Radioactive tracers diffusion measurement

Membrane Diffusion in Dilute Solution Environments. The measurement of ionic diffusion coefficients provides useful information about the nature of transport processes in polymer membranes. Using a radioactive tracer, diffusion of an ionic species can be measured while the membrane is in equilibrium with the external solution. This enables the determination of a selfdiffusion coefficient for a polymer phase of uniform composition with no gradients in ion or water sorption. In addition, selfdiffusion coefficients are more straightforward in their interpretation compared to those of electrolyte flux experiments, where cation and anion transport rates are coupled. 

Diffusion has often been measured in metals by the use of radioactive tracers. The resulting parameter, DT, is related to the self-diffusion coefficient by a correlation factor/that is dependent upon the details of the crystal structure and jump geometry. The relation between DT and the self-diffusion coefficient Dsclf is thus simply... 

Such a mechanism is not incompatible with a Haven ratio between 0.3 and 0.6 which is usually found for mineral glasses (Haven and Verkerk, 1965 Terai and Hayami, 1975 Lim and Day, 1978). The Haven ratio, that is the ratio of the tracer diffusion coefficient D determined by radioactive tracer methods to D, the diffusion coefficient obtained from conductivity via the Nernst-Einstein relationship (defined in Chapter 3) can be measured with great accuracy. The simultaneous measurement of D and D by analysis of the diffusion profile obtained under an electrical field (Kant, Kaps and Offermann, 1988) allows the Haven ratio to be determined with an accuracy better than 5%. From random walk theory of ion hopping the conductivity diffusion coefficient D = (e /isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by... 

Other techniques for the diffusion of gas through monolayers at the liquid interface have also been investigated (Blank, 1970). In these methods, the differential manometer system was used to measure the adsorption of gases such as C02 and 02 into aqueous solutions with and without the presence of monolayers. The Geiger-Mueller counter with a suitable sorbent and a radioactive tracer gas was used to measure the reduction of evolution of H2S and C02 from the surface solution when a monolayer was present. 

If one component is at a trace level but with variable concentrations (e.g., from 1 to 10 ppb) and concentrations of other components are uniform, the diffusion is called tracer diffusion. An example of tracer diffusion is diffusion into a melt of uniform composition (Watson, 1991b) when the concentration of is below ppb level. Usually only for a radioactive nuclide such as or " Ca, can such low concentrations be measured accurately to obtain concentration profiles. If a radioactive nuclide diffuses into a melt that contains the element (such as Ca diffusion into a Ca-bearing melt), it is still called tracer diffusion although it may be through isotopic exchange. 

The tracer-sectioning technique was employed for the diffusion measurement. The distribution of specific activity C of a radioactive tracer at fixed temperature and oxygen partial pressure is expressed as... 

During self-diffusion in a pure material, whether a gas, liquid, or solid, the components diffuse in a chemically homogeneous medium. The diffusion can be measured using radioactive tracer isotopes or marker atoms that have chemistry identical to that of their stable isotope. The tracer concentration is measured and the tracer diffusivity (self-diffusivity) is inferred from the evolution of the concentration profile. 

Schematic of device employed to determine long-term diffusion of dyes through hair. A similar set-up could be used for measurement of drugs employing radioactive tracers by placing the drug in the lower chamber. Removing aloquots from the top at regular intervals and measuring the radioactivity would then determine the breakthrough time.

The measurements were performed on a cholesterol monolayer spread at an air/water interface and at a temperature of 22 + 0.5 °C. The mass concentration lor the radioactive tracer molecule in the monolayer is given by Fick s second law lor surface diffusion [1.6.5.46)... 

Condit and Holt have reviewed the use of radioactive tracers in the study of oxidation. Radioactive platinum has been used to study the oxidation of cobalt and radioactive silver to study the oxidation of molybdenum. If the tracer element remains at the surface it indicates that the oxygen is diffusing into the metal, and if it is located some distance from the surface shows diffusion of the metal through the oxide. The tracer can be detected by autoradiography and its distribution studied by gradual removal of the oxide layer. Its distance from the surface can also be estimated by measurement of the energy of the emitted radiation at some point outside the surface . ... 

Translational self-diffusion and rotation of the water molecules. Since the above two models fail to explain the data, one may think of a model which combines both, and which is certainly more realistic. We h ve2tr e< such a possibility with p = 0.95 and D 1.6 x 10 cm /s. This last value is the long range self-diffusion coefficient of water in this membrane, measured by radioactive tracers. We found that no fit is possible with these values whatever D is chosen. As for the preceeding section, we find that the fiE improves considerably if we take either p or Dt as parameters. With Dt fixed, we should increase p to 3 A, as above, and with p fixed, we should increase D to 10 cm /s. These results suggest that one should think of a model which contains these two features. The simplest one is a model where the water molecules, more precisely the protons, are restricted to diffuse (diffusion goejjficient D) in a sphere of radius a, where we expect D 10 cm and a 3 S. 

