Abstract
The thermal diffusion behavior of dilute solutions of very long and thin, charged colloidal rods (fd-virus particles) is studied using a holographic grating technique. The Soret coefficient of the charged colloids is measured as a function of the Debye screening length, as well as the rod-concentration. The Soret coefficient of the fd-viruses increases monotonically with increasing Debye length, while there is a relatively weak dependence on the rod-concentration when the ionic strength is kept constant. An existing theory for thermal diffusion of charged spheres is extended to describe the thermal diffusion of long and thin charged rods, leading to an expression for the Soret coefficient in terms of the Debye length, the rod-core dimensions, and the surface charge density. The thermal diffusion coefficient of a charged colloidal rod is shown to be accurately represented, for arbitrary Debye lengths, by a superposition of spherical beads with the same diameter of the rod and the same surface charge density. The experimental Soret coefficients are compared with this and other theories, and are contrasted against the thermal diffusion behaviour of charged colloidal spheres.
Highlights
Thermal diffusion, which is known as the Ludwig–Soret effect, is the phenomenon where mass transport is induced by a temperature gradient in a multi-component system
The two uxes counter balance in a stationary state, from which it follows that the ratio of the concentration gradient and the temperature gradient in such a stationary state is equal to the Soret coefficient ST 1⁄4 DT/rD, where r is the number density of colloids
The Soret coefficient can be regarded as a response function, which measures the concentration gradient induced per unit of temperature gradient
Summary
Thermal diffusion, which is known as the Ludwig–Soret effect, is the phenomenon where mass transport is induced by a temperature gradient in a multi-component system. The mass ux induced by a temperature gradient VT is equal to ÀDTVT, where DT is the thermal diffusion coefficient. Thermal diffusion leads to gradients Vc in concentration, which in turn give rise to a mass ux equal to ÀDVc, where D is the mass diffusion coefficient. The two uxes counter balance in a stationary state, from which it follows that the ratio of the concentration gradient and the temperature gradient in such a stationary state is equal to the Soret coefficient ST 1⁄4 DT/rD, where r is the number density of colloids. The Soret coefficient can be regarded as a response function, which measures the concentration gradient induced per unit of temperature gradient. Note that o en a slightly modi ed de nition of the thermal diffusion coefficient is used in experimental contexts,[1] which contains an additional prefactor related to concentration (as discussed by Ning et al.,[2] and in Section 4 of the present paper)
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