Calculation of scattering from stretched copolymers using the tube model: a generalisation of the RPA

There are many experimental situations in which polymer chains are constrai ned or localised into a small region of space (e.g. melt chains confined to a "tube", network chains pinned by crosslinks). We show that detailed cons ideration of the quenched variables is vital in these experiments. This pap er provides a crucial link between microscopic models with localising const raints and scattering: patterns by a generalisation of the Random Phase app roximation (RPA) which allows for quenched translational variables. A metho d is developed which deals with correlations between the quenched variables brought about by incompressiblity (for example, in a polymer melt there ar e correlations between tubes because of the interaction between chains). As an example. the generalised RPA is applied to models based on the Warner-E dwards picture of the tube. Theoretical results for a melt of I-I-shaped co polymers are compared with experimental scattering. Early results suggest t hat to fit the scattering: we may be forced to relax one of the central ass umptions of the tube model, that the tube deforms affinely, that all chains retract by the same amount or that the tube diameter does not couple to th e strain.