Criterion of separation

To use the formula in Equation 38.2, it is necessary to define at what stage the two peaks representing the two masses are actually separate (Figure 38.4). The depth of the valley between the two peaks serves this purpose, with valley definitions of 5, 10, or 50%. A 5% valley definition is a much stricter criterion of separation efficiency than the 50% definition. 

The Archimedes number contains parameters that characterize the properties of the heterogeneous system and the criterion establishing the type of settling. The criterion of separation essentially establishes the separating capacity of a sedimentation machine. The product of these criteria is ... 

Resolution, like the separation factor, differs for each specific component pair and therefore fails as a global criterion of separation. For analytical separations, more universal criteria have evolved, such as plate height, number of plates, rate of generation of plates, and peak capacity (Chapter 5). While these indices differ somewhat from one component to another, they effectively establish a ballpark figure of merit for different systems and different conditions of operation. 

Once a suitable HPLC separation mode has been selected, the experimental conditions should be adjusted to suit the objective of the separation. To proceed in this way, either empirical or systematic (statistical or predictive) HPLC method development strategies can be used. Any method development necessitates a convenient measure of the quality of separation. The separation of two sample compounds is most often measured either by resolution or by peak separation function (see Section 1.1.2). The resolution is an especially useful criterion of separation as its definition Eq. (1.3) can be transformed to another expression relating directly to the experimental conditions of separation v/A k... 

Even with DRy equal to only 10, two successive batch extractions will transfer 99% of the material to the organic phase. If one chooses as a criterion of separation that substance A be at least 99% extracted and substance B no more than 1% extracted, then, from Equation 20.5, one must have > 100 and D Ry < 0.01 for a single (batch) extraction. 

There is however one major shortcoming of the Sigma concept the cut size is insufficient as a criterion of separation efficiency because different total efficiencies can be obtained at a given cut size, if the size distribution of the feed particles differs. Murkes recognized this but suggested a method which assumes a certain form of the feed distribution function, thus introducing an unnecessary limitation. 

Besides its use in assessing separation efficiency, entropy, in conjunction with internal energy, can also be used in deriving a criterion of separation . This is in analogy with chemical thermodynamics the value of the criterion wUl decide whether separation will take place spontaneously or not at all. Only a summary of the derivation is given in the following. 

To reiterate the definition of chromatographic resolution a separation is achieved in a chromatographic system by moving the peaks apart and by constraining the peak dispersion so that the individual peaks can be eluted discretely. Thus, even if the column succeeds in meeting this criterion, the separation can still be destroyed if the peaks are dispersed in parts of the apparatus other than the column. It follows that extra-column dispersion must be controlled and minimized to ensure that the full performance of the column is realized. 

Combination of Eq. 7 or Eq. 8 with the Young-Dupre equation, Eq. 3, suggests that the mechanical work of separation (and perhaps also the mechanical adhesive interface strength) should be proportional to (I -fcos6l) in any series of tests where other factors are kept constant, and in which the contact angle is finite. This has indeed often been found to be the case, as documented in an extensive review by Mittal [31], from which a few results are shown in Fig. 5. Other important studies have also shown a direct relationship between practical and thermodynamic adhesion, but a discussion of these will be deferred until later. It would appear that a useful criterion for maximizing practical adhesion would be the maximization of the thermodynamic work of adhesion, but this turns out to be a serious over-simplification. There are numerous instances in which practical adhesion is found not to correlate with the work of adhesion at ail, and sometimes to correlate inversely with it. There are various explanations for such discrepancies, as discussed below. 

A second criterion of performance sometimes used is an artificial thermal efficiency (tja) in which the energy in the fuel supply to the CHP plant is supposed to be reduced by that which would be required to produce the heat load (Qu) in a separate heat only boiler of efficiency (tjb). i e- by (Qu/ b)- The artificial efficiency (tja) is then given by... 

Mechanical strength becomes an important criterion, because wound cells (spiral-type construction), in which a layer of separator material is spirally wound between each two electrodes, are manufactured automatically at very high speed. Melt-blown polypropylene fleeces, with their excellent tensile properties, offer an interesting option. Frequently two layers of the same or different materials are used, to gain increased protection against shorts for button cells the use of three layers, even, is not unusual. Nevertheless the total thickness of the separation does not exceed 0.2 - 0.3 mm. For higher-temperature applications (up to about 60 °C) polypropylene fleeces are preferred since they offer a better chemical stability, though at lower electrolyte absorption [ 114"]. 

