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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.

Mussels attach to solid surfaces in the sea. Their adhesion must be rapid, strong, and tough, or else they will be dislodged and dashed to pieces by the next incoming wave. Given the dearth of synthetic adhesives for wet polar surfaces, much effort has been directed to characterizing and mimicking essential features of the adhesive chemistry practiced by mussels. Studies of these organisms have uncovered important adaptive strategies that help to circumvent the high dielectric and solvation properties of water that typically frustrate adhesion. In a chemical vein, the adhesive proteins of mussels are heavily decorated with Dopa, a catecholic functionality. Various synthetic polymers have been functionalized with catechols to provide diverse adhesive, sealant, coating, and anchoring properties, particularly for critical biomedical applications.

Geckos have evolved one of the most versatile and effective adhesives known. The mechanism of dry adhesion in the millions of setae on the toes of geckos has been the focus of scientific study for over a century. We provide the first direct experimental evidence for dry adhesion of gecko setae by van der Waals forces, and reject the use of mechanisms relying on high surface polarity, including capillary adhesion. The toes of live Tokay geckos were highly hydrophobic, and adhered equally well to strongly hydrophobic and strongly hydrophilic, polarizable surfaces. Adhesion of a single isolated gecko seta was equally effective on the hydrophobic and hydrophilic surfaces of a microelectro-mechanical systems force sensor. A van der Waals mechanism implies that the remarkable adhesive properties of gecko setae are merely a result of the size and shape of the tips, and are not strongly affected by surface chemistry. Theory predicts greater adhesive forces simply from subdividing setae to increase surface density, and suggests a possible design principle underlying the repeated, convergent evolution of dry adhesive microstructures in gecko, anoles, skinks, and insects. Estimates using a standard adhesion model and our measured forces come remarkably close to predicting the tip size of Tokay gecko seta. We verified the dependence on size and not surface type by using physical models of setal tips nanofabricated from two different materials. Both artificial setal tips stuck as predicted and provide a path to manufacturing the first dry, adhesive microstructures.I n the 4th century B.C., Aristotle observed the ability of the gecko to ''run up and down a tree in any way, even with the head downwards'' (1). Two millennia later, we are uncovering the secrets of how geckos use millions of tiny foot-hairs to adhere to even molecularly smooth surfaces. We tested the two currently competing hypotheses (2, 3) of adhesion mechanisms in gecko setae: (i) thin-film capillary forces (or other mechanisms relying on hydrophilicity) and (ii) van der Waals forces. First, we tested the capillary and van der Waals hypotheses experimentally. Second, we used our experimentally measured adhesion forces in a mathematical model (4) to generate an independent prediction of the size of a setal tip. We compared the predicted size with the empirical values measured by electron microscopy (5). Third, we fabricated a physical model of gecko setal tips from two different materials. We then compared the adhesive function of the physical model to predicted force values from the mathematical model. Previously, we showed by calculation that our direct force measurements of a single gecko seta (3) were consistent with adhesion by van der Waals forces, but we could not reject the only other untested mechanism-wet, capillary adhesion that relies on the hydrophilic nature of the surface. Capillary forces contribute to adhesion in many insects (6-13), frogs (14-16), and even some mammals (17). Unlike many insects, geckos lack glands on the surfaces of their feet...