Column maximum sample volume

Practical data for both the columns (Superose 5 and 12) have been announced by the supplier as follows maximum loading capacity, 5-10 mg-protein/column maximum sample volume, 200-300 pg-, maximum sample concentration, 30 mg/mL. Also the pore volumes ( of column volumes) have been determined to be 60 and 55 for Superose 6 and 12, respectively. Total protein and enzyme recoveries announced by the supplier are 90-100 % and 80 % for Superose 6 and 12, respectively. 

Maximum Sample Volume that Can Be Placed on a Chromatographic Column... 

Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

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, the maximum sample volume (Vi) that can be placed on the column that would restrict the increase to less than 5% has been shown to be. 

The effect of sample volume on peak width has been considered and treated theoretically in Chapter 6 however, it is of interest to determine the maximum sample volume that can be tolerated with modern columns packed with small particles. The maximum sample volume is defined by the following equation,... 

Equation (5) was used to calculate the maximum sample volume for a series of columns having different lengths and internal diameters and packed with particles 3 p... 

Figure 1. Curves Relating Maximum Sample Volume to Column Diameter for Columns of Different Length Packed with Particles 3 p in...

It is seen that columns having diameters less than 2 mm will only tolerate a maximum sample volume of a fraction of a microliter. Although larger volume valves can be used to inject sample volumes of this size, the dispersion from the valve is still likely... 

The use of 5 pm particles permits the use of much longer columns due to the increased permeability. This, in turn, permits the use of much larger sample volumes. In fact, for a column 20 cm long, eluting a solute at a (k ) of 5, the maximum sample volume that can be used without increasing the peak variance by more than 10% will... 

Extra-column dispersion can arise in the sample valve, unions, frits, connecting tubing, and the sensor cell of the detector. The maximum sample volume, i.e., that volume that contributes less than 10% to the column variance, is determined by the type of column, dimensions of the column and the chromatographic characteristics of the solute. In practice, the majority of the permitted extra-column dispersion should... 

There remains the need to obtain expressions for the optimum column radius (r(opt)), the optimum flow rate (Q(opt)), the maximum solvent consumption (S(sol)) and the maximum sample volume (v(sam))-... 

Maximum Sample Volume and Maximum Extra-Column Dispersion... 

In a packed column the HETP depends on the particle diameter and is not related to the column radius. As a result, an expression for the optimum particle diameter is independently derived, and then the column radius determined from the extracolumn dispersion. This is not true for the open tubular column, as the HETP is determined by the column radius. It follows that a converse procedure must be employed. Firstly the optimum column radius is determined and then the maximum extra-column dispersion that the column can tolerate calculated. Thus, with open tubular columns, the chromatographic system, in particular the detector dispersion and the maximum sample volume, is dictated by the column design which, in turn, is governed by the nature of the separation. 

TABLE 7.1 Recommended Maximum Sample Volumes for Different SEC Column Dimensions... 

Column dimension Bed height (cm) Maximum sample volume (mi)... 

Before progressing to the Rate Theory Equation, an interesting and practical example of the use of the summation of variances is the determination of the maximum sample volume that can be placed on a column. This is important because excessive sample volume broadens the peak and reduces the resolution. It is therefore important to be able to choose a sample volume that is as large as possible to provide maximum sensitivity but, at the same time insufficient, to affect the overall resolution. 

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 efficiency of the column. However, a sample does not consist of a single component, and it is therefore important that the resolution of any solute, irrespective of where it is eluted, is not... 

Now the total volume (Vc) of a column radius (r) and length (1) will be nr l. Furthermore, the volume occupied by the mobile phase will be approximately 0.6Vc (60% of the total column volume is occupied by mobile phase).Thus as a general rule the maximum sample volume that can be employed without degrading the resolution of the column is... 

The analyst can calculate the maximum sample volume (Vi) in a simple manner from the efficiency of a peak eluted close to the dead volume and the dimensions of the column. 

