Consolute Critical Phenomena in Dilute Silica Gel
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CONSOLUTE CRITICAL PHENOMENA IN DILUTE SILICA GEL
B.J. Frisken* , Fabio Ferri and David S. Cannell Department of Physics, University of California, Santa Barbara, CA 93106 *Current address, Department of Physics, Simon Fraser University, Burnaby BC V5A 1S6
ABSTRACT The effect of even dilute silica networks on the critical phenomena of binary liquid mixtures is profound. The network preferentially adsorbs one component, preventing a portion of the mixture from participating in critical fluctuations. Fluctuations in the remaining mixture are found to decay with a non-exponential correlation function near the consolute point. A correlation function consisting of the sum of an exponential decay and a non-exponential term of either an activated or stretched exponential form fits the data well. In the presence of the silica network, the mixtures are observed to phase separate near the critical temperature of the pure system, but while still in the one-phase region of the pure system.
INTRODUCTION A mixture of two simple liquids near the consolute or critical point is a particularly delicate system in terms of its response to being confined in small pores or to having even a very dilute (a few percent by volume) silica network (gel) embedded in it[1]. The same appears to be true of single fluids near their gas-liquid critical points[2], and of 4 He near the superfluid transition[3]. Although the critical behavior of these and other diverse systems is well understood in their pure states, the response of critical systems to the surface fields associated with pores or the strands of a gel network is complex and poorly understood at present. In general, confined fluids and mixtures near the critical points of the pure systems fail to exhibit the long range spatially correlated fluctuations and the concomitant extreme slowing down of temporal fluctuations associated with the critical points of the pure systems. Instead, the main response seems to be static time-independent fluctuations in concentration or density, which grow in amplitude as the critical region is approached. From a general point of view this is perhaps not too surprising. The linear response of a critical system to a field conjugate to its order parameter diverges at the critical point. If one models surfaces in term of surface fields which act on molecules or atoms at the surface and vanish elsewhere, then such fields would be expected to induce a large, possibly nonlinear, response in a critical system, provided the surface fields couple to the critical system's order parameter (concentration for a mixture, or density for a single fluid). In fact, it is well known that surfaces inevitably attract one of two species preferentially, or prefer either liquid or vapor phase when in contact with a single fluid. The challenge is to understand the static response of the critical system to the surface fields, and to use this knowledge to elucidate the effects of surfaces on the dynamical aspects of critical phenomena. This ambitious task is further complicated by
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