Common HPLC Calculations:

Capacity Factor / Retention Factor / Capacity Ratio:  k1 (K Prime)

k1 = T(R) - T(0) / T(0)
where T(R) equals the retention time of the peak in minutes and T(0) is
the retention time of an unretained peak. *For chromatography to take place, K Prime must be > 1.00 and for most modes of chromatography, should be greater than 1.5 or 2.0 for all samples !


Tailing Factor: USP: 't'

t = W(5.0)/tw/2

where tw equals the distance between peak front and T(R) at 5% of peak height units. W(5.0) equals peak width at 5% height, in minutes.


Theoretical Plates: USP and ASTM, 'N'

N = 5.54 x (T(R)/W(50))2          

Assumes width at peak half height (50)
* More info can be found at this link.


Resolution: USP, ASTM, 'R'

R = (T(R)(b)-T(R)(a)) x 2.35/(W(50)(b) + W(50)(a))/2

Assumes width at half height (50%) with peaks (a) and (b).

*Notes: Visually, "Baseline" resolution is R = 1.5. Your goal should be R = or > 2.0. ** R of 1.5 provides 99.8% separation which means you cannot accurately quantify a 0.1% impurity so develop the method to have a resolution value of at least 2.0.


Note: The appropriate formula(s) for use with your samples may depend on which of the many pharmaceutical guidelines and regulations apply in your country. Always consult the appropriate guidelines.

Determining the Data Acquisition Rate (Sampling Rate) For Your HPLC Detector

Another common question I am asked is how to set-up the HPLC detector’s sampling rate. This article is specific to commonly used UV/VIS, not mass selective detectors (Mass Spectrometer detectors are set-up in a similar manner, but you also want to take into account the numbers of MRM transitions for each peak and dwell time to account for the scanning delay. Typical values for MS are >10 points with 15-20 being best). 

Most HPLC (UHPLC) instrument manufacturer’s provide default sampling rate values within their software packages. Please do not use them as the values shown were just put there to fill in the data field and may not apply to your application or method. Many chromatographer's use these values without first understanding if they are appropriate for their own methods. This is a common mistake. Just as the manufacturer does not know what wavelength, flow rate or mobile phase you will use, they also do not know what sample(s), method and/or conditions are appropriate for your specific application. As such, they provide numerous default values in these data entry fields to satisfy the software's requirement. Just as you select an appropriate wavelength and bandwidth, you should always calculate and enter the correct detector data acquisition rate value yourself which is appropriate for your specific application, detector type and method. 

The Peak shape's role during integration: For each chromatographic analysis you must determine the optimum sampling rate for the chosen detector. An accurate value is critical for proper instrument set-up, quantification and integration of your sample(s) peaks. In the most basic sense, the area under a perfectly Gaussian peak requires at least ten points to describe it with some detail. Ten points will provide basic data about the shape of an ideal peak to the computer. Since peaks are rarely perfectly symmetrical, a larger number of points will provide more accurate integration of the peak’s actual shape and total area. This will improve run-to-run reproducibility and quantification. We suggest you include twenty to thirty data points to allow for a more detailed fit to the peak. Too few points across a peak and you lose detail and sacrifice reproducibility. Too many points and you start to introduce noise into the system. 


With these facts in mind we can next think about calculating the detector’s data acquisition rate. You must select a data rate (sampling rate) that is sure to provide the recommended 20 to 30 data points across the peak width (we use the commonly calculated peak width at half height as the time measurement). Select a detector sampling rate that will provide you with this degree of detail and resolution. This is best accomplished by initially looking at an actual chromatogram of your sample. Look at the chromatogram and use the narrowest sample or standard peak past the void time, with good retention as an example to determine the best acquisition rate. The narrowest peak will be the worst-case scenario and will insure that you have enough points across all of the remaining peaks in the sample. It's width is often measured in units of time (seconds/minutes). This data can often be read directly off of a generated data acquisition report.

Examples:

(a) If your narrowest peak has a peak width of 1.00 minute (60 seconds), then divide 30 points into 60 seconds for a result of 2 seconds per data point. The preferred sampling rate would be 2 seconds, 0.03 minutes or 0.5 Hz (depending on the units used by your detector).

(b) If your narrowest peak has a peak width of 0.20 minutes (12 seconds), then divide 30 points into 12 seconds  for a result of 0.4 seconds per data point. This equals a sampling rate of 2.5 samples per second or 2.5 Hz.

