SLIDE 1 Rheology of lamellar and smectic 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)
SLIDE 2 Outline
Background Rheology of lamellar phase Rheology of smectic phase
close to transition point
Summary
SLIDE 3 1D layered structures
1D solid + 2D fluid Thermotropic smectic phases (Sm A, Sm C) Lyotropic lamellar phases (Lα, Lβ)
thermotropic smectic phases lyotropic lamellar phases surfactant hydrophobic hydrophilic
SLIDE 4 Elastic energy
Layer displacement field: Elastic energy density:
f = K 2 (∇⊥
2u)2 + B
2 ∂u ∂z
2
K : bending constant
de Gennes (1969)
SLIDE 5
Shear thinning behavior of smectic phases: universality?
Meyer, Asnacios, Kleman (2001) Yamamoto, Tanaka (1995)
shear thinning C12E5
SLIDE 6 Outline
Background Rheology of lamellar phase Rheology of smectic phase
close to transition point
Summary
SLIDE 7 Dislocation loops in lamellar phases
Dissipation due to motion of dislocations
edge screw
SLIDE 8 Steady state stress: Birth and sink of dislocations: Steady state: Stress scaling:
Dynamics of dislocation loops
∂ρs ∂t = (˙ γ /ble)− (˙ γ ls /ξ)ρs σ ~ ρs τe ρs :screw density τe : edge line tension
Lu et al. (2008)
ξ
SLIDE 9 Temperature:
66~71 ℃ (339~344K)
Concentration:
30~45 wt%
Phase diagram of C12E5
Strey et al. (1990)
lamellar sponge Newtonian
Snabre, Porte (1990)
SLIDE 10
Flow curves
Lu et al. (2008)
SLIDE 11
Temperature effect
SLIDE 12 Concentration effect
MAK
SLIDE 13 Outline
Background Rheology of lamellar phase Rheology of smectic phase
close to transition point
Summary
SLIDE 14 Thermotropic LC: 8CB
4-n-alkyl-4’-cyano-bipheny (8CB)
smectic nematic isotropic
33.4℃ 40.5℃
~ 2nm
SLIDE 15
Rheology of 8CB
m = 2
Colby et al. (1997)
Universality ?
Panizza, Archambault, Roux (1995)
26℃ 31℃
SLIDE 16 Smectic-Nematic transition
Dislocation loop-mediated smectic melting Dislocation unbinding transition Free energy of a loop: Transition temperature: Divergence of defect size
Helfrich (1978)
F = τ− kBT(/b)ln p τ : line energy p : coordination number TSN = τb kBln(p)
Nelson, Toner (1981)
SLIDE 17
Flow curves of 8CB
TSN=33.4℃ Fujii et al. (2010)
SLIDE 18 Three different regimes
Regime 0: Hurschel-
Bulkely model
Regime I: power law
behavior
Regime II: Newtonian
σ = σ y + A ˙ γ
n
σ = C ˙ γ
1/m
T=33.1℃
SLIDE 19
Obtained parameters
Regime 0 Regime I
SLIDE 20
Microscope observation
a b c e f d
T=25℃ T=29℃ T=31℃
˙ γ =1s-1
T=33℃
˙ γ = 0.1s-1 1s-1 10s-1
Focal Conic Domains
SLIDE 21 Yield stress
Network of focal
conic domains with size L
Needed stress to
deform network
Constant K Unbinding behavior?
σ y ≈ K /L2
Fujii et al. (2010) Horn, Kleman (1978)
SLIDE 22
High shear stress region
heating rate=0.05K/min
SLIDE 23 Dynamic phase diagram
+ leek? perpendicular
- cf. Safinya, Sirota, Plano (1991)
Fujii et al. (2010)
SLIDE 24
Viscoelasticity of 8CB
T = 25℃ T = 29℃ T = 31℃ T = 33℃
SLIDE 25 Scaling of G’ with L
Relation between G’
and FCD size
Effective surface
tension
Similarity to onion
phases
G'~ 1/L σ eff ~ KB
SLIDE 26 Summary
Defect mediated rheology in lamellar and
smectic phases (structural rheology)
Lyotropic lamellar phase motion of dislocation loops Thermotropic smectic phase close to TSN growth of FCD effective surface tension
SLIDE 27 References
C.-Y. D. Lu, P. Chen, Y. Ishii, S. Komura, and
- T. 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).
