Column optimum sample size

One of the most important decisions that is left to the analyst when operating a liquid chromatograph is the choice of detector sensitivity. In some instruments the output from the sensor is monitored continuously over its entire dynamic range and so sensitivity is not an optional experimental parameter. Nevertheless, in this case, the sample size determines the concentration range over which the eluted solutes are monitored and thus an optimum sample size must be chosen. The detector should never be operated at its maximum sensitivity unless such conditions are enjoined by limited sample size or column geometry. Provided that there is adequate sample available, and the sample concentration when eluted is within the linear dynamic range of the detector, the maximum sample size that the column can tolerate should be used. This ensures that the detector noise is always minimal... 

Figure 18.6 Comparison of the true band profiles at the optimum sample size predicted by the noncompetitive model of Knox and Pyper (dotted lines) and by the ideal model with competitive Langmuir isotherms (solid lines) in the case of touching bands, fcg j = 6. a = 1.2. Isotherm coefficients = 2.4 2 = Column length 25 cm. Phase ratio F = 0.25. Mobile phase velocity 0.6 cm/s. (a) Feed composition 1 9. (b) Feed composition 3.6 1. (c) Feed composition 9 1. Reproduced with permission from S. Golshan-Shirazi and G. Guiochon, /. Chromatogr., 517 (1990) 229 (Figs. 3 to 5).

Knowing dp, it is easy to derive the length of the column for which N is maximmn. As there are usually several size grades of the selected stationary phase, it is possible to choose the particle size that gives the best possible efficiency. The column design is then optimized, and the optrmiun velocity is the one achieved when the column is operated imder the maximum pressure available. The optimum sample size is then easily derived by a simple series of experiments. 

The choice of sample size or bed size in preparative separations deserves as much attention as any other separation variable. Too large a sample for a bed of given size may lead to incomplete separation [e.g.. Fig. 4-1 (d)]. Too small a sample (or rather, too large a bed) frequently means a separation which requires more time, effort, and materials than is necessary. The optimum sample size in preparative separations (at least for sample sizes above 0.1 g) corresponds to the minimum adsorbent/sample ratio which yields adequate separation it is a complex function of separation conditions and of sample type. Samples of less than 0.1 g are commonly separated by thin-layer chromatography, while samples weighing more than 1 g are usually separated on columns. Loose-layer chromatography has been recommended for intermediate sample sizes (JO). As much as 100 g of sample have been separated by means of thin-layer chromatography (i/), but moderately difficult separations by this technique are normally limited to sample sizes of less than 1 g. 

Exploratory thin-layer separations are commonly used as guides in selecting the best separation conditions for corresponding preparative scale separations on columns. In this connection it should be possible to establish optimum sample size as well, using thin-layer chromatography. 

There is no single optimum sample size. Some general guidelines are available, however. Table 2.1 lists typical sample sizes for three types of columns. For the best peak shape and maximum resolution, the smallest possible sample size should always be used. 

Figure 14.5 Plot of the optimum velocity for minimum SLT vs. the concentration step height. Curves derived from Eq. 14.40. Curve 1, conditions used for Figure 14.4. Curve 2, experimental conditions 5 cm long home packed column mobile phase 50 50 methanol-water, sample 4-tert-butylphenol (kg = 10), sample size 0.2 fig. Symbols optimum velocity under linear conditions. Reproduced with permission from J. Zhu, Z. Ma and G. Guiochon, Biotechnol. Progr., 9 (1993) 421 (Fig. 8). 1993, American Chemical Society.

In the former case [32], the production rate of 99% pme enantiomers from the racemic mixture of R- and S-2-phenylbutyric acid was maximized as a function of the sample size and the mobile phase composition. The calculations were based on the column performance and the equilibrium isotherms of the two components (bi-Langmuir isotherms. Chapter 3). The separation was performed on immobilized bovine serum albumin, a chiral stationary phase, using water-methanol solution as the mobile phase. The retention times decrease with increasing methanol content, but so does the separation factor. For this reason, the optimum retention factor is around 3. Calculated production rates agree well with those measured (Table 18.4). The recovery yield is lower than predicted. 

