Dispersion in Chromatography Columns - Resistance to Mass Transfer Dispersion > Page 25

Resistance to Mass Transfer Dispersion

Both the resistance to mass transfer in the mobile phase and that in the stationary phase, can be treated quantitatively using the random walk model. Recalling that if each molecule of a group takes a series of steplike movements, (positive or negative) the direction being completely random, then after (p) steps have been taken, each step having an average length (s), the average of the molecules will have moved some distance from the starting position and will form a Gaussian type distribution curve with a variance of s2,

          where

                                           or             

                                    

In the first instance, consider that the distribution is energy controlled and not diffusion controlled, thus, a solute molecule will desorb from the stationary phase when it randomly has sufficient kinetic energy to break its association with a molecule of stationary phase (see Principles and Practice of Chromatography). Similarly, a molecule will be absorbed under the same conditions.