The HPLC separation process begins when a sample is introduced to a column filled with porous particles. The sample is injected and is transported through the column by a moving liquid phase (mobile phase). As analytes encounter stationary phase, they interact with it to differing degrees and separate into pure zones that can be analyzed or collected. Analytes that have a strong affinity to the stationary phase will stay on the column longer.
Resolution is an important HPLC performance indicator usually assessed by how quickly and how completely target components in a sample separate as they pass through a column. Resolution is measured by dividing the difference in peak retention times by the average peak width. Resolution can also be expressed in the Resolution Equation as a combination of the factors (separation, efficiency, and retention) that affect this value.
In nearly all modes of HPLC, some form of selective retention by the stationary phase is required for column resolution. In order to know whether a compound is retained, one must calculate the column void volume, V0, by measuring the retention time for an unretained solute at a given flow rate.
Once the column void volume or void time for a given flow rate is known, it will not change. If a solute elutes near or at the void, resolution caused by stationary phase interaction cannot occur.
Figure2. Resolution Equation
Retention factor is sometimes also referred to as capacity factor. It is a relative retention factor that defines retention in multiples of the time at which an unretained peak elutes, t0 or tM.
In the resolution equation, tR is the retention time of the analyte, and t0 is the void time (sometimes tM). The retention factor is a unitless number.
The k value for an unretained peak is 0. A k value for a peak that spends equal time in the stationary phase and mobile phase is 1. All solutes spend the same amount of time in the mobile phase and different amounts of time in the stationary phase. The column void volume in reverse phase mode is usually established by injection of a very polar compound such as uracil or thiourea. Several different methods can be used to confirm true void volume.
Most textbooks recommend that all peaks of interest be retained with a k of 1 or greater for reliable quantitation. A k of 2 to 3 is desired if it can be achieved. A k of more than 10 does little to improve resolution and it increases analysis time and dilutes the sample to make it harder to detect.
Figure3. Retention factor k
Once vM or tM at a given flow rate is established for a given column, it will not change. Selectivity or separation factor α (alpha) is calculated from the ratio of k values for adjacent peaks. The k for the later peak is always placed in the numerator so that k values are always equal to or greater than 1.
A good selectivity for HPLC is 1.1, which allows a resolution of 1.5 to be achieved with about 10,000 theoretical places. The critical pair in a separation is defined as adjacent solutes that have the smallest α value. Critical pair defines the minimum number of plates needed to achieve a defined resolution, which in turn defines the minimum particle size and column length.
Column efficiency, the rate of zone spreading measured by taking a ratio of retention time to peak width and squaring it, is usually expressed as N. When peak width is measured at half height, the constant is 5.54. If the peak width is measured at base, a constant of 16 must be used to arrive at about the same N value.
Retention time and peak width must be measured in the same units for a valid column efficiency determination.
Peak symmetry also affects column efficiency and, therefore, resolution. Strongly absorptive or active sites are often responsible for tailing peaks. Columns may show high efficiency and resolution for neutral solutes and very poor efficiency and resolution for bases or acids if such active sites are present.
Solute tailing is reported as peak broadening with an elongated right half of the peak. Excessive column activity for a solute is not necessarily a characteristic of an older column that has lost stationary phase. It can also be observed in new columns where the phase chemistry has not been optimized for that sample type and operating conditions.
The ASTM International standards organization recommends calculating column symmetry or asymmetry (As) as the back-to-front ratio of a bisected peak measured at 10% of height.
A tailing peak has a front of greater than 1.0, while a fronting peak has a front of less than 1.0. The U.S. Pharmacopeia (USP) has also recommended measuring tailing factor (T) as the back-to-front ratio of a bisected peak measured at 5% of height. The ratio is made by dividing the total width by twice the front width.
Both calculation methods give the same value of 1 for a symmetrical peak, but the USP method gives smaller values for tailing and fronting than the ASTM method. If using an automated method for symmetry calculation, check the data system to see which method is being used. Many data systems have both calculation methods available.
Increase N (efficiency) by:
Change α (selectivity) by:
Increase k (retention) by:
Notes on Resolution:
Much of the information presented on this page was originally delivered in the webinar series HPLC Column Fundamentals by Dr. Richard A. Henry, a retired Pennsylvania State University analytical chemistry professor and notable contributor to the field of separation technology.