Molecular assembly on cylindrical surfaces W. Hong, Z. Suo * Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA Received 22 December 2003; received in revised form 8 June 2004 Available online 17 July 2004 Abstract A molecule adsorbed on a metal surface carries an electric dipole moment, and diffuses on the surface. When a collection of identical molecules partially covers the surface, the dipole–dipole interactions, along with other thermo- dynamic forces, drive the molecules to aggregate into monolayer islands, in the shape of dots or stripes. The dipole– dipole interactions mediate through the electrostatic field in the space. If the space is shaped, the electrostatic field will be affected, and so will the molecular pattern. To illustrate this idea, we develop a model to evolve molecular pattern on the surface of a wire, or the inner surface of a tube. Molecules assemble into parallel rings on the wire, and parallel stripes on the internal surface of a tube. When the tube radius is comparable to, or smaller than, the island size, the stripes switch to the rings; occasionally, the stripes form spirals. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Self-assembly; Cylindrical surface; Phase pattern; Adsorbate 1. Introduction Molecules and atoms absorbed on metallic surfaces carry electric dipoles (Evans and Ulman, 1990; Kellogg, 1994). The adsorbates can diffuse on the substrate surfaces (Barth, 2000). The dipole–dipole interaction, together with other inter-adsorbate forces, causes the adsorbates to self-assemble into a pat- tern, such as dots and stripes (Bohringer et al., 1999; Dmitriev et al., 2002; Xu et al., 2003). Similar patterns and analogous physics have been found in diverse systems, including lipid monolayers at the air/water interface (McConnell, 1991), block copolymer films (Harrison et al., 2000; Cheng et al., 2003), homopol- ymer films (Chou and Zhuang, 1999; Schaffer et al., 2000), ferrofluids (Dickstein et al., 1993), ferromagnets (De’Bell et al., 2000; Ifti et al., 2001), monolayer mixture on solid surfaces (Plass et al., 2001), and superconductors (Bianconi and Saini, 2001). Models of such phenomena have been reviewed by Seul and Andelman (1995), and Ng and Vanderbilt (1995). When a system is isotropic, the self-assembled patterns lack long-range order. To break the symmetry, one can guide the adsorbate assembly with an external electric field (Gao and Suo, 2003; Suo and Hong, * Corresponding author. Tel.: +1-617-4953789; fax: +1-617-4960601. E-mail address: suo@deas.harvard.edu (Z. Suo). 0020-7683/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2004.06.014 International Journal of Solids and Structures 41 (2004) 6895–6903 www.elsevier.com/locate/ijsolstr