Elution defined

Figure 18.213-D plot of the hybrid objective function representing the total production cost in elution (defined in Eq. 18.62). Plot for the less retained component of a 3 1 mixture at a separation factor a = 1.5 and a retention factor = 6. A. Felinger and G. Guiochon, AIChE ]., 40 (1994) 594 (Fig. 8). Reproduced by permission of the American Institute of Chemical Engineers. 1993 AIChE. All rights reserved.

The identities of the solutes are defined such that solute A always has the smaller retention time. Accordingly, the selectivity factor is equal to 1 when the solutes elute with identical retention times, and is greater than 1 when is greater than fr A-... 

Now that we have defined capacity factor, selectivity, and column efficiency we consider their relationship to chromatographic resolution. Since we are only interested in the resolution between solutes eluting with similar retention times, it is safe to assume that the peak widths for the two solutes are approximately the same. Equation 12.1, therefore, is written as... 

An eluted solute was originally identified from its corrected retention volume which was calculated from its corrected retention time. It follows that the accuracy of the measurement depended on the measurement and constancy of the mobile phase flow rate. To eliminate the errors involved in flow rate measurement, particularly for mobile phases that were compressible, the capacity ratio of a solute (k ) was introduced. The capacity ratio of a solute is defined as the ratio of its distribution coefficient to the phase ratio (a) of the column, where... 

Reiterating the conditions for a chromatographic separation once again, for two solutes to be resolved their peaks must be moved apart in the column and maintained sufficiently narrow for them to be eluted as discrete peaks. However, the criterion for two peaks to be resolved (usually defined as the resolution) is somewhat arbitrary and is usually defined as the ratio of the distance between the peak maxima to half the peak width (a) at the points of inflection. To illustrate the various degrees of resolution that can be obtained, the separation of a pair of solutes 2o, 3o, 4o, 5o and 6o apart are shown in Figure 12. Although, for baseline resolution, it is clear that the peak maxima should be separated by at least 6o for most quantitative analyses. 

It is seen that the chromatographer can arrive at the minimum (aA/e) value for a pair of solutes that the column can resolve directly, from either the resolution, as defined by Giddings, or from a simple function of the number of effective plates. However, again it must be emphasized that this will not be a unique value for any column, as it will also depend on the (k ) of the eluted solute. 

Equation (22) allows the maximum sample volume that can be used without seriously denigrating the performance of the column to be calculated from the retention volume of the solute and the column efficiency. In any separation, there will be one pair of solutes that are eluted closest together (which, as will be seen in Part 3 of this book, is defined as the critical pair) and it is the retention volume of the first of these that is usually employed in equation (22) to calculate the maximum acceptable sample volume. 

Now, all the curves are describing the same chromatogram thus, by simple proportion, the ratios of the variance of each elution curve to the square of the retention (in the respective units in which the variables are defined) will all be equal. 

The second and third peaks will be the pair of peaks in the mixture that are eluted closest together and, thus, the most difficult to separate (usually given the term the critical pair as they define the severity of the separation). Finally, the fourth peak will be that which is eluted last from the mixture and will determine when the analysis is complete and establishes the total analysis time. The chromatographic system must be designed to separate the critical pair and, as this is the pair that is eluted closest together, all other peaks should also be resolved... 

The choice of variables remaining with the operator, as stated before, is restricted and is usually confined to the selection of the phase system. Preliminary experiments must be carried out to identify the best phase system to be used for the particular analysis under consideration. The best phase system will be that which provides the greatest separation ratio for the critical pair of solutes and, at the same time, ensures a minimum value for the capacity factor of the last eluted solute. Unfortunately, at this time, theories that predict the optimum solvent system that will effect a particular separation are largely empirical and those that are available can be very approximate, to say the least. Nevertheless, there are commercially available experimental routines that help in the selection of the best phase system for LC analyses, the results from which can be evaluated by supporting computer software. The program may then suggest further routines based on the initial results and, by an iterative procedure, eventually provides an optimum phase system as defined by the computer software. 

Column design involves the application of a number of specific equations (most of which have been previously derived and/or discussed) to determine the column parameters and operating conditions that will provide the analytical specifications necessary to achieve a specific separation. The characteristics of the separation will be defined by the reduced chromatogram of the particular sample of interest. First, it is necessary to calculate the efficiency required to separate the critical pair of the reduced chromatogram of the sample. This requires a knowledge of the capacity ratio of the first eluted peak of the critical pair and their separation ratio. Employing the Purnell equation (chapter 6, equation (16)). 

