Diffusion measurement calculation

Atwood and Goldstein [16] examined the effect of pressure on solute diffusivity and an example of some of their results is shown in Figure 7. It is seen that the diffusivity of the solutes appears to fall linearly with inlet pressure up to 40 MPa and the slopes of all the curves appear to be closely similar. This might mean that, in column design, diffusivities measured or calculated at atmospheric pressure might be used after they have been appropriately corrected for pressure using correction factors obtained from results such as those reported by Atwood and Goldstein [16]. It is also seen that the... 

Due to the inherent variability of these assays either by agar-plate diffusion measurement or turbidimetry measurement, the fiducial hmits are calculated according... 

Independent self-diffusion measurements [38] of molecularly dispersed water in decane over the 8-50°C interval were used, in conjunction with the self-diffusion data of Fig. 6, to calculate the apparent mole fraction of water in the pseudocontinuous phase from the two-state model of Eq. (1). In these calculations, the micellar diffusion coefficient, D ic, was approximated by the measured self-dilfusion coefficient for AOT below 28°C, and by the linear extrapolation of these AOT data above 28°C. This apparent mole fraction x was then used to graphically derive the anomalous mole fraction x of water in the pseudocontinuous phase. These mole fractions were then used to calculate values for... 

The ionic mobility and diffusion coefficient are also affected by the ion hydration. The particle dimensions calculated from these values by using Stokes law (Eq. 2.6.2) do not correspond to the ionic dimensions found, for example, from the crystal structure, and hydration numbers can be calculated from them. In the absence of further assumptions, diffusion measurements again yield only the sum of the hydration numbers of the cation and the anion. 

We have also reported on the ordinate axis of Fig.3 the values of the translational diffusion coefficient calculated from radius values measured by transient electric birefringence, using ... 

Absolute methods provide the molecular weight and the degree of polymerization without any calibration. Their calculation from the experimental data requires only universal constants such as the gas constant and Avogadro s number, apart from readily determinable physical properties such as density, refractive index, etc. The most important methods in use today are mass spectrometry, osmometry, light scattering, and - to some extent - sedimentation and diffusion measurements. Also, some chemical and spectroscopic methods (determination of end-groups) are important because of their relative simplicity. 

From H NMR self-diffusion measurements, the molecular diffusion coefficients could be calculated. Since the diffusion coefficients depend on the size and... 

In contrast to liquid water, a detailed mechanistic understanding of the physical and chemical processes occurring in the evolution of the radiation chemical track in hydrocarbons is not available except on the most empirical level. Stochastic diffusion-kinetic calculations for low permittivity media have been limited to simple studies of cation-electron recombination in aliphatic hydrocarbons employing idealized track structures [56-58], and simplistic deterministic calculations have been used to model the radical and excited state chemistry [102]. While these calculations have been able to reproduce measured free ion yields and end product yields, respectively, the lack of a detailed mechanistic model makes it very difficult... 

In Illustrative Example 19.2 we discussed the flux of trichloroethene (TCE) from a contaminated aquifer through the unsaturated zone into the atmosphere. The example was based on a real case of a polluted aquifer in New Jersey (Smith et al., 1996). These authors compared the diffusive fluxes, calculated from measured TCE vapor concentration gradients, with total fluxes measured with a vertical flux chamber. They found that the measured fluxes were often several orders of magnitude larger than the fluxes calculated from Fick s first law. In these situations the vapor profiles across the unsaturated zone were not always linear. The authors attributed this to the influence of advective transport through the unsaturated zone. In order to test this hypothesis you are asked to make the following checks ... 

The diffusion coefficients calculated from a simulation employing a flexible framework were all between 5 and 10 times larger than those calculated from fixed lattice simulations. A comparison between flexible framework results and NMR measurements (57) illustrated the influence of the cations in the experimental sample calculated diffusion coefficients from the cation-free (flexible) framework were approximately 5 times higher than the experimental results. The increase in diffusion coefficient as a function of loading found in experimental studies was reproduced by the simulations. 

Ueberreiter and collaborators (12, 13, 14) but have remained relatively unknown. In their earlier work the authors tried to calculate the heat conductivity X from these thermal diffusivity measurements by means of the relation... 

Diffusion coefficients can be related to molecular weight in three ways first by application of the Stokes-Einstein equation, second by combination with sedimentation data, and third by consideration of homologous polymer solutions. In the first method, an equivalent spherical size of the molecules is calculated from Dt, and an approximate molecular weight is found by combining these data with the appropriate density. In the second method, diffusion measurements are coupled with those of sedimentation velocity to give molecular weights, and in the third method, molecular weights may be determined directly from measurements of diffusion coefficients alone once a calibration has been... 

