Dynamics of a polymer test chain in a glass forming matrix: The Hartree Approximation

In this paper the Martin-Siggia-Rose formalism is used to derive a generalized Rouse equation for a test chain in a matrix which can undergo the glass transition. It is shown that the surrounding matrix renormalizes the static properties of the test chain. Furthermore the freezing of the different Rouse modes is investigated. This yields freezing temperatures which depend from the Rouse mode index.