SURFACTANT SELF-ASSEMBLY IN THREE DIMENSIONS K. P. Santo 1,2 , Andriy Kovalenko 1,2 and Maria Stepanova 2 1 Department of Mechanical Engineering, University of Alberta, Edmonton, Canada 2 National Institute of Nanotechnology, NRC, Canada. Abstract: The off-lattice self-consistent field theory (SCFT) is an efficient tool for modelling the mesoscopic phase behaviour of complex polymeric systems. Here, we make an extensive use of it to study the morphologies and the thermodynamics of phase separation in amphiphilic lipid air-water systems in three dimensions. We present results for both lipids with saturated and unsaturated tail groups and analyze the nature of the transition between their different morphological phases. Keywords: Surfactant, co-polymer, phase transition, statistical mechanics 1. THE SELF-CONSISTENT FIELD THEORY AND THE MESOSCOPIC PHASE SEPERATION IN PHOSPHO- LIPID SYSTEMS The ability of surfactant molecular systems to exhibit microscopic phase separation is the key factor that is responsible for their biologically important functions as well as their applications in industry ( de Bruijn et al, 2002), Swalen et al, 1987) . Surfactants are block co-polymers with regions that are hydrophilic and hydrophobic, and thus are termed amphiphilic. Different blocks in the copolymer interact differently within the blocks and with the medium, resulting in phase separation that leads to different morphologies in the microscopic level (Schmid, 1998). Such morphologies could be of different geometries, such as spherical micelle, cylindrical micelle and lamellae, depending on the lipid concentration, temperature and other conditions. The surfactants which are the essential ingredients of biological membranes are the phospholipids (Cullis et al, 1985, Kik et al, 2005,Luzatti et al, 1968) . Phospholipids are also the major content of the pulmonary surfactant, which regulate the alveolar functions in the lung during the breathing cycle (Ghodrat 2006, Piknova et al,2002). Despite considerable experimental (Binder et al, 2001, Discher et al, 1999) as well as theoretical ( Drolet et al, 1999, Muller et al, 1998) attempts the complete understanding of the functions of the pulmonary surfactant is still lacking in the literature. Modelling complex polymer systems has always been a challenge in polymer physics. While molecular dynamics (MD) simulations are limited to smaller length and time scales, a mean field approach may lead to loss of information at the molecular level. However, in the length scales where the micro copolymer phases are exhibited, the mean-field approaches have been used with considerable success. The self-consistent field theory (SCFT) combines a mean-field description of the segment interactions with the chain connectivity and has been successfully used to describe the block copolymer phases (Helfand, 1975). In this formalism, the interaction fields and the density distributions of the components are interdependent and therefore are calculated in a self-consistent manner. Here, we consider a system consisting of branched lipids, air, and water. We model the molecules according to the Flory-Huggins theory ; the head (A) and tail (B) groups of the lipid are linear polymer chains that consist of several segments, while the air (V) and water (W) molecules consists of two segments (lattice points). Using the statistical theory of polymers (Flory, 1969), one can obtain the Greens function q c (r ,s) of molecule c, which obeys ) , ( ) , ( 6 ) , ( 2 2 s r q s r q a s s r q c is c c       . (1) Here, a is the Kuhn length of the polymer and s is the arc length parameter.  is is the mean field interaction of the s th segment, which is of type i (i=A, B,...V, W). According to the standard Gaussian copolymer theory, the volume