Growth of a colloidal crystallite of hard spheres

We examine the growth of a single nucleus of hard spheres in a super-saturated colloidal dispersion of hard spheres. A model developed by Bruce Ackerson and Klaus Schätzel based on a Wilson-Frenkel growth law is used. Our emphasis is on the profile of the radial density distribution around the growing (but still spherically symmetric) grain and its Fourier transform, the grainʹs form factor, which can be observed under small scattering angles in a dynamic light scattering experiment. Depending on the value of the supersaturation we can identify two limiting cases of different growth exponents and density profiles: one is the Frank theory of diffusion-limited growth and the other is reaction-limited growth. In both cases a characteristic depletion zone appears, the shape of which can be modelled.