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Resolution in Gel filtration
The success of high resolution separations in gel filtration depend, primarily on:
- Choosing conditions that provide enough space between the relevant sample zones i. e. achieving a sufficient selectivity.
- Counteracting the zone broadening effects i.e. achieving a sufficient efficiency in the
As exemplified in Figure 5.1 these two parameters are interdependent with regard to resolution. In the chromatogram to the left the two peaks show no overlap when the peaks are kept narrow i.e. when the zone broadening effects are effectively counteracted (blue trace). However, when the peak width is doubled (red trace) the overlap becomes massive. In fact, a doubling of the distance between the centers of the peaks is necessary to restore the non-overlap situation (chromatogram to the right).
Figure 5.1. The dependence of resolution on the selectivity
and the counteraction of zone broadening.
To describe phenomena as shown in Figure 5.1, resolution (Rs) is defined by the following expression:
(Vr2 - Vr1) thus represents the distance between the peaks and 1/2 (W1 + W2) the mean peak width of the two peaks (Fig 5.2).
Fig 5.2. Parameters used for defining resolution (Rs).
The distance between the peaks (Vr2 - Vr1) (the selectivity) is determined by two factors in GF:
- The selectivity curve of the medium.
The steeper the slope of the selectivity curve, the larger the DKav and consequently (Vr2 - Vr1) (Fig 5.3). 
Fig 5.3. Relation between elution differance and
differance in Mr for two proteins.
Observe however, that (Vr2 - Vr1) is not linearly related to the difference in Mr, but to the ratio between the respective Mr or to be more precise
(Vr2 - Vr1) is proportional to log(Mr1 / Mr2) for globular proteins.
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Figure 5.4 Examples on how to match fractionation
range and Mr of sample molecules.
- The length of the column.
GF is an isocratic technique meaning that elution conditions are constant throughout the entire experiment (no gradients or steps). Each sample component will thus move down the column with its own specific and constant speed . Consequently distance between the peaks increases steadily with travel distance and the longer the column, the larger the (Vr2 - Vr1). However, the sample zones broaden during their passage through the column and the longer the column, the broader the zones. This zone broadening will in part counteract what is gained in separation by the larger (Vr2 - Vr1).
In reality one need to increase the column length four times to double the resolution.
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Figure 5.5. Column length and resolution -
Effect of using two columns in series.
Peak width is affected by the following factors:
- Uniformity of the beads and of the packed bed.
These factors influence the uniformity of the flow through the column and thus the shape of the sample zones. When the stationary phase consists of irregular, non-uniform beads or when the gel bed in the column contains irregularities, the path length for the sample may vary in different parts of the column. As a result, broad asymmetric sample zones will be formed when passing the column (Fig 5.6). This type of effect is assigned the term eddy diffusion and is independent on time and flow rate.
Eddy diffusion should not be confused with the type of effects described below which depend on diffusion rather than cause it.
Figure 5.6. Eddy diffusion -
Zone broadening caused by bed irregularities.
- Bead size and flow rate.
Bead size and flow rate both influence the efficiency (the ability to keep peaks narrow) of the chromatographic process though in different ways.
Consider a zone of sample molecules moving down a GF column and involved in a continuous partitioning process between the mobile and the stationary phases (Fig 5.7) The mobile phase transports the sample molecules down the column, but acts only on the sample molecules present in the mobile phase. The molecules present in the pores of the stationary phase escape this type of transportation.
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Figure 5.7 Mass transfer directions
in a travelling sample zone.
However, the transport creates an uneven distribution of “stationary” and “mobile” sample molecules in that the concentration profile in the mobile phase will always be slightly ahead of that in the stationary phase.
The partitioning mechanism strives to correct this resulting in a mass transfer of sample molecules from the mobile phase to the pores at the front of the sample zone and a mass transfer in the opposite direction at the rear end of the zone.
This positional discrepancy in concentration profiles causes broadening of the sample zone and is a consequence of the chromatographic process itself i.e. the continuous re-partitioning.
Though always present, the extent of this type of zone broadening depends on:
- Mass transfer rate.
- Mobile phase flow rate.
To minimize it, mass transfer must be allowed time enough for equilibration (figure 5.8):
The flow rate has to be balanced against the mass transfer rate.
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Figure 5.8. Zone broadening caused
by incomplete mass transfer.
However, zone broadening caused by diffusion along the column (axial diffusion) in the mobile phase increases with the time the zone spends in the column.
Since zone broadening due to incomplete mass transfer and to axial diffusion react in opposite ways on flow rate, there exists a flow rate where the sum of these effects is at a minimum.
The diagrams in Figure 5.9 illustrate the flow rate dependence of the three different zone broadening effects discussed above for small and large molecules:
- Incomplete mass transfer dominates zone broadening at high flow rates (2). This is less pronounced for small molecules, since they diffuse faster than large molecules.
- Axial diffusion dominates at low flow rates (4). This time the effect is more pronounced for small molecules due to their higher diffusion rates.
- Eddy diffusion reflecting inhomogeneities of the gel bed is independent on flow rate (3).
- The sum total zone broadening shows a minimum (1).
Three important conclusions can be drawn:
1. Excessively high flow rates should be avoided with large molecules, while low flow rates are less detrimental.
2. With small molecules on the other hand, flow rates lower than the optimum one (minimum of curve 1 in Figure 5.9) should be avoided.
3. The optimum flow rate (minimum of curve 1) is lower for large molecules than for small ones. Moreover, curve 1 for small molecules is rounder around the minimum than that for large molecules.
Figure 5.10. Peak width and bead size -
shows the practical consequences of the effects
explanied above for three molecules with wide differing Mr.
The effects of flow rate on zone broadening discussed above applies to all chromatographic techniques based on re-partitioning.
One can facilitate the mass transfer by reducing the bead size. This will shorten distances between the beads and above all increase the "active" surface of the stationary phase, all circumstances that aid in increasing the mass transfer rate in the re-partitioning process.
The higher the mass transfer rate, the closer you get to equilibrium conditions and the lesser the zone broadening (figure 5.11). (For a given molecule the efficiency is inversely proportional to the square of the bead diameter, all other conditions being constant !)
Figure 5.11. Peaks are narrower with smaller beads
and higher flow rates may be used.
In fact, modern HPLC techniques capitalises mainly on facilitating mass transfer by employing small beads.
The chromatograms in figure 5.12 demonstrate the effect of employing smaller beads. As seen in Figure 5.11, not only will the peaks provided by 10 mm beads be narrower than those provided by 100 mm beads, they are also far less sensitive to higher flow rates.
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Figure 5.12. Effect of bead size on resolution.
The effect of bead size on zone broadening discussed above applies to all chromatographic techniques based on re-partitioning. |
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