Short-time dynamics of monomers and dimers in quasi-two-dimensional colloidal mixtures

We report on the short-time dynamics in colloidal mixtures made up of monomers and dimers highly confined between two glass plates. At low concentrations, the experimental measurements of colloidal motion agree well with the solution of the Navier-Stokes equation at low Reynolds numbers; the latter takes into account the increase in the drag force on a colloidal particle due to wall-particle hydrodynamic forces. More importantly, we find that the ratio of the short-time diffusion coefficient of the monomer and that of the center of mass of the dimmer is almost independent of both the dimer molar fraction, $x_d$, and the total packing fraction, $\varphi$, up to $\varphi \approx 0.5$. At higher concentrations, this ratio displays a small but systematic increase. A similar physical scenario is observed for the ratio between the parallel and the perpendicular components of the short-time diffusion coefficients of the dimer. This dynamical behavior is corroborated by means of molecular dynamics computer simulations that include explicitly the particle-particle hydrodynamic forces induced by the solvent. Our results suggest that the effects of colloid-colloid hydrodynamic interactions on the short-time diffusion coefficients are almost identical and factorable in both species.

Figure 1

(a) Cartoon of the colloidal mixture of monomers and dimers confined between two glass plates separated by spacers. (b) Experimental (circles) and simulated (diamonds) points in the parameter space, $x_d$ vs $\varphi$, considered in this work. Inset: Snapshots (a–f) of experimental equilibrium configurations.

Figure 2

Cartoon of (a) a sphere of diameter $\sigma$ far away from and near a flat wall, (b) a sphere confined between two glass plates, (c) a dimer far away from and near a hard wall, and (d) a dimer confined between two plates; the plates are separated by distance $d$. When the particles are very close to a wall, the short-time diffusion coefficient is hindered and becomes a function of the distance, $z$, between the center of the particle and the wall. The reduction in the diffusion can be described by the factor $\lambda \left(z\right)$ given by Eq. (2).

Figure 3

Mean-square displacement, $W\left(t\right)$, of a monomer. Symbols are experimental data and lines simulation results for the state points indicated by diamonds in Fig. 1. Inset: Comparison in the short-time regime of two particular cases ($\varphi =0.142,x_d=0.450$ and $\varphi =0.573,x_d=0.020$).

Figure 4

Mean-square displacement, $W\left(t\right)$, of the center of mass of the dimer. Symbols are experimental data and lines simulation results for the state points indicated by diamonds in Fig. 1. Inset: Comparison in the short-time regime of two particular cases ($\varphi =0.142,x_d=0.450$ and $\varphi =0.573,x_d=0.020$).

Figure 5

Experimental short-time diffusion coefficients, $D^s$, of the sphere and center of mass of the dimer as a function of the total packing fraction obtained from the expression $W\left(t\right)=4D^{s}t$.

Figure 6

Mean-square displacement, $W\left(t\right)$, for the parallel displacement, with respect to the main axis, of a dimer. Symbols are experimental data and lines simulation results for the state points indicated by diamonds in Fig. 1. Inset: Comparison in the short-time regime of two particular cases ($\varphi =0.142,x_d=0.450$ and $\varphi =0.573,x_d=0.020$).

Figure 7

Mean-square displacement, $W\left(t\right)$, for the perpendicular displacement, with respect to the main axis, of a dimer. Symbols are experimental data and lines simulation results for the state points indicated by diamonds in Fig. 1. Inset: Comparison in the short-time regime of two particular cases ($\varphi =0.142,x_d=0.450$ and $\varphi =0.573,x_d=0.020$).

Figure 8

Mean-square angular displacement of a dimer, $W{\left(t\right)}_{\mathrm{rot}}$. Symbols are experimental data and lines simulation results for the state points indicated by diamonds in Fig. 1. Top-left inset: Comparison in the short-time regime of two particular cases ($\varphi =0.142,x_d=0.450$ and $\varphi =0.573,x_d=0.020$). Lower-right inset: Experimental concentration dependence of the short-time angular diffusion coefficient.

Figure 9

Experimental (open symbols) and simulation (filled symbols) results for the ratio of the short-time diffusion coefficients of the center of mass of the dimer (dim) and monomer (mon) and the ratio of the transversal (trans) to the parallel (par) short-time diffusion coefficients of the dimer as a function of the total packing fraction. Solid lines are guides for the eye.