Retardation factors

The position of a substance zone (spot) in a thin-layer chromatogram can be described with the aid of the retardation factor Rt. This is defined as the quotient obtained by dividing the distance between the substance zone and the starting line by the distance between the solvent front and the starting line (see Fig. 3)  

Zs = distance of the substance zone from the starting line [mm] 

Zp = distance of the solvent front from the solvent hquid level [mm] 

From this formula, one obtains an observed Ri value, which describes the position of a spot in the chromatogram in a simple numerical way. It gives no information about the chromatographic process used or rmder what other boimdary conditions this result was obtained. This calculated Ri is always 1. As it has been foimd to be inconvenient in routine laboratory work always to write a zero and a decimal point, the Ri value is multiphed by 100, referred to as the hRf value, quoted as a whole number, and used for the quahtative description of thin-layer chromatograms. 

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Recovery factor Reduced column length Reduced plate height Reduced velocity Relative retention ratio Retardation factor d Retention time Retention volume Selectivity coefficient Separation factor... 

The retardation factor ft governs the rate of transport of polymer to the crystal surface and as we are considering the actual crystallization process it is... 

The ionic mobilities Uj depend on the retarding factor 0 valid for a particular medium [Eq. (1.8)]. It is evident that this factor also influences the diffusion coefficients. To find the connection, we shall assume that the driving force of diffusion is the chemical potential gradient that is, in an ideal solution,... 

The traditional method of determination of the numerical values of the retardation factor, Rjn quasi-automatically assumes the following preconditions ... 

With a growing implementation of the thin-layer chromatographic laboratories with densitometric scanners and particularly in the case of PLC, it seems quite important to reconsider definition of the Rp coefficient and the ways of its determination. Further, it seems strongly advisable to recommend the retardation factor in its i P(max) form as a more practical one for the preparative layer chromatographic usage. 

Finally, an officially updated definition of the retardation factor, R, issued by lUPAC is important to the whole field of planar chromatography (the linear and the nonlinear TLC mode included). The importance of such a definition has two reasons. First, it is promoted by the growing access of planar chromatography users for densitometric evaluation of their chromatograms and second, by the vagueness of the present definition in the case of skewed concentration profiles with the samples developed under mass overload conditions. 

The migration rate of a groundwater constituent, relative to the groundwater flow rate, is controlled by the retardation factor, where Ri = 1 + Ki. Where Ki 1 (e.g., for Th and Ra), Ri Ki, and Iads + Iw = IwRi- Note that ki and k-i are element-specific but not isotope-specific. All isotopes that decay slower than desorption, so that k-i have a value of Ki that is equal to that of a stable isotope (Eqn. 3). The value of Ki may be lower for the shortest-lived nuclides (see Fig. 2b), and so a series of equations derived from Equation (3) applied to different isotopes of the same element may be used to obtain absolute values for the separate rate constants. 

Behavior of Ra in groundwater. The general behavior of Ra has been examined under laboratory conditions and in various environments (see Osmond and Cowart 1992). A major goal of field studies of Ra isotopes have aimed at obtaining bulk, in situ values of adsorption rates and so the retardation factors. Note that Ba serves as a very close chemical analogue to Ra but is typically 10 times more abundant, and so its behavior is related to that of Ra. 

There are various parameters and assumptions defining radionuclide behavior that are frequently part of model descriptions that require constraints. While these must generally be determined for each particular site, laboratory experiments must also be conducted to further define the range of possibilities and the operation of particular mechanisms. These include the reversibility of adsorption, the relative rates of radionuclide leaching, the rates of irreversible incorporation of sorbed nuclides, and the rates of precipitation when concentrations are above Th or U mineral solubility limits. A key issue is whether the recoil rates of radionuclides can be clearly related to the release rates of Rn the models are most useful for providing precise values for parameters such as retardation factors, and many values rely on a reliable value for the recoil fluxes, and this is always obtained from Rn groundwater activities. These values are only as well constrained as this assumption, which therefore must be bolstered by clearer evidence. 

Krishnaswami S, Graustein WC, Turekian KK, Dowd F (1982) Radium, thorium, and radioactive lead isotopes in groundwaters application to the in-situ determination of adsorption-desorption rate constants and retardation factors. Water Resour Res 6 1663-1675 Krishnaswami S, Bhushan R, Baskaran M (1991) Radium isotopes and Rn in shallow brines, Kharaghoda (India). Chem Geol (Isot Geosci) 87 125-136 Kronfeld J, Vogel JC, Talma AS (1994) A new explanation for extreme " U/ U disequilibria in a dolomitic aquifer. Earth Planet Sci Lett 123 81-93... 

McKinley IG, Alexander WR (1996) On the incorrect derivation and use of in-situ retardation factors from natural isotope profiles. Radiochim Acta 74 263-267... 

The fundamental parimeter used to characterize the position of a saaple zone in a TLC chromatograa is the retardation factor, or Rf value. It represents the ratio of the distance migrated by the saaple compared to that traveled by the solvent front. With respect to Figure 7.1, the Rf value for linear development is given by equation (7.1)... 

Retardation-factor models, which incorporate a simple retardation factor derived from a linear- or linearized-distribution coefficient... 

Empirically determined retardation factors (either partition coefficients or breakthrough curve measurements, which are the change in solute concentration measured over time in laboratory or field experiments) have been widely used because of their inherent simplicity.162 Modeling of specific geochemical partition and transformation processes is not necessary if the retardation factor can be determined empirically. 

The problems with linear-distribution coefficients apply equally to any retardation factor derived from them. Field measurements can be made but are expensive to obtain and highly site specific. Nevertheless, retardation factors provide some insight into organic chemical transport. 

Lesser retardation factor (slowing of migration with groundwater due to sorption to aquifer matrix). 

In simple cases, the mobility in the subsurface of a sorbing contaminant can be described by a retardation factor. Where contaminated water passes into a clean aquifer, a reaction front develops. The front separates clean, or nearly clean water downstream from fully contaminated water upstream. Along the front, the sorption reaction removes the contaminant from solution. The retardation factor describes how rapidly the front moves through the aquifer, relative to the groundwater. A retardation factor of two means the front, and hence the contamination, will take twice as long as the groundwater to traverse a given distance. 

By similar logic, the retardation factor for a solute that sorbs according to a Freundlich isotherm is... 

Fig. 21.3. Transport of benzene within an aerobic aquifer, as depicted in Figure 21.2, calculated assuming the species not only biodegrades, but sorbs to organic matter in the aquifer. Benzene in the simulation sorbs with a distribution coefficient of 0.16 x 10-3 mol (g sediment)-1, equivalent to a retardation factor R of 2. Fine lines show non-reactive case.

When half the aquifer s pore volume has been displaced, the inlet fluid in the simulation changes to uncomtaminated water. At this point, the contamination has progressed across one-quarter of the aquifer, reflecting the retardation factor of two. 

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