Summary:  

     To Determine the Data Acquisition Rate For Your Detector You Need To:

• Calculate the best data rate for each method and not use a generalized value (though similar methods will often use the same rate).
• Use your existing sample integration data results to identify the narrowest chromatographic peak in your analysis (at the baseline or half-height).
• Record the width value of this peak (usually in units of time).
• Divide this number by thirty (30) to determine the preferred sampling rate.
• Use this value, or a value close to it, for your detector’s sampling rate.

HPLC Capillary Tubing Connection Volumes:

The length and internal diameter of the HPLC interconnecting tubing used in your system really does matter. The total volume contained in the tubing can dilute your sample or separated peaks. This can effectively undue the work of separating the peak(s) on a column. Extra volume in the tubing can also have the effect of increasing the gradient delay factor for your method (the greater the volume of the tubing from the pump head to the column inlet, the greater the delay in the solvent mixture arriving at the column). In general, keep the the total delay volume as low as possible. This is accomplished by connecting the various modules together using the shortest lengths of tubing possible. For systems which use standard sized HPLC columns (e.g. I.D.'s of 3.0 to 4.6mm and lengths from 100mm to 300mm) the tubing internal diameter should be 0.17mm (0.007"). For systems which use very short, mini or micro bore sized HPLC columns (e.g. I.D.'s of 1.0 to 2.1 mm and lengths from 50mm to 250mm) the tubing internal diameter should be 0.12mm (0.005"). Looked at another way, if the total column volume is less than 750 ul, consider using the smaller internal diameter tubing (0.17mm) to reduce band broadening. 

Here are some tubing volumes to help you evaluate the effect changing the I.D. or length has on the tubing that you use.

I.D. (mm)	I.D. (inches)		ul / cm	ul / inch
0.12	0.005		0.127	0.323
0.17	0.007		0.249	0.632
0.25	0.010		0.507	1.288
0.51	0.020		2.026	5.146
1.02	0.040		8.103	20.581

HPLC Mobile Phase Filtering & Solvent Inlet Filters

HPLC Mobile Phase Filtering: 



The tubing and valve passageways of the HPLC system are very narrow and clogs can result from using solutions which have not been properly filtered. Columns are expensive and will also clog up with particulate matter causing increased back pressure and/or changes in retention times. Running clean, particulate free HPLC grade solvents through your chromatograph is a basic maintenance requirement. High grade chromatography solvents (and ultra pure water) are often pre-filtered through 0.2 micron filters by the manufacturer to meet their grade for use in chromatographic systems. However, there are times when you also prepare (mix) your own mobile phases using theses solvents with or without chemical reagents and additives. When you prepare mobile phase using these reagent grade chemicals or additives you should also take the extra time to filter the final mixture through a 0.2 micron glass or steel filter prior to use. This helps to insure that you start with as clean a solution as possible. *This is a critical procedure to follow with buffer solutions. When using aqueous solutions, possible bacterial and algae growth can occur so remember to date the solutions and dispose of them after a suitable time period (Make up only what you will use in one week). Do not re-filter these solutions and then use them again.


HPLC Solvent Inlet Filters:

Most HPLC manufacturer's supply solvent inlet filters on the lines which draw solvent into the pump head. To protect the pump and components downstream, these lines often incorporate a filter. These solvent pre-filters are usually made from plastic (PEEK or PEAK), glass or stainless steel. Their porosity is typically ten or twenty microns. A smaller porosity could be used, but it would restrict the lines ability to draw up fresh solvent into the pump head at the required flow rate so a compromise in pore size is necessary. The filter is primarily designed to stop the pump from drawing up any large particles or debris which could cause damage to the system and is NOT used to filter the solution (as mentioned above, the solutions used should be pre-filtered). These filters can clog up over time and so should be monitored for restrictions. Stainless steel filters can be cleaned using sonication and heat. Plastic filters should usually be replaced with new ones. Glass filters, which are often made of sintered glass, can be washed, but should never be sonicated to clean them as this can cause the glass to fracture and plug them up even worse. When in doubt, replace them with new filters. Filters used with clean organic solvents often last for many years. Filters which are used with aqueous solutions last for shorter times due to build up of undesirable biological matter.

• Another way in which you can insure a clean source of liquid for your HPLC system is to make sure that your mobile phase reservoir bottles are clean and free of dirt and dust during use. Keep them covered. Always wipe off any dust and debris from the solvent bottles before you uncap them and pour them into another container (much of the dust in the mobile phase comes from dirt that falls into the bottles). Instead of 'topping-off' bottles, replace them with clean bottles containing new solution.