15 Classically the optimum flow rate is given by the differential of the van Deemter equation;
Resulting in;
Equation 3. Optimal flow rate equation
It should be noted that the assumption here is that the ‘A’ term is flow independent, which is generally agreed not to be the case [10-13] for the more developed models of dispersion within a packed bed. However this simple treatment will allow for an understanding of how temperature affects the optimal flow rate and also how it affects the band dispersion process.
Figure 1. Variation of viscosity with temperature
Equation 4. Variation of the optimal flow rate as a function of temperature
Plotting vopt as a function of temperature will show the dependency of the optimal flow rate (where the minimum dispersion is seen) with the operating temperature. Figure 1 shows this plot and Figure 2 shows, schematically, the effect of changing the temperature on the optimal flow using this model. It can be seen from both figures that increasing the temperature results in the optimal flow rate increasing, and Figure 2 demonstrates that by increasing the flow rate the ‘C’ term dependency reduces. As a result the separation scientist is able to operate at flow rates higher than the optimal flow without a substantial loss in column performance.
Column Stability
An issue that needs to be discussed is the stability of silica based columns at extreme temperatures. Certainly most bonded silica is not stable [14, 15] and peak deterioration and retention time shift can be expected when running at temperatures above 60°C as demonstrated by Figure 3.
However, there are mechanisms by which silica-based stationary phases can be modified to increase thermal stability:
• use of a more stable ligand binding [16] • use of hybrid phases [17] • encapsulation of the silica [18]
Other phases are available which will also offer thermal stability when compared to traditional silica phases, these include, alumina [19,20], zirconia [21,22] and finally porous graphitic carbon [23-25]. The most interesting of these phases is the porous graphitic carbon phase [23] which is very stable to extremes of operating temperature and pH, with part of the manufacturing involving heating the material to temperatures in excess of 2000°C (although in an inert environment).
Figure 3b shows how the choice of a suitable stationary phase can be beneficial. In this example, the performance of the column was measured at the start of a high temperature investigation and at the end, after 6 weeks, where the column was operated at up to 200°C [26]. It can be seen that the two test chromatograms, taken at the start and the end of the six week test period, are virtually identical, with the efficiency of the last peak decreasing by less than 10%.
Compound Stability
Compound stability has often been proposed as a reason not to use elevated temperatures in liquid chromatography. Indeed, there are many examples of compounds which are not stable at elevated temperatures [27-30] and the use of elevated temperatures over long periods of time is clearly not advantageous for compound stability. However, this statement needs to be investigated in more detail, since many compounds that are thermally labile do actually require some time to decompose and also the environment that they are in will also affect the rate of decomposition.
Figure 4 demonstrates that it is a combination of time and temperature which cause compounds to thermally degrade. Thus in the first chromatogram the temperature used is lower than in the second, but the compound takes longer to elute which results in more degradation than compared to the elevated temperatures used in the second separation. Thus, by careful manipulation of the temperature it is possible to overcome some of the issues associated with thermal instability.
Figure 3b. Hypercarb column stability under high temperature conditions. Before and after 6 weeks of use at high temperatures. Column: Hypercarb 5 µm, 100x4.6mm; mobile phase: MeOH/H2O (95:5, v/v); flow rate: 0.8mL/min; detection: UV@254nm; analytes: 1) acetone; 2) phenol; 3) p-cresol; 4) 3,5-xylenol..
Figure 2. Plot of HETP vs the linear velocity, showing the effect that varying the temperature has on the plot, with the optimal flow rate increasing, and the flatter curve at higher temperatures.
Figure 3a. After 6 hours at 60°C the column exhibits extreme tailing effects and increased peak width using the Pursuit XRs Ultra column.
INTERNATIONAL LABMATE - JANUARY/FEBRUARY 2013
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