Diffusion penetration depth

For the discussed example investigated by Huang et al, the diffusion penetration depth reaches dp = 380nm for the diffusion coefficient of Dg = 3 x 10 mm s and increases to dp = 1.2 pm for Dg = 3x 10 mm s as seen in Figure 9. These data illustrate that a more homogenous distribution of y x] is established in gel with small thickness dh or for large diffusion coefficients Dg. 

Eor t7-limonene diffusion in a 50-pm thick vinyUdene chloride copolymer film, steady-state permeation is expected after 2000 days. Eor a 50- pm thick LDPE film, steady-state permeation is expected in less than one hour. If steady-state permeation is not achieved, the effective penetration depth E for simple diffusion, after time /has elapsed, can be estimated with equation 8. 

Many inorganic solids lend themselves to study by PL, to probe their intrinsic properties and to look at impurities and defects. Such materials include alkali-halides, semiconductors, crystalline ceramics, and glasses. In opaque materials PL is particularly surface sensitive, being restricted by the optical penetration depth and carrier diffusion length to a region of 0.05 to several pm beneath the surface. 

X-ray scattering studies at a renewed pc-Ag/electrolyte interface366,823 provide evidence for assuming that fast relaxation and diffu-sional processes are probable at a renewed Sn + Pb alloy surface. Investigations by secondary-ion mass spectroscopy (SIMS) of the Pb concentration profile in a thin Sn + Pb alloy surface layer show that the concentration penetration depth in the solid phase is on the order of 0.2 pm, which leads to an estimate of a surface diffusion coefficient for Pb atoms in the Sn + Pb alloy surface layer on the order of 10"13 to lCT12 cm2 s i 820 ( p,emicai analysis by electron spectroscopy for chemical analysis (ESCA) and Auger ofjust-renewed Sn + Pb alloy surfaces in a vacuum confirms that enrichment with Pb of the surface layer is probable.810... 

The terms in Eq. (6) include the gravitational constant, g, the tube radius, R, the fluid viscosity, p, the solute concentration in the donor phase, C0, and the penetration depth, The density difference between the solution and solvent (ps - p0) is critical to the calculation of a. Thus, this method is dependent upon accurate measurement of density values and close temperature control, particularly when C0 represents a dilute solution. This method has been shown to be sensitive to different diffusion coefficients for various ionic species of citrate and phosphate [5], The variability of this method in terms of the coefficient of variation ranged from 19% for glycine to 2.9% for ortho-aminobenzoic acid. 

It is of considerable practical importance to have some idea of how far an atom or ion will diffuse into a solid during a diffusion experiment. An approximate estimate of the depth to which diffusion is significant is given by the penetration depth, xp, which is the depth where an appreciable change in the concentration of the tracer can be said to have occurred after a diffusion time t. A reasonable estimate can be given with respect to the root mean square displacement of the diffusing... 

The diffusion coefficients in Table II can be compared with penetration depths measured by XPS profiling through the relationship (9),... 

The penetration depth for diffusion is small compared to the thickness of the liquid layer. 

Eor illustration purposes, we consider here a simple scenario of this interplay. We evaluate the effectiveness factor at a fixed cell voltage and thus at a fixed rig. We can express the corresponding current density as a two-variable function, jg =f f, Sqi), where the reaction penetration depth, CL/ depends on rjg. This function can be used to determine the effectiveness factor, rcL- In the case of severely limited oxygen diffusion, the following relations for local oxygen partial pressure and current density can be obtained ... 

The diffusion theory states that interpenetration and entanglement of polymer chains are additionally responsible for bioadhesion. The intimate contact of the two substrates is essential for diffusion to occur, that is, the driving force for the interdiffusion is the concentration gradient across the interface. The penetration of polymer chains into the mucus network, and vice versa, is dependent on concentration gradients and diffusion coefficients. It is believed that for an effective adhesion bond the interpenetration of the polymer chain should be in the range of 0.2-0.5 pm. It is possible to estimate the penetration depth (/) by Eq. (5),... 

A further benefit of the low absorbtivity of most samples in the NIR is that measurements involving scattering effects (both diffuse transmission and diffuse reflectance) are possible. The penetration depth of the sampling beam in diffuse reflectance measurements of powders in the NIR can be on the scale of millimeters, despite the numerous refractive index interfaces and extended optical path involved. Thus relatively large volumes of material can be interrogated, avoiding problems of surface contamination and sample nonhomogeneity. 

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