The hydrodynamic radius is determined from the self-diffusion coefficient ( D) via the Stokes–Einstein equation ( D = k B T/6πη r), (13−15) and D is determined through analyzing the so-called “taylorgram”, which is the temporal record of the optical absorbance of the particle band at a given distance from the injection point. (7) The rate of band-broadening is defined by the velocity profile and translational diffusion coefficient of the particles. The velocity profile of the laminar flow disperses the homogeneous band of the injected particles, which creates a concentration and induces a spontaneous net transport of particles via translational self-diffusion. Taylor dispersion is the combination of three independent phenomena: optical extinction, translational self-diffusion, and sheer-enhanced dispersion of particles subjected to a steady laminar flow in a microfluidic channel, usually driven by a pressure gradient in a cylindrical capillary tube. The consequence is that such treatment may be necessary whenever Taylor dispersion analysis is not optimized for a given size but dedicated to characterize broad groups of particles of varying size and material. Second we show that the accuracy of the technique may be recovered by treating Taylor dispersion as a linear time-invariant system, which we prove by analyzing the Taylor dispersion spectra of two iron-oxide nanoparticles measured under identical experimental conditions. First we show that these practical requirements bias the analysis when the self-diffusion coefficient of particles is high, which is typically the case of small nanoparticles. It requires a finite sample volume, a finite detector area, and a finite detection time for measuring absorbance. While Taylor dispersion grants the ability to measure radius within nearly 5 orders of magnitude, the detection of particles is never instantaneous.
The physical principles underpinning Taylor dispersion offer a high dynamic range to characterize the hydrodynamic radius of particles.
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