J. Phys.: Condens. zyxwvuts Matter 6 (1994) A395-A402. Printed in zyxwv the zyxwv UK Formation of two-dimensional colloid crystals in liquid fdms under the action of capillary forces P A Kralchevskyt, N D Denkovt. V N Paunovt, 0 D Velevt, I B Ivanovt, H Yoshimura and K Nagayme zyxw t Laboratory of Thermodynamics and Physico-chemical Hydrodynamics. University of Sofia, I126 Sofia, Bulgaria $ Protein Array Project. ERATO. IRDC, 5-9-1 Tokodai, Tsukuba 300-26, Japan Received 25 October 1993 Abstract. When two similar small particles are attached to a liquid interface they attract each other due to a lateral capillay force. This force appears because the gravitational potential energy of the floating particles decreases when they are approaching each other. This force is proportional to zyxwvut R6 (R is the particle radius), so it decreaxs very fast with panicle size and becomes negligible for R zyxwvut c 10 Km. zyxwv We found that the situation is quite different when ihe particles (instead of being freely floating) are panidly immersed in a liquid layer on a substrate. In this case the energy of capillary attraction is propaltional to zyx R2 and "s out to be much larger than kT even with particles of diameter about 10 nm. The effect is related to the particle three-phme contact angle, i.e. to the intermolecular forces, rather than to gravity. The experiments show that the lateral capillary forces can bring about the formation of a zy two- dimensional anay (20-crystal) hm both micrometre-size and submicrometre particles: latex spheres. protein globules. etc. 1. Introduction A fast and convenient method for formation of a two-dimensional (2D) protein array on a mercury surface has been recently developed [1,2]. The good quality of the samples thus obtained allowed investigation of the protein orientation and structure by electron microscopy combined with image reconstruction. Highly ordered 2D crystals can thus be obtained in a controllable way; this technique could lead to further development of the controlled building up of well ordered protein monolayers and multilayers-a possible step towards a future high technology at the macromolecular level [Z]. 2D arrays on solid substrates can find applications in various modern techniques, such as data storage, optical devices and microelectronics [3]. The occurrence of the ZD array formation with proteins [1,2,41 in many aspects resembles the ordering process with larger latex particles [5,6]. It can be. expected that the capillary interparticle forces play an important role in both these systems. The capillary forces between particles attached to an interface have been studied both experimentally [7,8] and theoretically [9-121. In the present paper we present a short review of our recent theoretical and experimental studies [13-18] on the different kinds of capillary force. Our aim is to attract the reader's attention to the variety of capillary interactions taking place at two different boundary conditions on the particle surfaces: fixed contact angle and fixed contact line. Particle-wall interactions, giving rise to the so-called 'capillary image forces' are also studied [ 19,201. 0953-8984/94/SAO395+8$19.50 @ 1994 LOP Publishing Ltd A395