Carbon diffusion coefficient

The deviation from the linear law of growth is based on the decrease of the supersaturation and even an increase of carbon diffusion coefficient does not compensate this effect. 

In the hyperstoichiometric UC, + phase, it is expected that the diffusion of carbon would occur through interstitial atoms, as substantiated by the increase of carbon diffusion coefficient with the increase of carbon content, but in the hypostoichiometric UC, j, phase, further careful examination of the composition dependence of the carbon diffusion coefficient must be undertaken before a reliable conclusion could be drawn. 

We call the correlation time it is equal to 1/6 Dj, where Dj is the rotational diffusion coefficient. The correlation time increases with increasing molecular size and with increasing solvent viscosity, equation Bl.13.11 and equation B 1.13.12 describe the rotational Brownian motion of a rigid sphere in a continuous and isotropic medium. With the Lorentzian spectral densities of equation B 1.13.12. it is simple to calculate the relevant transition probabilities. In this way, we can use e.g. equation B 1.13.5 to obtain for a carbon-13... 

Reasonable prediction can be made of the permeabiUties of low molecular weight gases such as oxygen, nitrogen, and carbon dioxide in many polymers. The diffusion coefficients are not compHcated by the shape of the permeant, and the solubiUty coefficients of each of these molecules do not vary much from polymer to polymer. Hence, all that is required is some correlation of the permeant size and the size of holes in the polymer matrix. Reasonable predictions of the permeabiUties of larger molecules such as flavors, aromas, and solvents are not easily made. The diffusion coefficients are complicated by the shape of the permeant, and the solubiUty coefficients for a specific permeant can vary widely from polymer to polymer. 

Carbon Dioxide Transport. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. A variety of methods ate used however, the simplest method uses the Permatran-C instmment (Modem Controls, Inc.). In this method, air is circulated past a test film in a loop that includes an infrared detector. Carbon dioxide is appHed to the other side of the film. AH the carbon dioxide that permeates through the film is captured in the loop. As the experiment progresses, the carbon dioxide concentration increases. First, there is a transient period before the steady-state rate is achieved. The steady-state rate is achieved when the concentration of carbon dioxide increases at a constant rate. This rate is used to calculate the permeabiUty. Figure 18 shows how the diffusion coefficient can be deterrnined in this type of experiment. The time lag is substituted into equation 21. The solubiUty coefficient can be calculated with equation 2. 

In tire transition-metal monocarbides, such as TiCi j , the metal-rich compound has a large fraction of vacairt octahedral interstitial sites and the diffusion jump for carbon atoms is tlrerefore similar to tlrat for the dilute solution of carbon in the metal. The diffusion coefficient of carbon in the monocarbide shows a relatively constairt activation energy but a decreasing value of the pre-exponential... 

In the kinetics of formation of carbides by reaction of the metal widr CH4, the diffusion equation is solved for the general case where carbon is dissolved into tire metal forming a solid solution, until the concentration at the surface reaches saturation, when a solid carbide phase begins to develop on the free surface. If tire carbide has a tirickness at a given instant and the diffusion coefficient of carbon is D in the metal and D in the carbide. Pick s 2nd law may be written in the form (Figure 8.1)... 

The mobilities of ions in molten salts, as reflected in their electrical conductivities, are an order of magnitude larger than Arose in Are conesponding solids. A typical value for diffusion coefficient of cations in molten salts is about 5 X lO cm s which is about one hundred times higher Aran in the solid near the melting point. The diffusion coefficients of cation and anion appear to be about the same in Are alkali halides, wiAr the cation being about 30% higher tlrair Are anion in the carbonates and nitrates. 

Fig. 18. Diffusion coefficient D12 for hydrogen+carbon dioxide. measure-...

Fig. 20. Diffusion coefficient JDia for nitrogen4-carbon dioxide. A, measurement of Boardman and Wild A > Waldmann V, Boyd, et al. O, Schafer, Corte, and Moesta , Andrew.

Lithiated carbons are mostly multiphase systems. Hence, the determination of chemical diffusion coefficients for Li1 causes experimental problems because the propagation of a reaction front has to be considered. 

The formation of carbon dioxide depends on both the isocyanate and water concentrations in the paint film. The carbon dioxide concentration in the paint film depends on the diffusion coefficient, the film thickness and the difference in carbon dioxide concentration between paint film and gas phase ... 

Diffusion coefficients can be estimated with the aid of the mathematical description of the diffusion of carbon dioxide from the paint film (Scheme II). Film thickness, saturation concentration and carbon dioxide equilibrium concentration are known. The emission curves of carbon dioxide calculated by the model have been fitted with the actual emission curves in Figure 7. In this case carbon dioxide is not formed chemically. 

Figures 9 and 10 give the calculated carbon dioxide concentration in the paint film, using different values for the diffusion coefficient and reaction rate constants.

A supercritical fluid exhibits physical-chemical properties intermediate between those of liquids and gases. Mass transfer is rapid with supercritical fluids. Their dynamic viscosities are nearer to those in normal gaseous states. In the vicinity of the critical point the diffusion coefficient is more than 10 times that of a liquid. Carbon dioxide can be compressed readily to form a liquid. Under typical borehole conditions, carbon dioxide is a supercritical fluid. 

Supercritical fluid extraction (SFE) is a technique in which a supercritical fluid [formed when the critical temperature Tf) and critical pressure Pf) for the fluid are exceeded simultaneously] is used as an extraction solvent instead of an organic solvent. By far the most common choice of a supercritical fluid is carbon dioxide (CO2) because CO2 has a low critical temperature (re = 31.1 °C), is inexpensive, and is safe." SFE has the advantage of lower viscosity and improved diffusion coefficients relative to traditional organic solvents. Also, if supercritical CO2 is used as the extraction solvent, the solvent (CO2) can easily be removed by bringing the extract to atmospheric pressure. Supercritical CO2 itself is a very nonpolar solvent that may not have broad applicability as an extraction solvent. To overcome this problem, modifiers such as methanol can be used to increase the polarity of the SFE extraction solvent. Another problem associated with SFE using CO2 is the co-extraction of lipids and other nonpolar interferents. To overcome this problem, a combination of SFE with SPE can be used. Stolker et al." provided a review of several SFE/SPE methods described in the literature. 

Sassiat, P.R., Mourier, P., Caude, M.H. and Rosset, R.H. (1987) Measurement of diffusion coefficients in supercritical carbon dioxide and correlation with the equation of Wilke and Chang. Analytical Chemistry, 59 (8), 1164-1170. 

Cyclic voltammetry, square-wave voltammetry, and controlled potential electrolysis were used to study the electrochemical oxidation behavior of niclosamide at a glassy carbon electrode. The number of electrons transferred, the wave characteristics, the diffusion coefficient and reversibility of the reactions were investigated. Following optimization of voltammetric parameters, pH, and reproducibility, a linear calibration curve over the range 1 x 10 6 to 1 x 10 4 mol/dm3 niclosamide was achieved. The detection limit was found to be 8 x 10 7 mol/dm3. This voltammetric method was applied for the determination of niclosamide in tablets [33]. 

Diffusion of dioxygen occurs 102 105 times more slowly with the diffusion coefficient D 10 7 10 10 cm2 s 1 Carbon-centered atom of P changes its orbital hybridization in this reaction and changes the C—C bond angles from 120° to 109°. Since P is macroradical and is surrounded by segments of macromolecules, this process occurs with an activation energy Solubility of dioxygen in the amorphous phase of polymer is about 3 x 10 4-2 x 10 3 mol L 1 atm-1... 

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