The true physical meaning of the corrected retention volumes in GC

Abstract

SummaryThrough a straightforward mathematical derivation it is shown that the compressibility correction factor equals the ratio of gas pressure at the column outlet to the average pressure in the column, j = po/p. Therefore, by multiplying by this factor, the experimentally measured retention volumes can be recalculated to the average pressure in the column. Corrected retention volumes thus represent the volume of the mobile phase under real conditions of chromatography in the column. Appropriate definitions for corrected retention volumes and factor ] are formulated. the pressure drop that matters, but the absolute value of the pressure.Without having said in plain words what is wrong with the retention volumes measured experimentally at the column outlet and why and in what direction these values have to be corrected, Ettre and Hinshaw present a detailed derivation of the compressibility correction factor. In these complicated mathematical exercises, it escaped the attention of the authors that the crucial steps in the derivation are integrations of functions (written for the gas flow rate or any other gradually changing quantity) along the column from the pressure Pi at the column inlet to pressure Po at the outlet. These integrations do not resemble any extrapolation to a hypothetical case of zero pressure drop. Instead, the mathematical meaning of the integration within a definite range of pressures is that it is replacing a gradually changing value of pressure by an equivalent, value, averaged over this range.

Chromatographic investigation of the effect of dissolved carbon dioxide on the glass transition temperature of a polymer and the solubility of a third component (additive)

“…The experimental results are given in Table I, where the retention volume data have been "corrected" to the commonly accepted standard state temperature for an ideal gas by a factor of 273/T. This correction step has been questioned in the chromatographic literature 19,20 but is historically the standard method for reporting chromatographic retention volume data.…”

Revisiting the problem of correcting retention parameters for pressure and temperature in gas chromatography

“…Therefore, it is not possible to calculate meaningful specific retention volumes at a standard temperature in the simple way suggested in formula (7). Instead, this formula significantly distorts the actual relations as exemplified in [2] by two different analytes which are eluted with identical (specific) retention volumes when chromatographed at two different temperatures. The analyte of higher relative mass, that requires a higher temperature for elution, was shown to produce a smaller "specific retention volume at 0 ~ after multiplying by the corresponding "temperature correction factor, 273.15/Tc", as compared to the lower relative mass analyte eluted at a smaller Tc.…”

“…The reason for making this mistake is the absence of a precise definition of the factor j that re-flects its physical meaning. To fill this important gap, we suggest [1,2] the following definition: "the mobile phase compressibility correction factor, j" is the ratio of the gas pressure at the column outlet to the average gas pressure in the column j = Po/Pc. This definition prevents inappropriate application of the factor to quantities other than volume and flow rate.…”

“…As shown in detail in [2], no further assumptions (and no extrapolations) are needed, in order to derive the averaged, over the whole column length, pressure Pc of the carrier gas in the column. Crucial steps in the derivation are two integrations of modified differentials (2) and (3) over the column length with pressures changing from Pi to Po as time t changes from 0 to tM.…”

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SummaryIt has been shown [1,2] that the compressibility correction factor equals the ratio of gas pressure at the column outlet to the average pressure in the column, j = Po/Pc, and, therefore, by multiplying by this factor, all experimentally measured retention volumes and flow rates are converted from ambient pressure to the average pressure in the column. This makes retention volumes corrected in this way independent of pressure.

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