Polymers show very interesting viscoelastic properties. They can be elastic, bridle or rigid as solids or show flow properties very similar to those of liquids, which allows Taylor design of materials with unique mechanical properties. This fact is related to the wide range of relaxation times relevant for the local dynamics of the polymer chains. On short time and length scales the dynamics is dominated by the local relaxation of the polymer chain segments, while on longer time and length scales constrains (tube or reputation model) no the diffusivity, imposed by other polymer chains, of a monomer are of increasing relevance. Connecting this local information to the viscoelastic properties is essential for the design and understanding of new materials.
The distinct scattering properties of hydrogen and deuterium for neutrons allow the study of single polymer chains in the matrix of other chains. Structural and dynamical information can be extracted, for examples, from small angle neutron scattering (SANS) and neutron spin echo experiments (NSE), respectively. However, for dense polymer solutions or melts such experiments are challenging, since for SANS one has to discriminate between the structure and single chain form factor, while for NSE Doppler scattered neutrons may superimpose the information on single chain dynamics. We show that by approximating the unknown structure using piecewise straight segments an analytical expression for the form factor can be derived. We fit the SANS data for a semi-dilute entangled polystyrene solution under in situ shear flow. The character of the deformation lies between that of a single ideal chain (viscous) and a cross-linked network (elastic rubber) and the extracted values of mechanical stress are in fairly good agreement with rheology literature.
Fig. 1: An entangled polymer chain under shear flow. Its structure is defined by the distribution of distances between all monomer pairs. Conceptually, it is subdivided into two linear regimes. Under shear the the anisotropy on the short scale (red ellipses), is just a few percent, but grows much bigger on a large scale (blue ellipse). The chain gradually stretches along the flow, and shrinks perpendicular to it.
The structure of polymers under shear load has to be complemented with information on the dynamics. In particular, in the intermediate shear rate regime, where chain stretching is not expected but the polymer already shows shear thinning effects changes in the topological interactions responsible for the shear thinning may manifest in convective constrain release resulting in a faster local dynamics of the single polymer chains. This information can be extracted from NSE measurements.