Colloidal nanocrystals (NCs) are hybrid organic/inorganic nano-objects composed of an inorganic core a few nanometer across terminated by an organic capping or ligand shell. This ligand shell has been compared to self-assembled monolayers (SAM) on surfaces. The way SAMs organize themselves on solid surfaces is generally described in terms of the combined effect of headgroup-substrate and chain-chain interaction. In the case of colloidal nanocrystals, however, the understanding of ligand exchange or the interplay between ligand binding and nanocrystal properties is typically discussed in terms of headgroup-substrate interactions rather than on chain-chain interactions. Nevertheless, already in the case of two-component SAMs containing molecules with identical headgroups yet slightly dissimilar chains, ligand-ligand interactions can cause phase separation into nanometer scale molecular domains, a size commensurate with that of a nanocrystal surface facet. Here, we propose a combined experimental and theoretical study on two-component ligand shells of colloidal quantum dots made by ligand exchange. Taking oleate-capped CdSe quantum dots as a model system, we first show by nuclear magnetic resonance (NMR) spectroscopy that exposure to other fatty acids results in a one-for-one exchange that leaves the net ligand/excess cadmium ratio unchanged. In the case of single chain saturated carboxylic acids, this results in a progressive exchange where a two-component ligand shells is formed that has the same composition as the reaction mixture. With a branched carboxylic acid, on the other hand, only part of the original ligands can be exchanged, regardless of the concentration of the branched acid.  Describing the quantum-dot surface using a two dimensional lattice model, we attribute this to a combination of a tit-for-tat exchange reaction and a difference in chain volume. Whereas such a model cannot distinguish a randomly distributed from a phase-separated two-component ligand shell, molecular dynamics simulations support an interpretation where the particular surface chemistry of CdSe QDs restricts the adsorption of branched carboxylic acids to the edges of crystal facets. This indicates that in the case of quantum dots of binary semiconductors, two-component ligand shells can phase separate by the joined effect of facet-specific adsorption, ligand-ligand interaction and ligand densities imposed by the surface excess of metal cations.