A Model of Capillary Rise of Nematic Liquid Crystals Alejandro D. Rey* Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2 Received August 29, 2002. In Final Form: December 4, 2002 A general model for the capillary rise for uniaxial nematic liquid crystals has been derived using fundamental principles and classical liquid crystal physics and partially validated using existing experimental data. A rigorous formulation of the contributions of surface and bulk nematic elasticity was implemented. The surface contribution is a function of the surface anchoring strength at the liquid crystal- capillary wall. The exact bulk elasticity contribution is a function of the director field in the meniscus. The specific form of the capillary rise equation for four typical nematic textures was developed and analyzed. It is found that capillary rise depends on the presence of bulk disclinations and on the orientation field close to the contact line. It is found that orientation gradients at the contact line are the most significant nematic contribution to capillary rise. The model explains unusual features in experimental capillary rise measurements, including why parallel nematic orientation at the capillary wall exhibits a higher capillary rise than orthogonal orientation. Introduction The capillary rise method is a standard and popular procedure to measure surface tension of liquids. 1 In this method the height h of a liquid column in a capillary above a reference level in a large reservoir is measured. For isotropic liquids the height of the liquid is where A is the cross section, L is the wetted perimeter, γ is the liquid surface tension, θ is the static contact angle, and ΔF is the density difference between the liquid and the ambient gas. Depending on the contact angle, the height can take any value in the interval -L/ΔFgA < h <+L/ΔFgA. The capillary rise method is one of the most accurate means to measure surface tension. Details of the method can be found in the literature. 1 The only material property that enters in the equation used to measure surface tension using the capillary rise method is the surface tension itself. For soft matter, such as complex fluids, the equation is inapplicable because long- and short-range bulk elastic modes are not included in eq 1. This paper presents an analysis of capillary rise for a typical single-component single-phase complex fluid, a low molar mass nematic liquid crystal, 2 in the absence of transitional phenomena. Nematic liquid crystals are anisotropic viscoelastic liquid crystals, 2 whose orienta- tional order is described by a unit vector n, known as the director. Spatial director gradients (∇n * 0) store long- range elastic energy, known as Frank elasticity. 2 Since nematic liquid crystals are orientationally ordered ma- terials, they can exhibit defects; linear defects are known as disclinations 2 and arise due to incompatibilities due to geometry or orienting fields. In the capillary rise of nematic liquid crystals, defects arise due to the presence on orienting surfaces. The surface physics of liquid crystals has been recently reviewed. 3-5 Surface tension measure- ments and theories for low molar mass thermotropic nematic liquid crystals using the Wilhelmy method are available. 6-8 The importance, magnitude, and mathemati- cal description of the nematic ordering contributions have not been discussed in the literature but are certainly critical given the central importance of the capillary rise method in surface science and the need of interpreting experimental surface tension data of a nematic liquid crystal (NLC). 9 A unique model equation of the capillary rise method for NLC such as eq 1 does not exist because the measure- ments involve the selection of one out of several bulk distortion modes, depending among other things on the NLC-capillary surface properties. Thus, distortion mode selection is at the core of the problem. The orientation at the free surface of NLC can also be tangential, planar, or tilted, and thus the magnitude and even sign of the orientation-dependent part of the surface tension, known as anchoring energy, 3-5 will depend on the nature of the NLC in question. The approach taken in this work is to derive the governing balance equation for the capillary rise and then apply it to a number of realistic particular cases. No attempts at modeling the capillary rise method are currently available, but they are certainly necessary to interpret and use existing experimental data. 9 Capillary rise measurements of several low molar mass rodlike nematic liquid crystals have been performed, using several carefully controlled physicochemical treatments of the capillary walls containing the liquid crystals. 9 The physicochemical treatments produce fixed orientation of the NLC, known as strong anchoring condition. The carefully conducted experiments show that when the * E-mail: alejandro.rey@mcgill.ca. Tel: (514) 398-4196. Fax: (514) 398-6678. (1) Hiemenz, P. C. Principles of Colloid and Surface Chemistry, 2nd ed.; Marcel Dekker: New York, 1986. (2) de Gennes, P. G.; Prost, J. The Physics of Liquid Crystals; Clarendon Press: Oxford, 1993. (3) Je´roˆme, B. Rep. Prog. Phys. 1991, 54, 391. (4) Sonin, A. A. The Surface Physics of Liquid Crystals; Gordon and Breach: Amsterdam, 1995. (5) Yokoyama, H. In Handbook of Liquid Crystal Research; Collins, P. J., Patel, J. S., Eds.; Oxford University Press: New York, 1997; Chapter 6, p 179. (6) Gannon, M. G. J.; Faber, T. E. Philos. Mag. 1978, 37, 117. (7) Chandrasekhar, S. Liquid Crystals, 2nd ed.; Cambridge University Press: New York, 1992. (8) Rey, A. D. Langmuir 2000, 16, 845. (9) Tsvetkov, V. A.; Tsvetkov; O. V.; Balandin; V. A. Mol. Cryst. Liq. Cryst. 1999, 329, 305. h ) γL cos θ ΔFgA (1) 3677 Langmuir 2003, 19, 3677-3685 10.1021/la020750h CCC: $25.00 © 2003 American Chemical Society Published on Web 03/27/2003