Self diffusion experiments

Brady J.B. and McCallister R.H. (1983) Diffusion data for clinopyroxenes from homogenization and self-diffusion experiments. Am. Mineral. 68, 95-105. 

Figure 4.38 Schematic illustration of a self-diffusion experiment in which (a) a thin layer of radioactive nickel is deposited on one surface of a nonradio active nickel specimen. After heating and time (b), the radioactive nickel has diffused into the sample, as monitored with a radioactive detector. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission John Wiley Sons, Inc.

Self-Diffusion Experiments. Diffusion was measured in a U-tube cell constructed in halves which could be clamped together with the disk or skin separating the arms of the U. Cells were secured on the arms of a shaker in a thermostat bath. Unlabeled aqueous salicylic acid solution (3... 

In a typical tracer self-diffusion experiment, the tracer concentration probability, p, depends upon position, whereas the total interstitial concentration probability, p, does not. 

The authors thank MinistAre de 1 Education Nationale, Brussels for a grant (2.4516.82) in support of their NMR studies. Jean Grandjean gratefully acknowledges support from Fonds National de la Recherche Scientifique, Brussels to perform self-diffusion experiments at the University of Uppsala, Sweden. These measurements were only made possible thanks to the hospitality and the expertise of Professor Peter Stilbs, now at Stockholm, and Dr. R. Rymdem, in Uppsala. 

Results of Self-Diffusion Experiments. Self-diffusion coefficient studies with fused salts really began to gather momentum after radioisotopes became... 

Balinov, B., Soderman, O., and Warnheim, T. Determination of water droplet sizes in margarines and low-calorie spreads by means of the NMR self-diffusion experiment, /. Am. Oil Chem. Soc., 71, 513, 1994. 

In the self-diffusion experiments a is obtained through the following relation ... 

General three-component diffusion equations may be reduced in two ways to concern only two chemically different components. One of these ways leads to the ordinary two-component equation presented above. The other leads to equations for self diffusion of a component in a mixture with a second component (Lamm > > ). The former component is split in two parts, (ideally) labelled by the isotope tracer procedure, which form a diffusion gradient. The latter component is assumed to have a constant concentration during the self-diffusion experiment (the more general case is of minor interest). We will mainly reproduce here the result which has a bearing upon the (relative) constancy of the resistivities. Let the chemically different components be a and b. The former is composed of two isotopically different, but with respect to diffusion properties identical, substances (a) 1 and (a)2 c = -(- c. In view of what has been stated... 

Self-diffusion experiments show that grain boundary diffusion of oxygen is faster than bulk diffusion [54, 55], whereas for Al, these processes are about equally... 

Figure 18 Illustration of the double-oil self-diffusion experiment with a cyclohexane-hexadecane mixture. K = D /D2, where D and Dj are the cyclohexane and hexadecane diffusion coefficients, respectively. In the pure oil mixture the ratio of the two diffusion coefficients is K = Kq— 1.69. For a water-in-oil droplet structure the two oil molecules have the same diffusion coefficient, that of the micelle, and the ratio A equals unity. In a bicontinuous structure, on the other hand, a molecular diffusion mechanism is dominating and the ratio K equals that of the pure oil mixture, Kq. By monitoring the diffusion coefficient ratio, the droplet-to-bicontinuous transition could be studied.

To confirm that the systems change from discrete aggregates to becoming bicontinuous, NMR self-diffusion experiments were performed. The results are shown in Figure 3.12. This technique [28, 29] measures the diffusion of the surfactants and the oils, and can thus be used to determine whether the studied structures consist of discrete aggregates or are bicontinuous. 

It is perhaps of interest to note that instead of a single label, particles can be assigned a set of labels, I, = (/,i, /,-2,..., /ic) for particle i, with one label for each of a set of probabilities p = (pi, P2> > Pc) for label change determination. Since each value of p is expected to yield a different steady-state number density gradient, one can, with a single molecular dynamics trajectory, perform a number of self-diffusion experiments. Moreover, a different set of labels can be used to label particles with respect to crossings of the y-boundaries and, in three dimensions, a third set iP can be used with respect to the 2-boundaries. 

The authors are grateful to Dr. Berni J. Alder and Dr. Thomas E. Wainwright for discussions of their methods. We are also grateful to Dr. Brad L. Holian for permission to discuss the nonequilibrium self-diffusion experiment and for calling to our attention the question of generalizing (35) to soft interactions. Finally we acknowledge the continued counsel of Professors E. G. D. Cohen and J. R. Dorfman. 

Si self-diffusion experiments at 14GPa and 1400 to 1800C. The lattice diffusion coefficients for the [110] and [001] directions could be expressed as ... 

In order to perform accurate measurements, it is necessary that the temperature in the probe is very stable (preferably an accuracy better than < 0.05°) and accurately determined. For a thorough discussion on these matters the reader is referred to ref. 15. Secondly, a careful calibration of the field gradient strength is very important. In addition, the effect of temperature gradients has to be very accurately determined, since such a problem can be substantial, even at temperatures close to room temperatures. With these careful efforts in maximizing the accuracy of the self-diffusion experiments, errors smaller than 1% may be obtained, a prerequisite for separating spherical from prolate or oblate structures (as will be discussed further below). 

H kansson, B., Nyden, M. and Soderman, O., The influence of polymer molecular-weight distributions on pulsed field gradient nuclear magnetic resonance self-diffusion experiments. Colloid Polym. Set, 278, 399-405 (2000). 

NMR self-diffusion experiments have been a very important experimental tool for investigating microemulsion structures. In this experiment, the molecular selfdiffusion coefficients of water, oil and surfactant can be determined within the same experiment and by comparing their diffusion coefficients important information is obtained about the structure. In particular it is more or... 

A hydrodynamic radius can also be obtained from collective diffusion, Dc, data measured by using dynamic light scattering (DLS). In Figure 17.14, we have also included some results obtained from DLS measurements. By extrapolating the Dc values to infinite dilution, we find the same value of Do as that obtained from the self-diffusion experiments. 

The micellar to bicontinuous transition can easily be detected by self-diffusion experiments. For example, in the case of an oil-in-water droplet structure, the surfactant and oil diffusion coefficients are essentially equal, and correspond to the self-diffusion coefficient of the micelle. On the other hand, in a bicontinuous microemulsion the two are no longer necessarily equal. Generally, one finds that the oil diffusion coefficient is higher than the surfactant diffusion coefficient (typically an order of magnitude difference). Furthermore, the selfdiffusion coefficients are generally much higher in the bicontinuous structure when compared to the micellar microemulsion. 

With nonionic surfactants, it is possible to generate an oil-in-water droplet to bicontinuous structural transition at constant composition by increasing the temperature. This transition can be studied in more detail by using self-diffusion experiments with mixed solvents. In a system where the oil was an equal weight mixture of cyclohexane (1) and hexadecane (2) the transition from normal oil-swollen micelles to a bicontinuous microstructure was studied by monitoring the variation of the self-diffusion coefficient ratio, K = as a... 

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