Statistical model for the structure and gelation of smectite clay suspensions

Abstract

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.