Tracer diffusion is a measure of the ease and frequency with which radioactive or tagged atoms are diffusing in a matrix. It can be shown that = /cor- ion where for is a correlation coefficient that depends... 

To illustrate the subtle differences and nuances between the various diffusion coefficients, it is instructive to take an example such as NiO, which was considered earlier in Worked Example 7.6. To obtain a measure of how fast Ni diffuses into NiO, one can carry out a tracer diffusion experiment, as described earlier. By analyzing the concentration profile of the radioactive tracer, it is possible to determine the so-called tracer diffusivity Dtr of Ni in NiO. The tracer diffusivity is then related to the self-diffusivity Disii by a correlation coefficient /cor- The coefficient /cor has been calculated for many structures and can be looked up. " ... 

To measure the tracer diffusivity of oxygen, typically a crystal is exposed to a gas in which the oxygen atoms are radioactive. 

The diffusion constant and activation energy can be measured directly by radioactive tracer techniques in which the initial distribution of radioactive ions is followed as a function of time and distance. Values of the diffusion constant and activation energies thus determined are then compared with values from ionic conductivities. 

Sharma and Laskar [129] measured the self-diffusion of potassium in melt-grown potassium azide using a radioactive tracer sectioning technique. The diffusion coefficient in the range 85-254°C was found to be (0.19 0.03) exp [(- 0.80 0.06) eV/kT] cm sec. They concluded that the cation is the predominantly mobile species, with diffusion occurring by a vacancy mechanism. The value of 0.80 0.06 eV (77 kJ/mole) for the enthalpy of migration agrees well with the results of Maycock and Pai Verneker [127]. 

Verbrugge and coworkers have employed a radioactive tracer method to measure the methanol diffusivity in a Nation membrane which was... 

Finally, it can be noted that adding alcohols to an aqueous CaCl2 solution was found to strongly affect the sizes of both the hydrated Ca and Cn ions, when calculated from the measurements of the self-diffusion coefficients of and Cl as radioactive tracers [167]. Surprisingly... 

Tracer diffusion coefficient D eif is usually difficult to direcdy measure. As stated earlier, it is more convenient to measure the diffusion coefficient of a radioactive or mass isotope. This measured coefficient is called the tracer diffusion D, which is close to but not the same as Dseiri because the motion of the tracer atoms is not in a completely random manner. Successive jumps are mumaUy correlated, so ffiat every jump is dependent on the previous one. Therefore, D eif and D can be related by the following equation ... 

Very slow diffusion and self-diffusion processes in solids can be determined using radiotracers. Two methods are used. In one, a thin surface containing tracer is applied to the sample. After some time has elapsed, the sample is sliced parallel to the surface and the radioactivity of each slice is measured. Another method is to use an a- or jS-active tracer. As the tracer diffuses into the sample, a direct measurement of the surface radioactivity gives information about the diffusion process. 

Another diffusion coefficient—the tracer—or self-diff-usion coefficient Z>rr is defined, which can be measured at electrochemical equilibrium by using a radioactive isotope. Under certain conditions, for example, for vacancy diffusion, the tracer diffusion coefficient Djj is related to the component diffusion coefficient by ... 

The diffusion coefficients of tracers and the displacement of lattice atoms and their activation energies can also be measured (Sudar et al. 1977). Using fast neutrons, radioactive tracers can be produced homogeneously in extended samples. For example, the measurement of the diffusion coefficient of the Na produced in Al(n,a) reaction for different alloys has a great practical importance, because a number of alloys used in reactor technology contain aluminum (e.g., the reactor fuel can). 

Radioactive tracers, with their high sensitivity and ease of detection, are also an excellent tool for the study of surface reactions. Usually, rapid exchange occurs between a chemical species in a solution or gas and that on a solid. Then follow much slower processes involving species in the deeper layers of the solid, i.e., diffusion and recrystalli2ation. These reactions are easily observed by establishing contact between the solid and a solution of a tracer followed by the separation of the two phases and activity measurement. 

The simplest case occurs when two substances which are only very slightly soluble in one another, such as Al-Ge [7], are pressed together and annealed at diffusion temperatures (400 C for Al-Ge). The chemical diffusion coefficient D is then equal to the diffusion coefficient of the solute metal, which may be assumed to be independent of concentration, and which can be directly measured, for example by means of radioactive tracers or stable isotopes. A radioactive tracer atom moves in the dilute solution on the average in exactly the same way as a solute atom moves in the solvent. It thus-follows from eq. (7-4) that ... 

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