Separation parameter

From these volumes, we can calculate three factors, kf, a, and N (Fig. 4.2), which will then be used to describe a resolution equation (Fig. 4.3).This equation predicts the effect of variations in these factors in controlling resolution within the FIPLC column. They are presented here to discuss the variables controlling each of them, their limits, and how you can use them to achieve your separations in a rational manner. 

They also serve as a common language when discussing separation problems. With these quantities in hand, it is generally unnecessary to detail other operating conditions. Finally, their most important use is as a diagnostic tool for column problems. 

The first factor, the retention factor (kf), is the relative retention of each peak on the column. In our example, kf B, the retention factor for the blue peak is determined by dividing the difference between VB and Va by V0. It effectively tells us how long it takes the center of peak B to come off the column relative to Va. We can derive a similar factor for the red dye (k A) or for any peak in a multi-peak mixture. 

The next factor, the separation factor (a), represents the relative separation between any two peaks centers on a chromatogram. It is defined as the retention factor of the longer retaining peak divided by the retention factor of the faster peak. Any pair of peaks in the chromatogram will have their own a. 

The final factor, the efficiency factor (N), measures the degree of sharpness of a given peak. It is determined by the retention volume of the peak (i.e., VB) by the peak width. Two different widths are commonly used for this calcula- 

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The Optimum Velocity Profile. The optimum velocity profile (41), that is the velocity profile that yields the maximum value for the flow pattern efficiency, is one in which the mass velocitypv is constant over the radius of the centrifuge except for a discontinuity at the wall of the centrifuge (r = rP). This optimum velocity profile is shown in Figure 14a. For this case the following values for the separation parameters of the centrifuge are obtained... 

The Two-Shell Veloeity ProHle. A second simple velocity profile (41) is shown ia Figure 14b ia which the flow consists of two thin streams, one situated at radius flowing upward, and the other situated at the wall (r = flowing downward. For this case the values of the separation parameters are... 

The separation parameters have been calculated for a centrifuge in which the behavior of the circulating gas is described by Martin s equation. The flow pattern efficiency is shown in Figure 15(b) as a function of the dimensionless parameter M, where M is equal to (ME /2RT). In this case the maximum flow pattern efficiency attainable is 0.956. 

This chapter illustrates the improvements in SEC column technology and modern applications of SEC separations. The better understanding of SEC column design and separation parameters described in the theoretical sections of this chapter will help the reader fine-tune his or her own work. The same is true for column performance tests, which should be applied regularly, especially after a column purchase. In order to obtain reproducible results, it is recommended to choose column manufacturers who can assure constant quality and performance and to invest in knowledgeable, well-trained support personnel and experienced application chemists. 

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

In our early evaluations, three parameters were utilized for the resolving power of the columns (3,4,7). These were the valley-to-peak height ratio, v, the peak separation parameter, P, and the parameter mentioned earlier, Djcr. The valley-to-peak height ratio is defined as... 

TABLE 21.4 Peak Resolution Parameters Valley-to-Peak Ratios, v, and Peak Separation Parameters, P, for Batch 52 Gel... 

The final step in the process of standardizing our columns was to try and maintain the high quality of columns from batch to batch of gel from the manufacturer. This was done by following the basic procedures outlined earlier for the initial column evaluation with two exceptions. First, we did not continue to use the valley-to-peak ratios or the peak separation parameters. We decided that the D20 values told us enough information. The second modification that we made was to address the issue of discontinuities in the gel pore sizes (18,19). To do this, we selected six different polyethylenes made via five different production processes. These samples are run every time we do an evaluation to look for breaks or discontinuities that might indicate the presence of a gel mismatch. Because the resins were made by several different processes, the presence of a discontinuity in several of these samples would be a strong indication of a problem. Table 21.5 shows the results for several column evaluations that have been performed on different batches of gel over a 10-year period. Table 21.5 shows how the columns made by Polymer Laboratories have improved continuously over this time period. Figure 21.2 shows an example of a discontinuity that was identified in one particular evaluation. These were not accepted and the manufacturer quickly fixed the problem. 

Much of our present day knowledge of sweetness intensity, both at the threshold level, where taste begins, and above the threshold level, derives from the application of psychophysical techniques. It is now evident that the psychophysical procedure used measure separate aspects of sweetness perception. Hedonic responses cannot be predicted from intensity of discrimination data, and vice versa. The taste-panel evaluation of sweetness is of fundamental importance in the development of worthwhile structure-taste relationships. Therefore, it is vital that the appropriate psychophysical method and experimental procedure be adopted for a particular objective of investigation. Otherwise, false conclusions, or improper inferences, or both, result. This situation results from the failure to recognize that individual tests measure separate parameters of sensory behavior. It is not uncommon that the advocates of a specific method or procedure seldom... 

Hydrodynamic volume of polymer (here considered equivalent to the separation parameter KM Table II for GPC calibration)... 

In the first attempt to characterize the reservoir, all 15 layers were treated as separate parameter zones. An initial guess of300 md was used for the permeability of each zone. A diagonal weighting matrix Q, with elements y j (t j) 2 was used. 

Sample adsorption to the silica wall is a problem in HPCE, one that is highly undesirable. As we mentioned earlier, adsorption can be minimized by proper buffer selection, additives, or chemical modification of the surface. The selection of pH is one of the simplest separation parameters to manipulate and is critical to the success of all electrophoretic separations. The pH of the media will determine the charge of the sample and the charge of the silica surface. At low values of pH, the capillary wall is protonated, the EOF... 

In order to explain this, we need to recall some basic separation parameters. The resolution between two SC peaks of the same height is defined as... 

Estimation of the Separation Parameters The extension of the SDO procedure to 2D separations implies that the 2D map is divided into many strips considered as ID separations on which computations are performed. Different... 

The 2D autocovariance function was computed on the digitized map signal using Equation 4.28 and the separation parameters were estimated according to Equation 4.30. The results obtained are reported in the following table (Pietrogrande et al., 2005). 

The various separation parameters should be adjusted to provide optimum resolution. These include mobile phase flow rate, stationary phase particle size, gradient elution, and column temperature (using an optional column oven). 

The chromatographic parameters discussed above were calculated for packed beds (increased dispersion and bed length), and for expanded beds with moderate, higher and lower dispersion. The results indicated that the corresponding separation parameters of packed beds and expanded beds are commensurable, therefore, expanded beds can be successfully employed in liquid chromatography even in the case of trace analysis of synthetic dyes in waste water and sludge [75],... 

The concentration of the chiral selector, for instance, has considerable influence on the mobility and separation of the enantiomers. Optical resolution varies with the chiral selector concentration and reaches a maximum value at a given optimum concentration. Wren and Rowe proposed a model that describes the influence of the selector concentration on selectivity, and which was extended by Vigh s group ° by including the pH as a separation parameter for weak acidic enantiomers. The latter model shows that the chiral selectivity is determined by the complex s relative mobility, the CD concentration, the degree of dissociation... 

Rathore, A. S., and Horvath, C. S. (1996). Separation parameters via virtual migration distances in high-performance liquid chromatography, capillary zone electrophoresis and electrokinetic chromatography /. Chromatogr. A 743, 231-246. 

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