High performance liquid chromatography is defined as a separation of mixtures of compounds due to differences in their distribution equilibrium between two phases, the stationary phase packed inside columns and the mobile phase, delivered through the columns by high pressure pumps. Components whose distribution into the stationary phase is higher, are retained longer, and get separated from those with lower distribution into the stationary phase. The theoretical and practical foundations of this method were laid down at the end of 1960s and at the beginning of 1970s. The theory of chromatography has been used as the basis for System- Suitability tests, which are set of quantitative criteria that test the suitability of the chromatographic system to identify and quantify drug related samples by HPLC at any step of the pharmaceutical analysis.
Retention Time (tR), Capacity Factor k' and Relative Retention Time (RRT)
The time elapsed between the injection of the sample components into the column and their detection is known as the Retention Time (tR). The retention time is longer when the solute has higher affinity to the stationary phase due to its chemical nature. For example, in reverse phase chromatography, the more lypophilic compounds are retained longer. Therefore, the retention time is a property of the analyte that can be used for its identification.
A non retained substance passes through the column at a time t0, called the Void Time. The Retention Factor or Capacity Factor k' of an analyte is measured experimentally as shown in Figure 3 and Eqn 1:
The Capacity Factor describes the thermodynamic basis of the separation and its definition is the ratio of the amounts of the solute at the stationary and mobile phases within the analyte band inside the chromatographic column:
Where Cs is the concentration of the solute at the stationary phase and Cm is its concentration at the mobile phase and ? is the ratio of the stationary and mobile phase volumes all within the chromatographic band.
The Retention Factor (Eqn 1a) is used to compare the retention of a solute between two chromatographic systems, normalizing it to the column's geometry and system flow rate. The need to determine the void time can be tricky sometimes, due to the instability of the elution time of the void time marker, t0, therefore, when the chromatogram is complex in nature, and one known component is always present at a certain retention time, it can be used as a retention marker for other peaks. In such cases the ratio between the retention time of any peak in the chromatogram and the retention time of the marker is used (tR (Peak) / tR (Marker)) and referred to as the Relative Retention Time (RRT). RRT is also used instead of the capacity ratio for the identification of the analyte as well as to compare its extent of retention in two different chromatographic systems.
Figure 3: Example of Capacity factor calculation in LC. In this case: tR = 0.739, t0 = 0.17, therefore k' = (0.739-0.176)/0.176 = 3.20
Efficiency: Plate Count N and Peak Capacity Pc
Figure 4 describes a chromatogram with 4 peaks and a detected void peak. The parameters of the System Suitability are displayed in the inserted table. The sharpness of a peak relative to its retention time is a measure of the system's efficiency, calculated as N, plate count. Band-broadening phenomena in the column such as eddy diffusion, molecular diffusion, mass-transfer kinetics and extra-column effects reduce the efficiency of the separation (33). The sharpness of a peak is relevant to the limit of detection and limit of quantification of the chromatographic system. The sharper the peak for a specific area, the better is its signal-to-noise; hence the system is capable of detecting lower concentrations. Therefore, the efficiency of the chromatographic system must be established by the system suitability test before the analysis of low concentrations that requires high sensitivity of the system, such as the analysis of drug impurities and degradation products.
The efficiency of the separation is determined by the Plate Count N when working at isocratic conditions, whereas it is usually measured by Peak Capacity Pc when working at gradient conditions (34). The following equation for the plate count is used by the United States Pharmacopoeia (USP) to calculate N (See Figure 5):
Where w is measured from the baseline peak width calculated using lines tangent to the peak width at 50 % height (See Figure 5). European and Japanese Pharmacopoeias use the peak width at 50% of the peak height (See Figure 5), hence the equation becomes:
Peak Capacity Pc is defined as number of peaks that can be separated within a retention window for a specific pre-determined resolution. In other words, it is the runtime measured in peak width units (34). It is assumed that peaks occur over the gradient chromatogram. Therefore, Peak Capacity can be calculated from the peak widths w in the chromatogram as follows:
Where n is the number of peaks at the segment of the gradient selected for the calculation, tg. Thus peak capacity can be simply the gradient run time divided by the average peak width. The sharper the peaks the higher is the peak capacity, hence the system should be able to resolve more peaks at the selected run time as well as detect lower concentrations.
