**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 %**

**Slide 6**

**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)

**Slide 11**

**Upscaling: spherical harmonic expansions &
mesoscopic projections**

**Slide 13**

**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

**Slide 18**

**Slide 19**

**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**

**Slide 39**

**Slide 40**

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

**Slide 42**

**“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**

**Slide 45**

**Slide 46**

**Slide 47**

**Transition from bulk
homogeneous phase response to structure**

**Structure in shear cells: leaving the longwave limit **

mesoscopic 2^{nd} 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

**Slide 54**

**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**

**Slide 59**

**Slide 60**

**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**

**Slide 66**

**Slide 67**

**Slide 68**

**Slide 69**

**Slide 70**

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