A common transient method is the line source technique, and such an apparatus was developed by Lobo and Cohen41 which could be used with melts. Oehmke and Wiegmann42 used the line source technique for measurements as a function of temperature and pressure. A hot wire parallel technique43 yielded conductivity and specific heat from the same transient, and then diffusivity was calculated. Zhang and Fujii44 obtained conductivity, diffusivity and the product of density and specific heat from a short hot wire method. 

The seriousness of this oversight is apparent in Sefcik and Schaefer s analysis of Toi s transport data (24) in terms of their NMR results (28) The value of the so-called "apparent" diffusion coefficient calculated from Toi s time lag data increases by 25% for an upstream pressure range between 100 mm Hg and 500 mm Hg On the other hand, the value of Deff(c) calculated from Toi s data changes by 86% over the concentration range from 100 to 500 mm Hg The difference in the two above coefficients arises from the fact that Da is an average of values corresponding to a range of concentrations from the upstream value to the essentially zero concentration downstream value in a time lag measurement Deff > on t le other hand, has a well-defined point value at each specified concentration and is typically evaluated (independent of any specific model other than Fick s law) by differentation of solubility and permeability data (22) ... 

Because the thermal diffusivity of SC water is comparable to that of many high quality insulation materials, gross radial temperature gradients can easily exist in a flow reactor. As shown in Figure 2, radial temperature gradients within the annular flow reactor are negligible. A computer program, which accurately accounts for the effects of the various fluid (solvent, solvent and solute, air) compressibilities on flow measurements, calculates mass and elemental balances for each experiment. A typical experiment evidences mass and elemental balances of 1.00+0.05. 

Sedimentation, used in conjunction with diffusion measurements, has been used for the determination of the molecular weights of macromolecules. At 20°C in a dilute aqueous solution, the sedimentation coefficient of hemoglobin, density 1.33 g/cm3, is 4.3 x 10"13 s. Its diffusion coefficient is 6.9 x 10 cm2/s. Calculate the molecular weight. How is this result affected by the hydration shell ... 

The importance of the measurements that we have presented so far for the diffusion of embedded tracer atoms becomes evident when we now use these measurements and the model discussed in Section 3 to evaluate the invisible mobility of the Cu atoms in a Cu(00 1) terrace. The results presented in Section 2 imply that not just the tracer atom, but all atoms in the surface are continuously moving. From the tracer diffusion measurements of In/Cu(0 0 1) we have established that the sum of the vacancy formation energy and the vacancy diffusion barrier in the clean Cu(0 01) surface is equal to 717 meV. For the case of self-diffusion in the Cu(0 01) surface we can use this number with the simplest model that we discussed in Section 3.2, i.e. all atoms are equal and no interaction between the vacancy and the tracer atom. In doing so we find a room temperature hop rate for the self-diffusion of Cu atoms in a Cu(00 1) terrace of v = 0.48 s-1. In other words, every terrace Cu atom is displaced by a vacancy, on average, about once per two seconds at room temperature and about 200times/sec at 100 °C. We illustrate this motion by plotting the calculated average displacement rate of Cu terrace atoms vs. 1 /kT in Fig. 14. 

The soot temperature was found to exceed the gas temperature as measured by thermocouples in the absence of droplet injection but decayed at a similar rate. This is attributed to bulk heating effects associated with the localized burning of vaporized material. A detailed diffusion flame calculation for a cylindrical source of reactants and relative velocity on the same order as these experimental data, indicate that this bulk heating effect is reasonable. 

An example of a diffusion potential that be can described by Equation 3.11 occurs at the open end of the special micropipettes used for measuring electrical potential differences across membranes (Fig. 3-6). The fine tip of the glass micropipette provides an electrically conducting pathway into the cell or tissue. Ions diffusing through this fine tip give rise to a diffusion potential between the interior of the micropipette and the aqueous compartment into which the tip is inserted. To estimate the magnitude of this potential for KC1 as the electrolyte, we will assume that there is 3000 mol m-3 (3 m) KC1 in the micropipette (Fig. 3-6) and 100 mol m-3 KC1 in the cell. The chloride mobility, uci, is about 1.04 times uK, so the diffusion potential calculated from Equation 3.11b at 25°C is... 

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