## Wednesday, 2 September 2009

### What is HPLC column efficiency?

PEAK SOLUTIONS
A resource for chromatographers
Column efficiency, also known as plate count, is a measure of the dispersion of a peak. Narrow peaks take up less space in the chromatogram and thus allow more peaks to be separated. They are also easier to integrate since they give better resolution and less overlapping. Efficiency is usually explained using the concept of theoretical plates. This model supposes that the column contains a large number of separate layers. Separate equilibrations of the sample between the stationary and mobile phase occur in these plates. The analyte moves down the column by transfer of equilibrated mobile phase from one plate to the next. It is important to remember that the plates do not actually exist, they are a means to help understand the process at work in the column. They also give a measure of column efficiency by stating the number of theoretical plates in a column, N. A high value for efficiency indicates that more peaks can be separated. The number of plates will increase with the length of the column. The calculation for efficiency is related to the peak width and is as follows:

where t is the retention time of the peak of interest and W is the peak width at the base (as shown in Figure 1).
Figure 1
Similar to the measurement for resolution, the measurement for efficiency may also be performed using the peak width at half height:

where Wh/2 is the peak width as half height. It can be seen that N is related to the analyte peak and thus the column behaves as if there are different numbers of plates for each solute in a mixture. When the peak width increases resulting in broad peaks, it is due to band broadening. There are a number of different reasons for band broadening:

1. The path taken by the analyte molecules through the column varies due to chance. Some molecules will travel in a fairly straight line whereas others will undergo several diversions. The effect of this is that not all the molecules will elute at the end of the column at exactly the same time.
2. Sample molecules in a solvent will spread out without any external influence due to molecular diffusion.
3. Analyte molecules travel from the moving mobile phase to the surface of the particle, through stagnant mobile phase in the pores to the internal surface on the packing. It interacts with the stationary phase and then is transported back to the moving mobile phase. This process is referred to as mass transfer and not all molecules will experience mass transfer in an identical way therefore band broadening will occur.
4. The mobile phase travels in a laminar flow between the stationary phase particles, the flow being faster in the centre than near a particle. Thus some molecules travel more quickly than others. This flow distribution is reduced by ensuring that the particles in the packing have a narrow particle size distribution.
5. The tubing in the HPLC instrumentation contributes to band broadening, this is known as the extra-column effect.

HPLC columns which contain packing of smaller particle sizes give better efficiency because the diffusion paths are shorter allowing solutes to transfer in and out of the particle more quickly and thus reducing band broadening.

A typical acceptance criterion for efficiency would be > 2000. Although the value for new columns would usually be very much higher than this (values in the tens of thousands) the system suitability acceptance should be based on a value which indicates that the efficiency is no longer sufficient for the separation. These calculations only apply to isocratic separations. For gradient methods the peak width remains fairly constant throughout the run due to the changing mobile phase composition and therefore the value for N would appear to increase with retention time. A more useful measure of the column efficiency would be the peak width at half height for the analyte. Monitoring this value could provide a measure of when the column efficiency is no longer sufficient for the separation. Resolution depends indirectly on efficiency and therefore if resolution is a parameter in the system suitability test then a measure of efficiency is already included.

The calculation for efficiency using the peak width at half height is common to the USP, EP and JP although the terminology and notations used are not identical. However, due to a slight difference in rounding, the constant in the equation is 5.54 in the USP and EP but is 5.55 in the JP.

This blog post is an excerpt from 'An Introduction to HPLC for Pharmaceutical Analysis' by Oona McPolin, available to purchase through the MTS website.

#### 1 comment:

1. So for gradient is measurement at half height appropriate?