Diffusion characterization

The steady-state transport of A through the stagnant gas film is by molecular diffusion, characterized by the molecular diffusivity DAg. The rate of transport, normalized to refer to unit area of interface, is given by Fick s law, equation 8.5-4, in the integrated form... 

Similarly, the transport of A through the liquid film is by molecular diffusion, characterized by DA(, and the flux (the same as that in equations 9.2-2 and -3 at steady-state) is... 

The above-mentioned results can be easily extended to anisotropic diffusion characterized by a diffusion tensor D . In this case the hydrodynamic speed is given by... 

The spin-lattice relaxation process is usually exponential. Theoretically, the effect of spin-diffusion, characterized by the coefficient D (order of 1(T12 cm2 s 1), has an influence on T, relaxation times when ix > L2/D, where Lis the diffusion path length. NMR studies of model systems f6r rubber networks, based on a styrene-butadiene-styrene block copolymer (SBSy, in which styrene blocks act as a crosslink for polybutadiene rubber segments of known and uniform length, indicate that spin diffusion operating between PS and PB phases causes a lowering of Tg for the PS component in SBS (as compared to the pure PS) and hindering of the motion of the PB component (as compared to the pure PB)51). 

The effective diffusion coefficient becomes negative for some range of composition when x is sufficiently large. The separation of phases requires an up-hill diffusion (characterized by negative Deff) in which the material moves against concentration gradients. The kinetics of the separation and the morphology of separated phases depend on the details of such diffusion. 

Brownian motion of a single noninteracting particle can be described in terms of self-diffusion characterized by Do, the particle self-diffusion coefficient in the infinite dilution limit. The probability / (Ar. r) of a particle displacement Ar in time r satisfies the diffusion equation... 

Whereas mutual diffusion characterizes a system with a single diffusion coefficient, self-diffusion gives different diffusion coefficients for all the particles in the system. Self-diffusion thereby provides a more detailed description of the single chemical species. This is the molecular point of view [7], which makes the selfdiffusion more significant than that of the mutual diffusion. In contrast, in practice, mutual diffusion, which involves the transport of matter in many physical and chemical processes, is far more important than self-diffusion. Moreover mutual diffusion is cooperative by nature, and its theoretical description is complicated by nonequilibrium statistical mechanics. Not surprisingly, the theoretical basis of mutual diffusion is more complex than that of self-diffusion [8]. In addition, by definition, the measurements of mutual diffusion require mixtures of liquids, while self-diffusion measurements are determinable in pure liquids. 

In the past decades, great progress has been made in various fields related to molecular sieves and porous materials, such as synthesis and catalysis, structural chemistry, adsorption and diffusion, characterization, and porous composite chemistry. In particular, the overlap of molecular sieve science with other related sciences, including physics, mathematics, computer science, materials science, and biology, has promoted the in-depth development of the chemistry of molecular sieves and porous materials. 

P (Q Q) and Q(Q -> n) are the probabilities that a molecule will rotate in the redistribution processes of trans cis optical transition and cis =i trans thermal recovery respectively. The orientational hole burning is represented by a probability proportional to cos 9. The last terms on the right-hand side of Eq. 11 describe the rotational diffusion due to Brownian motion. This is a Smoluchowski equation for the rotational diffusion characterized by a constant of diffusion for the cis (trans) configur-... 

In Equation 6.23 the transport in the pore fluid is modeled as free diffusion in the macropores and mesopores, but the diffusion coefficient Dpo. i is usually smaller than the molecular diffusivity characterizing transport in the liquid mobile phase due to the random orientations and variations in the diameter of the pores (tortuosity) (Section 6.5.8). 

Low moisture diffusivities are found in nonporous and sugar-containing foods, whereas higher values of moisture diffusivity characterize porous food materials. Diffusivities higher than the self-diffusivity of water are indicative of vapor diffusion in porous solids. 

At temperatures above the upper break temperature, the strength of steric interaction decreases and the probability of occurrence of the more tightly packed conformation lib decreases. The orienting potential diminishes and the nitroxide rotation can be characterized by a simple Brownian axially symmetric rotational diffusion characterized by the rotational parameters given in Fig. 16 and by the angle P close to 40°. The presence of the conformations revealed by these calculations can be accepted as an explanation of the experimental data only, provided that the effects omitted in the calculations, in particular the neglect of solvent effect and of interactions mediated by polymer chain(s), would increase the probability of occurrence of the more tightly packed nitroxide conformation. 

A chemical reaction progresses as a result of three processes chemical kinetics, which is characterized by the chemical time zc micromixing, which is linked to molecular diffusion (characterized by the micromixing time 7d - equation [10.8]) and macromixing (termed stirring in this chapter), which pertains to the process of turbulent dispersion as described in Chapter 8. 

In its simplest version, the method consists of two equal and rectangular gradient pulses of magnitude g and length (5, sandwiched on either side of the 180° RF-pulse in a simple Hahn echo experiment. For molecules undergoing free (Gaussian) diffusion characterized by a diffusion... 

Borca-Tasciuc, T, Mazumder, M., Son, Y., Pal, S. K., Schadler, L. S., Ajayan, P. M. (2007), Anisotropic thermal diffusivity characterization of aligned carbon nanotube-polymer composites. Journal of Nanoscience and Nanotechnology, 7,1581-8. 

Temperature conductivity (heat diffusivity) characterizes how fast the temperature in the material is spreading. 

In addition there is normal self-diffusion, characterized by T and the rotation of the water molecule, with a time constant T. Furthermore, diffusion from one such region into another... 

---