DYNAMICS OF A POLYMER TEST CHAIN IN A GLASS-FORMING MATRIX - THE HARTREE APPROXIMATION

We consider the Langevin dynamics of a Gaussian test polymer chain cou pled with a surrounding matrix which can undergo the glass transition. The Martin-Siggia-Rose generating functional method and the nonpertub ative Hartree approximation are used to derive the generalized Rouse e quation for the test chain. It is shown that the interaction of the te st chain with the surrounding matrix renormalizes the bare friction an d the spring constants of the test chain in such a way that the memory function as well as the bending dependent elastic modulus appear. We find that below the glass transition temperature T-G of the matrix the Rouse modes of the test chain can be frozen and moreover the freezing temperatures (or the ergodicity-nonergodicity transition temperature) T-c(p) depends from the Rouse mode index p. modulus appear.