Editing High-performance liquid chromatography (section)

===Theoretical===
The theory of high performance liquid chromatography-HPLC is, at its core,  the same as general chromatography theory.<ref>{{Cite journal |last1=Martin |first1=A. J. P. |last2=Synge |first2=R. L. M. |date=1941-12-01 |title=A new form of chromatogram employing two liquid phases |url=https://portlandpress.com/biochemj/article/35/12/1358/34734/A-new-form-of-chromatogram-employing-two-liquid |journal=Biochemical Journal |language=en |volume=35 |issue=12 |pages=1358–1368 |doi=10.1042/bj0351358 |issn=0306-3283 |pmc=1265645 |pmid=16747422}}</ref> This theory has been used as the basis for ''system-suitability'' tests, as can be seen in the USP Pharmacopeia,<ref>{{Citation |title=〈621〉 CHROMATOGRAPHY |date=2022-12-01 |url=https://www.usp.org/sites/default/files/usp/document/harmonization/gen-chapter/harmonization-november-2021-m99380.pdf |access-date=2025-01-21 |publisher=U.S. Pharmacopeial Convention |doi=10.31003/uspnf_m99380_06_01}}</ref> which are a set of quantitative criteria, which test the suitability of the HPLC system to the required analysis at any step of it.

This relation is also represented as a normalized unit-less factor known as the ''retention factor'', or retention parameter, which is the experimental measurement of the capacity ratio, as shown in the Figure of Performance Criteria as well. t<sub>R</sub> is the retention time of the specific component and t<sub>0</sub> is the time it takes for a non-retained substance to elute through the system without any retention, thus it is called the Void Time.

The ratio between the retention factors, k', of every two adjacent peaks in the chromatogram is used in the evaluation of the degree of separation between them, and is called '''selectivity factor''', α, as shown in the Performance Criteria graph.

The plate count N as a criterion for system efficiency was developed for isocratic conditions, i.e., a constant mobile phase composition throughout the run. In gradient conditions, where the mobile phase changes with time during the chromatographic run, it is more appropriate to use the parameter '''''peak capacity'' ''P''<sub>c</sub>''' as a measure for the system efficiency.<ref>{{Cite journal |last=Wren |first=Stephen A. C. |date=2005-06-15 |title=Peak capacity in gradient ultra performance liquid chromatography (UPLC) |url=https://www.sciencedirect.com/science/article/pii/S0731708505000142 |journal=Journal of Pharmaceutical and Biomedical Analysis |volume=38 |issue=2 |pages=337–343 |doi=10.1016/j.jpba.2004.12.028 |pmid=15925228 |issn=0731-7085|url-access=subscription }}</ref> The definition of ''peak capacity'' in chromatography is the number of peaks that can be separated within a retention window for a specific pre-defined resolution factor, usually ~1. It could also be envisioned as the runtime measured in number of peaks' average widths. The equation is shown in the Figure of the performance criteria. In this equation tg is the gradient time and w(ave) is the average peaks width at the base.

[[File:SST Equations single peak.jpg|alt=Basic Chromatography Equations|thumb|658x658px|The quantitative parameters and equations which determine the extent of performance of the chromatographic system]]
The parameters are largely derived from two sets of chromatographic theory: plate theory (as part of [[partition chromatography]]), and the rate theory of chromatography / ''[[Van Deemter equation]]''. Of course, they can be put in practice through analysis of HPLC chromatograms, although rate theory is considered the more accurate theory.

They are analogous to the calculation of [[retention factor]] for a [[paper chromatography]] separation, but describes how well HPLC separates a mixture into two or more components that are detected as peaks (bands) on a chromatogram. The HPLC parameters are the: efficiency factor(''N''), the retention factor (kappa prime), and the separation factor (alpha). Together the factors are variables in a resolution equation, which describes how well two components' peaks separated or overlapped each other. These parameters are mostly only used for describing HPLC reversed phase and HPLC normal phase separations, since those separations tend to be more subtle than other HPLC modes (''e.g.'', ion exchange and size exclusion).

Void volume is the amount of space in a column that is occupied by solvent. It is the space within the column that is outside of the column's internal packing material. Void volume is measured on a chromatogram as the first component peak detected, which is usually the solvent that was present in the sample mixture; ideally the sample solvent flows through the column without interacting with the column, but is still detectable as distinct from the HPLC solvent. The void volume is used as a correction factor.

Efficiency factor (''N'') practically measures how sharp component peaks on the chromatogram are, as ratio of the component peak's area ("retention time") relative to the width of the peaks at their widest point (at the baseline). Peaks that are tall, sharp, and relatively narrow indicate that separation method efficiently removed a component from a mixture; high efficiency. Efficiency is very dependent upon the HPLC column and the HPLC method used. Efficiency factor is synonymous with plate number, and the 'number of theoretical plates'.

[[Retention factor]] (''kappa prime'') measures how long a component of the mixture stuck to the column, measured by the area under the curve of its peak in a chromatogram (since HPLC chromatograms are a function of time). Each chromatogram peak will have its own retention factor (''e.g.'', ''kappa''<small>1</small> for the retention factor of the first peak). This factor may be corrected for by the void volume of the column.

Separation factor (''alpha'') is a relative comparison on how well two neighboring components of the mixture were separated (''i.e.'', two neighboring bands on a chromatogram). This factor is defined in terms of a ratio of the retention factors of a pair of neighboring chromatogram peaks, and may also be corrected for by the void volume of the column. The greater the separation factor value is over 1.0, the better the separation, until about 2.0 beyond which an HPLC method is probably not needed for separation.
Resolution equations relate the three factors such that high efficiency and separation factors improve the resolution of component peaks in an HPLC separation.