The General Form of Dynamic Equation

The most advanced theories of relaxation phenomena in a system of entangled macromolecules is based on the dynamics of a single macromolecule. Dynamics of the tagged macromolecule is simplified by the assumption that the neighbouring macromolecules can be described as a uniform structureless medium and all important interactions can be reduced to intramolecular interactions. The dynamic equation for a macromolecule can be written as a modification of equation (2.1) for dynamics of macromolecule in viscous liquid 

Indeed, the intramacromolecular forces, both dissipative and elastic, do not affect motion of the coil as a whole. 

The fourth term on the right hand side of (3.4) represents the elastic forces on each Brownian particle due to its neighbours along the chain the forces ensure the integrity of the macromolecule. Note that this term in equation (3.4) can be taken to be identical to the similar term in equation for dynamic of a single macromolecule due to a remarkable phenomenon - screening of intramolecular interactions, which was already discussed in Section 1.6.2. The last term on the right hand side of (3.4) represents a stochastic thermal force. The correlation function of the stochastic forces is connected 

In virtue of the results, described in the previous section, it is natural to present the extra dissipative terms in equation (3.4) in an integral forms. One has to require the resistance forces to be independent of the rotation of the coordinate system with constant angular velocity and, assuming also the proper covariance and linearity in the velocities of particles, determines (Pokrovskii and Volkov 1978a) the general form of the terms 

One can assume that each Brownian particle of the chain is situated in a similar environment, which is approximately correct for long chains, so that we can rewrite the memory functions in (3.6) and (3.7) as 

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