Rotational Diffusion of Spherical Colloids Close to a Wall

There is currently no experimental technique available to probe spatially resolved rotational diffusion of nanoparticles in the vicinity of a wall. We present the first experimental study of rotational diffusion of small spherical colloids, using dynamic evanescent wave scattering. A setup is used where the wave vector components parallel and perpendicular to the wall can be varied independently, and an expression is derived for the first cumulant of the intensity correlation function in VH evanescent wave geometry for optically anisotropic spheres. The experimental results are in agreement with theoretical predictions that take particle-wall hydrodynamic interactions into account.

Figure 1

Experimental geometry. Laser light is totally internally reflected at the planar surface of a glass hemisphere, setting up an evanescent wave at the glass-fluid interface. Scattered photons pass through an angled polarizer on the detector, which can be placed anywhere on the surface of a solid quadrant. The “horizontal” and “vertical” polarizations are indicated.

Figure 2

Initial relaxation rates as functions of the square of the scattering vector. Open circles: experimental data from a bulk VH experiment. Black squares or blue triangles: EWDLS results from normalized penetration depths of $(\kappa a{)}^{-1}=0.6$ and 1.2. Lines (see text).

Figure 3

Rotational contribution to the initial relaxation rates as a function of the square of the $z$ component of the unit vector ${\mathbf{n}}_S$. Symbols: data obtained from VH experiments at penetration depths of $(\kappa a{)}^{-1}=0.6$ (black squares) and 1.2 (blue triangles). Full lines: linear regressions representing an attempt to determine the $\kappa$-averaged rotational diffusion coefficients.

Figure 4

$\kappa$-averaged rotational diffusion coefficients as functions of the penetration depth. Symbols and error bars: experimental data as determined by linear regression [Eq. (6)]. Red: rotation around an axis normal to the wall. Black: rotation around an axis lying in the plane of the wall. Lines: see text.