Scattering directional diffusion coefficient

The second part of ISO 17497 specifies a method of measuring the directional diffusion coefficient of surfaces in a free field (ISO, 17497-2, 2012). The diffusion coefficient characterizes the sound reflected from a surface in terms of the uniformity of the reflected polar distribution. The directional diffusion coefficient is a frequency dependent value derived from the polar distribution of the scattered sound (Cox and D Antonio, 2009). First the scattering from a surface is measured in terms of a polar distribution. Then the diffusion coefficient is evaluated at 1/3 octave bandwidth intervals, which has the advantage of smoothing out some of the local variations in the polar responses. 

Many statistical parameters can be used to describe a diffusion coefficient from measurements of polar sound distributions. In the standard, an autocorrelation function is used to measure the scattered energy s spatial similarity with receiver angles. A surface which scatters sound uniformly to all receivers produces high values in a spatial autocorrelation function conversely a surface which concentrates scattered energy in one direction has a low value (Cox and D Antonio, 2009). By using the directional diffusion coefficient calculated by Eq. (6.10), the normalized directional diffnsion coefficient can be obtained by ... 

ISO 17497-2,2012. Acoustics—Sound-scattering properties of surfaces—Part 2 Measurement of the directional diffusion coefficient in a free field. 

The above experimental results largely relate to spectroscopic techniques, which do not give direct information about the spatial scale of the molecular motions. The size of the spatial heterogeneities is estimated by indirect methods such as sensitivity of the dynamics to the probe size or from the differences between translational and rotational diffusion coefficients (rotation-translation paradox). It might be expected that the additional spatial information provided by neutron scattering could help to discriminate between the two scenarios proposed. 

For small chains in solution the translational diffusion significantly contributes to the overall decay of Schain(Q>0- Therefore precise knowledge of the centre of mass diffusion is essential. Combing dynamic light scattering (DLS) and NSE revealed effective collective diffusion coefficients. Measurements at different concentrations showed that up to a polymer volume fraction of 10% no concentration dependence could be detected. All data are well below the overlap volume fraction of (p =0.23. Since no -dependence was seen, the data may be directly compared with the Zimm prediction [6] for dilute solutions ... 

Diffusion of atoms from the point at which they dissociate on a metal surface to the edge of the metal crystallite is one of the component steps of hydrogen spillover. Quasielastic neutron scattering experiments have produced direct evidence for the diffusion coefficients of hydrogen on the surface of catalysts. The mean time between diffusional jumps for hydrogen on a Raney Ni surface has been found to be 2.7 0.5 x 10 9s at 150°C.72 For H on the surface of Pt crystals dispersed within a Y type zeolite the mean time between surface jumps was found73 to lie between 3.0 and 8 x 10-9s at 100 °C. 

The diffusion coefficient for a suspension of monosized particles can be measured directly by photon correlation spectroscopy [12] (quasielastic light scattering). For distributions of different particle sizes, the average diffusion coefficient is determined by photon correlation spectroscopy. 

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 has been utilized to directly measure droplet diffusion coefficients in near-critical and supercritical fluids. Blitz et al.f and Fulton et measured the effect of pressure on... 

Direct observation of the AFGP in solution by quasi-elastic light scattering also did not show any conformational changes that could be related to function (Ahmed et al., 1975). Comparisons of measurements of diffusion coefficients, at different temperatures and at... 

The difference between elastic and "quasielastic" measurements is that in the latter, small changes in the frequency due to the translational ("Brownian") movement of the scattering particles are also measured. The broadness of the intensity distribution of the emitted light for frequencies around the primary monocluomatic beam frequency is directly related to the diffusion coefficient of the particles, which can then be related to the hydrodynamic radius if a model for the particle shape is available Dynamic light scattering can thus be used to follow the kinetics of particle coagulation by following the decrease in diffusion coefficient as the particle size increases. ... 

Fig. 21 Steady state incoherent intermediate scattering functions d> (r) as functions of accumulated strain yt for various shear rates y the data were obtained in a col loidal hard sphere dispersion at packing fraction

---