Weakly-Coupled Macromolecules

The main subject of the following discussion is the mechanical behaviour of networks in terms of the behaviour of the system of weakly coupled macromolecules. The network modulus of elasticity is small in comparison to the values of the elasticity modulus for low-molecular solids (Dusek and Prins 1969 Treloar 1958). Nevertheless, large (up to 1000%) recoverable deformations of the networks chains are possible. 

To calculate stresses for a system of weakly coupled macromolecules, nonequilibrium correlation functions (71), (74) and (75), specified for the memory function (45), can be used to write down the stresses in linear approximation with respect to the velocity gradients. In this way, the stresses are determined by the velocity gradients in all the previous moments of time. Further... 

The expression for the strain-optical coefficient 0 u ) for a system of weakly-coupled macromolecules is quite similar to the expression for the dynamic modulus, if the stress-optical coefficient C does not depend neither on frequency nor on the relaxation branch. In this case components of the strain-optical coefficient can be calculated according to formula (131) and have the same form as the components of the dynamic modulus, which are shown in Fig. 3. However, to explain experimental data [123, 124], we must admit that the stress-optical coefficient C depends either on frequency or on the relaxation branch. So as the different relaxation branches are assumably connected with different types of motion, one ought to ascribe different values of the stress-optical coefficient to contributions from different relaxation branches, and the expression for the strain-optical coefficient aquires the following form... 

As a rule, the weak coupling case is observed in solution, the intermediate coupling case in crystalline solids and oriented membranes, and the strong coupling case within conjugated macromolecules. In order to quantify the energy transfer, we will consider a molecular complex composed of two molecules a and b. The Hamiltonian of this system is given by... 

Keywords. Birefringence, Localisation of macromolecule. Polymer dynamics, Viscoelasticity, Weakly-coupled chains... 

M. Ottiger, F. Delaglio, J.L. Marquardt, N. Tjandra, A. Bax, Measurement of dipolar couplings for methylene and methyl sites in weakly oriented macromolecules and their use in structure determination, J. Magn. Reson. 124 (1998) 365—369. 

Figure 2. Schematisation of amorphous polymeric material. Macromolecules are coupled with weak van der Waals forces. At T > Tg, the system is in a fluid state, and the thermal motion makes the macromolecules move besides each other. At T < Tg, the system is in a glassy state, large-scale conformations of the chains are frozen, and a macromolecule can change its neighbours at the deformation of the material only.

Borsali, R., Vilgis, T. A., and Benmonna, M., Viscosity of weakly-charged polyelectrolyte solutions the mode-mode coupling approach. Macromolecules, 25, 5313-5317 (1992). 

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