Chromatographic peaks have width and this means that molecules of a single compound, despite having the same capacity factor, take different lengths of time to travel through the column. The longer an analyte takes to travel through a column, the more the individual molecules making up the sample spread out and the broader the band becomes. The more rapidly a peak broadens the less efficient the column. Detailed mathematical modelling of the processes leading to band broadening is very complex.1 The treatment below gives a basic introduction to the origins of band broadening. The causes of band broadening can be formalised in the Van Deemter equation (Equation 3) as applied to liquid chromatography:
H is the measure of the efficiency of the column (discussed above); the smaller the term the more efficient the column.
u is the linear velocity of the mobile phase; simply how many cm/s an unretained molecule travels through the column and A is the 'eddy' diffusion term; broadening occurs because some molecules take longer erratic paths while some, for instance those travelling close to the walls of the column, take more direct paths thus eluting first. As shown in Figure 10.3, for two molecules of the same compound, molecule X elutes before molecule Y. In liquid chromatography the eddy diffusion term also contains a contribution from streaming within the solvent volume itself, i.e. A (see the Cm term) is reduced if the diffusion coefficient of the molecule within the mobile phase is low because molecules take less erratic paths through not being able to diffuse out of the mainstream so easily.
B is rate of diffusion of the molecule in the liquid phase which contributes to peak broadening through diffusion either with or against the flow of mobile phase; the contribution of this term is very small in liquid chromatography. Its contribution to band broadening decreases as flow rate increases and it only becomes significant at very low flow rates.
C, is the resistance to mass transfer of a molecule in the stationary phase and is dependent on its diffusion coefficient in the stationary phase and upon the thickness of the stationary phase coated onto silica gel:
d2 thickness r =-
Ds where d2 thickness is the square of the stationary phase film thickness and D, is the diffusion coefficient of the analyte in the stationary phase.
Obviously the thinner and more uniform the stationary phase coating, the smaller the contribution to band broadening from this term. In the example shown in Figure 10.4, molecule Y is retarded more than molecule X. It could be argued that this effect evens out throughout the length of the column, but in practice the number of random partitionings during the time required for elution is not sufficient to eliminate it. As might be expected, Cs makes less contribution as u decreases.
Resistance to mass transfer of a molecule within a particle of stationary phase.
Mobile phase flow
Mobile phase flow
Cm is resistance to mass transfer brought about by the diameter and shape of the particles of stationary phase and the rate of diffusion of a molecule in the mobile where d2 packing is the square of the stationary phase particle diameter and Dm is the diffusion coefficient of the analyte in the mobile phase.
The smaller and more regular the shape of the particles of stationary phase, the smaller the contribution to band broadening from this term. In Figure 10.5 molecule X is retarded more than molecule Y both in terms of pathlength (this really belongs to the eddy diffusion term) and contact with stagnant areas of solvent within the pore structure of the stationary phase. With regard to the latter effect, the smaller the rate of diffusion of the molecular species (Dm) in the mobile phase, the greater the retardation will be. There are an insufficient number of random partitionings during elution for these effects to be evened out.
C, m d2 packing
Band broadening due to resistance to diffusion of a molecule within the mobile phase, contained within the pores of a stationary phase and due to irregularities in stationary phase pore structure.
Thus, a low diffusion coefficient for the analyte in the mobile phase increases efficiency with regard to the A term but decreases efficiency with respect to the C„, term. On balance, a higher diffusion coefficient is more favourable. Higher column temperatures reduce mass transfer effects because the rate of diffusion of a molecule in the mobile phase increases.
In practice the contributions of the A, Csu and Cmuln terms to band broadening are similar except at very high flow rates where the Csu terms predominate. At very low flow rates, the B term makes more of a contribution. A compromise has to be reached between analysis time and flow rate. Advances in chromatographic techniques are based on the minimisation of the effects of the various terms in the Van Deemter equation and it has provided the rationale for improvements in the design of stationary phases.
Indicate which of the following parameters can decrease or increase column efficiency in liquid chromatography.
• Large particle size of stationary phase
• Small particle size of stationary phase
• Thick stationary phase coating
• Thin stationary phase coating
• Regularly shaped particles of stationary phase
• Irregularly shaped particles of stationary phase
• High temperature
• Low temperature
• Uneven stationary phase coating
• Even stationary phase coating
• Uniform stationary phase particle size
• Non-uniform stationary phase particle size
• Low diffusion coefficient in the mobile phase
• High diffusion coefficient in the mobile phase
• Low diffusion coefficient in the stationary phase
• High diffusion coefficient in the stationary phase.
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