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March 25-30, 2001, Halle, ECLC2001
VAN DER WAALS AND STRUCTURAL FORCES:STABILITY OF THIN LIQUID-CRYSTALLINE FILMS
Andreja [arlah1
Primo` Ziherl,2,3 and Slobodan @umer1,3
1. Department of Physics, Faculty of Mathematics and Physics, University ofLjubljana, Jadranska 19, 1000 Ljubljana, Slovenia
2. Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104-6396 USA
3. J. Stefan Institute, Jamova 35, 1000 Ljubljana, Slovenia
MOTIVATION
# observed instability of very thinnematic films
# search for systems with pronouncedCasimir effect
View of spinodal dewetting of a42.8-nm-thick film (T=33.5 °C).The image size 460 µm x 460 µm.
F. Vandenbrouck, M. P. Valignat in A.M. Cazabat, PRL 82, 2693 (1999)
I. Dreven{ek (2000)
(IN)STABILITY OF THIN LIQUID DEPOSITIONS
wrinkling of the freeliquid surface due tothermal fluctuations
decomposition of film into drops
enhanced fluctuations
stable film
decreased fluctuations
(IN)STABILITY OF THIN LIQUID DEPOSITIONS
capillary waves:
STRUCTURAL FORCE MEAN-FIELD & FLUCTUATION-INDUCED FORCE
STRUCTURAL FORCE
mean-field part
fluctuation-induced(pseudo-Casimir) force
free energy of LC film
mean-field force
mean-field structure harmonic fluctuations
0 5 10 15 20 25-10
-5
0
5
10
∆ T = T - TNI
∆ T = -11 K ∆ T = -5 K ∆ T = -1 K
Π [
Pa]
d [nm]
# weak short ranged force (weak, localizeddeformation)# non-monotonic thickness dependence# marginal thickness
> strong homeotropic anchoring (free surface; excess order)> weak planar anchoring
0.0 0.2 0.4 0.6 0.8 1.0-15
-10
-5
0
5
10
15
~
Λ = 0.01 Λ = 0.06 Λ = 0.1 Λ = 0.5
Π/Π
d [dc]
attraction repulsion
pseudo-Casimir forcemean-field force
VAN DER WAALS FORCE
van der Waals potentialbetween two molecules
van der Waals potentialbetween two half-spaces
Hamaker approach:
sum of pair-wise interactions(ideal gas approximation),neglecting retardation
Lifshitz approach:
continuum theory (taking intoaccount many-body interactions),retardation effects
# dispersion interaction:interaction of fluctuatingdipoles arising fromdynamic redistribution ofelectrons in molecules
# orientational interaction:interaction of permanent,yet fluctuating electricdipoles
VAN DER WAALS FORCEBETWEEN ANISOTROPIC MEDIA
0 50 100-50
0
50
Π [P
a]d [nm]
0 50 100
d [nm]
Hamaker constant for anisotropic media
> uniaxial symmetry> optical axis parallel to
the surface normal
the relevant parametersareinstead of averages
LC in the isotropic phaseLC in the nematic phase (Lifshitz)LC in the nematic phase (Hamaker)
VAN DER WAALS FORCE
# non-monotonic thicknessdependence# marginal thickness
four layer systemshort distance limit (non-retarded)long distance limit (non-retarded)
0 2 4 6 8 10-100
-80
-60
-40
-20
0
20
40
0 5 10-200
0
200
Π [k
Pa]
d [nm]
Π [k
Pa]
d [nm]
LC in nematic phaseLC in nematic phase (non-retarded)LC in isotropic phase
inset
VAN DER WAALS FORCEin wetting geometry
10 20 30 40 50 60 70 8010-2
10-1
100
101
102
103
mean-field force
van der Waals force
Π [P
a]
d [nm]
d: thickness of the wetting layer which isvery delicately tuned by the temperature(the plotted thickness interval correspondsto )
# non-zero van der Waals force actingon the wetting layer# both, mean-field and van der Waalsforce are repulsive and are decreasingwith the increasing thickness, yieldinggrowing of the wetting layer onapproaching
# van der Waals force Si - SiOx - 5CB - air
repulsion attraction
# pseudo-Casimir force>
>
= stable nematic film= spinodal decomposition
TOTAL FORCE BETWEEN CONFINING SURFACESMEAN-FIELD, PSEUDO-CASIMIR & VAN DER WAALS CONTRIBUTION
0 5 10 15 20 25-100
-80
-60
-40
-20
0
20
40
mean-field force van der Waals force pseudo-Casimir force total force
Π [k
Pa]
10 15 20 25-1
0
1
d*
Π [k
Pa]
d [nm]
temperature dependentextrapolation lengths
increase of the marginalthickness on approaching thebulk NI transition temperature
STABILITY OF A THIN HYBRID NEMATIC FILM
# stable nematic film# spinodal decomposition
20 22 24 26 28 30 32 34 36
20
40
60
80
100
120 Λ =0.25 Λ =0.5
d* [
nm]
T [°C]
SUMMARY & CONCLUSIONS
The effect of the anisotropy ofthe dielectric permittivity of themedia on the magnitude andcharacter of the van der Waalsinteraction is discussed.
Some of the effects discussed havebeen observed in a study ofspinodal dewetting of 5CB on asilicon substrate.
The confinement-induced features ofthe film are especially prominent inthe vicinity of structural transitions.
In highly frustrated geometries thestructural forces, originating indeformed nematic ordering andmodified spectrum of fluctuations,can play an important role in thestability of the film.
The Hamaker constant foranisotropic media with uniaxialsymmetry has been derived.
In some casestaking into accountthe anisotropy iscrucial.
REFERENCES
F. Brochard Wyard and J. Daillant, Can. J. Phys. 68, 1084 (1990) [(in)stability of thin liquid depositions]
Israelachvili, Intermolecular & Surface Forces (Academic Press, London, 1985) [van der Waals force]
J. Mahatny and B. W. Ninham, Dispersion Forces (Academic Press, London, 1976) [van der Waals force]
A. Mertelj and M. ^opi~, PRL 81, 5844 (1998) [temperature dependence of the extrapolation length]
A. [arlah, P. Ziherl, and S. @umer, submitted to MCLC [Orientational fluctuations and pseudo-Casimir in confinednematic liquid crystals]
S. @umer, A. [arlah, P. Ziherl, and R. Podgornik, accepted for publication in MCLC [Casimir interactions and stabilityof thin nematic films]
A. [arlah and S. @umer, to be published [Van der Waals interaction between anisotropic dielectric bodies]
P. Ziherl, R. Podgornik, and S. @umer, PRL 82, 1189 (1999) [Wetting driven Casimir force in nematic liquid crystals]
