Chemical Analysis. Francis Rouessac

Chemical Analysis - Francis Rouessac


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into account the hold‐up time tM spent by the compound in the mobile phase. The three equations then become:

      (1.17)upper N Subscript e f f Baseline equals StartFraction t prime Subscript upper R Superscript 2 Baseline Over sigma squared EndFraction

Schematic illustration of retention factors and separation factor (or selectivity factor) between two adjacent compounds.

      (1.19)upper N Subscript e f f Baseline equals 5.54 StartFraction t prime Subscript upper R Baseline squared Over delta squared EndFraction

      Currently, it is considered that these last three equations are not very useful.

      

      1.6.3 Plate Height

      For a long time in gas chromatography, an adjustment value called the effective plate height Heff was calculated using the true efficiency, instead of the theoretical efficiency.

      Reduced plate height

      In liquid chromatography, when the column is filled with spherical particles, a parameter known as the reduced plate height h is often encountered. This parameter takes into account the mean diameter dm of the particles. This eliminates the effect of the particle size for better comparison of columns with different mean diameter values. Columns with the same reduced plate height h will yield similar performance.

      1.7.1 Retention Times

      The definition of retention times has been given previously (Section 1.2).

      1.7.2 Retention Volume (or Elution Volume) VR

      The retention volume VR of an analyte represents the volume of mobile phase necessary to enable its migration from one end of the column to the other. To estimate this volume, different methods (direct or indirect) that depend of the physical state of the mobile phase may be used. On the chromatogram, it corresponds to the volume of mobile phase that flows through between the time of injection and the time when the peak reaches its maximum point. If the flow rate F is constant, then:

      (1.22)upper V Subscript normal upper R Baseline equals t Subscript normal upper R Baseline dot upper F

      The volume of a peak Vpeak corresponds to that volume of the mobile phase in which 95% of the solute is diluted when leaving the column. It is defined by:

      (1.23)upper V Subscript p e a k Baseline equals omega dot upper F

      1.7.3 Hold‐up Volume (or Dead Volume) VM

      The volume of the mobile phase in the column (known as the dead volume), VM, corresponds to the accessible interstitial volume. It can be calculated from a chromatogram, provided a solute not retained by the stationary phase is present. The dead volume is deduced from tM and the flow rate F:

      (1.24)upper V Subscript normal upper M Baseline equals t Subscript normal upper M Baseline dot upper F

      1.7.4 Stationary Phase Volume

      This volume designated by Vs is not directly accessible from the chromatogram. In simple cases, we calculate it by subtracting the volume of the mobile phase from the total internal volume of the empty column. A column, whatever its design, may always be characterized by its phase ratio β defined as:

      (1.25)beta equals StartFraction upper V Subscript upper M Baseline Over upper V Subscript s Baseline EndFraction

      1.7.5 Retention (or Capacity) Factor k

      When a compound of total mass mT is introduced onto the column, it separates into two quantities: mM, the mass in the mobile phase, and mS, the mass in the stationary phase. During the solute’s migration down the column, these two quantities remain constant. Their ratio, called the retention factor k, is constant and independent of mT:

      (1.26)k equals StartFraction m Subscript normal upper S Baseline Over m Subscript normal upper M Baseline EndFraction equals StartFraction upper C Subscript normal upper S Baseline Over upper C Subscript normal upper M Baseline EndFraction dot StartFraction upper V Subscript normal upper S Baseline Over upper V Subscript normal upper M Baseline EndFraction equals upper K StartFraction upper V Subscript normal upper S Baseline Over upper V Subscript normal upper M Baseline EndFraction equals upper K slash beta

      The retention factor k, also known as the capacity factor, is a very important parameter in chromatography for defining column performance. Though it does not vary with the flow rate or the column length, k is not a constant, as it depends upon the experimental conditions. k is dependent via K (Nernst distribution law) on the intensity of solute–stationary phase interactions, and via β on the column’s design. For this reason, it is


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