new materials by design - newton gateway to mathematics · k. stratford et al nature comms (2014)...

New Materials By Design

• Continuum / phase field models of emulsions and liquid crystals

• Lattice Boltzmann method

• Topological defects: walls and lines

• Colloidal particles + their defect interaction

• Bijels: possible battery materials

• Particle-doped liquid crystals: possible display materials

• Biomimetic media: active liquid crystals

• Crawling emulsion droplets

Collaborators: D Marenduzzo, K Stratford, I Pagonabarraga, R Adhikari, J Lintuvuori, E Tjhung, G Foffi, A Tiribocchi, O Henrich....

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• Topological defects: lines and walls

• Lattice Boltzmann simulations







Continuum / Phase Field Models for Complex Fluids

Isothermal Navier Stokes fluid:

Additional stress S depends on internal degrees of freedom




Binary fluid mixtures (emulsions):

Scalar composition f




Binary fluid mixtures (emulsions):

Scalar composition f

Liquid crystals:

Orientational alignment tensor Q na


Equations of motion for internal fields:

Additional stress

Liquid crystal:

S describes rotation of rodlike objects in flow

Additional stress S: complicated but known

Free energy functional F is known in both cases

na

Lattice Boltzmann Method for Forced NSE

• each site x has velocity set {ci}: ci t = lattice vector

• fi(x,t): population of fluid “particles” at x with velocity ci

(x,t) = ∑i fi fluid density v(x,t) = ∑i fi ci fluid velocity

• local streaming, and relaxation

fi(x+ci,t+1) – fi(x,t) = ∑j Lij (fj(x,t) – fj

0(x,t)) F.cfi • continuum limit: forced Navier Stokes equation

• select

Complex Fluids: Hybrid Lattice Boltzmann

Couple LB to finite difference code for f, Q dynamics

Read in required velocity field from LB

Update order parameters via FD

Pass stress to LB as NSE solver

D. Marenduzzo, E. Orlandini, MEC, J. Yeomans, PRE 76, 031921 (2007)

et seq.

LUDWIG Parallel coding and curation: K. Stratford, O. Henrich (Edinburgh)

https://ccpforge.cse.rl.ac.uk/gf/project/ludwig/

fluid-fluid phase separation: domain walls

defect core

proliferating disclination lines in chiral liquid crystal

Colloidal Inclusions Spherical hard particles; no slip boundary conditions Energetics: particles attracted to topoplogical defects Physics: covering up the defect saves energy!

fluid interface disclination line

both cases:

Colloidal Inclusions Additional Physics

fluid interface: wettability

liquid crystals: anchoring

q

defaults: q = p/2 no anchoring

Designing New Materials by Computer Binary fluid phase separation + colloidal particles Concept: • Coarsening interfaces sweep up particles

• Particles form jammed monolayer: coarsening stops

• Percolating 2D layer rigidifies entire structure

• Bicontinuous Interfacially Jammed Emulsion Gel = Bijel MEC et al. Patents 2005, K. Stratford et al, Science 2005

without colloids with colloids

BIJELS – Bicontinuous interfacially jammed emulsion gels

BIJELS – Bicontinuous interfacially jammed emulsion gels

Bijels: Confocal Microscopy Confocal Microscopy M. Reeves et al, PRE 2015

robust, waxy material tricontinuous fluid/fluid/solid

Bijels: Timeline Computational proof-of-concept; patents 2005 K. Stratford et al. Science 2005 First lab realization 2007 E. Herzig et al. Nature Materials 2007 Reliable fabrication, templating 2011 J. Tavacoli et al Adv. Func. Materials 2011, Lee and Mohraz, Adv. Materials 2011 Extended range of solvent pairs, particles 2011-2016 M. N. Lee et al Adv. Func. Materials 2013 + ongoing Sample production for Li-ion battery research 2012- now J. Thijssen, P. Bruce et al. (Oxford-Edinburgh collaboration)

Bijels for Batteries Li-ion / Li-air batteries: mobile phones to electric cars anode / electrolyte /cathode Tricontinuity: Conduction paths for cations, anions, electrons Soft solid: Electrodes expand/contract on charge / discharge

research continues...

Bistable (powerless) Liquid Crystal Displays

Bistable LC displays

each pixel: two metastable defect configurations

power used only to switch, not maintain

supermarket display tags (ZBD), e-paper, etc.

microfabricated

substrate: defect anchor

Bistable LC displays

each pixel: two metastable defect configurations

power used only to switch, not maintain

supermarket display tags (ZBD), e-paper, etc.

microfabricated

substrate: defect anchor

Can bistability be achieved by self-assembly alone?

Colloids in Blue Phases

Fast-switching device properties of BPs

W. Cao et al, Nat Mat (2002)

can we add bistability?

Phase diagram of cholesteric liquid crystals

t temperature

k chirality zero field: e = 0

BPIII: amorphous lattice O. Henrich et al PRL 2011

BPI,II: Ordered lattices of disclinations

ISOTROPIC

CHOLESTERIC

(defect free)

Colloids in BPI/II: Weak anchoring

Numerical energy minimization

Colloids replace energy “hotspots” of pre-existing structures

M Ravnik, J. Yeomans et al., PNAS (2011)

Colloids in BPI: Full dynamics

Initial state: isotropic phase, 1% colloids

Quench into BPI

weak anchoring on particles strong

lock-in of metastable amorph

K. Stratford et al Nature Comms (2014)

Colloids in BPI: Confined system

slab geometry, 1% colloids

top

side



Colloids in BPI: Confined system

Slab geometry; 4% colloids

top

side



Colloids in BPIII

K. Stratford et al Nature Comms 5, 3954 (2014)

Colloids in BPIII: external field


Colloids in BPIII: field switching+ bulk multistability

no field field on field off (showing particles only)


Active Liquid Crystals Oriented phase of self-propelled fibres Inspired by the cytoskeleton: polymerizable actin filaments + myosin motors Synthetic versions: “cell extracts” e.g. microtubule bundles: Dogic group, Nature 2014 Catalytic colloidal nanorods in fuel bath Sen group, JACS 2004

etc

Active Liquid Crystals Oriented phase of self-propelled fibres Inspired by the cytoskeleton: polymerizable actin filaments + myosin motors Standard equations for polar liquid crystal (P replaces Q) + 2 active terms:

Active Liquid Crystals Oriented phase of self-propelled fibres Inspired by the cytoskeleton: polymerizable actin filaments + myosin motors Standard equations for polar liquid crystal (P replaces Q) + 2 active terms:

P = <ni>

Active Liquid Crystals Oriented phase of self-propelled fibres Inspired by the cytoskeleton: polymerizable actin filaments + myosin motors Standard equations for polar liquid crystal (P replaces Q) + 2 active terms: contractile stress in fibres

Cell Crawling in Eukaryotes

Keratocyte on glass

Biomimetic /modelling agenda: • polar LC emulsion droplet • self-advection in wall layer • contractile stress everywhere • anchoring at drop interface • no slip of fluid at wall

Active emulsion droplet emulates crawling cell

E. Tjhung et al, Nat Comms (2015)

Morphological Zoo

keratocyte on glass:

lamellipodium one of several shapes

static fried egg phagocytic cup

lamellipodium filopod

Morphological Zoo

immobile platelet lamellipodium

cup-like pseudopod

E Tjhung et al, Nat Comms (2015)

Morphological Zoo

immobile platelet lamellipodium

cup-like pseudopod

strong anchoring

low motor activity

just right

E Tjhung et al, Nat Comms (2015)

new materials by design - newton gateway to mathematics · k. stratford et al nature comms (2014)...

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