The Role of Nanoscale Forces in Colloid Dispersion Rheology
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The Role of
and the maximum packing fraction. For example, the following correlation of colloid rheology (the Krieger–Dougherty equation),
Nanoscale Forces in Colloid Dispersion Rheology
Norman J. Wagner and Jonathan W. Bender Abstract Advances in our fundamental understanding of and control over interparticle colloidal forces have enhanced our ability to formulate stable, complex fluids with colloidal and/or nano-sized particles with specific rheological properties. This understanding stems from advances in experimental methods that probe these forces, either directly or indirectly, as well as theoretical treatments and simulation methods linking macroscopic suspension properties to the dynamics and interactions between colloidal particles. This article highlights recent experimental developments in the structure–property relationships for colloidal dispersions, with emphasis on the sensitivity of colloid rheology to nanometer-scale interactions. Examples of applications are used to illustrate these relationships. Keywords: colloidal dispersions, rheology, surface forces, nanoparticles.
Introduction and Background It has long been recognized that interparticle interactions between colloidal particles control the stability, phase behavior, and low-shear rheology of colloidal dispersions such that modern formulators of these materials can “tune” the thermodynamic and rheological properties over a broad range of parameters for specific applications (see, e.g., References 1 and 2). However, formally exact theoretical predictions valid for the rheology of dense dispersions are elusive.3–5 Paint formulations, photographic emulsions, cosmetics, body lotions, and pharmaceutical preparations are examples of large-scale technological applications of colloids, while photonic devices are representative of emerging technologies that can benefit from the rational formulation of concentrated colloidal dispersions. In such applications, as the colloid volume fraction increases, interparticle interactions dominate the rheological behavior of the dispersion. Equation 1 suggests how the average surface-to-surface separation 100
h changes in a liquid dispersion with particle volume fraction :6–8
h 2 a
max
1/3
1 .
1 max
(1)
The maximum packing fraction max is typically taken to be in a range from 0.58 (which corresponds to the colloidal hard-sphere glass transition) to 0.64 (random close packing) or 0.71 (the maximum packing extrapolated from high-shear viscosities). Thus, when 0.2, the average distance between particle surfaces is about equal to the particle radius a. As maximum packing approaches, the colloidal surfaces are brought into close proximity such that subtle changes in interparticle forces acting over nanometers can have a dramatic influence on the dispersion’s phase behavior, stability, and rheology. This sensitivity is evident in the common equations postulated by Krieger9 and others10 that empirically relate the suspension zero-shear viscosity to the suspension volume frac
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