Capacity factor

Theory of HPLC retention based on the adsorption from solutions can help to establish the relationships of measurable retention values (VR, tR, and k') with the thermodynamic parameters, such as adsorption equilibrium constant (K), or free Gibbs energy ().

Capacity factor is the ratio of the reduced retention volume to the dead volume:

          (20)
  

From the basic retention equation we can get

          (21)
  

For the low analyte concentration, in the absence of the analyte-analyte interactions in solution and on the surface, the equation (14) could be applied for the description of adsorption isotherm. At very low concentrations the limit of the derivative of the excess adsorption by concentration is equal to:

          (22)
  

From equations (21) and (22) we can conclude that capacity factor may be expressed in form

k' = K - 1

Thermodynamic equilibrium constant is an energetical parameter. Its logarithm is equal to the difference of the free Gibbs energy of the analyte and solvent in the adsorption system,

         (23)
  

where DH is the difference of the enthalpy of adsorption of analyte and solvent and DS is the corresponding difference of their entropy. If the solvent interacts with the adsorbent surface stronger than analyte, it will be preferentially adsorbed. The free Gibbs energy value will be negative and the equilibrium constant will be less then 1. From the equation (23) we can conclude that the capacity factor of that analyte will be negative. This actually means that analyte will move through the column faster than eluent. The analyte which have a negative adsorption will not penetrate in the adjacent to the adsorbent surface part of the volume (adsorbed eluent molecules will not allow it, as they have stronger surface interactions). As a result, this analyte will occupy less volume while it is moving through the column and will move faster than the eluent.

This is one of the experimental facts which could not be explained on the basis of partitioning theory.