Unfortunately, the magnitude of the variance contribution from each source will be different and the ultimate minimum size of each is often dictated by the limitations in the physical construction of of the different parts of the apparatus and consequently not controllable. It follows that equipartition of the permitted extra column dispersion is not possible. It will be seen later that the the maximum sample volume provides the maximum chromatographic mass and concentration sensitivity. Consequently, all other sources of dispersion must be kept to the absolute minimum to allow as large a sample volume as possible to be placed on the column without exceeding the permitted limit. At the same time it must be stressed, that all the permitted extra column dispersion can not be allotted solely to the sample volume. 

It is seen from equation (34) that for a fully optimized column the maximum sample volume depends solely on the extra column dispersion (oe) This again emphasizes the importance of not only using equipment with low extra column dispersion but, also, knowing the value of (oe) for the particular chromatograph being used. 

The curves in figure (5) show the relationship between maximum sample volume and the separation ratio of the critical pair for a fully optimized column and were obtained using equation (20) The curves give the first, indication of the limitations of open tubular columns in LC and the reason why they have not achieved the popularity and success of the packed column... 

The properties of open tubular columns shown in figures (I) to (6) indicate that the areas where such columns would have practical use is very restricted. At pressures in excess of 10 ps.i., and whatever the nature of the separation, whether simple or difficult, the optimum column diameters are so small that they would be exceedingly difficult to fabricate or coat with stationary phase. The maximum sample volumes and extra column dispersion that couid be tolerated would also be well below that physically possible at this time. At relatively low pressures, that Is at pressures less than 10 p.s.l. the diameter of the optimum column is large enough to fabricate and coat with stationary phase providing the separations required are difficult i.c. the separation ratio of the critical pair must be less than 1.03. However, even under these conditions the sample volume will be extremely small, the extra column dispersion restricted to an almost impossibly low limit and the analysis time would be very long Nevertheless, open tubular columns used for very difficult separations... 

It Is seen from equation (9) that the maximum sample volume depends on the square of the radius and inversely on the square root of the column inlet pressure. Now, although (r) and (P) are not mathematically interdependent, there is a practical dependance of (r) on (P). The column must, physically, be able to withstand the the pressure (P) and thus, the column walls must be sufficiently thick to accommodate the pressure for any given radius (r). The aspect of column strength, and weight will be discussed further in due course. Now, if the mass of the selected solute that is required per separation is (M) and is placed on the column in the maximum permissible sample volume (Vj),... 

What happens when the sample injection volume constraint is removed Calculations can be made from the data presented by Cooke et al. (25). For these calculations, the data required is that relating to the maximum sample volumes that can be injected on the various columns while a given number of theoretical plates is maintained. This data, shown in Table IV, was calculated by using eq 3 ... 

By assuming that a proportional increase in the amount of sample injected results in a proportional increase in the detector response for the solute band of interest, the detector response for chromatogram I in Figure 7 will increase 14 times when the maximum sample volume of 7 /xL is injected. However, for the 4.6-mm i.d. column, the detector response will increase 400 times when the maximum sample volume of 200 (lL is injected. By taking into account the relative detector responses for the 0.5-/xL injection, at the maximum sample injection volumes, the 4.6-mm i.d. column with the 20-/liL detector flow cell will produce approximately five times the detector response of the 1-mm i.d. column with the 5-/zL flow cell. In most cases, studies can be designed to provide excess sample because aqueous environmental samples are seldom limited with respect to volume. 

Additionally, the combination of trace enrichment and microbore columns can effectively increase the maximum sample volume injectable without seriously degrading efficiency. Slais et al. (29) evaluated this combination for the determination of polynuclear hydrocarbons and chlorinated phenols in water. By using reversed-phase HPLC and am-perometric detection, Slais et al. (29) reported lower limits of detection from 20 to 280 ng/L of water (parts per trillion) when 1-mL sample enrichments were carried out directly on the analytical microbore column. 

The concept of maximum sample volume as it relates to miniaturization can be illustrated as follows, assuming that both a conventional analytical column (4.6 mm I.D.) and a narrow-bore column (2 mm I.D.) have equal efficiency, length, and porosity. To switch a method from the analytical column to the narrow-bore column and still maintain optimum performance on the narrow-bore column, Eq. (8.1) may be rewritten as... 

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