Statistical model for the structure and gelation of smectite clay suspensions

The sol-gel transition in a suspension of monodisperse, charged, disklike platelets (Laponite, i.e., a synthetic clay) is examined within a simplified statistical model. The initial ''primitive'' model of uniformly charged disks surrounded by microscopic co ions and counterions is reduced to a model of nonintersecting disks carrying a rigid point quadrupole, resulting from the electric double layers around the disks. The quadrupolar interactions favor edge-to-face pair configurations that counteract the tendency of parallel (nematic) alignment of bare disks at high densities. The local structure and phase behavior of the quadrupolar disk model is studied over a broad range of clay concentrations and quadrupole moments (which depend on the concentration of added salt) by extensive Monte Carlo simulations. The model suspension is found to undergo a reversible sol-gel transition above a critical quadrupolar coupling. The gel phase lacks long-range order, and is reminiscent of a ''house-of-cards'' structure in which most of the particles are edge-to-face to each other. The critical concentration and quadrupolar coupling constant are not inconsistent with recent experimental data on the gelation of Laponite suspensions.