A SEC material should be hydrophilic if it is to be used for biological applications. One such material, introduced by PolyLC in 1990 (8), is silica with a covalently attached coating of poly(2-hydroxyethyl aspartamide) the trade name is PolyHYDROXYETHYL Aspartamide (PolyHEA). This material was evaluated for SEC of polypeptides by P.C. Andrews (University of Michigan) and worked well for the purpose (Fig. 8.1). Because formic acid is a good solvent for polypeptides, Dr. Andrews tried a mobile phase of 50 mM formic acid. The result was a dramatic shift to a lower fractionation range for both Vq and V, (Fig. 8.2) to the point that V, was defined by the elution position of water. 

Hydrodynamic volume refers to the combined physical properties of size and shape. Molecules of larger volume have a limited ability to enter the pores and elute the fastest. A molecule larger than the stationary phase pore volume elutes first and defines the column s void volume (Vo). In contrast, intermediate and smaller volume molecules may enter the pores and therefore elute later. As a measure of hydrodynamic volume (size and shape), SE-HPLC provides an approximation of a molecule s apparent molecular weight. For further descriptions of theoretical models and mathematical equations relating to SE-HPLC, the reader is referred to Refs. 2-5. 

The ability of a GC column to theoretically separate a multitude of components is normally defined by the capacity of the column. Component boiling point will be an initial property that determines relative component retention. Superimposed on this primary consideration is then the phase selectivity, which allows solutes of similar boiling point or volatility to be differentiated. In GC X GC, capacity is now defined in terms of the separation space available (11). As shown below, this space is an area determined by (a) the time of the modulation period (defined further below), which corresponds to an elution property on the second column, and (b) the elution time on the first column. In the normal experiment, the fast elution on the second column is conducted almost instantaneously, so will be essentially carried out under isothermal conditions, although the oven is temperature programmed. Thus, compounds will have an approximately constant peak width in the first dimension, but their widths in the second dimension will depend on how long they take to elute on the second column (isothermal conditions mean that later-eluting peaks on 2D are broader). In addition, peaks will have a variance (distribution) in each dimension depending on... 

The basis of chromatography is in the differential migration of chemicals injected into a column. The carrier fluid takes the solutes through the bed used for elution (mobile phase). The bed is the stationary phase. Based on mobility, the retention-time detectors identify the fast and slow-moving molecules. Based on internal or external standards with defined concentration, all unknown molecules are calculated in a developed method by software. GC columns are installed in an oven which operates at a specified temperature. A diagram of an oven with GC column is shown in Figure 7.16. 

Finally, ion chromatography can be used to determine the a-sulfo fatty acid esters. The chromatographic column is a nonpolar poly sty rene/divinylbenzene column and the ion pair reagent is 0.005 M ammonia. In order to reduce the elution time, acetonitrile is added as a modifier with increasing concentration. This gradient technique makes it possible to separate simultaneously ester sulfonates and disalts by chain length. Determination is achieved by standards with defined chain length [107]. 

Detector Sensitivity or the Minimum Detectable Concentration has been defined as the minimum concentration of an eluted solute that can be differentiated unambiguously from the noise. The ratio of the signal to the noise for a peak that is considered decisively identifiable has been arbitrarily chosen to be two. This ratio originated from electronic theory and has been transposed to LC. Nevertheless, the ratio is realistic and any peak having a signal to noise ratio of less than two is seriously obscured by the noise. Thus, the minimum detectable concentration is that concentration that provides a signal equivalent to twice the noise level. Unfortunately, the concentration that will provide a signal equivalent to twice the noise level will usually depend on the physical properties of the solute used for measurement. Consequently, the detector sensitivity, or minimum detectable concentration, must be quoted in conjunction with the solute that is used for measurement. 

How then are these ions/decompositions chosen Before considering this we must define, very carefully, the requirements of the analysis to be carried out. Is a single compound to be determined or are a number of compounds of interest If a single compound is involved, its mass spectrum and MS-MS spectra can be obtained and scrutinized for any appropriate ions or decompositions. If the requirement is to determine a number of analytes, their chromatographic properties need to be considered. If they are well separated, different ions/decompositions can be monitored for discrete time-periods as each compound elutes, thus obtaining the maximum sensitivity for each analyte. If the analytes are not well separated, this approach may not be possible and it may then be necessary to monitor a number of ions/decompositions for the complete duration of the analysis. If this is the case, the analyst should attempt to find the smallest number of ions/decompositions that give adequate performance for all of the analytes (remember the more ions/decompositions monitored, then the lower the overall sensitivity will be). 

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