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1296 FANG, KRÖGER, AND ÖTTINGER
profile to the flow. As a result, the flow ‘‘loses its grip’’ on the molecules, leading to
anomalously low friction and hence low viscosity.
D. Convective constraint release „CCR…
Marrucci 1996 and Ianniruberto and Marrucci 1996 proposed a CCR mechanism
which removes the problem just mentioned above. They proposed a model for which,
under flow conditions, relaxation of chain orientation occurs by two mechanisms. One of
them is ordinary diffusion reptation and double reptation due to thermal motion, which
of course also takes place in the absence of flow. The second mechanism is CCR, i.e., the
topological obstacles on a probe chain are renewed through the relative motion among
chains due to chain retraction. In fast flow situations, this mechanism leaves the chain
much freer to relax than is possible only by the previously described mechanism, and
hence prevents the tube segments from becoming highly oriented in the flow direction.
E. Anisotropic tube cross sections
Ianniruberto and Marrucci 1998 introduced the idea that during deformation an
initial circular tube cross section may become elliptical. They derived the corresponding
expression for the stress tensor, but did not present a time-evolution equation for the tube
cross section in flow. It was shown that the idea of anisotropic tube cross section has an
important influence mainly on the ratio of normal-stress difference in shear flow. In view
of the well know intimate relation between the time evolution of the structural variables
and the stress tensor expression implied by various approaches to nonequilibrium thermodynamics,
Öttinger 2000 developed a thermodynamically admissible reptation
model with anisotropic tube cross section and the constraint release mechanisms associated
with double reptation and CCR. For that model, he proposed relationships between
the ratio of normal-stress differences and the mean-square curvature of the tube cross
section in shear flow.
Very recently, reptation models incorporating all the well-established phenomena except
for anisotropic tube cross sections have been formulated by two groups, based on a
full-chain stochastic approach suitable for computer simulations by Hua and Schieber
1998 and Hua et al. 1998, 1999 and on rather complicated coupled integraldifferential
equations by Mead et al. 1998. It is encouraging that these reptation models
can quite successfully reproduce the experimentally observed rheological behavior in a
large number of flow situations. In a previous work by Öttinger 1999b, which is referred
to as part I of the present work, a new reptation model including anisotropic tube
cross sections, chain stretching, double reptation, and CCR, while avoiding the IA approximation,
has been developed under the guidance of nonequilibrium thermodynamics.
Two versions of the model, referred to as ‘‘uniform’’ and ‘‘tuned,’’ have been proposed.
The purpose of this paper is to give a detailed model evaluation of the recommended
‘‘uniform’’ model in shear and extensional flows by numerical simulations. Because the
experimentally observed features listed in the beginning of Sec. I can be explained
without considering anisotropic tube cross sections their implementation seems to be
nontrivial to us, and they weakly affect the ratio of predicted normal stress differences for
which experimental data is rarely available, the variable Q representing a tube cross
section in the previously proposed model has been omitted here. On this simplified level,
the model has only four degrees of freedom, which will be recalled in Sec. II. Note that
our model takes into account only a single relaxation time reflecting the linear viscoelastic
response of the material. This limitation can be released by considering