Measurement of diffusion coefficients

Gosnell, DL Zimm, BH, Measurement of Diffusion Coefficients of DNA in Agarose Gels, Macromolecules 26, 1304, 1993. 

Another group of surveys has focused on the direct modeling of some effective transport phenomena which are essential for predicting parameters that have an important role in underground gas sequestration process such as diffusivity and convection. Azin et al., in 2013, have conducted study regarding correct measurement of diffusivity coefficient [114]. 

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. 

Up to now, no direct measurements of diffusion coefficients have been reported for any system that show the low-temperature upturn just described, and it may well be that for most systems involving hydrogen such effects would occur only at ultra-low temperatures and minuscule diffusion rates. Also, the impurities and imperfections always present in real materials might well trap nearly all the diffusant atoms at the low temperatures at which coherent transport might be expected in ideal material. However, a recent measurement by Kiefl et al. (1989) of the (electronic) spin relaxation rate of muonium in potassium chloride over a range of temperatures gives spectacular support to the concept of coherent tunneling at low temperatures. (See Fig. 6 of Chapter 15 and the associated discussion.)... 

Dixon, A. M. and Larive, C. K. (1997). Modified pulsed-field gradient NMR experiments for improved selectivity in the measurement of diffusion coefficients in complex mixtures application to the analysis of the Suwannee River fulvic acid, Anal. Chem., 69, 2122-2128. 

Seki, T., Mochida, J., Okamoto, M., Hosoya, 0., Juni, K., and Morimoto, K. Measurement of diffusion coefficients of parabens and steroids in water and 1-octanol, Chem. Pharm. Bull, 51(6) 734-736, 2003. 

The solvent mobility in atactic polystyrene-toluene solutions has been studied as a function of temperature using NMR. The local reorientation of the solvent was studied using deuterium NMR relaxation times on the deuterated solvent. Longer range motions were also probed using the pulsed-gradient spin-echo NMR method for the measurement of diffusion coefficients on the protonated solvent. The measurements were taken above and below the gel transition temperatures reported by Tan et al. (Macromolecules, 1983. 16, 28). It was found that both the relaxation time measurements and the diffusion coefficients of the solvent varied smoothly through the reported transition temperature. Consequently, it appears that in this system, the solvent dynamics are unaffected by gel formation. This result is similar to that found in other chemically crossed-linked systems. 

This is the correct expression for use in the analysis of closed diffusion-cell experiments for the measurement of diffusion coefficients. Equation (48) is known as Fick s First Law of Diffusion. Note that Na = — NB corresponds to saying that w = 0. 

Further measurements of diffusion coefficients of long-chain organic molecules and highly polar substances. 

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... 

Chronoamperometry has proven useful for the measurement of diffusion coefficients of electroactive species. An average value of it1/2 over a range of time is determined at an electrode, the area of which is accurately known, and with a solution of known concentration. The diffusion coefficient can then be calculated from it1/2 by the Cottrell equation. Although the electrode area can be physically measured, a common practice is to measure it electrochemically by performing the chronoamperometric experiment on a redox species whose diffusion coefficient is known [6]. The value of A is then calculated from it1/2. Such an electrochemically measured surface area takes into account any unusual surface geometry that may be difficult to measure geometrically. 

The explanation of Graham s law given by Hoogschagen is not complete, as subsequent authors (17,18) stated. However, the attempts of these authors to give a more complete explanation for the law are not convincing. It is known that at conventional measurements of diffusion coefficients in binary gas mixtures using wide capillaries, equal velocities of counterdiffusion of the components are observed. From the considerations developed... 

The most convenient of these methods is viscosity measurement of a liquid in which particles coated with a polymer are dispersed, or measurement of the flow rate of a liquid through a capillary coated with a polymer. Measurement of diffusion coefficients by photon correlation spectroscopy as well as measurement of sedimentation velocity have also been used. Hydrodynamically estimated thicknesses are usually considered to represent the correct thicknesses of the adsorbed polymer layers, but it is worth noting that recent theoretical calculations52, have shown that the hydrodynamic thickness is much greater than the average thickness of loops. 

