Fractal Structure and Fractal Time in Silica Sol-Gels
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FRACTAL STRUCTURE AND FRACTAL TIME IN SILICA SOL-GELS JAMES E. MARTIN AND JESS WILCOXON Sandia National Laboratories, Albuquerque, NM 87185 ABSTRACT
Near the gel point, light scattering studies of silica sol-gels reveal fractal clusters whose size diverges as a power law, in accord with the predictions of percolation theory. More surprising is the appearance of a fractal time description of the dynamics of these clusters. This novel dynamics has recently been revealed by quasielastic light scattering from the density fluctuations that occur at the sol-gel transition. Since the relaxation of fluctuations in these branched polymer systems is self-similar, decay processes occur on all time scales (fractal time), and average decay times diverge. An interpretation of this observation will be presented that relies on a length-scale-dependent viscosity and the geometrical self-similarity of the sol-gel transition. The scattering theory is extended to the calculation of time- and frequency-dependent viscoelastic properties, as well as mechanical properties such as the shear modulus, steady state creep compliance, and viscosity. The viscoelastic predictions are found to be in good agreement with experimental data. INTRODUCTION
Silica gels are technologically important materials with a rich chemistry, yet relatively little is known about the evolution of structure of these complex materials. In part, the complexity of silica gels arises from the wealth of synthetic routes used to produce them. A typical synthetic process depends on such parameters as the pH, concentration of monomer, water, catalyst, salt etc., and these parameters are usually varied in an empirical fashion to produce a suitable gel time, gel density and so forth. That the evolution of structure in these gels is so poorly understood is partially due to the fact that researchers are unable to agree on exactly what is meant by structure. Once a suitable definition of structure is adopted, one might then ask some very basic questions, such as "What structural characteristics are strongly affected by the chemistry and what properties are largely immutable?" Since the most dramatic physical changes occur in the vicinity of the sol-gel transition, this regime would seem to offer the most fruitful initial avenue of investigation. The investigations we have made on the sol-gel transition include relatively Mat. Res. Soc. Symp. Proc. Vol. 180. 91990 Materials Research Society
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The investigations we have made on the sol-gel transition include relatively straightforward static structure measurements as well as more complex determinations of dynamical properties. To interpret these measurements we have used the well known analogy [1-4] between the sol-gel transition and a second-order thermodynamic phase transition to develop theories of the elastic and inelastic light scattering behavior, and viscoelastic phenomena. In this article we give a overview of the various aspects of the sol-gel transition in silica, and briefly discuss the less universal aspects of gr
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