In this paper we study the conditions under which comicellization occurs for a bimodal distribution of diblock copolymers in a selective solvent. The formation of pure micelles or comicelles depends on the relative concentration of the two species of diblock copolymers in solution. Regions of pure micelles in equilibrium with the free chains belonging to the two species exist in the phase diagram at low concentrations of one or other species, but for high enough concentrations of both species, comicelles may be present depending on the interaction parameter of the bimodal core. We consider the effects of varying this interaction parameter. We also discuss the interfacial behavior of mixed copolymer systems, and the conditions under which mon- odisperse or bimodal brushes of adsorbed polymer will form on an attractive surface. I. Introduction The macromolecular analogues of micelle-forming sur- factants, amphiphilic diblock copolymers AC in a selective solvent, have been extensively studied.l+ Various the- oretical models have been put forward to gain a better understanding of these micelle-forming diblock copolymers and have been used to explain some of the experimental observations.10 We consider the case of a highly selective solvent in which one of the blocks, say A, is incompatible with the solvent and with the C block and forms a near-molten core, excluding most of the solvent and the C polymer. The other block C solubilizes preferentially in the solvent and forms a corona* fanning outward from the core. This region is analogous to a set of terminally attached polymers on the molten core/corona interface. The asymmetry of the diblock copolymer is character- ized by the parameter PAC = Nc~/~NA-'/~. This is simply the ratio of the sizes in the solvent of the two blocks making up the diblock copolymer. (We assume that the statistical lengths of A and C species are equal and choose units so that this length 1 = 1.) In most practical cases where the diblock copolymer is in selective solvent, j3 # 1. Diblock copolymers are also used to study the physical properties of polymer-coated particles.11 They impart stability on colloidal particles and prevent the particles from coagulating or flocculating in a dispersion. The block that has a high affinity for the surface and interacts unfavorably with the solvent precipitates onto the colloid surface and the block that has a lower surface affinity then forms the solvated corona, which acts as a stabilizing layer. If the thickness of the solvated layer is much smaller than the radius of the colloidal particle, then the stabilizing layer can be modeled as a grafted layer on a flat surface. This has been extensively studied by many authors.l2-19 This approximation is not unreasonable and provides the route for calculating the interaction between colloidal particles.11 These two problems-formation of micelles and ad- sorption-have been previously addressed by Marques et a1.l who assumed a monodisperse distribution of diblock copolymer chains in solution. In many experimental situations it is of some interest to modulate the micelles and adsorbed layer characteristics-for instance, the mi- celle aggregation number or the thickness of the adsorbed layer-by mixing molecules of different types. In this paper we present an extension of the model of ref 1 to a bimodal distribution of diblock copolymers. We consider two species of diblock copolymers AC and BC with asymmetry parameter j3~c and BBC, respectively. Their degrees of polymerization (DP) are (NA + NJ and (NB + N2), respectively. For simplicity we restrict our attention to the case NA = NB = N. Both A and B are in bad solvent and hence in a collapsed state, while for C the solvent is good; each C block forms a dangling tail attached to a molten head of A or B. The objectives of this paper are to consider situations under which composite micelles (comicelles) can arise from the two different species. This represents the simplest case of a more general problem involving the statistics of micelle formation from a distribution of diblock copolymers in a selective solvent. There is a close analogy with the theory of competitive adsorption by different species and we will consider this problem within the same framework. Diblock copolymers make good theoretical models for studying micellization (even though their critical micellization concentrations are small). This is because polymeric interactions and free energies are more universal and better understood than the forces between smaller molecules. Strictly speaking our results apply only for asymptotically long chains, but many of the qualitative aspects should hold for short chains also. With this in mind, we deliberately use rather small values of the DP when illustrating our results with numerical phase diagrams.