On the validity of Stokes–Einstein–Debye relations for rotational diffusion in colloidal suspensions

Abstract

According to the Stokes-Einstein-Debye (SED) relation, the rotational diffusion coefficient of a colloidal tracer sphere scales with the inverse of the solvent viscosity. Here we investigate the generalization of the SED relation to tracer diffusion in suspensions of neutral and charged colloidal host spheres. Rotational diffusion coefficients are measured with dynamic light scattering and phosphorescence spectroscopy, and calculated including two-and three-particle hydrodynamic interactions. We find that rotational tracer diffusion is always faster than predicted by the SED relation, except for large tracer/host size ratios l. In the case of neutral particles this observation is rationalized by introducing an apparent l-dependent slip boundary coefficient. For charged spheres at low ionic strength, large deviations from SED scaling are found due to the strongly hindered host sphere dynamics. Finally, we present some first experiments on tracer sphere diffusion in suspensions of host rods, showing that hydrodynamic hindrance by rods is much stronger than by spheres. We conclude by pointing to some interesting unresolved issues for future research. I IntroductionThe rotational diffusion coefficient of a single colloidal sphere with radius a T suspended in a solvent with shear viscosity Z 0 is given by the familiar Stokes-Einstein-Debye (SED) relationwith k B T the thermal energy and f r 0 the Stokesian friction factor. Eqn. (1) assumes that the particle is large enough for the solvent to behave as a structureless continuum with vanishing response time. Moreover, stick boundary conditions are assumed, i.e. the velocity of the fluid on the tracer surface equals that of the tracer. Eqn. (1) holds quantitatively not only for colloidal particles but,

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres

“…(34). The pronounced sensitivity of D r on the ionic strength has been observed also experimentally [40]. For larger amounts of added salt, the lower limiting curve for D r describing neutral hard spheres is reached (see red symbols in Fig.…”

“…For optically anisotropic spheres, characterized in their orientation by a unit vectorû(t), rotational dynamics can be probed by experimental techniques sensitive to their orientation [40,74]. In a depolarized dynamic light scattering measurement, e.g., the rotational self-dynamic correlation function [39],…”

“…Numerically exact results for the translational and rotational short-time self-diffusion coefficients [35], for the shorttime collective diffusion coefficient [36], and for the high-frequency limiting shear viscosity of hard spheres [37], valid up to second and third order in the particle volume fraction, respectively, have been derived recently by Cichocki and collaborators. With regard to the rooted cluster expansion method for charge-stabilized particles truncated at the three-body level, approximate expressions for the equilibrium triplet distribution functions are required, since these are not known analytically [38][39][40]. The most comprehensive theoretical scheme available so far to calculate short-time properties is the renormalized density fluctuations (named δγ) expansion approach of Beenakker and Mazur [32,[41][42][43][44], commonly referred to as the δγ scheme.…”

Hydrodynamic and electrokinetic effects on the dynamics of charged colloids and macromolecules

“…The description of the host suspension surrounding a colloidal probe sphere as a continuous medium without local inhomogeneities, characterized by η ∞ , is strictly valid only when the probe sphere is much larger than the host spheres. In fact, for a colloidal tracer sphere of radius a immersed in a host suspension of neutral spheres of radius a H , the slip-stick parameters of the tracer increase from 0 for a/a H → 0 (i.e., zero excess friction) up to the value 1 for a/a H → ∞, in accord with the expectation that the GSE relations become exactly valid only in the continuum limit of the host dispersion (c.f., [35,36]). In figures 9a and 9b, we show the slip-stick parameters for hard spheres and deionized charged spheres, respectively, as obtained from the ASD data in figures 7 and 8 using equation (17).…”

“…Out of various GSE proposals, we will explore the following three short-time relations [30,34,35,36] …”