Although the systems investigated here exhibited predominantly macropore control (at least those with pellet diameters exceeding 1/8" or 0.32 cm), there is no reason to believe that surface diffusion effects would not be exhibited in systems in which micropore (intracrystalline) resistances are important as well. In fact, this apparent surface diffusion effect may be responsible for the differences in zeolitic diffusion coefficients obtained by different methods of analysis (13). However, due to the complex interaction of various factors in the anlaysis of mass transport in zeolitic media, including instabilities due to heat effects, the presence of multimodal pore size distribution in pelleted media, and the uncertainties involved in the measurement of diffusion coefficients in multi-component systems, further research is necessary to effect a resolution of these discrepancies. 

Naturally, all experimental techniques that allow the measurement of diffusion coefficients must be compared to PCS, which is the most widely employed method for the study of polymer diffusion processes. 

The self-diffusion coefficients in supercritical ethylene were measured using the pulsed NMR spectrometer described elsewhere (9,10), automated for the measurement of diffusion coefficients by the Hahn spin echo method (11). The measurements were made at the proton resonance frequency of 60 MHz using a 1 1.2 kG electromagnet. 

FIGURE 9.3 Pulse sequence for measurement of diffusion coefficient D by the pulsed field gradient spin echo technique. The gradient G is applied for a period 8 both before and after the 180° pulse, with separation A. 

A can be measured accurately, and the value of G8 need not be known precisely so long as it is the same for the two magnetic field pulses. This technique permits accurate measurement of diffusion coefficients for one substance dissolved in another or for self-diffusion of a single substance. By Fourier transforming the echo, diffusion coefficients for several substances can be determined. In conjunction with spatial localization methods provided by NMR imaging, studies of diffusion can be quite valuable, as we point out in Chapter 14. 

In 1978, Karlberg and Thelander [5] described the flow injection extraction (FIE) technique, and in 1979 Murray [6] improved the microextraction, reducing the amount of solvent to 200 pL. The main disadvantage of these methods was the necessity to use complicated equipment. Jeannot and Cantwell [7] and, independently, Hee and Lee [8] introduced a simpler kind of microextraction in which a solvent drop is applied, single drop microextraction (SOME). They designed a microreactor with 8 pL of -octane in a Teflon tube (Fig. 14.3) [7]. The authors performed measurements of diffusion coefficients and the kinetics of the system, which suggested a mass transfer model. 

The sensitivity of the measurement of diffusion coefficients in solids depends primarily on the method applied. By the radiation-absorption method mentioned above, diffusion coefficients down to about 10 ° cm s can be measured in the case of p emitters and down to about 10" cm s in the case of a emitters. The recoil method makes it possible to measure diffusion coefficients down to the order of 10 cm s . Relatively low sensitivity D > 10 cm s ) is achieved with the method of mechanical slicing, whereas diffusion coefficients down to about 10 cm s are obtained with the method of dissolution in steps. Mechanical slicing and dissolution in steps have the advantage that the actual concentration in the solid is obtained. 

By inspection of Eqs. (87)-(89) it is seen that measurement of the rotating disk current may provide information concerning the value of n, C%, Da, vy., or ks,f if the remaining parameters are known. Accuracy in determination of n values depends mainly on how accurately the value of Da for the compound in question is known. For the majority of organic compounds, diffusion coefficients in the common organic solvents have not been measured, but comparison with a suitable compound of similar structure for which both n and D are known can often solve the problem (assuming the same value of D for the two substrates). Since Da appears only to the power of in Eq. (88), the resulting n value is only moderately dependent on variations in the Da estimate. The measurement of diffusion coefficients by means of the RDE technique has been the subject of a number of papers [248,253] and need not be treated further at this place. 

B. Robertson, B. Tribollet, and C. Deslouis, "Measurement of Diffusion Coefficients by DC and EHD Electrochemical Methods," Journal of The Electrochemical Society, 135 (1988) 2279-2283. 

T. Seki, M. Okamoto, O. Hosoya and K. Juni. Measurement of diffusion coefficients of parabens by the chromatographic broadening method. /. Pharm. Sci. Technol., Jpn. 60, 114-7 (2000)... 

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