Torsion Balance for Measurement of Capillary Immersion Forces Ceco D. Dushkin,* ,† Peter A. Kralchevsky, † Vesselin N. Paunov, † Hideyuki Yoshimura, ‡ and Kuniaki Nagayama ‡ Laboratory of Thermodynamics and Physico-chemical Hydrodynamics, Faculty of Chemistry, University of Sofia, 1126 Sofia, Bulgaria, and Protein Array Project, ERATO, JRDC, 5-9-1 Tokodai, Tsukuba 300-26, Japan Received July 10, 1995. In Final Form: October 6, 1995 X Particle-particle and particle-wall capillary interactions were measured as a function of the separation distance. The “particles” were vertical thin glass cylinders and/or small glass spheres, protruding from an air/liquid interface. The particles attract each other due to the overlapping of the menisci formed around each of them. The force of interaction is detected by a sensitive torsion microbalance. It is based on counterbalancing the moment of a couple of forces, acting between two pairs of particles, by the torsion moment of a thin platinum wire. By varying the wire diameter, we accessed forces differing by several orders of magnitude, from about 5 dyn at small separation between the particles down to 0.001 dyn at large separation. The smallest force was measured with two cylinders of diameters about 300 µm. For two spheres (diameters 1.2 mm) we obtained difference in the forces corresponding to different heights of protrusion from the liquid surface. For interacting sphere and glass cylinder the force follows similar trends as the forces between two spheres or two cylinders. In the case of sphere and glass wall, however, the force first increases with decreasing the distance and then decreases close to the wall passing through a maximum. The predictions of the theory of capillary immersion forces are in quantitative agreement with the experimental results. 1. Introduction For a long time capillary forces were believed to play an important role in the interaction between colloidal particles attached to a liquid interface. 1 This importance was stressed recently in connection with the formation of two-dimensional arrays of fine particles. 2 It was observed experimentally that, despite of their size (micrometer, 3 submicrometer, 4 or nanometer 5 ), the particles confined in a thin suspension film on a substrate form an ordered monolayer due to a sort of long range lateral attractive force (capillary force). This force arises in the course of thinning the suspension film down to a thickness of less than the particle diameter 3,6 when the particles protrude from the liquid-air interface. The cause of the lateral capillary forces is the deformation of the liquid surface around the particle which allowed theoretical computation of the force by solving the Laplace equation of capillarity in relevant geometry (for a review see ref 7). The forces acting on particles partially immersed in a wetting liquid film on a substrate, called immersion capillary forces, should be distinguished from the flotation capillary forces acting on particles floating freely on a liquid interface. The origin of the flotation forces is the particle weight causing a deformation of the liquid surface whereas the immersion forces are related to the wetting properties of the particle surface rather than to gravity. 7 The immer- sion forces, being much stronger due to their origin, can be significant even for nanometer size particles compared to the flotation forces which practically vanish for particles smaller in size than 10 µm. Here we consider forces acting among particles constrained on a liquid-air interface which are a sort of capillary immersion forces. As shown theoretically 8,9 the capillary interaction between two spherical particles can be successfully approximated by the interaction between two vertical cylinders used recently for experimental determination of the capillary forces. 10 The force balance developed in ref 10 allowed measurement of the force between two glass capillaries immersed in liquid: one of them attached to a stepper motor gradually approaches the other one attached to the sensitive core of a pressure transducer. The force was determined from the transducer output voltage plotted on chart recorder versus the separation distance. For a couple of capillaries of diameters 740 and 630 µm the measured force ranged from about 0.1 to 4 dyn depending on the separation distance. At one and the same distance the force measured for pure water was roughly twice the force obtained for surfactant solution which could be explained simply by twice larger surface tension in the former case than in the latter, in agreement with the theoretical predictions. 8,9 Despite of the experimental work 10 there are questions which still remain open: (i) About the force between spherical particles which are much closer in shape to the real colloidal particles than the model cylinders. There is only one attempt 11 to measure the force between two spheres attached to a water-oil interface in an oil film spread on water. Unfortunately, the experimental data obtained in ref 11 could not be quantitatively interpreted by means of the * Author for correspondence † University of Sofia. ‡ Protein Array Project. X Abstract published in Advance ACS Abstracts, December 15, 1995. (1) Nicolson, M. M. Proc. Cambridge Philos. Soc. 1949, 45, 288. (2) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Nature (London) 1993, 361, 26. (3) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Langmuir 1992, 8, 3183. (4) Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Chem. Phys. Lett. 1993, 204, 455. (5) Nagayama, K. Materials Sci. Eng. 1994, C1, 87. (6) Dimitrov, A. S.; Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Langmuir 1994, 10, 432. (7) Kralchevsky, P. A.; Nagayama, K. Langmuir 1994, 10, 23. (8) Kralchevsky, P. A.; Paunov, V. N.; Ivanov, I. B.; Nagayama, K. J. Colloid Interface Sci. 1992, 151, 79. (9) Kralchevsky, P. A.; Paunov, V. N.; Denkov, N. D.; Ivanov, I. B.; Nagayama, K. J. Colloid Interface Sci. 1993, 155, 420. (10) Velev, O. D.; Denkov, N. D.; Paunov, V. N.; Kralchevsky, P. A.; Nagayama, K. Langmuir 1993, 9, 3702. (11) Camoin, C.; Roussell, J. F.; Faure, R.; Blanc, R. Europhys. Lett. 1987, 3, 449. 641 Langmuir 1996, 12, 641-651 0743-7463/96/2412-0641$12.00/0 © 1996 American Chemical Society