Marker experiments

Flow markers are often chosen to be chemically pure small molecules that can fully permeate the GPC packing and elute as a sharp peak at the total permeation volume (Vp) of the column. Examples of a few common flow markers reported in the literature for nonaqueous GPC include xylene, dioctyl phthalate, ethylbenzene, and sulfur. The flow marker must in no way perturb the chromatography of the analyte, either by coeluting with the analyte peak of interest or by influencing the retention of the analyte. In all cases it is essential that the flow marker experience no adsorption on the stationary phase of the column. The variability that occurs in a flow marker when it experiences differences in how it adsorbs to a column is more than sufficient to obscure the flow rate deviations that one is trying to monitor and correct for. 

Figure 3.22 Illustration to show how marker experiments can identify the diffusing components (in the case considered they are the metal atoms) during oxidation process.

Inert markers have been used to obtain additional information regarding the mechanism of spinel formation. A thin platinum wire is placed at the boundary between the two reactants before the reaction starts. The location of the marker after the reaction has proceeded to a considerable extent is supposed to throw light on the mechanism of diffusion. While the interpretation of marker experiments is straightforward in metallic systems, giving the desired information, in ionic systems the interpretation is more complicated because the diffusion is restricted mainly to the cation sublattice and it is not clear to which sublattice the markers are attached. The use of natural markers such as pores in the reactants has supported the counterdiffusion of cations in oxide spinel formation reactions. A treatment of the kinetics of solid-solid reactions becomes more complicated when the product is partly soluble in the reactants and also when there is more than one product. 

Photolysis of the acyclic trisilane 57 produces 1,2,4-trisilacyclopentanes 42 in moderate yields (67-79%) (Equation 4). Marker experiments suggest that the reaction proceeds via a bimetallic silylene bridged dimer, which collapses to give the cyclic carbosilane <20020M503>. 

This binary system is worth further investigation, especially in the region of non-parabolic layer-growth kinetics. Marker experiments are also desirable, with inert markers embedded in both intermetallic layers. 

All attempts to carry out marker experiments with Ni-Zn and Co-Zn diffusion couples in the same way as with Ni-Bi ones (see Section 1.8 of Chapter 1) were unsuccessful because of crack formation, not allowing an unambiguous determination of the diffusing species in the growing intermetallic layers. These proved, however, extremely useful for understanding the mechanism of multiple-layer formation. Namely, it became quite clear that this phenomenon is most frequently a result of secondary reactions occurring in cracked couples. 

It is clear that in cases like this, there is even no need to do marker experiments to reveal the main diffusing species. Formation of duplex structures provides by itself sufficient evidence for the dominant diffusion of one of two components. If, in addition, the ratio of sublayer thicknesses coincides with a theoretically calculated value, then it can definitely be concluded that the layer growth undoubtly takes place exclusively at the expense of diffusion of that component. 

O. Thomas, L. Stolt, P. Buaud, J.S. Poler, F.M. d Heurle. Oxidation and formation mechanisms in dicilicides VSi2 and CrSi2, inert marker experiments interpretation // J.Appl.Phys.- 1990.- V.68, No. 12.- P.6213-6223. 

Lawrence Stamper Darken (1909-1978) subsequently showed (Darken, 1948) how, in such a marker experiment, values for the intrinsic diffusion coefficients (e.g., Dqu and >zn) could be obtained from a measurement of the marker velocity and a single diffusion coefficient, called the interdiffusion coefficient (e.g., D = A ciiD/n + NznDca, where N are the molar fractions of species z), representative of the interdiffusion of the two species into one another. This quantity, sometimes called the mutual or chemical diffusion coefficient, is a more useful quantity than the more fundamental intrinsic diffusion coefficients from the standpoint of obtaining analytical solutions to real engineering diffusion problems. Interdiffusion, for example, is of obvious importance to the study of the chemical reaction kinetics. Indeed, studies have shown that interdiffusion is the rate-controlling step in the reaction between two solids. 

A brass (Cu-Zn) bar, wound with molybdenum wire, was plated with copper metal. The specimen was annealed in a series of steps, in which the movements of the molybdenum wires were recorded. The inert markers had moved from the interface towards the brass end of the specimen, which contained the fastest diffuser - zinc. This is now called the Kirkendall effect. A similar marker experiment had actually been performed by Hartley a year earlier while studying the diffusion of acetone in cellulose acetate (Hartley, 1946), but most metallurgists were not familiar with this work (Darken and Gurry, 1953). 

Lawrence Stamper Darken (1909-1978) subsequently showed how, in such a marker experiment, values for the intrinsic diffusion coefficients (e.g. Dcu and Dz )... 

Table 4. Summary of Marker Experiments Used To Study Metal Silicide Formation...

Fig. 2.13. Result of a Kirkendall marker experiment carried out by Rutherford backscattering spectroscopy. The upper part shows the marker shifts (A m and A ) for the tungsten marker and the Zr edge from the backscattering spectrum. The lower part compares the experimental data with the expected behavior of the marker shift when only one species moves (dashed lines). Within experimental error, it is found that only Ni moves (see [2.46] for details)...

The nature of the mobile ionic species was questionable for a long period of time. For passive Al, Verwey [47] assumed in 1935 that exclusive transport of Al-cations occurs in a fixed oxygen matrix. The idea of mobile cations dominated the oxide formation theories for the next 30 years. It seemed to be reasonable, as the volumes of cations are much smaller than -anions (e.g. by a factor of 20 for AP+), even if the experimental results indicated a combined transport. Marker experiments in the sixties proved cation-transference numbers in the range from 0.3 to 0.7 for many systems (Al, Be, Nb, Ta, Ti, V, W) coming closer to 0.5 with increasing current density, that is, cations and anions move in fact simultaneously (Table 1). This indicates that effects of charge distribution become more important than individual ion properties like size or polarizability [25]. Exceptions are the crystalline oxides on Hf and Zr, which are pure oxygen conductors. 

Figure 2.6 Electrochemical version of the marker experiment to investigate the dispersion of electrolyte through the reactor.

FIGURE 24 Flow marker experiments for pin barrel extruder of Yabushita et al. [Yl]. (a) Cross sections of vulcanized rubber strip removed from the area between the first and second grooves (extruder run without pin application). Operating conditions Tb = 80°C, = 80°C, N = 10min" ... 

If marker experiments are performed for the case in which Da > then it is expected that the markers will remain at the A B, /A phase boundary, while the product layer grows at the B/A B boundary. Whether it is useful in this case to speak of a Kirkendall effect in the sense of section 7.1,2 is debatable. It is observed experimentally, however, that in such a case the continual removal of A atoms from the A B /A phase boundary leads to the formation of pores, so that ideal contact is no longer maintained. The assumption that local thermodynamic equilibrium is maintained at the phase boundaries, which is the assumption upon which the above calculations are based, will then no longer hold true. Therefore, when performing such experiments for the purpose of testing the theory, one should apply external pressure in order that the contact between the individual phases will remain ideal. 

Fig. 3. Molecular weight dependence of the of PS as a function of M from various techniques ERD of PS into d-PS(Q) ERD of d-PS into PS(A) Holographic grating technique(O) NMR(—) and the RBS marker experiment ( ) (reproduced from ref. 20).

The availability of an oxygen tracer permits us to consider several types of marker experiments. One of these which we are undertaking can be understood by reference to Fig. 1. Two spheres can be prepared, one having its surface layer labeled with tracer, and the other without tracer. The distribution of the tracer within the neck area after a sinter anneal as Compared with the initial distribution should provide a clue about the mechanism of neck formation. The following should be mentioned ... 

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