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 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
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