Stokes-Einstein equation size-dependent diffusion

Photon correlation spectroscopy (PCS) has been used extensively for the sizing of submicrometer particles and is now the accepted technique in most sizing determinations. PCS is based on the Brownian motion that colloidal particles undergo, where they are in constant, random motion due to the bombardment of solvent (or gas) molecules surrounding them. The time dependence of the fluctuations in intensity of scattered light from particles undergoing Brownian motion is a function of the size of the particles. Smaller particles move more rapidly than larger ones and the amount of movement is defined by the diffusion coefficient or translational diffusion coefficient, which can be related to size by the Stokes-Einstein equation, as described by... 

This work, along with all other diffusion studies in ionic liquids, depends on the validity of the Stokes-Einstein equation and here lies the main discrepancy with the analysis of most difhision coefficient data in ionic liquids. To be strictly accurate, the distance term, R, in Eqnation 1.3 should be replaced by the correlation length, which is only really equivalent to the radius of the diffusing species when the size of the diffusing particle is large conpared with the solvent particles [27]. Eqnation 1.3 was initially derived to describe the random movement of... 

Pulsed-Field Gradient Spin-Echo NMR Diffusion NMR experiments resolve different compounds in a mixture based on their diffusion coefficients, depending on physical parameters such as size and shape of the molecules, temperature, and viscosity. The diffusion NMR technique is often referred to as diffusion-ordered spectroscopy (DOSY) or pulsed-field gradient spin-echo (PGSE) NMR. A series of NMR diffusion spectra are acquired as a function of the gradient strength G (Fig. 2.19) [56], and the slope of the peak decay is used to obtain the diffusion coefficient D. Furthermore, the hydrodynamic radius can be obtained from the Stokes-Einstein equation (Eq. 2.3). 

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