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Chromatography Today Help Desk Capillary Columns and Dispersion
In March the Chromatographic Ssociety celebrated its 60th anniversary at the Institute for Electrical Technology in London. The theme for the meeting was capillary chromatography and this prompted the Chromatography Today help desk to think about the issues that we have seen when moving to very narrow column diameters.
A common problem, experienced by many chromatographers as they start in the field of capillary chromatography, is the sudden importance of the dispersion effect within the chromatographic system. This is highlighted as the column diameter is decreased from the traditionally used size of 4.6 mm to the significantly smaller sub 1 mm i.d. dimension. So why is this the case? In this issue the help desk investigates why changing diameter of the column affects the apparent efficiency of the column, and what steps can be taken to avoid this.
In order to properly evaluate the impact of dispersion on efficiency, one common misconception much be clarified. It is generally the chromatographic efficiency of the whole HPLC system that is measured and not just the HPLC column. When larger id columns such as the traditional 4.6 mm i.d. size are used, their void volumes are smaller than the extra column volume of the chromatographic system. When the size of the column is decreased to 1 mm .i.d., however, the extra column volume becomes larger relative to the dispersive contribution from the column and the impact of the dispersion is much more apparent.
The rationale for this occurrence is that within the fluidic pathways there are random dispersion processes, due to molecular diffusion occurring that cause an increase in the peak width under both isocratic and gradient conditions resulting in a reduction in the performance of the separation. This dispersion is due to the random nature of movement of small molecules, and even though there is a general direction to the flow of the mobile phase, this random nature of dispersion will result in elements of the mobile phase moving at different linear velocities through the fluidic pathways.
All molecules will have a degree of energy that can be utilised for movement within the space that they occupy. When looking at a large number of molecules there is a tendency for the molecules to preferentially move from areas of high concentration to areas of lower concentration. This can be summarised by Fick’s first and second laws of diffusion [1], relating to spatial and temporal concentration variations, which are given by;
• The concentration of the solute is very dilute • The solute molecules do not interact with each other • There are no interactions with a container of any description
In a standard chromatography environment, the first of these two assumptions are valid. However, it is very evident that there will be a wall effect observed which will alter the effective dispersion processes within the tubing. Thus, it must be considered that when the diffusion in the mobile phase is contained in a fluidic pathway, the result will be in drag at the surfaces causing a parabolic flow profile across the tube, comparable to a bowl. Improving the radial movement of molecules will reduce this issue, as will reducing the diameter of the tubing, however for common connector dimensions the radial dispersion does not overcome the parabolic flow profile associated with the flow rates found in capillary HPLC. As a consequence of this effect increases in the flow rate will result in a greater variance, due to the frictional effects of the surface of the tubing being greater than the relative reduction in retention time within a capillary at the typical flow rates observed in capillary systems. This is typically measured by a parameter referred to as the variance.
The variance measures the amount of peak broadening and is the standard measure of how much dispersion there is within a chromatographic system. The smaller the variance, the less dispersion there will be. The degree of diffusion or dispersion has been effectively modelled by Aris and Taylor [2] resulting in this equation for a laminar flow system.
Where Deff
is the effective dispersion coefficient
U is the average linear velocity r is the internal radius of the connector D is the measured dispersion coefficient
The important parameters to consider that will affect the dispersion rate are;
Viscosity of mobile phase These models do rely on a couple of assumptions though;
The mobile phase can have an effect on the dispersion processes, with the viscosity of the mobile phase being the most predominant parameter which will affect the dispersion. Thus, if a mobile phase is more viscous there is a tendency for the diffusion of the analyte to be less than that if the analyte were in a less viscous mobile phase. The change in the viscosity can be caused by a range of external effects, however the buffer concentration and also the temperature are the parameters which will have the greatest effect on the viscosity.
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