Chemical Analysis. Francis Rouessac

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

      (1.17)

(1.18)

Figure 1.7 Retention factors and separation factor (or selectivity factor) between two adjacent compounds. Each compound has its own retention factor. On this figure, the separation factor is around 1.3. α alone is not enough to determine whether separation is really possible.

      (1.19)

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

      

      1.6.3 Plate Height

The height equivalent to a theoretical plate H, as already defined (Eq. (1.4)), is calculated for reference compounds to permit a comparison of columns of different lengths. However, H does not behave as a constant; its value depends upon the compound chosen and upon the experimental conditions.

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

The calculation of H_eff from the real efficiency uses Eq. (1.20):

(1.20)

      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 d_m 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.

(1.21)

1.7 RETENTION PARAMETERS

      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) V_R

      The retention volume V_R 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)

      The volume of a peak V_peak 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)

      1.7.3 Hold‐up Volume (or Dead Volume) V_M

      The volume of the mobile phase in the column (known as the dead volume), V_M, 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 t_M and the flow rate F:

      (1.24)

      1.7.4 Stationary Phase Volume

      This volume designated by V_s 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)

      1.7.5 Retention (or Capacity) Factor k

      When a compound of total mass m_T is introduced onto the column, it separates into two quantities: m_M, the mass in the mobile phase, and m_S, 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 m_T:

      (1.26)

      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