Bimodal colloid gels of highly size-asymmetric particles

We report a type of colloidal gel, induced by a minute incremental addition of mutually attractive small particles (size $\sim 12$ nm) to a suspension of highly charged large particles (size $\sim 500$ nm). The gel's morphological behavior does not follow the typical power-law scaling for fractal clusters. Its unique scaling behavior has two distinct power-law indices, based on particle volume fraction. We show the unique scaling behavior arises when nonfractal networks of large particles are bridged by small-particle clusters, which occurs between a lower and upper critical boundary of small particle volume fraction.

Figure 1

Effect of adding small particles (silica) to a suspension of large particles (PS). Steady shear viscosity as a function of shear stress for a suspension of 0.1 vol% silica (open circles), 5.0 vol% PS (closed circles), and a mixture of 5.0 vol% PS and 0.1 vol% silica (closed triangles).

Figure 2

The rheological properties for (a) the suspension of small particles (silica) and (b) the bimodal suspensions (PS+silica).

Figure 3

Power-law scaling of plateau modulus with volume fraction of total particles for the silica suspension (open circles) and the bimodal suspensions of fixed PS concentration at 2.0 vol% (open triangles), 5.0 vol% (closed triangles), and 10.0 vol% (open diamonds). Solid lines and dashed lines are the results of fits to power-law equations, $G_p^{\prime }=A{\varphi }^v$ . For bimodal suspensions, fitting was performed separately for the data in the high- and low-exponent regions.

Figure 4

Microstructure of two representative samples, one each from a high-exponent region (low small-particle loading) and a low-exponent region (high small-particle loading). (a) SAXS data of PS 5.0 vol% + silica 1.0 vol% (open triangles) and PS 5.0 vol% + silica 0.1 vol% (open circles) in which solid lines are fitted to the equation $I=q^{-D_f}$, (b) cryo-SEM image of PS 5.0 vol% + silica 1.0 vol%, (c) cryo-SEM image of PS 5.0 vol% + silica 0.1 vol%.

Figure 5

Phase diagram of bimodal suspensions of repulsive large particles and attractive small particles ($d_{\mathrm{large}}=500\mathrm{nm}$ and $d_{\mathrm{small}}=12\mathrm{nm}$). Open circles represent a fluid consisting of discrete clusters of large and small particles, closed stars represent a bimodal gel in which small-particle clusters bridge large particles, and closed circles represent a bimodal gel in which both small and large particles form fractal structures. The lower and upper dashed lines illustrate the experimentally observed critical boundary of phase behavior as a function of small particle volume fraction, ${\varphi }_{L,C}$ and ${\varphi }_{U,C}$.