Rheology of lamellar andsmectic phases
S. Komura, T. Kato (Tokyo Metropolitan University)
S. Fujii (Nagaoka University of Technology)
Y. Ishii (Waseda University)
C.-Y. D. Lu (National Taiwan University)

OutlineBackgroundRheology of lamellar phase

Rheology of smectic phaseclose to transition point
Summary1D layered structures

1D solid + 2D fluid
Thermotropic smectic phases (Sm A, Sm C)
Lyotropic lamellar phases (Lα, Lβ)surfactant
hydrophilic

thermotropic
smectic phases

lyotropic
lamellar phases

hydrophobic

Elastic energyLayer displacement field:

Elastic energy density:2
K 2 2 B ∂uf = (∇ ⊥u) +  
22  ∂z K : bending constant€de Gennes (1969)

Shear thinning behavior ofsmectic phases: universality?
Yamamoto, Tanaka (1995)

C12E5

shear thinning

Meyer, Asnacios, Kleman (2001)

OutlineBackground

Rheology of lamellar phase

Rheology of smectic phaseclose to transition point
SummaryDislocation loops in lamellar
phases

Dissipation due to motion of dislocations
edgescrewLu et al. (2008)

Dynamics of dislocation loops
Steady state stress: σ ~ ρs τ eρs : screw densityτ e : edge line tension

Birth and sink of dislocations:€∂ρs= (γ˙ / ble ) − (γ˙ ls / ξ )ρs€∂t€



Steady state:Stress scaling:€ξStrey et al. (1990)

Phase diagram of C12E5


Concentration:

30~45 wt%Temperature:

66~71 ℃ (339~344K)

spongeNewtonianSnabre, Porte (1990)

lamellarFlow curves

Lu et al. (2008)

Temperature effectConcentration effect
MAKour theory

Outline

BackgroundRheology of lamellar phaseRheology of smectic phaseclose to transition point
SummaryThermotropic LC: 8CB


4-n-alkyl-4’-cyano-bipheny (8CB)
~ 2nm

33.4℃

smectic

40.5℃

nematicisotropic

Rheology of 8CB
Panizza, Archambault, Roux (1995)

31℃

m=2

Colby et al. (1997)

26℃

Universality ?

Helfrich (1978)
Nelson, Toner (1981)

Smectic-Nematic transition

Dislocation loop-mediated smectic melting

Dislocation unbinding transitionFree energy of a loop:τ : line energyF = τ − k BT ( / b) ln pp : coordination number

Transition temperature:€€  Divergence€ of defect sizeτb
TSN =k Bln( p)Fujii et al. (2010)

Flow curves of 8CB

TSN=33.4℃

Three different regimes


T=33.1℃

Regime 0: HurschelBulkely modelσ = σ y + Aγ˙ nσ = Cγ˙1/ m€
€Regime I: power lawbehavior
Regime II: Newtonian

Obtained parameters
Regime 0Regime I

Microscope observation
T=25℃

T=29℃

T=31℃

abcγ˙ = 1s-1
dFocalConic
Domainsfe

T=33℃

γ˙ = 0.1s-11s-110s-1

Horn, Kleman (1978)

Yield stress

Network of focal
conic domains withsize L
Needed stress todeform networkσ y ≈ K / L2
€Constant K
Unbinding behavior?

Fujii et al. (2010)

High shear stress region
heating rate=0.05K/min

Fujii et al. (2010)

Dynamic phase diagram+perpendicularleek?

cf. Safinya, Sirota, Plano (1991)

Viscoelasticity of 8CB

T = 25℃

T = 29℃

T = 31℃

T = 33℃

Scaling of G’ with LRelation between G’and FCD size
G' ~ 1/ L€€

Effective surfacetension
σ eff ~ KB
Similarity to onionphases

Summary

Defect mediated rheology in lamellar andsmectic phases (structural rheology)
Lyotropic lamellar phasemotion of dislocation loops

Thermotropic smectic phase close to TSNgrowth of FCD



effective surface tensionReferences

C.-Y. D. Lu, P. Chen, Y. Ishii, S. Komura, andT. Kato, Eur. Phys. J. E 25, 91-101 (2008).
S. Fujii, Y. Ishii, S. Komura, and C.-Y. D. Lu,Europhys. Lett. 90, 64001 (2010).