A simple theory is developed that accounts for many of the observed physical properties of micelles, both globular and rod-like, and of bilayer vesicles composed of ionic or zwitterionic amphiphiles. The main point of departure from previous theories lies in the recognition and elucidation of the role of geometric constraints in self-assembly. The linking together of therrnodynamics, interaction free energies and geometry results in a general framework which permits extension to more complicated self-assembly problems.

From a review of the major factors responsible for surfactant mesophase structure, a model phase diagram is deduced which shows phase structure as a function of surfactant volume fraction and micelle curvature. To test this model the phase behaviour of a series of pure polyoxyethylene surfactants (C, EO,) with water has been studied using optical microscopy over the temperature range 0-100 OC. The compounds

Organic Geochemismealworm beetle (~enebrio molitor) that reveals the layeis of cuticle overlapping at different angles; (C try Unit, School Of University Of BristOl, Canan SEM image of afractured edge of cuticle of the specimen illustrated in (A) that shows chitinous fibers; tock's Close, Bristol BS8 ITS, UK. M, Wuttke, Landesamt fijr Denkmalpflege Rheinland-and D) an SEM image of the shale matrix that contains the fossil insects and reveals that pennate Pfalz, Referat Erdgeschichtliche Denkmalpflege, Am diatoms are the dominant constituent. (Images were made with a Cambridge Stereoscan 250 Mk3 SEM Obstmarkt 13, D-55126 Mainz, Germany.at 7 to 12 kV after specimens were coated with gold.)www.sciencemag.org SCIENCE VOL. 276 6 JUNE 1997

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A theory of self-assembly of surfactant molecules into micelles and bilayers is critically examined and extended to include vesicles and microemulsions. The notion of hydrophilic-lipophilic balance is quantified. The theory gives a unified account of type, size and shape of the aggregates which form under various conditions. Observed trends due to change in salt concentration, temperature and oil type, and due to the addition of cosurfactants, are correlated and emerge from a simple global framework.