Glass transition in colloidal hard spheres: mode-coupling theory analysis
Figure 1 shows a representative set of ISF’s, made at wave vectors below, near, and above the position qm of the main peak in S(q). Increasing the concentration from freezing (ø /—0.494) to φ "0.574 lengthens the overall decay time of f ( q y r ) by nearly four decades, from about 10s to 109 /is, and significantly three relaxation stages become increasingly apparent; the crossover times between these stages are indicated by points of inflection which, for 0 "0.574, occur at around 104 and 107 /is. The fastest of these processes [indicated by the dashed curve in Fig. 1(b)] is associated with the microscopic diffusive motions of particles within their instantaneous neighbor cages and accounts for the initial few percent of the decay of f (q, r). This is followed by two slower pro cesses whose time scales lengthen and separate with in creasing concentration. When the concentration is in creased further by only 1%, from 0.574 to 0.581, f ( q y τ) saturates to an almost constant value indicating the pres ence of concentration fluctuations whose duration significantly exceeds 1000 s. Thus, the occurrence of the kinetic GT is indicated at a concentration фс (0.574 <фс< 0.581) by the cessation of large-scale diffusion and arrest of the fluid structure on the experimental time scale.