Modeling the pipeline of high performance, nano-composite materials and effective properties, I

Acknowledgements

On the Theme of this Workshop

Relationships evolve through a dance that goes something like this

  Designer Molecules (particles) at low vol %

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Why the difficulty?  Conspiring factors in                                   nematic polymer nano-composites



These lectures address elements of the nematic polymer, nano-composite materials pipeline.

Anisotropic molecular liquids:  scales of relevance (apologies to chemistry friends)

Multi-scale descriptive variables
linking theory for flowing, anisotropic macromolecules        & experiments (& effective properties tomorrow)

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Upscaling:  spherical harmonic expansions & mesoscopic projections

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What happens at rest to bulk phases? 
Onsager phase diagram of quiescent hard-rod liquids  Kinetic simulations:  Larson-Ottinger ’91;  Faraoni et al. ’99; FWZ ’04,’05 Rheol. Acta I,II

The Onsager diagram is deceptive if you don’t read the fine print: 
Orientational degeneracy of nematic phases

What happens when you drive this O(3)-degenerate phase transition with weak fields?
De Gennes:  “very little is known, even less is understood”

 Flow-molecular interactions
Spiders instruct us to make fibers

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The Couette cell—model system for shear-dominated flow of complex anisotropic fluids: Imposed kinematics first (the longwave limit)
then morphology due to confinement

What happens?  Rheological oscillators
 Onsager’s nightmare:  Mesophase oscillators in steady shear flow.....the cast of transient bulk attractors

Rheological oscillators in steady shear

A Kayaking Orbit of kinetic theory:  A “dynamical circle of equilibria” selected from orientational degeneracy in weak shear

Period doubling route to chaos &
associated normal stress differences

 Chaotic Sheared Bulk Phases from Kinetic Simulations
(arises from complex bifurcation sequence as flow rate increases)  Grosso et al. 02, FWZ 04

Why?  What molecular & flow properties pick the response(s)?  A Mesoscopic-Microscopic “Predictor-Corrector” Strategy

Monodomain selection criteria

Weak-shear selection criteria
vs. aspect ratio & concentration

Example: Doi closure

All persistent steady states in the weak shear limit vs. molecule aspect ratio and nematic concentration &
phase transitions, steady and unsteady!

Steady-unsteady phase transition diagnostic:  mesoscopic Leslie “tumbling parameter”
Sensitivity to Closure Rule (FWZ)

Downscaling to Kinetic PDF “survivors” in weak shear:
a=1, Pe=0.1  using AUTO

Bifurcations vs Flow Rate
at a fixed nematic concentration
all orbits, stable and unstable

Virtual Bifurcations versus Molecular Aspect Ratio
N=6, Pe=5 in FA regime when r=3, 1/3

Shear-driven mesoscopic flow-phase diagram:   numerical continuation software (AUTO)                                  Doi closure; Forest & Wang, ’03, Rheol. Acta

Molecular-scale kinetic theory:
robust vs closure-sensitive behavior

Kinetic monodomain phase diagram
of attractors versus vol % and shear rate

First & second order phase transitions between regions:  bifurcation city

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Devices to explore planar flows combining shear and extension:  4 roll mill, G.I. Taylor

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“Finesse” monodomain response in linear, planar flows from pure shear! PRE 2002; JNNFM 2004; PRL 2004

Correspondence principle:  extrapolating from pure shear to linear planar flows by varying molecular aspect ratio

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Transition from bulk homogeneous phase response to structure

Structure in shear cells:  leaving the longwave limit 
mesoscopic  2nd moment models & full kinetic simulations We are looking for lengthscale genesis, propagation, interactions…. & “structure attractors”

Mesoscopic model equations for nano-composite       structure development in flow processing

Idealized 1-d model of flow-mesophase structure:  onset, evolution & correlations

Aspects of molecular mesostructure induced during laminar processing

Structure scaling laws due to
  Confinement--bulk motion interactions

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Read off structure scaling properties
parametrized by device and molecular conditions

Numerical continuation studies:  Resonating new flow-nematic structures as asymptotics fails

Macroscopic-mesoscopic steady-state structure correlations (unpublished, FWZZ):  here we find a temporal-to-spatial “kayaking” transference

Dynamic structure formation in steady processes:  midgap tumbling layer with finite oscillations near plates & defect core fluctuations

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Full kinetic structure simulations:  Spherical harmonic expansion for orientational configuration space

Er=500, De=1, Probe effect of normal anchoring:
Creation of internal dynamic structure layer

Er=500, De=6, normal anchoring:  Probe effects due to increasing the plate (processing) speed
Timescales & extent of dynamic structure region change!

Transition to defect-laden attractors
associated with transient structures & spatial T-W transition

Blowup of defect cores:  local space-time crashing of Flory order parameter of the PDF, signaling complete defocusing of orientational distribution

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Anisotropy, Dynamics, & Heterogeneity of Nematic Polymer Shear-driven Flows