Breakdown of the Yukawa model in de-ionized colloidal suspensions

We study effective colloidal interactions in de-ionized colloidal mixtures through sedimentation-diffusion equilibrium. We derive a coarse-grained effective model (EM) and compare its density profiles with those of the computationally much more expensive primitive model (PM) of colloids and counterions in gravity. The EM, which contains not only standard pairwise screened-Coulomb interactions, but also explicit many-body effects by means of a so-called volume term, can quantitatively account for all observed sedimentation phenomena such as lifting of colloids to high altitudes, segregation into layers in mixtures, and floating of heavy colloids on top of lighter ones. Without the volume term there is no quantitative agreement between the PM and EM, even in the present high-temperature limit of interest, showing that de-ionized colloidal suspensions cannot be described by a pairwise Yukawa model.

Figure 1

Packing fraction profiles ${\eta }_1\left(z\right)$ for de-ionized monodisperse suspensions of colloidal spheres with diameter $\sigma$, gravitational length $L_1=10\sigma$, charge $Z_1=10$, and sample height $H=100\sigma$, for average packing fractions ${\overline{\eta }}_1=0.055$ (a), 0.099 (b), and 0.128 (c). The PM simulations (noisy curves, taken from [11]), the EM simulations (dashed curves), and the EM calculations based on hydrostatic equilibrium (solid curves) are all in good agreement, while the YM calculations (dotted curves) clearly differ. This indicates the importance of the volume term in the EM.

Figure 2

Sedimentation profiles for a de-ionized binary mixture of equal-sized colloids with diameter $\sigma$, gravitational lengths $L_1=10\sigma$ and $L_2=5\sigma$, average packing fractions ${\overline{\eta }}_1={\overline{\eta }}_2=0.0144$, and colloidal charges $Z_1=10$ and (a) $Z_2=10$, (b)$Z_2=20$, (c) $Z_2=30$, and (d) $Z_2=40$. There is quantitative agreement, in all cases, between the PM simulations (noisy curves), EM simulations (dashed curves), and EM calculations based on hydrostatic equilibrium (solid curves).

Figure 3

Mean height $h_i$ (see text) as a function of the colloidal charge ratio $Z_2/Z_1$ for binary mixtures with the parameters given in Fig. 2, showing mutual quantitative agreement between PM simulations (squares), EM simulations (circles), and EM calculations (solid curves). The mean height of the YM from simulation (crosses) and hydrostatic equilibrium calculations (dashed curves) cannot account for the PM results.

Figure 4

Sedimentation profiles of a de-ionized equimolar three-component colloidal system with average packing fractions ${\overline{\eta }}_i=0.0031$, charges $Z_i=50,20,10$, and gravitational lengths $L_i/\sigma =4,6,6$ for the three species $i=1,2,3$, respectively, as obtained from PM simulations (noisy curves) and EM simulations (dashed curves) and pairwise Yukawa simulations without volume term (dot-dashed curves).