Figure 4.14
Effects of diffusion and mass transfer on peak width. (a) Concentration profiles
of a solute at the beginning of a separation. (b) Concentration profiles of a solute
after passing some distance through the system.travels through the system. Attempts to define efficiency in terms of diffusion and mass transfer effects
are numerous, the most useful being those of van Deemter 3 and of Giddings^4. Based on their approach,
the following simplified equation can be derived:
where is the mean linear flow rate of the mobile phase, and A, B and C are terms involving diffusion
and mass transfer.
A is the 'multiple path' term which accounts for different portions of the mobile phase, and consequently
the solute, travelling different total distances because of the various routes taken around the particles of
stationary phase. The effect is minimized by reducing particle size but increases with length of column
or surface.
B/ is the 'molecular diffusion' term and relates to diffusion of solute molecules within the mobile phase
caused by local concentration gradients. Diffusion within the stationary phase also contributes to this
term, which is significant only at low flow rates and increases with column length. As B is proportional
to the diffusion coefficient in the mobile phase, the order of efficiency at low flow rates is liquids >
heavy gases > light gases.
C is the 'mass transfer' term and arises because of the finite time taken for solute molecules to move
between the two phases. Consequently, a true equilibrium situation is never established as the solute
moves through the system, and spreading of the concentration profiles results. The effect is minimal for
small particle size and thin coatings of stationary phase but increases with flow rate and length of
column or surface.
Experimental values of H, obtained from equation (4.46) and plotted against the rate of flow of mobile
phase for a given solute and set of conditions, produce a hyperbolic curve showing an optimum flow
rate for maximum efficiency (Figure 4.15). The position of the maximum varies with the solute, and a
family of curves can be derived for the components of a mixture. The most efficient flow rate for a
particular sample is, therefore, a matter of compromise. The equation also indicates that the highest