Surviving Structure in Colloidal Suspensions Squeezed from 3D to 2D

Combining colloidal-probe experiments and computer simulations, we analyze the solvation forces $F$ of charged silica colloids confined in films of various thicknesses $h$. We show that the oscillations characterizing $F(h)$, for sufficiently large $h$, are determined by the dominant wavelength of the bulk radial distribution function. As a consequence, both quantities display the same power-law density dependence. This is the first direct evidence, in a system treatable both by experiment and by simulation, that the structural wavelength in bulk and confinement coincide, in agreement with predictions from density functional theory. Moreover, theoretical and experimental data are in excellent quantitative agreement.

Figure 1

Dominant wavelength ${\lambda }_b$ characterizing $h_b(r)=g_b(r)-1$ as a function of the volume fraction according to HNC (solid line) and MC (diamonds). Also shown are the HNC data for ${\lambda }_s$ (dashed line) and the corresponding SANS data (filled circles, with error bars). The inset shows two MC results for the function $\ln (r|h_b(r)|)$ (circles). The asymptotic fit functions are plotted as dashed lines.

Figure 2

Two examples of the solvation pressure $f(h)$ as obtained by GCMC (filled circles) together with the asymptotic fits (solid line) obtained with the bulk values of $q_1=2\pi /{\lambda }_b$ and $q_0$. Included are the resulting structural forces $F(h)/2\pi R$ (dashed line). The inset shows a logarithmic plot of $f(h)$.

Figure 3

Experimental curves for $F(h)$ obtained by CP-AFM for three different particle concentrations (the data have been vertically offset for ease of viewing). The curves are fitted according to the formula $F/2\pi R=A\exp (-h/{\xi }_f)\cos (2\pi h/{\lambda }_f+{\theta }_f)+\mathrm{\text{offset}}$.

Figure 4

Comparison of the various wavelengths from theory and experiment in bulk and confinement. Not included are the theoretical results for ${\lambda }_s$ since these are very similar to the SANS data (see Fig. 1). The inset shows the same data on a logarithmic scale.