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How are column efficiency, peak asymmetry factor, tailing factor and resolution calculated?
How are column efficiency, peak asymmetry factor, tailing factor and resolution calculated?
#Asymmetry ; #Column efficiency.
Column efficiency calculation:
Column efficiency calculation:
Column efficiency, indicated as the number of theoretical plates per column, is calculated as N = 5.54 (tR / w0.5)2 where tR is the retention time of the analyte of interest and w0.5 the width of the peak at half height.
This half-height method enables the determination of the number of theoretical plates per column (N) even if the peak is not fully separated from a neighbouring peak (poor resolution), as long as the valley between the peaks is lower than the half-height of the peak. Half-height measurements commonly is the method of choice for automatic determination by data systems.
The larger the number of theoretical plates per column, the sharper the peak! Should you need to calculate the number of theoretical plates per meter, you must use the following equation:
Number of theoretical plates per column x 100/length of HPLC column (cm)= Number of theoretical Plates per m
Peak Asymmetry Factor:
Peak Asymmetry Factor:
Peak Asymmetry Factor, often presented as As is calculated with the following equation As = b/a where b is the distance from the peak midpoint (perpendicular from the peak highest point) to the trailing edge of the peak measured at 10% of peak height and a is the distance from the leading edge of the peak to the peak midpoint (perpendicular from the peak highest point) measured at 10% of peak height. If As > 1 : tailing, et si As < 1 : fronting.
Tailing Factor:
Tailing Factor:
Tailing Factor (Tf) is the USP coefficient of the peak symmetry. It is calculated using the following equation: Tf = (a+b)/2a where a is the distance from the leading edge of the peak to the peak midpoint (perpendicular from the peak highest point) measured at 5% of peak height and b is the distance from the peak midpoint (perpendicular from the peak highest point) to the trailing edge of the peak measured at 5% of peak height.
Resolution:
Resolution:
Resolution (Rs) is a measure of the separation quality. In order to determine the resolution between 2 peaks we need to measure the retention times of the 2 peaks of interest (tr2 and tr1) and the width of the 2 peaks at baseline (w1 and w2) between tangents drawn to the sides of the peaks. It is normally calculated as:
Rss = (tr2 – tr1) / ((0.5 * (w1 + w2)
Since nearly every peak shows some degree of tailing, so to allow for a small amount of tailing and still retain a bit of flat baseline between the peaks, Rs ≥ 2.0 generally is desired for proper resolution between 2 peaks of interest.
This equation is extremely convenient and gives good results for peak resolution calculations, but it is only useful when the peaks are resolved at baseline level. However, we are often confronted to situation where peaks are marginally separated. Peaks overlap at the bottom, and measurement of the peak width at baseline is virtually impossible.
In these cases, just like we measured the efficiency at mid peak height, the same approach can be used for the calculation of the resolution with the following equation:
Rs = (tR2 – tR1) / ((1.7 * 0.5 (w0.5,1 + w0.5,2))
where w0.5,1 and w0.5,2 are the peak widths measured at half the peak height. Note that the factor of 1.7 is added to the denominator to adjust for the difference in width at the half-height. The half-height technique is the way many data systems measure resolution, because it is simpler to measure than the baseline width.
The number of theoretical plates per column (performance)/symmetry factor/Tailing Factor/Resolution can and will change depending on the type of analysis and analytical conditions used.
From Cytiva-Column efficiency testing (ref- https://cdn.cytivalifesciences.com/api/public/content/digi-13432-original )
Commonly used sample/eluent systems that fulfill these requirements are acetone in water, and salt systems, which are monitored by measurement of absorbance and conductivity, respectively. Depending on the chemistry of the chromatography medium, the following sample and eluents are recommended:
For all media, except for hydrophobic synthetic polymers, RPC and HIC media: Eluent: water Sample: 1% - 2% acetone in water
For RPC and HIC: Eluent: 20% ethanol Sample: 1% - 2% acetone in at least 20% ethanol
For all media: Eluent: 0.4 M NaCl in water Sample: 0.8 M NaCl in water (use this always for Asymmetry)
For the use of NaCl as a tracer, a minimum of 0.4 M NaCl (35 - 40 mS/cm) in the eluent has to be used to suppress charge interaction effects between the tracer and the chromatography medium (otherwise, misleading test results may be observed).
Summary: Specifications for qualification of optimal column efficiency may be defined as:
h: Reduced plate height h ≤ 3
As: Asymmetry factor 0.8 < As < 1.8
These specifications rely on the use of optimized test conditions and parameters including:
•An inert tracer substance to avoid interaction with the medium
•Optimal liquid velocity enabling highest theoretical efficiency
•Low external volume
•A low sample volume in the pulse test (1% of VC)
Specifications for column qualification as well as test procedures should always be reviewed with regard to specific application needs as well as practical constraints that may not allow for application of optimal test conditions. The specification for reduced plate height and asymmetry may very well be different for different purification steps in the process. In addition to the efficiency test described in this application note, additional parameters could be used to track the process (e.g., pressure of the bed and retention volume of the product).
References 1. Hagel, L. et al. Handbook of process chromatography 2nd ed., John Wiley and Sons, Inc., New York (2008)
h = HETP/dp
h: Reduced plate height
HETP: Height equivalent of a theoretical plate
As: Asymmetric Factor
dp :Particle diameter
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