Entropically driven microphase transitions in mixtures of colloidal rods and spheres

Although the idea that entropy alone is sufficient to produce an ordered state is an old one in colloid science1, the notion remains counter-intuitive and it is often assumed that attractive interactions are necessary to generate phases with long-range order. The phase behaviour for both rods and spheres has been studied experimentally1,2,3,4,5,6,7, theoretically8,9 and by computer simulations10. Here we describe the phase behaviour of mixtures of colloidal rod-like and sphere-like particles (respectively viruses and polystyrene latex or polyethylene oxide polymer) under conditions in which they act like hard' particles2,3. We find a wealth of behaviour: bulk demixing into rod-rich and rod-poor phases and microphase separation into a variety of morphologies. One microphase consists of layers of rods alternating with layers of spheres11; in another microphase of unanticipated complexity, the spheres reversibly assemble into columns, which in turn pack into a crystalline array. Our experiments, and previous theory and computer simulations11, suggest that this phase behaviour is entropically driven by steric repulsion between particles. The phenomena are likely to be quite general, applying also for example to low-molecular-mass liquid crystals12. This kind of microphase separation might also be relevant to systems of amphiphiles13 and block copolymers14, to bioseparation methods and DNA partitioning in prokaryotes15, and to protein crystallization16,17 and the manufacture of composite materials.