Modeling planar degenerate anchoring and wetting

Modeling planar degenerate anchoring and wetting

J.-B. Fournier & P. Galatola

SMMM, Cortona (2005)

Nematic order

0 < S < 1 - ½ < S < 0 S > 0 , b ≠ 0

uniaxial biaxial

Introduction

Anchoring

homeotropic (S > 0) homeotropic (S < 0)

planar (S > 0) planar degenerate (S > 0)

Introduction

Wetting

T > T NI

P. Sheng (1976) - K. Miyano (1979)

Introduction

Model

Model anchoring and wettingin this situation :

planar degenerate (S > 0)

NB. ≠ homeotropic with S < 0 :● Sluckin et al. (1985)

● Allender et al. (1997)

● Stark et al. (2005)

Model

Free energies

degenerate

Surface potential favoringplanar degenerate

Model

Surface potential Model

Minimization problemModel

bulk :

boundary :

transitionτ =1

In the nematic phaseResults

S

b

Θ / 90˚ S0 = 1, τ = 0.8,

w1 = w

2 = 2

P†

z / ξ

Planarwith biaxiality

Sb

z / ξ

In the isotropic phase- large coupling -

Results

Θ / 90˚ S0 = 1, τ = 1.1,

w1 = w

2 = 2

P†Planar

with biaxiality

S

b = 0z / ξ

In the isotropic phase- weak coupling -

Results

S0 = 1, τ = 1.1,

w1 = w

2 = 0.26

Hn

Θ / 90˚

Homeotropicnegative

Phase diagram

Results

S0 = 1

w1 = w

2 = w

second order

first ordercritial

end-point

NB. s0 < s

tr

Phase diagram: for s0>s

tr

Results

S0 = 1.5

w1 = w

2 = w

second order

first order

tricritial point

complete wetting

S

z

Conclusions

● Compatible with experiments of Tarczon and Miyano (1980) observing pretransitional uniaxial negative birefringence with optical axis perpendicular to the surface (i.e., Hn) for MBBA in contact with silane-treated substrate, giving planar degenerate anchoring in the nematic phase.

● Useful tool to study anchoring/wetting problems with degenerate planar anchoring (defects around particles, capillary interactions, colloids suspensions, etc.)

● Liquid emulsions as colloids?

Detail of the second order transition