Using the discrete dipole approximation and holographic microscopy to measure rotational dynamics of non-spherical colloidal particles

Abstract

We present a new, high-speed technique to track the three-dimensional translation and rotation of non-spherical colloidal particles. We capture digital holograms of micrometer-scale silica rods and sub-micrometer-scale Janus particles freely diffusing in water, and then fit numerical scattering models based on the discrete dipole approximation to the measured holograms. This inverse-scattering approach allows us to extract the position and orientation of the particles as a function of time, along with static parameters including the size, shape, and refractive index. The best-fit sizes and refractive indices of both particles agree well with expected values. The technique is able to track the center of mass of the rod to a precision of 35 nm and its orientation to a precision of 1.5• , comparable to or better than the precision of other 3D diffusion measurements on non-spherical particles. Furthermore, the measured translational and rotational diffusion coefficients for the silica rods agree with hydrodynamic predictions for a spherocylinder to within 0.3%. We also show that although the Janus particles have only weak optical asymmetry, the technique can track their 2D translation and azimuthal rotation over a depth of field of several micrometers, yielding independent measurements of the effective hydrodynamic radius that agree to within 0.2%. The internal and external consistency of these measurements validate the technique. Because the discrete dipole approximation can model scattering from arbitrarily shaped particles, our technique could be used in a range of applications, including particle tracking, microrheology, and fundamental studies of colloidal self-assembly or microbial motion.

Brownian motion of a particle with arbitrary shape

“…(40). The evolution of the traceless symmetric part of H(t) is associated with five other eigenvalues, −f (2) i , −f (+) and −f (−) as the characteristic exponents in the time decay, where…”

“…In general, these scales differ from each other, and a careful analysis of the timedependence at long times in needed. It is always true that τ (1) i ≥ τ (2) i and τ (−) ≥ τ (+) , but τ (1) i can be smaller or larger than τ (−) , depending on the particle geometry.…”

“…Brownian motion of particles with arbitrary shapes has been recently investigated in many different contexts, including proteins, DNA, nanofibers, actins or other biological nano and micro objects [1][2][3][4][5][6][7]. There is a rapidly growing number of experimental and numerical studies, which give rise to interesting fundamental questions, challenging for theoreticians.…”

“…where k is the remaining third index, k = i, j, and the characteristic exponents f (1) i and f (2) j are given in Eqs. (40)-(43).…”

Random-subset fitting of digital holograms for fast three-dimensional particle tracking [Invited]

“…This inverse approach has been used for high-precision measurements in fluid dynamics [16] and colloid and interface science [17]. Recent work has extended the fitting technique to clusters of spheres [18,19] and nonspherical particles [20].…”