Simultaneous characterization of rotational and translational diffusion of optically anisotropic particles by optical microscopy

Abstract

We probe the roto-translational Brownian motion of optically anisotropic particles suspended in water with a simple and straightforward optical microscopy experiment that does not require positional or rotational particle tracking. We acquire a movie of the suspension placed between two polarizing elements and we extract the translational diffusion coefficient D T and the rotational diffusion coefficient D R from the analysis of the temporal correlation properties of the spatial Fourier modes of the intensity fluctuations in the movie. Our method is successfully tested with a dilute suspension of birefringent spherical colloidal particles obtained by polymerizing an emulsion of droplets of liquid crystal in a nematic phase, whose roto-translational dynamics is found to be well described by theory. The simplicity of our approach makes our method a viable alternative to particle tracking and depolarized dynamic light scattering.

Differential dynamic microscopy microrheology of soft materials: A tracking-free determination of the frequency-dependent loss and storage moduli

“…p-DDM is a recently introduced extension of DDM allowing the simultaneous measurement of the rotational and translational dynamics of dispersed optically anisotropic colloidal particles observed between suitably oriented polarizing elements [20].…”

“…(6), while f R (t) = e −3 θ 2 (t) and f RT (q,t) = f R (t)f T (q,t) are the rotational and the rototranslational intermediate scattering functions, respectively [17,20] (6)]. α(q) is a weighting factor determined by the optical properties of the particles and by the angle between the polarizing elements [20].…”

“…(6), while f R (t) = e −3 θ 2 (t) and f RT (q,t) = f R (t)f T (q,t) are the rotational and the rototranslational intermediate scattering functions, respectively [17,20] (6)]. α(q) is a weighting factor determined by the optical properties of the particles and by the angle between the polarizing elements [20]. As described in detail in Appendix B, by combining p-DDM and bright-field DDM measurements, we were able to remove the purely translational contributions from the image structure function, obtaining an estimate of the rotational intermediate scattering function f R (t), from which AMSD is extracted as…”

“…In general, the measurement with optical means of the rotational dynamics is technically more challenging than its translational counterpart and usually requires the use of specialized shape [14][15][16] or optically [17][18][19][20] anisotropic tracers. Rotational diffusion microrheology has been initially demonstrated by using a light streak tracking method enabling the time-resolved measurement of the axial orientation of a single, optically trapped microdisk [14].…”

“…In particular, DDM has been recently proven to be an effective tool to measure also the rotational dynamics of anisotropic colloidal particles in solution. This can be accomplished, for example, by introducing in the microscope set-up suitably oriented polarizing elements (polarized DDM or p-DDM [20]) or by adopting a dark-field imaging condition (dark-field DDM or DF-DDM [16,36]). …”