### abstract

- A two-dimensional lattice model, originally introduced by Granek etal. [J. Chem. Phys. 101, 4331 (1994)], is used to demonstrate the intricate coupling between the intramicellar interactions that determine the optimal aggregation geometry of surfactant molecules in dilute solution, and the intermicellar interactions that govern the phase behavior at higher concentrations. Three very different scenarios of self-assembly and phase evolution are analyzed in detail, based on Monte Carlo studies and theoretical interpretations involving mean-field, Landau–Ginzburg, Bethe–Peierls, and virial expansion schemes. The basic particles in the model are ‘‘unit micelles’’ which, due to spontaneous self-assembly or because of excluded area interactions, can fuse to form larger aggregates. These aggregates are envisaged as flat micelles composed of a bilayerlike body surrounded by a curved semitoroidal rim. The system’s Hamiltonian involves one- through four-body potentials between the unit micelles, which account for their tendency to form aggregates of different shapes, e.g., elongated vs disklike micelles.Equivalently, the configurational energy of the system is a sum of micellar self-energies involving the packing free energies of the constituent molecules in the bilayer body and in rim segments of different local curvature. The rim energy is a sum of a line tension term and a 1D curvature energy which depends on the rim spontaneous curvature and bending rigidity. Different combinations of these molecular parameters imply different optimal packing geometries and hence different self-assembly and phase behaviors. The emphasis in this paper is on systems of ‘‘curvature loving’’ amphiphiles which, in our model, are characterized by negative line tension. The three systems studied are: (i) A dilute solution of stable disklike micelles which, upon increasing the concentration, undergoes a first-order phase transition to a continuous bilayer with isolated hole defects. An intermediate modulated ‘‘checkerboard’’ phase appears under certain conditions at low temperatures. (ii) A system of unit micelles which in dilute solution tend to associate into linear micelles. These micelles are rodlike at low temperatures, becoming increasingly more flexible as the temperature increases. Upon increasing the concentration the micelles grow and undergo (in 2D) a continuous transition into nematic and ‘‘stripe’’ phases of long rods. At still higher concentrations the micellar stripes fuse into continuous sheets with line defects. (iii) A system in which, already in dilute solution, the micelles favor the formation of branched aggregates, analogous to the branched cylindrical micelles recently observed in certain surfactant solutions. As the concentration increases the micelles associate into networks (‘‘gels’’) composed of a mesh of linear micelles linked by ‘‘T-like’’ intermicellar junctions. The network may span the entire system or phase separate and coexist with a dilute micellar phase, depending on the details of the molecular packing parameters.