Forces Acting on the Chain

The translational friction coefficient ft of the polymer chain at infinitely dilute solutions is calculated by equating the net force acting on the chain, — and —fR, where R is the net drift velocity of the center of mass of the chain... 

Note that the internal viscosity is a residual of internal relaxation process in the case, when the slow deformation is considered. In a more general case, the elastic and internal viscosity forces acting on the chain, according to equations (2.2) and (2.28), can be written as... 

Figure 5. The results of computer simulations of the variation of the average end force/acting on the chains in a pearl necklace network. The system consisted of 20 identical chains, each with Nb — 14 bonds of length a, 13 free with one tethered. For the latter, the fixed end-to-end distance r — 6.62a. The reduced temperature was T —4.

The total force acting on the chain molecule is related to the frictional... 

The boundary condition (6.82) can be visualized tensile force acting on the chain ends (see Fig. 6.8a) ... 

Fo is the force acting on the bond located at the center of the chain under consideration 8 is the distance necessary to stretch the bond to break... 

In the system of the mechanics signs the deformation forces acting on the random chain into ball along /-axes of the t/-dimensional space are equal to / = dF(x) / dxi. By differing (27) we will obtain... 

The description of the chain dynamics in terms of the Rouse model is not only limited by local stiffness effects but also by local dissipative relaxation processes like jumps over the barrier in the rotational potential. Thus, in order to extend the range of description, a combination of the modified Rouse model with a simple description of the rotational jump processes is asked for. Allegra et al. [213,214] introduced an internal viscosity as a force which arises due to a transient departure from configurational equilibrium, that relaxes by reorientational jumps. Thereby, the rotational relaxation processes are described by one single relaxation rate Tj. From an expression for the difference in free energy due to small excursions from equilibrium an explicit expression for the internal viscosity force in terms of a memory function is derived. The internal viscosity force acting on the k-th backbone atom becomes ... 

Now one can return to the equation (2.1) for the dynamics of the macromolecule in the flow of a viscous liquid. The dissipative forces acting on the particles of the chain have generally non-linear forms, but the assumptions, when these force can be written in linear approximation, were discussed in the previous sections, so that we are able to write, in terms of the normal co-ordinates introduced previously and by taking into account all the considerations described above, the dynamic equation... 

Figure 4. (a) Schematic illustrating an ideal chain with end atoms held in place by external forces, (b) Schematic representation of the force acting on a chain in a stretched network when the chain vector R makes an angle 6 with the stretch axis x. Shown are fR and fy, the axial and transverse components of the chain force f. 

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