Apparent diffusion parameter

This expression has subsequently been evaluated and modified by Ponec and co-workers,illustrating that the rate of diffusion of labelled oxygen into the bulk can be significant in exchange studies. This modified expression allows the determination of the apparent diffusion parameter in addition to the three individual Rq, Ri and R2 rate constants. 

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. 

As the alternative, a phenomenological description of turbulent mixing gives good results for many situations. An apparent diffusivity is defined so that a diffusion-type equation may be used, and the magnitude of this parameter is then found from experiment. The dispersion models lend themselves to relatively simple mathematical formulations, analogous to the classical methods for heat conduction and diffusion. 

The rapid transport of the linear, flexible polymer was found to be markedly dependent on the concentration of the second polymer. While no systematic studies were performed on these ternary systems, it was argued that the rapid rates of transport could be understood in terms of the dominance of strong thermodynamic interactions between polymer components overcoming the effect of frictional interactions this would give rise to increasing apparent diffusion coefficients with concentration 28-45i. This is analogous to the resulting interplay of these parameters associated with binary diffusion of polymers. 

Thus, with the simple cubic autocatalytic rate law, we have been able to find an analytical expression for the time and space dependence of a steady reaction-diffusion wave and make various quantitative and qualitative comments about the behaviour of the wave in terms of the kinetic and diffusion parameters. We now turn to the apparently simpler kinetics of a quadratic autocatalysis, hoping for similar rewards. 

The only published work on the diffusion of gas in coals of different rank appears to be that of Bolt and Innes (2) who studied the diffusion of carbon dioxide from eleven samples of coal at 38°C. They found the diffusion coefficient to range from 3.5 to 9.2 x 10 8 sq. cm./sec., with no apparent correlation with coal rank. Diffusion data on coals of different rank at temperatures higher than 38°C. have only been reported by the present authors (6). It has been shown (7) that the diffusion of inert or noble gases from coal above room temperatures can be rigorously analyzed by using simple diffusion theory, and that true diffusion parameters of the micropore systems can be obtained. In this paper our measurements on the unsteady state release of argon from coals of various rank, over a temperature range, are reported. 

What is this parameter called the apparent diffusion coefficient, Dapp As indicated earlier, it is a measure of the rate of charge transport in a multilayer film at an electrode surface. What Dapp physically means depends on the type of film being investigated. If the electroactive species is free to diffuse through... 

Additionally, the lack of adequate mixing with a continuous flow method results in pronounced diffusion (Ogwada and Sparks, 1986a,b) and the determination of apparent rate parameters. 

We have seen that MR parameters like Tl, T2, proton density, diffusion-weighting or apparent diffusion... 

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. 

For a given sequence, Bloch equations give the relationship between the explanatory variables, x, and the true response, i]. The / -dimensional vector, 0, corresponds to the unknown parameters that have to be estimated x stands for the m-dimensional vector of experimental factors, i.e., the sequence parameters, that have an effect on the response. These factors may be scalar (m — 1), as previously described in the TVmapping protocol, or vector (m > 1) e.g., the direction of diffusion gradients in a diffusion tensor experiment.2 The model >](x 0) is generally non-linear and depends on the considered sequence. Non-linearity is due to the dependence of at least one first derivative 5 (x 0)/50, on the value of at least one parameter, 6t. The model integrates intrinsic parameters of the tissue (e.g., relaxation times, apparent diffusion coefficient), and also experimental nuclear magnetic resonance (NMR) factors which are not sufficiently controlled and so are unknown. 

It is difficult to make an exhaustive list of the applications of quantitative imaging, because a large number of parameters are quantifiable proton density, relaxation time T, T2, T2 or T 2, T p), data qualifying interaction of pools by magnetization transfer, apparent diffusion coefficients, indices characterizing diffusion phenomena from tensor estimation or a (/-space approach, temperature difference, static magnetic field, B1 field amplitude, current density or values related to dynamic MRI contrast agent uptake. 

Recently, kinetic models have been combined with the equilibrium data of the interfacial processes, taking into account that soils and rocks are heterogeneous and consequently have different sites. These models are called nonequilibrium models (Wu and Gschwend 1986 Miller and Pedit 1992 Pedit and Miller 1993 Fuller et al. 1993 Sparks 2003 Table 7.2). These models describe processes when a fast reaction (physical or chemical) is followed by one or more slower reactions. In these cases, Fick s second law is expressed—that the diffusion coefficient is corrected by an equilibrium thermodynamic parameter of the fast reaction (e.g., by a distribution coefficient), that is, the fast reaction is always assumed to be in equilibrium. In this way, the net processes are characterized by apparent diffusion coefficients. However, such reactions can be equally well described using Equation 1.126. 

Apparently the parameters of stochastic models are quite different from those of classic (deterministic) models where the permeability, the porosity, the pore radius, the tortuosity coefficient, the specific surface, and the coefficient of the effective diffusion of species represent the most used parameters for porous media characterization. Here, we will present the correspondence between the stochastic and deterministic parameters of a specified process, which has been modelled with a stochastic and deterministic model in some specific situations. 

