Diffusion from dynamic light scattering

Figure 5. Collective diffusion coefficient D c= Tlq1 (left) and Rayleigh ratio Rdyn (right) from dynamic light scattering intensity in PNIPA gels at 20°C at equilibrium with aqueous solutions containing different concentrations ce of phenols. Symbols are the same as in Figure 1.

Though we cannot determine the fine internal structure of the particle with the current technique by using dynamic light scattering, the dependence of the diffusion coefficient obtained from dynamic light scattering strongly depends on the shell structure of vesicles 36]. 

Diffusion coefficient from dynamic light scattering for dilute polystyrene solutions in the good solvent toluene (open circles). The lines show the limiting power laws with slopes expected by Eq. (8.23) (i/=ij2 inside the thermal blob and i/ = 0.588 at higher molar--------... 

Figure 7.2 Concentration dependences of the collective diffusion coefficient (DJ obtained from dynamic light scattering (open symbols) and surfactant self-diffusion...

The hydrodynamic radius of colloidal particles can be obtained from dynamic light scattering (DLS), also known as photon correlation spectroscopy (PCS). Here, the temporal fluctuations of scattered light intensity are measured to provide the autocorrelation function, analysis of which provides the translational diffusion coefficient. Then the Stokes-Einstein equation (Eq. 1.9) is used to determine a hydrodynamic radius. This method is described further in Section 1.9.2. 

The existence of the cluster has also been proposed from dynamic light scattering experiments the time corrdation function obtained for solutions of some ionic polymers at low salt concentrations showed two or three dynamic modes, fast and slow. The very slow mode was first reported by Lin, Lee, and Schurr, who coined the term ordinary-extraordinary transition for its appearance at low salt concentrations [11]. Several authors have also observed essentially the same phenomena by DLS [bb-TO]. The slow mode has been attributed to the translational diffusion of (temporal) cluster by Schmitz [66], or of multi-chain domains (dusto s) by Sedlak [68,70]. We also observed two modes for polystyrenesulfonate solutions we attributed the slow mode to the translational diffusion of the localized ordered structures [71]. 

Does light scattering spectroscopy actually measure the mutual diffusion coefficient Extensive early experiments confirmed that QELSS obtains the same diffusion coefficient as classical techniques, at least for protein solutions. Limited sets of measurements(18,19) compare Dm from dynamic light scattering and from... 

W. Brown and R. M. Johnson. Diffusion coefficients in semidilute solutions evaluated from dynamic light scattering and concentration gradient measurements as a function of solvent quality. 1. Intermediate molecular weights. Macromolecules, 18 (1984), 379-387. 

Photon Correlation Spectroscopy. Photon correlation spectroscopy (pcs), also commonly referred to as quasi-elastic light scattering (qels) or dynamic light scattering (dls), is a technique in which the size of submicrometer particles dispersed in a Hquid medium is deduced from the random movement caused by Brownian diffusion motion. This technique has been used for a wide variety of materials (60—62). 

The rotational diffusion coefficient Dr of a rodlike polymer in isotropic solutions can be measured by electric, flow, and magnetic birefringence, dynamic light scattering, and dielectric dispersion. However, if the polymer has some flexibility, its internal motion makes it difficult to extract Dr for the end-over-end rotation of the chain from data of these measurements. In other words, Dr can be measured only for nearly rodlike polymers. 

In contrast, in dynamic light scattering (DLS) the temporal variation of the intensity is measured and is represented usually through what is known as the intensity autocorrelation function. The diffusion coefficients of the particles, particle size, and size distribution can be deduced from such measurements. There are many variations of dynamic light scattering, and... 

This diffusion constant can be measured by dynamic light scattering. Tanaka and Filmore originally considered the case K P fi, for which swelling occurs from the boundary with the relaxation rate n2D/R2 and the thickness of the diffusion layer is (Df)1/2 after a change of the boundary condition at t = 0. However, this normal diffusion behavior is altered for swelling near the point K = 0. 

In dynamic light scattering (DLS), or photon correlation spectroscopy, temporal fluctuations of the intensity of scattered light are measured and this is related to the dynamics of the solution. In dilute micellar solutions, DLS provides the z-average of the translational diffusion coefficient. The hydrodynamic radius, Rh, of the scattering particles can then be obtained from the Stokes-Einstein equation (eqn 1.2).The intensity fraction as a function of apparent hydrodynamic radius is shown for a triblock solution in Fig. 3.4. The peak with the smaller value of apparent hydrodynamic radius, RH.aPP corresponds to molecules and that at large / Hs,Pp to micelles. 

With respect to the virtually very low sample loads, one could argue that the determined diffusion coefficient is at infinite dilution. However, there is no possibility in FFF techniques to perform a safe extrapolation to infinite dilution as in analytical ultracentrifugation or dynamic light scattering. In addition there is a severe problem for all particles deviating from the spherical shape (see Sect. 4.2.3 for a detailed discussion), as the evaluation of D from the FFF experiments using the conventional theory is inappropriate. 

One of the practical applications of dynamic light scattering involves the determination of particle sizes in media dispersed as dilute suspensions in a liquid phase. This aspect of dynamic light scattering is the focus here. Analysis of the scattering data will yield the translational diffusion constant D for a dilute aqueous suspension of polystyrene spheres, and this is directly related to the radius of the spheres. In addition, scattering will be studied from dilute skim milk, which reveals that a distribution of particle sizes exists for this system. 

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