NDLI: Likelihood and expected-time statistics of monodomain attractors in sheared discotic and rod-like nematic polymers

Content Provider	Springer Nature Link
Author	Zheng, Xiaoyu Forest, M. Gregory Zhou, Ruhai Wang, Qi
Copyright Year	2004
Abstract	Employing a mesoscopic Doi tensor model, we develop transient statistical properties of sheared nematic polymer monodomains consistent with typical experimental protocols. Our goal is to convey to the experimentalist a list of expected outcomes, based not only on properties of the nematic liquid and imposed flow rate, but also on the timescale of the experiment and variability in the initial conditions. Step 1 is deterministic: we solve the model equations completely, then compile the flow-phase diagram of all monodomain attractors and phase transitions versus nematic concentration and Peclet number (shear rate normalized by molecular relaxation rate). Step 2 is to overlay on the phase diagram a statistical diagnostic of the expected time, 〈t〉 A , to reach a small neighborhood of every attractor A. The statistics are taken over the arbitrary quiescent director angle on the sphere, modeling experiments that begin from rest. Step 3 is to explore parameter regimes with multiple attractors, where we statistically determine the likelihood of convergence to each attractor. These statistical properties are critical for any application of theoretical models to the interpretation of experimental data. If 〈t〉 A is longer than the timescale of the experiment, attractor A is never fully resonated and the relevant stress and scattering predictions are those of the transients, not the attractor. In bi-stable and tri-stable parameter regimes, which are typical of nematic polymers, a distribution of monodomains of each type will populate the sample, so experimental data must be compared with weighted averages based on the likelihood of each attractor (see Grosso et al (2003) Phys Rev Lett 90:098304). The final step is to give statistics of shear stress and normal stress differences during the approach to each attractor type, as well as typical paths of the major director that are contrasted with the results of Van Horn et al (Rheol Acta (2003) 42(6):585–589) with Leslie-Ericksen theory.
Starting Page	219
Ending Page	234
Page Count	16
File Format	PDF
ISSN	00354511
Journal	Rheologica Acta
Volume Number	44
Issue Number	3
e-ISSN	14351528
Language	English
Publisher	Springer-Verlag
Publisher Date	2004-06-09
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nematic polymers Shear flow Transient rheology
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Condensed Matter Physics Materials Science

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