Direct measurement of osmotic pressure and interparticle interactions in colloidal dispersions

Abstract

Colloidal dispersions are widely found in systems ranging from natural environments to industrial materials.Their macroscopic properties such as viscosity and light scattering depend on their dispersibility, which is characterized by interparticle interactions. Osmotic pressure is induced in a solution with a concentration gradient, in which dispersity is one of the major factors governing the behavior of solutes. Thus, examining the relationship between the interparticle interactions and osmotic pressure may reveal colloidal dispersive properties. Although measuring the osmotic pressure is useful to understand dispersion systems, osmotic pressure is usually extremely low, and only limited experimental methods are available. In this study, we demonstrate that both osmotic pressure and interparticle interactions can be measured within the same experimental system, an optical tweezer system. The directly measured pressure is consistent with both the Brownian dynamics simulation and theoretical results based on the hard-sphere model, both of which were calculated using the interparticle interactions directly measured in the experiment. This agreement demonstrates the applicability of the proposed technique for investigating dispersive properties across multiple scales, linking microscopic particle-level interactions to macroscopic osmotic pressure within a single system. The proposed technique enables bottom-up design of colloidal materials through particle-level modifications.

Figures (6)

• Figure 1: Our optically trapped colloidal dispersion system. (a, b) Schematic of the sample cell in the $x$-$z$ (a) and $x$-$y$ (b) planes. Gravity $g$ acts along the negative $z$-direction. The gray and green particles represent optically trapped silica and freely suspended polystyrene particles, respectively. $o$ is the center of the the particle corral in the $x$-$y$ plane. Radius of the particle corral is $r_0$. (c) A typical microscope image of the dispersion. The scale bar is 10 µ m. (d) Probability distribution $P$ of radial displacement $\Delta r$ without inside particles (inset). The solid line represents the best-fitted curve with $\exp\left[-\frac{k(\Delta r)^2}{2k_\text{B}T}\right]$ where $k$ is $5.0 \times 10^{-2}$ pN/µ m. The scale bar of the inset is 10 µ m.
• Figure 2: Measurement of pair interaction potential $U_\text{pair}$. (a) Two particles are trapped by a Gaussian line trap. $l$ is the interparticle distance in the horizontal direction parallel to the line trap. The scale bar is 5 µ m. (b) Distribution of $l$, $P(l)$ (inset), and $U_\text{pair}$. The solid line is the best-fitted curve of $\epsilon \left(\frac{\sigma}{l}\right)^n$ with $\sigma = 5.34$, $\epsilon = 5.4 k_\text{B} T$, and $n=106$.
• Figure 3: Nondimensionalized osmotic pressure in the colloidal dispersion. The blue dots and red crosses represent experimental and numerical results, respectively. The solid curve is the theoretical values obtained using Eq.(\ref{['Eq:Pi_2']}).
• Figure S1: Our optical system.
• Figure S2: Accessible area $S$. The gray circle represents the area of the corral, $\pi r_0^2$. The red region represents the total of semicircular region of the corral particles, $24 \times A_{\text{c}}$. $A_{\text{c}}$ is the semicircular region. $B_\text{c}$ is the void formed when the inside particle (green) is in contact with the corral particles (black). $l_{NN}$ is the distance between two neighboring corral particles. The total of the void region is $23 \times B_\text{c}$. Notably, subtracting the red and blue regions from the gray region yields $S$ (yellow).