Stokes dynamic light scattering

Dynamic light scattering (DLS) Translational diffusion coefficient, hydrodynamic or Stokes radius branching information (when Rh used with Rg) Fixed 90° angle instruments not suitable for polysaccharides. Multi-angle instrument necessary. [3]... 

The final section (Section 5.8) introduces dynamic light scattering with a particular focus on determination of diffusion coefficients (self-diffusion as well as mutual diffusion), particle size (using the Stokes-Einstein equation for the diffusion coefficient), and size distribution. 

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. 

Diffusion coeffflcients can be readily measured by means of quasi-elastic or dynamic light scattering, also called photon correlation spectroscopy. For a description of the technique, we refer to sec. 1.7.8. In a dilute dispersion of spherical particles of bare radius a, the diffusion coefficient D can be directly related to d and a by the Stokes-Einsteln equation [1.6.3.321 ... 

Dynamic Light Scattering. The hydrodynamic radius, Rh, is defined as the Stokes radius from the mutual diffusion coefficient at infinite dilution (Do)... 

In 1953, Stockmayer and Fixman [2] observed that the ratio of hydrodynamic (Stokes) radii Rh), given by the symbol h, could also be used as a measure of branching. Although they presented their relationship as a ratio of intrinsic viscosities [see Eq. (11)], the relatively recent introduction of on-line dynamic light scattering (DLS) detectors... 

To measure the droplet size distribution of the primary emulsion (W/O in W/O/W or O/W in O/W/O) that has a micron range (with an average radius of 0.5-1.0 pm), a dynamic light-scattering technique (also referred to as photon correlation spectroscopy PCS) can be apphed. Details of this method are described in Chapter 19. Basically, the intensity fluctuation of scattered light by the droplets as they undergo Brownian diffusion is measured from this, the diffusion coefficient of the droplets can be determined, and in turn the radius can be obtained by using the Stokes-Einstein equation. 

The criterion however applies only to uncross-linked proteins, so that no conclusion can be drawn from the rather small increase, circa 20%, in the Stokes radius Rs upon heat denaturation measured by dynamic light scattering (DLS) for chymotrypsinogen, ribonuclease, and lysozyme [98], and for ribonuclease [99] for comparison, 5 M GuCl causes a 45% increase to / s of unreduced lysozyme [100],... 

A method for measuring the size of aggregates in aqueous environments is dynamic light scattering (DLS). This technique uses scattered light to measure diffusion rates (Brownian motion) of particles in stable suspensions to determine a size based on the Stokes-Einstein equation ... 

DLS (dynamic light scattering)—in dynamic light scattering laser light is scattered by the nanoparticles. Due to the Brownian motion of the particles, a time-dependent fluctuation is imparted to the scattered light intensity. Analysis of the signal intensity yields information about the diffusional motion of the particles, which is in turn related to the hydrodynamic size via the Stoke-Einstein equation. 

Another method for determining 5h is to apply dynamic light scattering, referred to as photon correlation spectroscopy (PCS). For this purpose, dilute monodisperse particles must be used. From measurements of the intensity fluctuations of scattered light by the particles as they undergo Brownian diffusion, one can obtain the diffusion coefficient D, which can be used to obtain the hydrodynamic radius by using the Stokes-Einstein equation (equation (20.19)). By measuring D for the particles, both with and without the polymer layer, one can obtain / h and / , respectively. One should make sure that the bare particles are sufficiently stable 8 is then equal to (/ h — / ) ... 

The micelle diameter can be calculated by measuring the micelle diffusion coefficient using the technique of dynamic light scattering (DLS). If one assumes that aU micelles are spherical in shape, the radius of a micelle in solution may be calculated by using the Stokes-Einstein relation ... 

In 1953, Stockmayer and Fixman observed that the ratio, h, of hydrodynamic or Stokes radii (/ h) of the branched and linear macromolecules could also be used as a measure of branching. The relatively recent introduction of online quasielastic light scattering (QELS, also known as dynamic light scattering and as photon correlation spectroscopy) detectors for SEC permits direct determination of h by... 

The Dynamic Light Scattering (DLS) technique was used to measure radii of the PS latex spheres with and without adsorbed polymer brushes. We could then deduce the polymer brush hydrodynamic layer thickness by taking the difference of the radii. DLS measures the intensity autocorrelation as a function of delay time, which gives information on the diffusion constant of particles in a dilute solution. The translational diffusion coefficient, D, is related to the solution temperature T, particle radius r, and solvent viscosity ri by the Stokes-Einstein relation ... 

Fig. 4.30 Measured size distributions from optical centrifugation analysis (OCA) and dynamic light scattering (90° and 173°), i.e. distribution of the effective hydrodynamic diameter Xi, efl 9o /i73° weighted by seattering intensity as well as of the Stokes diameter JtstokEs weighted by optical extinction pyrogenic silica (BET = 50 m /g)...

Dynamic light scattering (photon correlation spectroscopy, PCS) can also be applied to obtain the hydrodynamic radius of the micelle. By measuring the intensity fluctuation of scattered light by the micelles (when these undergo Brownian diffusion), one can obtain the diffusion coefficient of the micelles D, from which the hydrodynamic radius R can be obtained using the Stokes-Einstein equation ... 

Photon correlation spectroscopy — also dynamic light scattering (DLS) or quasi-elastic light scattering (QELS) — is a robust and rapid method for size determinations in the colloidal range (from about 5nm to 1 m ). In PCS, intensity fluctuations of the scattered light due to particle motion are measured in dependence on time. By the diffusion coefficient of the particles in the measurement fluid, the particle diameter can be calculated according the Stokes-Einstein Eq. (9.1) under the assumption of a spherical particle shape ... 

The translational diffusion coefficient D of a polymer coil can be found from the time-dependent correlation function of scattered intensity measured in dynamic light-scattering experiments. Using the Stokes-Einstein equation, the translational diffusion coefficient D can be related to the apparent hydro-dynamic radius (the radius of equivalent hard sphere). In the limit of nondraining for the solvent coil formed by infinitely long chain, the hydrodynamic radius is given by... 

In a simple case the diffusion coefficients of spheres can be determined via the Stokes-Einstein relationship see Section 12.6.4. While such a relationship was originally derived with hard spheres in mind, it can also be used with globular proteins such as bovine serum albumin (59). Dynamic light-scattering can be used to study aggregation, adsorption, and structural changes as well as chain dynamics. 

Dynamic light-scattering, sometimes called quasi-elastic light scattering or photon correlation spectroscopy, can be used to measure the diffusion coefficients of polymer chains in solution and colloids, a kind of Doppler effect see Section 3.6.6. In a dilute dispersion of spherical particles, the diffusion coefficient D is related to the particle radius, a, through the Stokes-Einstein equation. 

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