Mechanical Properties of Colloidal Gels Subject to Particle Rearrangement
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MECHANICAL PROPERTIES OF COLLOIDAL GELS SUBJECT TO PARTICLE REARRANGEMENT WAN Y. SHIH, WEI-HENG SHIH, and ILHAN A. AKSAY Department of Materials Science and Engineering; and Advanced Materials Technology Center, Washington Technology Centers, University of Washington, Seattle, WA 98195
INTRODUCTION In a colloidal suspension with attractive interaction, particles form aggregates that settle to the bottom of the container. As the concentration of particles is increased, the overlapping of the aggregates (flocs) produces a continuous network throughout the suspension before settling occurs and a colloidal gel is formed. Colloidal gels may be divided into hard gels and soft gels. 1 Hard gels are those formed by fine particles such as silica or boehmite of about 0.01 pm in size with high interparticle attraction energies. Under small shear rates, there is little restructuring in the gel network. The flocs that pack to form the gel network still retain their fractal structure, which gives rise to the scaling behavior of various mechanical properties of a gel with respect to particle concentration. For example, the storage modulus G' of a hard gel remains constant at small strain and increases in a power-law fashion with particle concentration, (p, as G' - p".nThere can be two regimes, a strong-link regime and a weak-link regime. In both regimes, the exponent n can be expressed in terms of the fractal dimension of the flocs, D, and the fractal dimension of the backbone of the flocs, x, while the form of n depends on what regime the system is in. Furthermore, a gel may crossover from the strong-link regime to the weak-link regime as the particle volume 2 fraction is increased. The soft gels are formed by particles with much smaller interparticle bonding energies. Gels formed by silica particles coated with surfactant are examples. Because of the small interparticle attraction energies, the storage modulus G' of a soft gel is about three orders of magnitude smaller than that of a hard gel at the same concentration. Furthermore, restructuring of the gel network occurs at even smaller shear strain. Therefore, the gel is no longer linear viscoelastic. The storage modulus G' does not increase with particle concentration with a power law as in hard gels. Instead, G' increases exponentially with particle concentration. A similar exponential behavior of G" with 4Pwas also observed with ordered polystyrene suspensions.3 The exponential behavior exhibited by a soft gel under small shear stress has also been observed with hard gels under high pressures. In the pressure filtration experiments of boehmite particulate gels, the applied pressure P increases exponentially with the final packing density (p of the gel as P - eOP in the pressure range from 0.1 to 10 MPa. The slope j3 decreases with increasing interparticle attraction energy. The exponential relationship between the shear modulus and the particle volume fraction of soft gels under small shear stresses and the exponential relationship between the applied pressure and the fina
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