Diffusive motions

Most of our ideas about carrier transport in semiconductors are based on tire assumption of diffusive motion. Wlren tire electron concentration in a semiconductor is not unifonn, tire electrons move diffuse) under tire influence of concentration gradients, giving rise to an additional contribution to tire current. In tliis motion, electrons also undergo collisions and tlieir temporal and spatial distributions are described by the diffusion equation. The... 

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). 

A procedure commonly used to extract dynamic data directly from experimental incoherent neutron scattering profiles is described in Ref. 17. It is assumed that the atomic position vectors can be decomposed into two contributions, one due to diffusive motion, fi /t), and the other from vibrations, Uijt), i.e.. 

The Q and ft) dependence of neutron scattering structure factors contains infonnation on the geometry, amplitudes, and time scales of all the motions in which the scatterers participate that are resolved by the instrument. Motions that are slow relative to the time scale of the measurement give rise to a 8-function elastic peak at ft) = 0, whereas diffusive motions lead to quasielastic broadening of the central peak and vibrational motions attenuate the intensity of the spectrum. It is useful to express the structure factors in a form that permits the contributions from vibrational and diffusive motions to be isolated. Assuming that vibrational and diffusive motions are decoupled, we can write the measured structure factor as... 

Specification of. S SkCG, CO) requires models for the diffusive motions. Neutron scattering experiments on lipid bilayers and other disordered, condensed phase systems are often interpreted in terms of diffusive motions that give rise to an elastic line with a Q-dependent amplitude and a series of Lorentzian quasielastic lines with Q-dependent amplitudes and widths, i.e.. 

Fig. 11a and b. Decay of the alignment echo height as a function of the mixing time x2 for different motional mechanisms, a Tetrahedral jumps as a model for conformational changes b Diffusive motion, the solid lines correspond to unrestricted rotational diffusion, the dashed lines to diffusion restricted to an angular region of 8°. Note the strong dependence of the decay curves on the evolution time t, in case of diffusive motion... 

Fig. 12a and b. Calculated 2H spin alignment spectra for diffusive motion, a unrestricted rotational diffusion for different mixing times x2 b diffusion restricted to angular regions as indicated for long mixing times t2... 

Note added in proof The calculated spin alignment spectra for diffusive motion plotted in Fig. 12 are incorrect, in particular the oscillations in the central part, due to a sign-error in the computer program. 

Various ligands bind to their protein sites in a diffusive motion. Similarly, the distance between different ends of a folded macromolecule changes in a way which can be described as a diffusive motion in the presence of a constraint potential (that keeps the parts of the molecule near their folded configurations). Brownian-type diffusive motion in the absence of a restrictive potential is characterized by a diffusion constant (Ref. 6)... 

From the image sequences, information on the velocities of nano-particles can be extracted. The statistical effect of Brownian motion on the flowing speed of the mixed liquid is found small enough to be ignored as shown in Fig. 37 where most of the particles trajectories in the liquid are straight lines and parallel with the wall basically. Therefore, Brownian diffusive motion is ignorable. 

WE WILL FIND THAT ALL DIFFUSION MOTION OCCURS BY DEFECT MOVEMENT IN THE LATTICE. ... 

Direct observation of molecular diffusion is the most powerful approach to evaluate the bilayer fluidity and molecular diffusivity. Recent advances in optics and CCD devices enable us to detect and track the diffusive motion of a single molecule with an optical microscope. Usually, a fluorescent dye, gold nanoparticle, or fluorescent microsphere is used to label the target molecule in order to visualize it in the microscope [31-33]. By tracking the diffusive motion of the labeled-molecule in an artificial lipid bilayer, random Brownian motion was clearly observed (Figure 13.3) [31]. As already mentioned, the artificial lipid bilayer can be treated as a two-dimensional fluid. Thus, an analysis for a two-dimensional random walk can be applied. Each trajectory observed on the microscope is then numerically analyzed by a simple relationship between the displacement, r, and time interval, T,... 

Figure 13.3 (a-c) Trajectories of the diffusion motion of a gold nanoparticle probe on a planar lipid membrane, (d) Mean-square displacement plots forthe diffusion shown in (a-c). Adapted from Ref [31] with permission. 

Springer T (1972) Quasielastic neutron scattering for the investigation of diffusive motions in solids and liquids. Springer, Berlin Heidelberg New York... 

Fig. 11 Free energy plot for an atom-transfer reaction in solution. Diffusive motion along the solvent coordinate opens the opportunity for a favourable atom transfer.

The connection between anomalous conductivity and anomalous diffusion has been also established(Li and Wang, 2003 Li et al, 2005), which implies in particular that a subdiffusive system is an insulator in the thermodynamic limit and a ballistic system is a perfect thermal conductor, the Fourier law being therefore valid only when phonons undergo a normal diffusive motion. More profoundly, it has been clarified that exponential dynamical instability is a sufRcient(Casati et al, 2005 Alonso et al, 2005) but not a necessary condition for the validity of Fourier law (Li et al, 2005 Alonso et al, 2002 Li et al, 2003 Li et al, 2004). These basic studies not only enrich our knowledge of the fundamental transport laws in statistical mechanics, but also open the way for applications such as designing novel thermal materials and/or... 

Femtosecond solvation dynamics experiments in water [147] clearly hint at the existence of a bimodal response of the solvent to a change in solute charge density that is produced by photon absorption for instance. Water appears to show an ultrafast component in the fl/ kT timescale and a slow component due to diffusive motions whose timescale would be in the 1/y range. 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

A more rigorous approach consists of considering that electron hopping between fixed redox sites is fundamentally a percolation problem, each redox center being able to undergo a bounded diffusion motion.16 If these are fast enough, a mean-field behavior is reached in which (4.24) applies replacing d2 by d2 + 3 Ad2, where Adr is the mean displacement of a redox molecule out of its equilibrium position. 

The relaxation of the stress resulting from a step strain can be observed experimentally and we can see that it is the result of diffusive motion of the microstructural elements. Although we can have a mechanistic picture, what does this mean in terms of our measurements We have the very striking result that our material classification must depend on the time t, i.e. the experimental or observation time. Hence, we can usefully classify material behaviour into three categories ... 

Although a mechanism for stress relaxation was described in Section 1.3.2, the Deborah number is purely based on experimental measurements, i.e. an observation of a bulk material behaviour. The Peclet number, however, is determined by the diffusivity of the microstructural elements, and is the dimensionless group given by the timescale for diffusive motion relative to that for convective or flow. The diffusion coefficient, D, is given by the Stokes-Einstein equation ... 

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