Apparent diffusion coefficient determination

The voltammetric behavior of compounds I" " and 2+ in aqueous media is characterized, as expected, by the reversible oxidation of the ferrocene group. All three unmodified CD hosts cause a substantial decrease of the currents associated with the ferrocene couple, indicating that complexation is taking place in all cases, fhe decrease in current levels results from the lower diffusion coefficient of the CD-bound ferrocene derivative as compared to the free compound. We have used the CD concentration dependence of the apparent diffusion coefficients (determined by rotating electrode voltammetry) to obtain the binding constants of all three CDs with compounds and 2" [8]. The values obtained from this kind of analysis are shown in Table 1. 

Relaxation times, MT ratios, and diffusion properties allow insight into the microstructure of various tissues. Determination of these parameters is possible by recording and analysing of a series of volume selective spectra, even for metabolites with relatively low concentrations in vivo. For recording series of spectra usually one parameter is changeable (e.g., inversion time TI for Ti measurements, echo time TE for T2 measurements, MT preparation for assessment of spin transfer and chemical reaction rates, or diffusion sensitizing gradients for assessment of apparent diffusion coefficients or even diffusion... 

Free diffusion of molecules in solution is characteristically a haphazard process with net directionality determined only by solute gradients and diffusion coefficients. Within cellular and extracellular spaces, however, diffusion can be strongly influenced by noncovalent interactions of solvent and solute molecules with membranes as well as the cellular and extracellular matrix. Channels and orifices can also alter the movement of solute and solvent molecules. These interactions can greatly alter the magnitude of the diffusion coefficient for a molecule from its isotropic value D in water to apparent diffusion coefficient D (which often can be directionally resolved into D, Dy, and D ). The parameter A, known as the tortuosity, equals DID y. In principle, A has X, y, and z components that need not be equal if there is any anisotropy in the local electrical fields or porosity of the matrix. 

In Section IB we presented experimental evidence that diffusion coefficients correlate with PVC main-chain polymer motions. This relationship has also been justified theoretically (12). In the previous section we demonstrated that the presence of CO2 effects the cooperative main-chain motions of the polymer. The increase in with increasing gas concentration means that the real diffusion coefficient [D in eq. (11)] must also increase with concentration. The nmr results reflect the real diffusion coefficients, since the gas concentration is uniform throughout the polymer sample under the static gas pressures and equilibrium conditions of the nmr measurements. Unfortunately, the real diffusion coefficient, the diffusion coefficient in the absence of a concentration gradient, cannot be determined from classical sorption and transport data without the aid of a transport model. Without prejustice to any particular model, we can only use the relative change in the real diffusion coefficient to indicate the relative change in the apparent diffusion coefficient. 

The apparent diffusion coefficient D is determined by minimizing the difference between the experimental and the calculated apparent velocity versus dp 16. Then we have to determine two parameters Km and Vmax. V, does not depend on the particule size so these two parameters are determined by studying the influence of myristic acid concentration on apparent velocity. 

According to Eq. (19), the data of R(q) are usable to determine the values of the apparent diffusion coefficients, D pp. The plots of against are shown in... 

The effect of using the sodium adsorption isotherm (equation 6) to determine the apparent diffusion coefficient can be seen by... 

An extended analysis of data using the time-derivative method provides for simultaneous determination of apparent sedimentation, and apparent diffusion coefficient, values at a particular concentration and temperature [9]. The apparent diffusion coefficient was calculated from the apparent sedimentation coefficient distribution by the following relationship ... 

The time, f,-, for the induction period (region I) to end is an important factor in determining the surface tension as a function of time, since only when that period ends does the surface tension start to fall rapidly. The value of f,- has been shown (Gao, 1995 Rosen, 1996) to be related to the surface coverage of the air-aqueous solution interface and to the apparent diffusion coefficient, Dap, of the surfactant, calculated by use of the short-time approximation of the Ward-Tordai equation (Ward, 1946) for diffusion-controlled adsorption (equation 5.6) ... 

The apparent diffusion coefficient, D, was determined for the particular leaching conditions of each of the thirteen experiments. This was accomplished using the measured chloride breakthrough (effluent concentration) curve and the analytical solution to Equation 7 with Kd==0. Examples of the observed and calculated chloride concentrations (determined by adjustment of D until a best fit was obtained) are presented for three different experiments (Experiments 7, 8, 11) in Figures 2-4. Values of D and the pore water velocity (v) determined for each experiment are presented in Table III. The value of D increased for cases with large v, and was different between soils for any particular v. This is consistent with the basic relationship be-... 

