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SynopsisVarious methods of solving the dynamical equation for defect polymers are discussed. It is shown that the Green's function (GF) can be conveniently used to reduce the order of the characteristic equation to the number of the degrees of freedom of a repeat unit in the case when the perturbation caused by each of the defects is localized within it. In the general case, the order of the reduced determinant depends on the range of the interaction forces between the defect unit and the regular chain.For a polymer chain containing one or two defect units, the Green's function method allows us to obtain the exact solution of the dynamical equation, while for a high concentration of randomly distributed defect units various approximation methods can be used. As a possible approach to the solution of the latter problem we suggest using either one of the versions of the perturbation theory (the dilute limit, the coherent potential approximation) or the cluster approximation.

At large defect concentrations the probability of forming impurity clusters in a region sharply increases. Lifshits pointed out the importance of such clusters for the formation of the crystal vibrational spectrum (1). When the distance between the defects i s small a s in the case of clusters the impurity level splitting could be s o large that a part of the impurity levels can shift into the region of the quasicontinuous spectrum. Then instead of local levels quasi-local levels appear where A m is the difference between the masses of the impurity atom and the basic one. Solving Dyson's equation (4) for the perturbation (2) and using the expression of the Green's function of the ideal chain (1) one may obtain the Green's function of

SynopsisA new method of calculating the Green's function (GF) for an arbitrary polymer chain is suggested.It makes it possible to obtain analytical expressions for this function in a number of cases of practical value.The calculation of the Green's function (GF) G(0)(w2) for a perfect system is an important and independent part of the solution of the dynamical equation for disordered solids. As shown in part I of this series,l the GF can be employed