Vesicle adhesion and microemulsion droplet dimerization: Small bending rigidity regime

To study the vesicle-substrate unbinding transition and the onset of microe mulsion aggregation, we calculate the curvature free energy of a vesicle ad hered to a substrate and of two microemulsion droplets forming a dimer. Ana lytical expressions are derived in the small bending rigidity regime in whi ch the length (k/sigma)(1/2), constructed from the rigidity constant of ben ding k and surface tension sigma, is small compared to the typical size of the vesicle (droplet), (k/sigma)(1/2)much less than R. The leading contribu tion to the curvature free energy is shown to be proportional to k(1/2). Th e formulas derived are used to understand the experimentally observed aggre gation of microemulsion droplets occurring in the direction of vanishing sp ontaneous curvature. In this way we intend to bridge the gap between the li quid state theories used to describe aggregation processes in microemulsion systems and the bending energy concept originally introduced by Helfrich t o describe vesicles shapes and fluctuations as well as phase diagrams of mi croemulsion systems. (C) 1999 American Institute of Physics. [S0021-9606(99 )71739-3].