Relative fractionation

Gas-liquid. From Equation (13), the relative fractionation between, for example, species i and Ar in the gas phase, ([i]/[Ar])g, can be related to the original ratio in the system ([i]/[Ar])x, after Bosch and Mazor (1988), by 

Taking the limits as Vg/Vi oo then ([i]/[Ar])g ([i]/[Ar])x, and as Vg/Vi 0 then ([i]/[Ar])g ([i]/[Ar])x(K i/K Ar)- Therefore as Vg/Vi becomes small, the noble gases are fractionated proportionally to their relative solubilities in the liquid phase, or more precisely including the effects of non-ideality on the solubility  

Liquid-liquid In a similar fashion the relative change in the [i]/[Ar] ratio in a liquid-liquid system can be assessed. For example, the high solubility of noble gases in oil relative to water can potentially result in significant and distinct fractionation of the noble gases where equilibrium has occurred between these two phases. Following Bosch and Mazor (1988), the [i]/[Ar] ratio in the oil phase, ([i]/[Ar])oii, is related to the original 

The magnitude of the fractionation seen in either phase is therefore proportional to the ratio between the noble gas relative solubilities in the two liquid phases. 

This decreases to a maximum of 4.3 for a light crude oil (API = 34) at the same temperature (Fig. 7b). Fractionation in any gas phase associated with oil decreases with increasing temperature, Vg/Vi and decreasing oil density. 

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Figure Bl.22.1. Reflection-absorption IR spectra (RAIRS) from palladium flat surfaces in the presence of a 1 X 10 Torr 1 1 NO CO mixture at 200 K. Data are shown here for tluee different surfaces, namely, for Pd (100) (bottom) and Pd(l 11) (middle) single crystals and for palladium particles (about 500 A m diameter) deposited on a 100 A diick Si02 film grown on top of a Mo(l 10) single crystal. These experiments illustrate how RAIRS titration experiments can be used for the identification of specific surface sites in supported catalysts. On Pd(lOO) CO and NO each adsorbs on twofold sites, as indicated by their stretching bands at about 1970 and 1670 cm, respectively. On Pd(l 11), on the other hand, the main IR peaks are seen around 1745 for NO (on-top adsorption) and about 1915 for CO (tlueefold coordination). Using those two spectra as references, the data from the supported Pd system can be analysed to obtain estimates of the relative fractions of (100) and (111) planes exposed in the metal particles [26].

Ft. The remainder was assumed to be surface atoms and Ao was allowed to vary to achieve the best fit to the data. The relative fraction of surface and bulk was assigned from the chemisorption measurement, l.e., 0.9 and 0.1, respectively. The results are given... 

Figure 5. Relative fraction of the different surface atoms as a function of Log H, where Mis the number of atoms, for a (111) and (100) facetted f.c.c, crystal when the surface morphology is equilibriated, E. refers to the edges between the (inn) and (111) faces, to the edges between two (111) faces. The (111) curve is drawn using the axes to the right,...

Special topographic features of the surfaces of small crystallites. The smaller the size of a crystallite, the larger will be the relative fraction of special ... 

Figure 15. Relative fraction of different kinds of surface sites in silver particles. (Reprinted from Reference [82], 1999, with permission from American Chemical Society).

The use of nuclear techniques allows the determination of C, N, H, O, and heavier contaminants relative fractions with great accuracy, and of the elements depth profile with moderate resolution (typically 10 nm). Rutherford backscattering spectroscopy (RBS) of light ions (like alpha particles) is used for the determination of carbon and heavier elements. Hydrogen contents are measured by forward scattering of protons by incident alpha particles (ERDA) elastic recoil detection analysis [44,47]. 

Figure 11. The clinopyroxene-liquid partition coefficient for 4+ ions entering the M2-site shown as a function of the ionic radins of the trace cation. Changes in clinopyroxene composition along a solid solntion lead to small changes in the dimensions of M2 (ro Jw 2>), which can lead in turn to changes in the relative fractionation between 4+ ions of similar ioiuc radii, such as and Th" (shown as vertical lines). We contrast the partitioning behavior of a diopside-rich clinopyroxene = 1 044 A) and a...

Fig. 3.3.6 Comparison of the relative fractions of stagnant and moving fluid obtained from the propagators for catalyst and glass beads.

Figure 5. Tomato cell suspensions exposed to peak 1 polar extract of spikerush culture. Plotted as relative fraction of cell volume over volume of medium vs. time.

In general, pores swell nonuniformly. As a simplification, fhe random network was assumed to consist of fwo types of pores. In fhis fwo-stafe model, nonswollen or "dry" pores (referred to later as "red" pores) permit only a small residual conductance due to tightly bound surface water, which solvates the charged surface groups. Swollen or "wet" pores (referred to later as "blue" pores) contain extra water in the bulk, allowing them to promote the high bulk-like conductance. Water uptake by the membrane corresponds to the swelling of wef pores and to the increase of their relative fraction. 

We may now argue whether or not a silicate melt can fractionate elements of the same group. The question is rather important for REE, whose relative fraction-... 

Sulfur isotope relative fractionation factors between various minerals and py-rite are shown in figure 11.40. As we can see, the isotopic compositions of sulfates reflect the relative fractionation effects induced by the 804 groups (compare figures 11.40 and 11.39). 

Low density PE foam sheets having a thickness of 10 mm were cut from a block produced by compression moulding and their thermal conductivities over the temperature range from 24 to 50C determined. The evolution of the properties along the block was analysed and the cell structure, apparent mean cell diameter, anisotropy, mean cell wall thickness and relative fraction of polymer determined using quantitative image analysis and a previously reported model utilised to predict the thermal conductivity of the foams. 30 refs. 

Table VIII shows the influence of base octane on the relative fractional ZSM-5 replacement rate required to achieve a 1 RON boost. Model estimates show that half as much ZSM-5 is required to achieve a +1 RON/+0.4 MON boost at a base octane of 88 as compared to an application with a base octane of 92.

For this example, the relative fractional replacement rate of ZSM-5 in the inventory decreases form 1 to 0.85. 

RON Relative Fractional ZSM-5 Replacement Rate ARON AMON... 

Relative Fractional Replacement Rate of ZSM-5 Required to Achieve a +1 RON Increase... 

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