Figure 18.29 Plot of the maximum production rate of the two components versus the retention factor of the first eluted one. Separation factor, a. = 1.5. All symbols correspond to the production rate of the optimum column, operated at the optimum velocity and sample size. Curve 1, first component, elution. Curve 2, second component, elution. Curve 3, first component, displacement. Curve 4, second component, displacement, (a) Feed composition 3 1. (b) Feed composition 1 3. Reproduced with permission ofWiley-Liss Inc., a subsidiary of John Wiley Sons, Inc. from A. Felinger and G. Guiochon, Biotechnol. Bioeng., 41 (1993) 134 (Fig. 4). (g)1993, John Wiley Sons.

The optimum use of SPE procedures requires investigation of different stationary phases, their masses, the volume of conditioning, sample load, wash, elution solvents, and the sample size. These variables are readily studied in column format. But it is costly or inconvenierit to use only a fraction of the 96 wells to perform all the studies. Hence, modular well plates have been developed that have small removable plastic SPE cartridges that fit tightly in the 96-hole base plate, and only a portion needs to be used to develop a method. 

For optimum performance the sample size should be such that only the first theoretical plate in the column is saturated. Since a theoretical plate has a very small capacity large samples will overload the column. The optimum size is that which gives the sharpest symmetrical peaks with adequate sensitivity. The limit is thus a function of column capacity and detector performance. 

The production rate in the elution mode increases with increasing volume and/or concentration of the sample injected on the column [66,67]. Since the bandwidth of all components increases in both cases, there is a limit to the sample size that can be used effectively. When the sample size increases from the very low levels typically used in analytical applications, the recovery yield remains constant, and the production rate increases linearly with increasing sample size. When the band of the compound of interest touches its neighbor, the recovery yield starts to decline with increasing sample size, since the wings of the elution band must be clipped to eUminate contamination. Eventually, a maximum value for the production rate is reached, but since the separation is carried out under nonlinear conditions, optimum separation conditions are no longer predictable from data obtained under analytical conditions. 

The cost of any chromatographic separation is indemnified in two currencies, pressure and time. In general, the highest pressure that is usable (normally determined by the life expectancy of the sample valve or, under some circumstances, the pump) determines the smdlest particle diameter that can be used. In fact, for a given maximum available (or usable) inlet pressure, there will be an optimum particle size that will achieve a given separation in the minimum time. A discussion of this aspect of column optimization is outside the scope of this book, but details are given elsewhere [1]. 

Sample size is defined by both the volume of the aliquot injected as well as by the concentration of the sample solution. Use of excessively large sample volumes can lead to significant band broadening, resulting in loss of resolution and errors in molecular weight measurement. As a rule of thumb, sample volumes should be limited to one-third or less of the baseline volume of a monomer or solvent peak measured with a small sample (10). The optimum injection volume is a function of the size and number of the columns employed but generally ranges between 25 and 200 j,l. 

Injection System— The chromatograph should be equipped with a splitting-type inlet device if capillary columns or flame ionization detection are used. Split injection is necessary to maintain the actual chromatographed sample size within the limits of column and detector optimum efficiency and linearity. 

Some gas chromatographs are equipped with on-column injectors and autosamplers which can inject small samples sizes. Such injection systems can be used provided that sample size is within the limit of the column and detectors optimum efficiency and linearity. 

The smallest size difference that can be resolved is related to the pore volume, the solute shape, and the efficiency of the column (see Fig. 2.6). However, this is at very low loadings. At higher loadings the sample volume will contribute to zone broadening and may, in some cases, be the dominating factor for resolution. Thus, for fractionation, an optimum exists with respect to column efficiency (represented by the flow rate as operational parameter) and sample volume for processing a particular volume of feed per unit time. As a rule of thumb this optimum can be found at a relative sample volume of 2-5% of the column volume (Hagel et al., 1989). 

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