This equation is based on a Gaussian distribution, similar to that of plate theory. Its simplified form, proposed by Van Deemter in 1956, is well known (expression 1.30). The expression links the plate high H to the average linear velocity of the mobile phase ¯u in the column (Figure 1.11).
The three experimental basic coefficients A, B and C are related to diverse physico-chemical parameters of the column and to the experimental conditions. If H is expressed in cm, A will also be in cm, B in cm2/s and C in s (where velocity is measured in cm/s).
This equation reveals that there exists an optimal flow rate for each column, corresponding to the minimum of H, which predicts the curve described by Equation 1.30.
The loss in efficiency as the flow rate increases is obvious, and represents what occurs when an attempt is made to rush the chromatographic separation by increasing the pressure upon the mobile phase.
However, intuition can hardly predict the loss in efficiency that occurs when the flow rate is too slow. To explain this phenomenon, the origins of the terms A, B and C must be recalled . Each of these parameters represents a domain of influence which can be perceived on the graph (Figure 1.11).
The curve that represents the Van Deemter equation is a hyperbola which goes through a minimum H
min
when:
Term A is related to the flow profile of the mobile phase passing through the stationary phase. The size of the particles (diameter d
), their dimensional distribution and the uniformity of the packing (factor characteristic of packing ) can all be the origin of flow paths of different length which cause broadening of the solute band and improper exchanges between the two phases. This results in turbulent or Eddy diffusion, considered to have little importance in liquid chromatography and absent for WCOT capillary columns in GC (Golay’s equation without term A, cf. paragraph 1.10.2). For a given column, nothing can be done to reduce the A term.
The three experimental basic coefficients A, B and C are related to diverse physico-chemical parameters of the column and to the experimental conditions. If H is expressed in cm, A will also be in cm, B in cm2/s and C in s (where velocity is measured in cm/s).
This equation reveals that there exists an optimal flow rate for each column, corresponding to the minimum of H, which predicts the curve described by Equation 1.30.
The loss in efficiency as the flow rate increases is obvious, and represents what occurs when an attempt is made to rush the chromatographic separation by increasing the pressure upon the mobile phase.
However, intuition can hardly predict the loss in efficiency that occurs when the flow rate is too slow. To explain this phenomenon, the origins of the terms A, B and C must be recalled . Each of these parameters represents a domain of influence which can be perceived on the graph (Figure 1.11).
The curve that represents the Van Deemter equation is a hyperbola which goes through a minimum H
min
when:
Term A is related to the flow profile of the mobile phase passing through the stationary phase. The size of the particles (diameter d
), their dimensional distribution and the uniformity of the packing (factor characteristic of packing ) can all be the origin of flow paths of different length which cause broadening of the solute band and improper exchanges between the two phases. This results in turbulent or Eddy diffusion, considered to have little importance in liquid chromatography and absent for WCOT capillary columns in GC (Golay’s equation without term A, cf. paragraph 1.10.2). For a given column, nothing can be done to reduce the A term.
Term B, which can be expressed from D
, the diffusion coefficient of the analyte in the gas phase and , the above packing factor, is related to the longitudinal molecular diffusion in the column. It is especially important when the mobile phase is a gas.
G
This term is a consequence of the entropy which reminds us that a system will tend spontaneously towards the maximum degrees of freedom, chaos, just as a drop of ink diffuses into a glass of water into which it has fallen. Consequently, if the flow rate is too slow, the compounds undergoing separation will mix faster than they will migrate. This is why one never must interrupt, even temporarily, a chromatography once underway, as this puts at risk the level of efficiency of the experiment.
Term C, which is related to the resistance to mass transfer of the solute between the two phases, becomes dominant when the flow rate is too high for an equilibrium to be attained. Local turbulence within the mobile phase and concentration gradients slow the equilibrium process CS⇔CM
. The diffusion of solute between the two phases is not instantaneous, so that it will be carried along out of equilibrium. The higher the velocity of mobile phase, the worse the broadening becomes. No simple formula exists which takes into account the different factors integrated in term CL. The parameter CG
is dependent upon the diffusion coefficient of the solute in a gaseous mobile phase, while the term C
depends upon the diffusion coefficient in a liquid stationary phase. Viscous stationary phases have larger C terms.
In practice, the values for the coefficients of A, B and C in Figure 1.11 can be accessed by making several measurements of efficiency for the same compound undergoing chromatography at different flow rates, since flow and average linear speed are related. Next the hyperbolic function that best satisfies the experimental values can be calculated using, by preference, the method of multiple linear regression.