Translational diffusion coefficient distribution

Fig. 25. Time evolution of the translational diffusion coefficient distribution G(D) for blend STVPh-9/PEMA after mixing, where the total polymer concentration is 1.0x10" g/ml, the weight ratio of STVPh-9/PEMA is 100 8, and the scattering angle is 15° [152]...

Conversion Between Translational Diffusion Coefficient Distribution... 

Fig. 14. Apparent weight distributions calculated from the translational diffusion coefficient distributions corresponding to low-mass (O) and high-mass ( ) copolymer segmented polyethylene terephthalate-co-caprolactone) (PET-PCL) containing 13% PET in tetrahydrofuran (THF) at 25 °C...

Fig. 16. Translational diffusion coefficient distributions G(D) of a simulated polymer mixture at two scattering angles ( , 17° and O , 14°). The mixture contains two polystyrene standards of distinctly different weight average molar masses (3.0 x 105 and 5.9 x 106 g/mol) and a high mass polystyrene...

In dynamic LLS, the Laplace inversion of each measured intensity-intensity time correlation function G q, t) in the self-beating mode can result in a line-width distribution G(L). G(7) can be converted into a translational diffusion coefficient distribution G(D) or further a hydrodynamic radius distribution /(Rh) via the Stokes-Einstein equation, Rh = (kBTI6nrio)/D, where kB, T and qo are the Boltzmann constant, the absolute temperature and the solvent viscosity, respectively. The time correlation functions were analyzed by both the cumulants and CONTIN analysis. 

For a single fluorescent species undergoing Brownian motion with a translational diffusion coefficient Dt (see Chapter 8, Section 8.1), the autocorrelation function, in the case of Gaussian intensity distribution in the x, y plane and infinite dimension in the z-direction, is given by... 

Laplace transformation of eqn 1.1 (often using the CONTIN program (Provencher 1982)) yields the distribution of relaxation times, A(t). The decay rates of the relaxation modes provide translational diffusion coefficients. 

Generally, mean size and size distribution of nanoparticles are evaluated by quasi-elastic light scattering also named photocorrelation spectroscopy. This method is based on the evaluation of the translation diffusion coefficient, D, characterizing the Brownian motion of the nanoparticles. The nanoparticle hydro-dynamic diameter, is then deduced from this parameter from the Stokes Einstein law. 

Dynamic light scattering allows measurement of the translational diffusion coefficient A of particles. For noninteracting particles, the first-order autocorrelation function g r) is directly proportional to A- Polydisperse systems are analyzed using the method of cumulants, in which a distribution of exponential terms C(r) is assumed ... 

Recently, we have developed a new method of data analysis which permits us to obtain an approximate distribution function in terms of translational diffusion coefficients or sizes (14,15). 

Siddiqu and Wu [31] used a dynamic laser light scattering method to characterise an unfractionated PI in chloroform at 25 °C. The relatively small angular and concentration dependencies and translational diffusion coefficients measured by this technique enabled the PI to be characterised from only one measurement at a finite concentration and small scattering angle. Thus, this method could be used to characterise the molecular weight distribution of PI from the measured line-width distribution. 

A, is the second virial coefficient, D is the translational diffusion coefficients, is the hydrodynamic radius, and iXy/iT)- is the width of the line width distribution... 

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