Saturation factor

Then, the MW power is increased in order to partially saturate the EPR transition. The degree of saturation is provided by the saturation factor s defined earlier (see equation (bl.l5.13fi. 

Raw Material Proportions. The three main considerations in proportioning raw materials for cement clinker are the potential compound composition the percentage of Hquid phase at clinkering temperatures and the bumabiUty of the raw mix, ie, the relative ease, in terms of temperature, time, and fuel requirements, of combining the oxides into good quaUty clinker. The ratios of the oxides are related to clinker composition and bumabiUty. For example, as the CaO content of the mix is increased, more C S can be formed, but certain limits cannot be exceeded under normal burning conditions. The lime saturation factor (LSF) is a measure of the amount of CaO that can be combined (20) ... 

An LSF of 100 would indicate that the clinker can contain only C S and the ferrite soHd solution. Time saturation factors of 88—94 are frequentiy appropriate for reasonable bumabiUty low LSF indicates insufficient C S for acceptable early strengths, and higher values may render the mix very difficult to bum. Several other weight ratios such as the siUca modulus and the iron modulus are also important (21). 

We have seen that in a steady field Hq a small excess, no, of nuclei are in the lower energy level. The absorption of rf energy reduces this excess by causing transitions to the upper spin state. This does not result in total depletion of the lower level, however, because this effect is opposed by spin-lattice relaxation. A steady state is reached in which a new steady value, n, of excess nuclei in the lower state is achieved. Evidently n can have a maximum value of o and a minimum value of zero. If n is zero, absorption of rf energy will cease, whereas if n = no, a steady-state absorption is observed. It is obviously desirable that the absorption be time independent or. in other words, that s/no be close to unity. Theory gives an expression for this ratio, which is called Zq, the saturation factor ... 

It is, therefore, desirable that the quantity y H, TiT2 be as small as possible. The rf field Hi should be of low power to prevent saturation. The saturation factor appears in the later treatment. 

Notice the appearance of the saturation factor in these equations. By working at small values of Hi these equations become... 

Once m has been calculated, the so-called saturation factor in 1D separation can be obtained from... 

The statistical model of peak overlap clearly explains that the number of observed peaks is much smaller than the number of components present in the sample. The Fourier analysis of multicomponent chromatograms can not only identify the ordered or disordered retention pattern but also estimate the average spot size, the number of detectable components present in the sample, the spot capacity, and the saturation factor (Felinger et al., 1990). Fourier analysis has been applied to estimate the number of detectable components in several complex mixtures. 

Bulk Density of Benthic Compartment (SDCHRG(2)) Benthic Saturation Factor (PCTWAG(2))... 

In this equation, the term in parentheses is called the saturation factor. This factor tends rapidly to 1 when t is increased. Thus, for t = 6r, the activity reaches a value of 98%. Experimentally, the time of irradiation never exceeds 4 to 5t. This method is usually reserved for radioelements with short half-lives. 

The term (1—e xtt) is referred to as the saturation factor and approaches unity as the time of irradiation becomes large with respect to the half-... 

The saturation factor gives the degree to which the applied radiofrequency (RF) field saturates the electron transition of all radicals in the sample and can range from 0 to 1. The saturation factor can be written as a function of the applied radiation power P,... 

From here, the saturation factor requires further discussion. Equation (9) is correct for radicals with a single ESR transition however, the picture becomes more complicated for radicals with more than one transition due to hyperfine splitting. The nitroxide radicals commonly used for ESR and DNP fall into this category,47 48 as the impaired electron in these molecules partially resides on a nitrogen nucleus with spin 1 (14N) or spin 1/2 (15N) giving three or two hyperfine lines, respectively. For the more common 14N nitroxide radicals, at low concentrations in aqueous solutions the right side of Equation (9) is multiplied by a factor of 1 /3, as only one hyperfine line can be saturated at a time.49 However, two processes can serve to mix the hyperfine lines and increase the saturation factor in the limit of infinite power (smax) of nitroxide radicals well beyond smax = 1/3. 

These descriptions of the saturation factor are based solely on classical Ti relaxation dynamics of the electron populations and do not include electron-nitrogen spin-spin (T2) relaxation effects due to spin coherences. To include electron-nitrogen T2 effects into the saturation factor, semi-classical relaxation theory25 54 can be used, and a recent paper by Sezer et al. presents a formalism to include these effects.55... 

A recent advance in the quantification of DNP came with the inclusion of nitrogen nuclear relaxation into the saturation factor. Inspired by the measurement of nitrogen spin-lattice relaxation times over a wide range of correlation times by Robinson et al.,52 Armstrong and Han developed a... 

As the discussion in this section shows, there remains somewhat conflicting reports on the proper way to measure the coupling factor and maximum saturation factor for nitroxide radicals. While this is not a concern for radicals (such as trityl) with only one hyperfine line, nitroxide radicals have been shown to give generally better DNP signal enhancements for solution-state systems than water-soluble trityl radicals at both 0.34 and 3.3 T.41 Because of the importance of nitroxide radicals, further work needs to be done to resolve all discrepancies. However, the most recent results show that theory and various experimental reports are closer in agreement than ever before. 

Figure 7 Plot of the change in the product of the coupling and maximum saturation factors as a function of macromolecular structure. At lower pH values, the spin-labelled lipids are present as vesicles and vesicular aggregates, while at higher pH values, micelles are formed. The higher psmax values for the micelles imply greater water accessibility to the radical site. The solid circles represent 16-DS (16-doxyl stearic acid, spin-labelled at the end of the lipid tail) while the open circles represent 5-DS (5-doxyl stearic acid, spin-labelled near the polar head group). Reproduced with permission from Ref. [70].

Saturation factor for small values of A, it equals At for t = t /2, it equals 0.5, the optimum irradiation time. 

AR = alumina ratio (alumina modulus). ASR = alkali silica reaction. LSF = lime saturation factor. SR = silica ratio (silica modulus). C, = analytical (total) concentration of x, irrespective of species, [x] = concentration of species x. x = activity of species x. RH = relative humidity. =... 

Lime saturation factor, silica ratio and alumina ratio... 

Lime saturation factor (LSF) = Ca0/(2.8Si02 -f I.2AI2O3 -f 0.65Fe2Oj)... 

Any more detailed interpretation demands that both activity coefficients and the existence of complex species be taken into account (B90,G58). Gartner el til. (G58) showed that, for most cements, the solution is saturated in CH within 12 min and that the saturation factor (defined as the activity product divided by its value at saturation) reaches a maximum of between 2 and 3 within 2h. For gypsum, saturation is reached within 6 min, but the saturation factor never exceeded 1.3 in the cases studied. With cements high in K,0, the solution can become saturated in syngenite. Gartner el id. found that the and Na concentrations increased rapidly during the first 12 min and only slowly, or not at all, during the subsequent period up to 3 h. 

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