Thorsten Teutenberg1, Terence Hetzel1, Denise Loeker1, Juri Leonhardt1
There are several strategies that can be used when we’re looking for a solution to a chromatographic separation problem. The Purnell-equation, often called the “Master Equation” of chromatography, specifies the parameters for the targeted optimization of the chromatographic resolution [1, 2].
By means of this equation, it is clear that three strategies exist for obtaining a separation with sufficient resolution R. These are the increase in selectivity α, the efficiency with respect to the number of theoretical plates N and the retention using the retention factor k. The aim is usually a minimum resolution of 1.5, so that a baseline separation can be obtained. Figure 1 shows the resolution plotted against the three variables α, k and N.
To achieve a separation, a sufficient retention is necessary.
However, retention factors of > 5 do not lead to a significant increase in the resolution. With this in mind, the elution strenght of the mobile phase should be adjusted to achieve a retention factor between 2 and 10. Retention factors of > 10 only lead to an increase in the analysis time and no significant impact on the resolution can be observed. The following theoretical example shows that the retention factor as a dimensionless quantity says nothing about the actual analysis time and that short analysis times are possible despite higher retention factors. If the column void time (t0) is one minute and the retention factor is 10, this equals a retention time (tR) of the component of
11 minutes – as can be seen when using of the following equation:
If, for example, the retention factor increases to 50 but the flow rate is not changed, the resulting retention time is 51 minutes. However, if it is possible to reduce the column void time to for example 6 seconds, the resulting retention time would only be 5.1 minutes even for a retention factor for 50.
Flow Rate and Linear Velocity
Minimizing the column void time can be achieved in two ways. If the inner diameter of the column remains constant, the absolute flow rate needs to be increased in order to increase the linear velocity (u0) of the mobile phase – this can be calculated using the following equation:
However, using a constant flow rate, the inner diameter of the column can also be decreased so that a higher linear velocity can be achieved. This, by the way, is one of the great advantages of Micro-LC. As can be seen in figure 2, due to the combination of a small diameter of 300 µm for Micro-LC columns and relatively low absolute flow rates of around 40 μL min-1, very high linear velocities can be achieved. The inner diameter of the column is plotted against the linear velocity (left y-axis) using the given flow rate or rather against the absolute flow rate (right y-axis) using the given linear velocity. Using the plotted data, it can be seen that at a constant absolute flow rate of 40 μL min-1, the linear velocity increases from 0.058 mm s-1 to 13.6 mm s-1 if the inner diameter is reduced from 4.6 mm to 300 μm. Based on a constant linear velocity of 13.6 mm s-1, the absolute flow rate increases from
40 μL min-1 up to 9.4 mL min-1 when the column inner diameter is increased from 300 μm to 4.6 mm. So when using the conventional column formats the absolute flow rate has to be drastically increased to achieve analysis times comparable to Micro-LC. This inevitably leads to a very high consumption of expensive and toxic solvents.
The question that then arises is, “What will be the loss in separation efficiency if such high linear velocities are used?” The data in figure 3 provide information on this. Here, the plate height H is plotted against the linear velocity u0 for different stationary phases.
It can be clearly seen that the increase in the C-term of the van-Deemter curve can be regarded as negligible when using either completely porous particles with a diameter of 1.9 µm or a core shell material with a diameter of 2.7 µm. In contrast, the sharper increase in the C-term for the monolithic phase and 3 µm porous particle packed column leads to an increase in the theoretical plate height and therefore a significant decrease in the number of theoretical plates N. Therefore, sub 2 µm particles should be used for fast analysis. Using the Master Equation for the resolution it is clear that the increase in the number of theoretical plates also leads to an improvement in the resolution, although the resolution only increases in proportion to the square root of N. Therefore, doubling the number of plates only results in a factor of 1.4. This means that for the targeted optimization of the resolution for a single peak pair, the selectivity of the phase system can be accepted as the key parameter. Relatively small changes in the α-values lead to considerable changes in the resolution, as shown in figure 1.
Selectivity is defined as the quotient of the retention factor of the component that elutes later to the retention factor of the component that elutes earlier:
If a component elutes at a k1-value of 2 and the second component at a k2-value of 12, the resulting α-value is 6. If the k2-value is 50 and the k1-value 40, the same difference in the k-value only leads to an α-value of 1.25. On the basis of this example it becomes impressively apparent that high k-values are not advantageous when the goal is to increase the selectivity and therefore the resolution of a single critical peak pair.
On a critical note, the concept presented here is only valid for isocratic separations. Furthermore, the focus is on only one single peak pair and the optimization of its separation. Having said that, the separation of a two component mixture cannot be described as complex. In the field of Life Sciences, the challenge nowadays, is to separate mixtures containing over 10,000 individual compounds. With such a high number of compounds, co-elution is unavoidable. The fact that a complete baseline separation of “only” 50 compounds in a chromatographic run represents a significant challenge is clear in the following example calculation that dates back to Calvin C. Giddings’ reflections in 1983 .
Giddings asked himself the question, how high the probability is to completely separate a mixture of m-components on an HPLC-column with a given peak capacity. So, if the sample consisted of 50 substances and the separation were to be carried out on a column with a peak capacity of 100, then 32 of the 50 compounds would co-elute. Only 18 peaks actually consisted of one compound. This results in the strategy that with complex samples the efficiency should be maximized rather than the selectivity. The large differences in the polarity of the compounds rules out isocratic elution. Therefore, instead of considering N the number of plates for isocratic separation, one has to consider nc, the peak capacity for gradient separations. In the next article we will therefore be describing the strategy for maximizing the peak capacity on the basis of one and two-dimensional separations.
Do you have questions regarding the application and technology in the field of Micro-LC and 2D-LC? Ask the experts at IUTA under: email@example.com
1Institute for Energy and Environmental Technology e. V., IUTA, Duisburg, Germany
Dr. Thorsten Teutenberg
Institute for Energy and Environmental Technology e. V. (IUTA)
Department Head Research Analysis
Project “Advanced Liquid Chromatography”: http://www.laboratory-journal.com/advanced-liquid-chromatography
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