Eur. Phys. J. B 12, 431-449 (1999)
https://doi.org/10.1007/s100510051025

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

I.R.C. in Polymer Science and Technology, Department of Physics, University of Leeds, Leeds, LS2 9JT, UK

Corresponding author: ^a d.j.read@leeds.ac.uk

Received: 26 October 1998
Revised: 19 March 1999
Published online: 15 December 1999

Abstract

There are many experimental situations in which polymer chains are constrained 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 consideration of the quenched variables is vital in these experiments. This paper provides a crucial link between microscopic models with localising constraints and scattering patterns by a generalisation of the Random Phase Approximation (RPA) which allows for quenched translational variables. A method is developed which deals with correlations between the quenched variables brought about by incompressiblity (for example, in a polymer melt there are correlations between tubes because of the interaction between chains). As an example, the generalised RPA is applied to models based on the Warner-Edwards picture of the tube. Theoretical results for a melt of H-shaped copolymers are compared with experimental scattering. Early results suggest that to fit the scattering we may be forced to relax one of the central assumptions 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 the strain.