In fact, X is a correction parameter for the Pick diffusion coefficient. This correction has a similar effect on the apparent diffusivity as the correction given in Eq. (14). When X is less then 1, the diffusivity increases with occupancy. This correction can also be applied to the Maxwell-Stefan diffusivity, which results in an even larger effect of concentration on the flux. The concentration dependence of the flux in the Maxwell-Stefan equations depends largely on the adsorption isotherm chosen, since this isotherm determines the thermodynamic factor. For Langmuir adsorption the concentration dependence of the flux increases in the following order using different models ... 

Fig. 13. Universal relation of apparent activation energy Q, real activation energy Qo, and the diffusion parameter -q.

Apparently the (2x1) phase cannot be attributed to the equilibrium structure at room temperature, but may be described as a quenched phase probably due a limited surface diffusion parameter. Aside of finding the ordered surface by LEED, the (4x1) structure has been imaged for the first time in real space by scanning tunneling microscopy [76] which is presented in Fig. 5 a. 

The decomposition of thorium hydride is controlled by kinetic rather than diffusion parameters [14]. The value of is 58 kJ mol for the decomposition of TI1H3 between 483 and 663 K and is 137 kJ mol" for the decomposition of ThH, 5 in the interval 873 to 1073 K. Reaction orders were reported to be 0.34 and 0.25, respectively. The evolution of hydrogen from PbH j proceeds [15] at about 463 K in steps during an increasing temperature programme and the apparent magnitude of , increases from 6.7 to 15 kJ moT as the hydrogen content decreases. 

Although the presence of buffering moieties on membrane surfaces reduces the apparent diffusion coefficient of a proton, it can enhance the probability that protons in the bulk phase will interact with groups on a membrane surface. This feature is demonstrated by the experiments presented in Figure 3. The measured parameter in these experiments was the protonation of a pH indicator adsorbed to the surface of a micelle made of uncharged detergent (Brij 58). The protons were released in the bulk from a hydrophilic proton emitter, 2-naphthol-3,6-disulfonate. The protons released in the bulk react by a diffusion-controlled reaction with the micelle-bound indicator and lead to a fast protonation phase. The perturbation then relaxes,... 

The diffusion data presented above indicate that all three phosphates quantitatively retain He at Earth surface temperatures (see Wolf et al. 1998 for a discussion of the minimal affects of diurnal heating and forest fires on He diffusion from apatite). As a result, all three minerals may be used to accurately date the formation of quickly cooled rocks, such as volcanics. Apatite has already been used for this purpose (Stockli, in preparation Farley et al. 2002). Because these phases are rare in volcanic rocks, the more likely application of phosphate He chronometry is to assessment of cooling histories. In slowly cooled rocks, the quantity t computed from the age equation (Eqn. 4) is an apparent age, which may or may not correspond to a specific geologic event. The simplest way to interpret such an apparent age is to associate it with cooling through a particular closure temperature, computed from the diffusion parameters (Dodson 1973). The diffusion arrays in Figure 5 indicate closure temperatures of 115°C and 220°C for xenotime, and monazite, respectively. For apatite, in which diffusivity is known to scale with inverse square of grain radius, the diffusivity data indicate a closure temperature of 73°C for a prism half-width of 75 pm. Half-widths of 50 and 100 pm yield closure temperatures of 68 and 77°C respectively. 

Fiehler, J. et al. Apparent diffusion coefficient decreases and magnetic resonance imaging perfusion parameters are associated in ischemic tissue of acute stroke patients. J Cereb Blood How Metab, 2001. 21(5) p. 577-84. 

Typical values useful for predictive purposes are given in the literature for water diffusion, its apparent activation energy, and sorbed concentration as a function of relative vapor pressure. The data in Table III Include values calculated for diffusion parameters at 5°C and 30°C as representative values for nominal temperature extremes for an environmental exposure cycle. It is seen that values may easily vary from polymer to pol)nner by four or more orders of magnitude. 

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 apparent diffusion coefficient, obtained from real structures or laboratory tests, is often also used as the parameter that describes the resistance of concrete to chloride penetration, e. g. when performances of different materials are compared. The lower D,pp is, the higher the resistance to chloride penetration is. It should, however, be observed that, while the diffusion coefficient obtained from pure (steady-state) diffusion tests can be considered as a property of the concrete, the apparent diffusion coefficient obtained from real stractures also depends on... 

In case a, future penetration of chlorides has to be evaluated in order to assess if the chloride threshold will be reached at the surface of the reinforcement before time tf. If this is expected, the concrete with a chloride content higher than the critical value has to be removed (and replaced with a chloride-free material that prevents further penetration of chloride). Equation (1), Chapter 6, may be used to evaluate the future penetration of chlorides. By fitting the present chloride profile, the surface content and the apparent diffusion coefficient Dj j, may be calculated at time Since these parameters are evaluated on the actual structure and usually after a long time of service, it is often reasonable to assume that they will not change significantly in the future (unless the conditions of exposure of the structure will change). Equation (1), Chapter 6, can then be used to plot the expected chloride profile at time tf. 

When the diffusing particles carry only one fluorescent label, the statistical characteristics of the diffusion of the labels exactly corresponds to that of point-like particles. Data points in Fig. 30 show the simulation data for particles carrying one label. The data are plotted using relative units On the vertical axis, we plot the ratio of the apparent diffusion time (i.e., that obtained from the fit of the autocorrelation function) to the true diffusion time (i.e., that which was an input parameter of the simulation). On the horizontal axis, we plot the ratio of the particle radius, R, and... 

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