Internal diffusion coefficient

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

Values too obtained by plotting Equation 19 and the internal diffusion coefficients calculated by Equation 18 are represented in Table II. Column 7 of the table displays diffusion coefficients of substances in nitrogen (6, 7, 10). 

Thus, in spite of a satisfactory agreement of Equation 17 with experimental data for systems with weakly convex adsorption isotherms, the internal diffusion coefficients, evaluated for these cases according to Equation 17, are in fact below their actual value. 

Hong et al. [45] used numerical solutions of the FOR model, under linear conditions, to determine the internal diffusion coefficient of rubrene in the particles of Symmetry-Ci8, with methanol/water solutions (90 to 100% methanol) as the mobile phase. The results derived from the analytical solution of the model in the Laplace domain and from the first and second order moments were in excellent agreement. 

A further, sometimes useful, quantity was originally defined by Monchick et al. (1965) and was defined in terms of effective cross sections by Viehland et al. (1978). It represents the transport of eneigy associated with internal degrees of freedom by a diffusion mechanism. This so-called internal diffusion coefficient is defined by... 

Figure 5. 1 -2iJ/3 - (1 - t relationship at 700 reduction temperature Table VI. Additives Effect on the Reduction Internal Diffusion Coefficient... 

Film diffusion coefficients normally are large and have very low temperature dependency (" - ). Internal diffusion coefficients can be activated (for pores 5-7 A in diameter with Fact of about 5 to 10 kcal) or nonactivated. For pores in the transitional size range, internal diffusion is of the Knudsen type with a low temperature dependency (T - ). 

Rotational diffusion coefficient, Dg, internal motion rate parameter, angle between the internal rotation axis and the internuclear axis... 

The advantage of the simulations compared to the experiments is that the correspondence between the tracer diffusion coefficient and the internal states of the chains can be investigated without additional assumptions. In order to perform a more complete analysis of the data one has to look at the quench-rate and chain-length dependence of the glass transition temperature for a given density [43]. A detailed discussion of these effects is far beyond the scope of this review. Here we just want to discuss a characteristic quantity which one can analyze in this context. 

The experimental value for Agl is 1.97 FT cirT1 [16, 3], which indicates that the silver ions in Agl are mobile with nearly a thermal velocity. Considerably higher ionic transport rates are even possible in electrodes, by chemical diffusion under the influence of internal electric fields. For Ag2S at 200 °C, a chemical diffusion coefficient of 0.4cm2s, which is as high as in gases, has been measured... 

Checking the absence of internal mass transfer limitations is a more difficult task. A procedure that can be applied in the case of catalyst electrode films is the measurement of the open circuit potential of the catalyst relative to a reference electrode under fixed gas phase atmosphere (e.g. oxygen in helium) and for different thickness of the catalyst film. Changing of the catalyst potential above a certain thickness of the catalyst film implies the onset of the appearance of internal mass transfer limitations. Such checking procedures applied in previous electrochemical promotion studies allow one to safely assume that porous catalyst films (porosity above 20-30%) with thickness not exceeding 10pm are not expected to exhibit internal mass transfer limitations. The absence of internal mass transfer limitations can also be checked by application of the Weisz-Prater criterion (see, for example ref. 33), provided that one has reliable values for the diffusion coefficient within the catalyst film. 

Further to aspects discussed in Section 23.5.1.2, the simplest strategy, if it is practical, is slow decompression. If the pressure can be reduced sufficiently slowly, the gas which is dissolved in the elastomer can diffuse out of the mbber without buUding up sufficient internal pressure to cause damage. The rate of decompression required may be roughly calculated if the diffusion coefficient of the gas and its solubility in the elastomer are known— but in practice it will probably require a laboratory simulation. 

Here, / is the electric field, k is the electrical conductivity or electrolytic conductivity in the Systeme International (SI) unit, X the thermal conductivity, and D the diffusion coefficient. is the electric current per unit area, J, is the heat flow per unit area per unit time, and Ji is the flow of component i in units of mass, or mole, per unit area per unit time. 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

Compound 6 contains seven iron-based units [ 12], of which the six peripheral ones are chemically and topologically equivalent, whereas that constituting the core (Fe(Cp)(C6Me6)+) has a different chemical nature. Accordingly, two redox processes are observed, i.e., oxidation of the peripheral ferrocene moieties and reduction of the core, whose cyclic voltammetric waves have current intensities in the 6 1 ratio. Clearly, the one-electron process of the core is a convenient internal standard to calibrate the number of electron exchanged in the multi-electron process. In the absence of an internal standard, the number of exchanged electrons has to be obtained by coulometry measurements, or by comparison with the intensity of the wave of an external standard after correction for the different diffusion coefficients [15]. 

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