Another measure of the column's chromatographic efficiency is the Height Equivalent to Theoretical Plate (HETP) which is calculated from the following equation:
Eqn 5: HETP = (L/N)
Where L is column length and N is the plate
count. HETP is measured in
micrometer. For example, in the
Figure 4: Example of a System Suitability Run’s Result
The behavior of HETP as function of linear velocity has been described by various equations (35). It is frequently called "The Van-Deemter curve", and it is frequently used to describe and characterize various chromatographic stationary phases' performance and compare them to each other (36-39). The lower are the values of HETP, the more efficient is the chromatographic system, enabling the detection of lower concentrations due to the enhanced signal-to-noise ratio of all the peaks in the chromatogram.
Figure 5: System Suitability measurements on a single peak
Peak Asymmetry Factor, Af and Tailing Factor T
The chromatographic peak is assumed to have a Gaussian shape under ideal conditions, describing normal distribution of the velocity of the molecules populating the peak zone migrating through the stationary phase inside the column. Any deviation from the normal distribution indicates non-ideality of the distribution and the migration process, therefore might jeopardize the integrity of the peak's integration, reducing the accuracy of the quantitation. This is the reason why USP Tailing is a peak's parameter almost always measured in the system suitability step of the analysis.
The deviation from symmetry is measured by the Asymmetry Factor, Af or Tailing Factor T. The calculation of Asymmetry Factor, Af is described by the following equation:
Where A and B are sections in the horizontal line parallel to the baseline, drawn at 10% of the peak height as shown in Figure 5.
The calculation of Tailing Factor, T, which is more widely used in the pharmaceutical industry, as suggested by the pharmacopeias, is described by the following equation:
Where A and B are sections in the horizontal line parallel to the baseline, drawn at 5% of the peak height, as also shown in Figure 5. The USP suggests that Tailing Factor should be in the range of 0.5 up to 2 to assure a precise and accurate quantitative measurement. The peaks in Figures 4 and 5 have a tailing factor within the USP requirements.
Selectivity Factor alfa and Resolution Factor Rs
The separation is a function of the thermodynamics of the system. Substances are separated in a chromatographic column when their rate of migration differs, due to their different distribution between the stationary and mobile phases. The Selectivity Factor?, a, and Resolution Factor, Rs, measure the extent of separation between two adjacent peaks. The Selectivity Factor? accounts only for the ratio of the Retention Factors, k', of the two peaks (k'2/k'1), whereas the Resolution Factor, Rs, accounts for the difference between the retention times of the two peaks relative to their width.
The equation that describes the experimental measurement of the Resolution Factor, Rs, is as follows:
Where tR is the retention time of peaks 1 and 2 respectively and w is their respective peak width at the tangents' baseline (see Figure 5). According to the pharmacopeias Rs should be above 1.5 for an accurate quantitative measurement. Figure 4 shows that the resolution measured between every two adjacent peaks in the chromatogram was above 1.5, therefore, it was above the minimum required.
The resolution is a critical value when working with complex samples such as drug impurities and degradation products, or when the formulation is complex and excipients might interfere with the quantitative measurements. Therefore, it is an essential part of the system suitability measurement stage before the quantitative work of these type of samples.
The sample used for the measurements of Rs during the system suitability runs is sometimes called Resolution Solution, as can be seen in Figure 4 It usually contains the components that are the most difficult to resolve.
The theoretical description of the Resolution Factor Rs equation is shown in Equation 9. It includes some of the above parameters, the plate count N, the selectivity a and the average of the two peaks' capacity factors k':
It can be clearly seen from this equation that the plate count is the most effecting parameter in the increase of the chromatographic resolution. Since the plate count increases with the reduction in particle diameter, it explains the reduction in particle diameter of the stationary phase material during the last 3 decades of HPLC. This is also the rational behind the recent trend in HPLC, the use of sub 2 micron particle columns and the development of a specially design of ultra performance HPLC systems to accommodate such columns (36, 40-42).
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