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 science(1), 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 experimentally(1-7), theoretically(8,9) and by computer simulations(10). Here we describe the phase behaviour of mixtures of colloidal rodlike and sphere-like particles (respectively viruses and polystyrene latex or polyethylene oxide polymer) under conditions in which they act like hard' particles(2,3). 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 spheres(11); 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 simulations(11), 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 crystals(12). This kind of microphase separation might also be relevant to systems of amphiphiles(13) and block copolymers(14), to bioseparation methods and DNA partitioning in prokaryotes(15), and to protein crystallization(16,17) and the manufacture of composite materials.