In application to very concentrated solutions, the optical anisotropy provides the important means for the investigation of slow relaxation processes. The evidence can be decisive for understanding the mechanism of the relaxation. 

The set of internal variables is usually determined when considering a particular system in more detail. For concentrated solutions and melts of polymers, for example, a set of relaxation equation for internal variables were determined in the previous chapter. One can see that all the internal variables for the entangled systems are tensors of the second rank, while, to describe viscoelasticity of weakly entangled systems, one needs in a set of conformational variables xfk which characterise the deviations of the form and size of macromolecular coils from the equilibrium values. To describe behaviour of strongly entangled systems, one needs both in the set of conformational variables and in the other set of orientational variables w fc which are connected with the mean orientation of the segments of the macromolecules. 

IR Dichroism. Two types of IR-dichroism experiments were used in this study to follow segmental orientation. First, dynamic differential dichroism was used to follow chain orientation while the sample was elongated at a constant strain rate. This experiment was performed with different IR peaks which allowed a comparison of the molecular orientations for each blend constituent. Second, a cyclic experiment was used where the film was strained to a predetermined elongation, relaxed at the same strain rate until the stress was reduced to zero, and then elongated to a higher level of strain, and so forth. 

The orientational relaxation of various parts of the star is depicted in Figure 9. Segments close to the branch point appear initially more oriented than those of the central block. The end part of an arm is clearly less oriented at short times. As relaxation proceeds, no difference can be made between the relaxation of the branch point and of the central block. The end block nevertheless relaxes faster. 

According to the Doi-Edwards theory, after time t = Teq following a step deformation at t = 0, the stress relaxation is described by Eqs. (8.52)-(8.56). In obtaining these equations, it is assumed that the primitive-chain contour length is fixed at its equilibrium value at all times. And the curvilinear diffusion of the primitive chain relaxes momentarily the orientational anisotropy (as expressed in terms of the unit vector u(s,t) = 5R(s,t)/9s), or the stress anisotropy, on the portion of the tube that is reached by either of the two chain ends. The theory based on these assumptions, namely, the Doi-Edwards theory, is called the pure reptational chain model. In reality, the primitive-chain contour length should not be fixed, but rather fluctuates (stretches and shrinks) because of thermal (Brownian) motions of the segments. 

Physical ageing can result from the spatial reorganization of polymer chains or segments (relaxation of enthalpy, volume, orientation or stress crystallization etc.), transport phenomena (penetration of a solvent, migration of additives) and superficial phenomena (e.g. cracking in a tension-active medium). 

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