VAN DER WAALS AND STRUCTURAL FORCES: STABILITY OF THIN LIQUID-CRYSTALLINE FILMS Andreja [arlah 1 Primo` Ziherl, 2,3 and Slobodan @umer 1,3 1. Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 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 March 25-30, 2001, Halle, ECLC2001
MOTIVATION # observed instability of very thin nematic films # search for systems with pronounced Casimir effect View of spinodal dewetting of a 42.8-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 free liquid surface due to thermal fluctuations decreased fluctuations enhanced fluctuations stable film decomposition of film into drops
capillary waves: (IN)STABILITY OF THIN LIQUID DEPOSITIONS
STRUCTURAL FORCE MEAN-FIELD & FLUCTUATION-INDUCED FORCE free energy of LC film mean-field part mean-field structure harmonic fluctuations mean-field force fluctuation-induced (pseudo-casimir) force STRUCTURAL FORCE
> strong homeotropic anchoring (free surface; excess order) > weak planar anchoring mean-field force pseudo-casimir force 10 5 15 10 5 Λ = 0.01 Λ = 0.06 Λ = 0.1 Λ = 0.5 Π [Pa] 0-5 T = T - T NI T = -11 K T = -5 K T = -1 K ~ Π /Π 0-5 -10-10 0 5 10 15 20 25 d [nm] -15 0.0 0.2 0.4 0.6 0.8 1.0 d [d c ] # weak short ranged force (weak, localized deformation) # non-monotonic thickness dependence # marginal thickness attraction repulsion
VAN DER WAALS FORCE # dispersion interaction: interaction of fluctuating dipoles arising from dynamic redistribution of electrons in molecules # orientational interaction: interaction of permanent, yet fluctuating electric dipoles van der Waals potential between two molecules van der Waals potential between two half-spaces Hamaker approach: sum of pair-wise interactions (ideal gas approximation), neglecting retardation Lifshitz approach: continuum theory (taking into account many-body interactions), retardation effects
VAN DER WAALS FORCE BETWEEN ANISOTROPIC MEDIA > uniaxial symmetry > optical axis parallel to the surface normal the relevant parameters are instead of averages Hamaker constant for anisotropic media 50 Π [Pa] 0-50 0 50 100 d [nm] 0 50 100 d [nm] LC in the isotropic phase LC in the nematic phase (Lifshitz) LC in the nematic phase (Hamaker)
VAN DER WAALS FORCE 40 20 0 Π [kpa] -20-40 -60 Π [kpa] 200 0-80 -200 0 5 10 d [nm] -100 0 2 4 6 8 10 d [nm] four layer system short distance limit (non-retarded) long distance limit (non-retarded) # non-monotonic thickness dependence # marginal thickness inset LC in nematic phase LC in nematic phase (non-retarded) LC in isotropic phase
VAN DER WAALS FORCE in wetting geometry 10 3 10 2 mean-field force Π [Pa] 10 1 10 0 10-1 van der Waals force # non-zero van der Waals force acting on the wetting layer # both, mean-field and van der Waals force are repulsive and are decreasing with the increasing thickness, yielding growing of the wetting layer on approaching 10-2 10 20 30 40 50 60 70 80 d [nm] d: thickness of the wetting layer which is very delicately tuned by the temperature (the plotted thickness interval corresponds to )
TOTAL FORCE BETWEEN CONFINING SURFACES MEAN-FIELD, PSEUDO-CASIMIR & VAN DER WAALS CONTRIBUTION Π [kpa] 40 20 0-20 -40 mean-field force -60 van der Waals force -80 pseudo-casimir force total force -100 0 5 10 15 20 25 # van der Waals force Si - SiO x - 5CB - air repulsion attraction # pseudo-casimir force > > Π [kpa] 1 0 = stable nematic film = spinodal decomposition -1 10 15 20 25 d [nm] d*
STABILITY OF A THIN HYBRID NEMATIC FILM 120 100 Λ =0.25 Λ =0.5 temperature dependent extrapolation lengths d* [nm] 80 60 40 20 20 22 24 26 28 30 32 34 36 T [ C] increase of the marginal thickness on approaching the bulk NI transition temperature # stable nematic film # spinodal decomposition
SUMMARY & CONCLUSIONS In highly frustrated geometries the structural forces, originating in deformed nematic ordering and modified spectrum of fluctuations, can play an important role in the stability of the film. The confinement-induced features of the film are especially prominent in the vicinity of structural transitions. The effect of the anisotropy of the dielectric permittivity of the media on the magnitude and character of the van der Waals interaction is discussed. In some cases taking into account the anisotropy is crucial. The Hamaker constant for anisotropic media with uniaxial symmetry has been derived. Some of the effects discussed have been observed in a study of spinodal dewetting of 5CB on a silicon substrate.
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 confined nematic liquid crystals] S. @umer, A. [arlah, P. Ziherl, and R. Podgornik, accepted for publication in MCLC [Casimir interactions and stability of 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]