Columns maximum efficiency

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. 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

It is seen that by a simple curve fitting process, the individual contributions to the total variance per unit length can be easily extracted. It is also seen that there is minimum value for the HETP at a particular velocity. Thus, the maximum number of theoretical plates obtainable from a given column (the maximum efficiency) can only be obtained by operating at the optimum mobile phase velocity. 

Thus, for significant values of (k") (unity or greater) the optimum mobile phase velocity is controlled primarily by the ratio of the solute diffusivity to the column radius and, secondly, by the thermodynamic properties of the distribution system. However, the minimum value of (H) (and, thus, the maximum column efficiency) is determined primarily by the column radius, secondly by the thermodynamic properties of the distribution system and is independent of solute diffusivity. It follows that for all types of columns, increasing the temperature increases the diffusivity of the solute in both phases and, thus, increases the optimum flow rate and reduces the analysis time. Temperature, however, will only affect (Hmin) insomuch as it affects the magnitude of (k"). 

For example, a 30-m column (regardless of diameter) should have a tR for argon or butane of approximately 100 sec. It appears better to set the linear velocity higher than the optimum rather than lower than the optimum to obtain good column efficiency. Determine the column temperature where the most difficult-to-separate compounds elute and set the linear velocity at that temperature. Now the column will exhibit its maximum resolving power at the point where it is needed most. 

As already stated any sample placed on a column will have a finite volume, and the variance of the injected sample will contribute directly to the final peak variance. It follows that the maximum volume of sample that can be placed on the column must be limited, or the column efficiency will be seriously reduced. Consider a volume Vi, injected onto a column. Normal LC injections will start initially as a rectangular distribution and the variance of the eluted peak will be the sum of the variances of the injected sample plus the normal variance of the eluted peak. 

The curve exhibits a minimum, which means that there is an optimum mobile phase velocity at which the column will give the minimum HETP and consequently a maximum efficiency. In practice this usually means that reducing the flow rate of a column will increase the efficiency and thus the resolution. In doing so, however, the analysis time will also be increased. As seen in figure 5, however, there is a limit to this procedure, as reducing the column flow rate so that the mobile phase velocity falls below the optimum will result in an increase in the HETP and thus a decrease in column efficiency. 

It is interesting to ascertain the effect of temperature at the optimum velocity where the value of (H) is a minimum and the column efficiency a maximum. 

It is seen that when operating at the optimum velocity that provides the minimum value of (H) and thus, the maximum efficiency, solute diffusivity has no effect on solute dispersion and consequently, the column efficiency is independent of temperature. 

The peak volume is directly proportional to the square of the column diameter and the column length and decreases with Increasing column efficiency (decreases for smaller particle packings). The concentration at the peak maximum, C—, is given by... 

The quantity H (equal to L/N) measures the efficiency of a given column (operated under a specific set of operating conditions) per unit length of the column (see van Deemter s equation in Chapter 14). Small H values mean more efficient columns and large N values. A very important goal in HPLC is to attain small H values that lead to maximum N and highest column efficiencies. 

Overloading effects seem even more complex at intermediate pH because silan-ols are now partially ionized and involved in the retention of bases. As mentioned previously, the overload of now-ionized silanols could at least be part of the cause of tailing peaks, even when very small amounts of ionized base are used [18,24]. However, it has been observed that as solute mass increases in experiments at pH 7, column efficiency may improve from an initially low value to a maximum, afterward declining in the usual way [33]. This observation could be due to the blocking or saffiration of ionized silanols by a portion of the sample, such that the rest interacts mainly by hydrophobic processes, resulting in better efficiency. At higher pH still, the solute should not be ionized if appreciably above its p a and therefore should... 

Equations (67) and (68) show that the efficient columns available today tolerate much smaller sample sizes than the columns used a few years ago. Wlicicua lui culuiiiiis With t>p - 25 fiin, h = 5, and /V - 200U tlic maximum permissible sample volume Vs,m is about 60 /xl. tne microparticulate columns can accept samples of only a few microliters without deterioration of the intrinsic column efficiency. 

This number, which is also called peak capacity, is inhni e n theory, but Jimiied in practice. Time considerations require that k noii exceed a certain limit, which in fact decreases when the column efficiency increases, because should not exceed a few hours except in very social circumstances. The maximum peak number is also limited by the fact that with increasing retention the width and height of the peak inpi ases dnd decreases, respectively. As a consequence of the limitations oil sample size, peaks whose maximum concentration at the column outlet is lower than the detection limits remain unnoticed. 

Primarily the Plate Theory provides the equation for the elution curve of a solute. Such an equation describes the concentration of a solute leaving a column, in terms of the volume of mobile phase that has passed through it. It is from this equation, that the various characteristics of a chromatographic system can be determined using the data that is provided by the chromatogram. The Plate Theory, for example, will provide an equation for the retention volume of a solute, show how the column efficiency can be calculated, determine the maximum volume of charge that can be placed on the column and permit the calculation of the number of theoretical plates required to effect a given separation. 

It is seen that the that the maximum sample volume that can be tolerated can be calculated from the retention volume of the solute concerned and the the efficiency of the column. A knowledge of the maximum sample volume that can be place on a column is important where the column efficiency available is only just adequate and the compounds of interest are minor components of the mixture to be analyzed and are only partly resolved. 

The time taken to achieve these efficiencies when eluting the last peak at a k value of 10 can be calculated employing equation (18). The results obtained are shown in figure 4 where the elution time obtained from columns of maximum efficiency are plotted against particle diameter. 

The analytical specifications must prescribe the ultimate performance of the total chromatographic system, in appropriate numerical values, to demonstrate the performance that has been achieved. The separation of the critical pair would require a minimum column efficiency and the number of theoretical plated produced by the column should be reported. The second most important requisite is that the analysis should be achieved in the minimum time and thus the analysis time should also be given. The analyst will also want to know the maximum volume of charge that can be placed on the column, the solvent consumption per analysis, the mass sensitivity and finally the total peak capacity of the chromatogram. The analytical specifications can be summarized as follows. 

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