Reliable analytical methods are available for determination of many volatile nitrosamines at concentrations of 0.1 to 10 ppb in a variety of environmental and biological samples. Most methods employ distillation, extraction, an optional cleanup step, concentration, and final separation by gas chromatography (GC). Use of the highly specific Thermal Energy Analyzer (TEA) as a GC detector affords simplification of sample handling and cleanup without sacrifice of selectivity or sensitivity. Mass spectrometry (MS) is usually employed to confirm the identity of nitrosamines. Utilization of the mass spectrometer s capability to provide quantitative data affords additional confirmatory evidence and quantitative confirmation should be a required criterion of environmental sample analysis. Artifactual formation of nitrosamines continues to be a problem, especially at low levels (0.1 to 1 ppb), and precautions must be taken, such as addition of sulfamic acid or other nitrosation inhibitors. The efficacy of measures for prevention of artifactual nitrosamine formation should be evaluated in each type of sample examined. 

Recalling the previous assertion that efficient fractionation requires liquid-liquid phase separation, we conclude that nitrobenzene and amyl acetate should be satisfactory solvents from which to fractionate polyethylene by successively lowering the temperature and that the better solvent xylene should be avoided for this purpose. The character of the phase diagram may, in fact, be used as a criterion of the efficacy of a given solvent for fractionation (see Chap. VIII, p. 344). If the curve representing the precipitation temperature plotted against concentration rises monotonically, crystalline separation is clearly indicated if it passes through a maximum at a low concentration, liquid-liquid separation is virtually assured, and the solvent may be assumed to be a satisfactory one to use for fractionation. 

In a practical sense, stability of a dispersion ofttimes is accompanied by a retarded separation of the phases. Unfortunately, a quantitative definition cannot be based on this rate of separation because of the overwhelming influence of density, viscosity, and thermal effects. In short, a kinetic criterion, such as sedimentation rate, is not as likely to portray stability as one based on thermodynamic considerations. In this latter category are sediment volumes, turbidity, consistency, and electrical behavior. 

As already mentioned, the criterion of complete ionization is the fulfilment of the Kohlrausch and Onsager equations (2.4.15) and (2.4.26) stating that the molar conductivity of the solution has to decrease linearly with the square root of its concentration. However, these relationships are valid at moderate concentrations only. At high concentrations, distinct deviations are observed which can partly be ascribed to non-bonding electrostatic and other interaction of more complicated nature (cf. p. 38) and partly to ionic bond formation between ions of opposite charge, i.e. to ion association (ion-pair formation). The separation of these two effects is indeed rather difficult. 

The classification of methods for studying electrode kinetics is based on the criterion of whether the electrical potential or the current density is controlled. The other variable, which is then a function of time, is determined by the electrode process. Obviously, for a steady-state process, these two quantities are interdependent and further classification is unnecessary. Techniques employing a small periodic perturbation of the system by current or potential oscillations with a small amplitude will be classified separately. 

It must be however underlined that, in measuring the peak-to-peak separation, a departure of 10-20 mV from the theoretical value (especially at relatively high scan rates) does not compromise the criterion of reversibility, in that the eventual presence of solution resistances not adequately compensated by the electrochemical instrumentation (see Chapter 3, Section 2) tends to lay down the forward/ reverse peaks system, thus increasing the relative Aisp value. 

A price calculation is relatively easy for a product with a track record of a regular industrial-scale production. On the other hand, it is difficult, if only a laboratory procedure exists and a calculation has to be made based on the virtual scaleup to industrial-scale production. The ability to perform this desk exercise in a quick and reliable fashion is an important competence criterion of a fine-chemical manufacturer. When setting a price, a separation of tasks must be made between the controller, who calculates the manufacturing cost, and the sales manager, who determines the sales price. If mistakes have been made and prices have to be changed, you will need facts to support your request. If a pivotal product is supplied, a supply contract is concluded. 

A typical application is given by Debets et al. A quality criterion for the characterization of separation in a chromatogram is modified by using Hermite polynomial coefficients in order to enhance the performance. The quality criterion can be used in... 

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