For half a century different theories have been and continue to be proposed to model chromatography and to explain the migration and separation of analytes in the column. The best known are those employing a statistical approach (stochastic theory), the theoretical plate model or a molecular dynamics approach.
To explain the mechanism of migration and separation of compounds on the column, the oldest model, known as Craig’s theoretical plate model is a static approach now judged to be obsolete, but which once offered a simple description of the separation of constituents.
Although chromatography is a dynamic phenomenon, Craig’s model considered that each solute moves progressively along a sequence of distinct static steps. In liquid–solid chromatography this elementary process is represented by a cycle of adsorption/desorption. The continuity of these steps reproduces the migration of the compounds on the column, in a similar fashion to that achieved by a cartoon which gives the illusion of movement through a sequence of fixed images. Each step corresponds to a new state of equilibrium for the entire column.
These successive equilibria provide the basis of plate theory according to which a column of length L is sliced horizontally into N fictitious, small plate-like discs of same height H and numbered from 1 to n. For each of them, the concentration of the solute in the mobile phase is in equilibrium with the concentration of this solute in the stationary phase. At each new equilibrium, the solute has progressed through the column by a distance of one disc (or plate), hence the name theoretical plate theory.
The height equivalent to a theoretical plate (HETP or H) will be given by equation (1.5):
To explain the mechanism of migration and separation of compounds on the column, the oldest model, known as Craig’s theoretical plate model is a static approach now judged to be obsolete, but which once offered a simple description of the separation of constituents.
Although chromatography is a dynamic phenomenon, Craig’s model considered that each solute moves progressively along a sequence of distinct static steps. In liquid–solid chromatography this elementary process is represented by a cycle of adsorption/desorption. The continuity of these steps reproduces the migration of the compounds on the column, in a similar fashion to that achieved by a cartoon which gives the illusion of movement through a sequence of fixed images. Each step corresponds to a new state of equilibrium for the entire column.
These successive equilibria provide the basis of plate theory according to which a column of length L is sliced horizontally into N fictitious, small plate-like discs of same height H and numbered from 1 to n. For each of them, the concentration of the solute in the mobile phase is in equilibrium with the concentration of this solute in the stationary phase. At each new equilibrium, the solute has progressed through the column by a distance of one disc (or plate), hence the name theoretical plate theory.
The height equivalent to a theoretical plate (HETP or H) will be given by equation (1.5):
This employs the polynomial approach to calculate, for a given plate, the mass distributed between the two phases present. At instant I, plate J contains a total mass of analyte m
of the analyte that has just arrived from plate J −1 carried by the mobile phase formerly in equilibrium at instant I −1, to which is added the quantity mT
which is composed of the quantity mSM
already present in the stationary phase of plate J at time I −1 (Figure 1.5).
of the analyte that has just arrived from plate J −1 carried by the mobile phase formerly in equilibrium at instant I −1, to which is added the quantity mT
which is composed of the quantity mSM
already present in the stationary phase of plate J at time I −1 (Figure 1.5).
If it is assumed for each theoretical plate that: m
S
=Km
M
and m
, then by a recursive formula, m
T
(as well as m
M
and m
), can be calculated. Given that for each plate the analyte is in a concentration equilibrium between the two phases, the total mass of analyte in solution in the volume of the mobile phase V
S
of the column remains constant, so long as the analyte has not reached the column outlet. So, the chromatogram corresponds to the mass in transit carried by the mobile phase at the N +1th plate (Figure 1.6) during successive equilibria. This theory has a major fault in that it does not take into account the dispersion in the column due to the diffusion of the compounds.
The plate theory comes from an early approach by Martin and Synge (Nobel laureates in Chemistry, 1952), to describe chromatography by analogy with distillation
and counter current extraction as models. This term, used for historical reasons, has no physical significance, in contrast to its homonym which serves to measure the performances of a distillation column.
The retention time t
, of the solute on the column can be sub-divided into two terms: t
M
R
(hold-up time), which cumulates the times during which it is dissolved in the mobile phase and travels at the same speed as this phase, and t
the cumulative times spent in the stationary phase, during which it is immobile. Between two successive transfers from one phase to the other, it is accepted that the concentrations have the time to re-equilibrate.
In a chromatographic phase system, there are at least three sets of equilibria: solute/mobile phase, solute/stationary phase and mobile phase/stationary phase. In a more recent theory of chromatography, no consideration is given to the idea of molecules immobilized by the stationary phase but rather that were simply slowed down when passing in close proximity.
S
=Km
M
and m
, then by a recursive formula, m
T
(as well as m
M
and m
), can be calculated. Given that for each plate the analyte is in a concentration equilibrium between the two phases, the total mass of analyte in solution in the volume of the mobile phase V
S
of the column remains constant, so long as the analyte has not reached the column outlet. So, the chromatogram corresponds to the mass in transit carried by the mobile phase at the N +1th plate (Figure 1.6) during successive equilibria. This theory has a major fault in that it does not take into account the dispersion in the column due to the diffusion of the compounds.
The plate theory comes from an early approach by Martin and Synge (Nobel laureates in Chemistry, 1952), to describe chromatography by analogy with distillation
and counter current extraction as models. This term, used for historical reasons, has no physical significance, in contrast to its homonym which serves to measure the performances of a distillation column.
The retention time t
, of the solute on the column can be sub-divided into two terms: t
M
R
(hold-up time), which cumulates the times during which it is dissolved in the mobile phase and travels at the same speed as this phase, and t
the cumulative times spent in the stationary phase, during which it is immobile. Between two successive transfers from one phase to the other, it is accepted that the concentrations have the time to re-equilibrate.
In a chromatographic phase system, there are at least three sets of equilibria: solute/mobile phase, solute/stationary phase and mobile phase/stationary phase. In a more recent theory of chromatography, no consideration is given to the idea of molecules immobilized by the stationary phase but rather that were simply slowed down when passing in close proximity.