Molecular modelling of entangled polymer fluids under flow The ...

1.7. ALTERNATIVE EXPERIMENTAL TECHNIQUES 11
This can be written more compactly as
∇
σ = − 1 ) (σ − GI . (1.20)
≈ τ ≈ ≈
Where the operator ∇ is known as an upper convected Maxwell derivative and the
general form of constitutive equation is called an upper convected Maxwell equation. In
the non-linear regime the choice of equation 1.5 as the starting point of the derivation is
arbitrary and other combinations of the finger tensor are equally permissible. Under this
empirical approach these choices can only be vindicated by comparison with observed
phenomena.
If the relaxation modulus is taken to be a sum over exponential Maxwell modes
(equation 1.15) then equation 1.20 can be solved for an independent set of non-linear
Maxwell modes to produce stress predictions.
1.7 Alternative experimental techniques
Although the measurement of mechanical stresses is the most common and arguably
the most industrially relevant measurement there are a range of additional experimental
techniques which can be used to provide information about polymer fluids under flow.
From an empirical point of view these measurements provide additional phenomena
that must be explained. However, they are particularly useful in the field of molecular
rheology since many of the experiments offer a more direct probe of the molecular
dynamics. Examples of these experiment include small angle neutron scattering (SANS)
[Müller et al. (1993), McLeish et al. (1999)], NMR [Cormier and Callaghan (2002)],
neutron spin echo [Wischnewski et al. (2002)] and dielectric relaxation [Watanabe et al.
(2002)]. The use of these measurements in the verification and development of molecular
models is a relatively new approach but they appear to provide new insight into the
behaviour of polymers under flow [McLeish (2002)].