In this way, Barrer and Riley 46) and Barrer and Brook 47) obtained apparent diffusion coefficients that were decreasing with concentration for propane, butane, and other gases in chabazites. However, the initial slopes frequently cannot be measured accurately if only very small crystals are available. In one case, it was found that diffusion in the macropores of pellets controls the rate of sorption 48) in another case at least the rate of desorption seems to be influenced by the transfer through the phase boundary, as different diffusivities were reported for sorption and desorption 49). The determination of diffusivities from sorption rates is thus impeded by several difficulties. The results that have been obtained thus far can be generalized only with respect to a few points ... 

Fiehler J, Knudsen K, Thomalla G et al (2005) Vascular occlusion sites determine differences in lesion growth from early apparent diffusion coefficient lesion to final infarct. AJNR Am J Neuroradiol 26 1056-1061... 

The self-diffusion coefficients reflect the molecular mobility in solution and are sensitive to temperature, solvent viscosity, and molecular mass. Similarly to other spectral parameters, the apparent self-diffusion coefficient is the weighted average for all species remaining in the equilibrium. Thus, when a small guest molecule interacts with a bigger host molecule its apparent diffusion coefficient decreases, allowing us to detect the formation of an inclusion complex. Moreover, the dependence of the self-diffusion coefficient of guest on the host molar fraction allows us to determine the association constant similarly to the chemical shift titration. 

The initiation time ( ) may be calculated as a function of the chloride transport properties of concrete (usually the apparent diffusion coefficient), the surface chloride content dictated by the environment, the thickness of the concrete cover and the critical chloride content determining the onset of corrosion. The arrival of the critical chloride content at the steel at depth x at time t is calculated using Fick s second law of diffusion (Chapter 6). 

Gros, J.B. and Ruegg, M., Determination of apparent diffusion coefficient of sodium chloride in model foods and cheese, in Physical Properties of Foods—2, Jowitt, R. et al. (eds.), Elsevier, London, U.K., 1987, pp. 71-108. 

Furthermore, the concentration dependence of the apparent diffusion coefficient has been investigated. The determination of the hydrodynamic radius from the diffusion coefficient is valid only when pure self-diffusion is measured, that is, when the experiment is performed in the dilute concentration range. In the semidilute or concentrated regime, interactions between individual solute molecules have to be considered. Whether interactions... 

Fig. 6.17 The apparent diffusion coefficient of charge transport (Z>app) obtained by chronoamper-ospectrometry as a function of the concentration of the Ru(bpy)3 species (c) in aNafion film. The inset shows the >app vs. cy function, where y is the electrochemically active fraction determined from optical absorbance. (Reproduced from [194] with the permission of Elsevier Ltd.)...

Fig. 1 shows typical cyclic voltammogr ams with and without large excess of CD. The shape of the voltammogr am is sensitive to the heterogeneous electron transfer rate[8] between the substrate and electrode, and also to the dissociation and formation rates. If the electron transfer is reversible, i.e., the concentrations of the electroactive species at the electrode surface are determined by the Nernst equation, and if the relative contribution of the latter factor is small, the cyclic voltammogram shows a typical shape[8] with reversible electron transfer and no chemical reaction. In this case, the electrochemical response is purely controlled by the diffusion process of the substrate, CD and the complex. The peak separation in this case is 57 mV at 25°C, which is not affected by addition of CD to the electrolyte solution. This situation is usually attained by the use of slow scan rates[9] in CV. Since complexation reaction can be assumed to remain at equilibrium everywhere in the diffusion layer in the present circumstance, the apparent diffusion coefficient, D from the voltammogram in the presence of CD is written as... 

The role of DWI has to be determined (Ducreux et al. 2001). The nidus usually has a low signal with a large and homogeneous increase of the apparent diffusion coefficient (ADC). However, to date DWI does not play a major role in AVMs. 

D. Myrand and collaborators (Myrand et al. 1992) determined the apparent diffusion coefficients for benzene, trichloroethylene, toluene and chlorobenzene in diffusion experiments in the laboratory on clay samples which were taken from drill cores of the same natural deposit. Similar apparent diffusion coefficients were determined as in the field experiments. On the assumption of effective diffusion coefficients as per Table 7.6, the... 

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