Column Resolution

Chromatographic separation is only achieved when there is a difference in the distribution coefficients of two components, i.e. the molecular interactions (dispersion forces, dipole interactions and hydrogen-

A value of Rs = 1.5 is normally considered to represent baseline separation for Gaussian-shaped peaks. To achieve the maximum peak resolution, both high selectivity and column efficiency (giving bands) are required.

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Linear flow rate

Figure 4 The van Deemter plot for LC and the variation of the terms A, B, Cs and Cm with flow rate. See text for details.

Linear flow rate

Figure 4 The van Deemter plot for LC and the variation of the terms A, B, Cs and Cm with flow rate. See text for details.

Increased resolution can always be achieved by an increase in column length since the peak separation (AtR) is proportional to the distance of migration down the column, but peak width is only proportional to the square root of the migration distance. The penalty for this, however, is longer retention times and an increased inlet pressure of mobile phase.

The Purnell equation shows how peak resolution is related to the retention factor (k), the plate number (N) and the relative retention (a):

where the subscript 2 refers to the second peak.

Conditions for obtaining maximum values of the plate number have already been discussed. In LC the relative retention is governed by the nature of the mobile phase as well as the stationary phase. In order to obtain a satisfactory separation, a balance must be achieved between the interactions (dispersion forces, dipole-dipole interactions, dipole-induced-dipole interactions, H-bonded forces), represented in Figure 5 by an interaction triangle.

If the interactions between the sample and stationary phase are too strong, the retention times will be excessively long, whereas if the interactions between sample and mobile phase are too strong, retention times will be too short. Modifications to the mobile phase (e.g. the addition of ion-pairing agents, chiral molecules) may also be used to change stationary-phase-mobile-phase interactions.

The interactions are maximized in the concept of 'like has an affinity for like'. Thus, for a sample which contains predominantly nonpolar species, a nonpolar stationary/mobile phase will optimize the dispersion forces, and polar interactions will be absent. For polar samples a polar stationary/mobile phase will maximize both dipole-dipole interactions and dipole-induced-dipole interactions and the effect of dispersion forces will be reduced. At least a partial separation can be achieved with a values as low as 1.01,

Figure 5 The interaction triangle in LC.

but values in the range 1.5-3.0 are preferable but above values of about 5.0 little additional resolution is achieved.

Peak resolution increases rapidly with increasing k values, but at values > 10 the term k2/(1 + k2) p 1 and the term plays no further part in the resolution. The use of k values < 1 gives very short retention times and poor resolution, so that the optimum for k is between 1 and 10. The retention equation tR = L/U(1 + k) shows that retention times are a function of both the mobile-phase velocity (U ) and the retention factor.

In LC, temperature has little effect on retention, because of the relatively small values of the enthalpies of solution involved. The van't Hoff equation describes the change in equilibrium constant with temperature and if the phase ratio ( VS/VM) is independent of temperature we can also write for the retention factor:

dT RT2

Figure 5 The interaction triangle in LC.

where AH is the enthalpy of solution (or adsorption) from the mobile phase to the stationary phase.

The main use of temperature control is to increase the reproducibility of retention times, and to increase column efficiency through the effect of temperature on viscosity and diffusion. The first choice to be made is, therefore, the choice of chromatographic mode (normal phase or reversed phase) and the stationary phase. In practice, the reversed-phase mode can be used for samples with a wide range of polarities and is usually the mode of choice. Bonded stationary phases with a hydrocarbon chain attached to the silica surface (e.g. Si-C18) are widely used; the polarity of the phase may be modified by introducing functional groups (e.g. - CN, -NH2) into the chain.

To select the mobile phase, the concept of solvent strength and polarity is utilized. A strong solvent is one which causes a sample to elute rapidly from the column. Various measures of solvent strength are used:

• solvent strength parameter (E°), based on the adsorption energies of the solvent on alumina

• solvent polarity parameter (P'), based on experimental solubility data which reSects the proton acceptor, proton donor and dipole interactions of the solvent molecule

• the Hildebrand solubility parameter (¿), which measures dispersion and dipole interactions, and hydrogen acceptor and donor properties.

Figure 1 for the general elution problem also shows values of k for different zones of the chromatogram. With low k values (k < 1) the peaks are eluted too rapidly and there is no time for separation. With high k values (k > 10) elution times are long, the peaks are broad and the peaks are over-resolved. This problem can be corrected using the technique of gradient elu-tion which is analogous to temperature programming in gas chromatography. Assuming that the chromato-gram in Figure 1 was obtained isocratically using a binary mixture of 50% methanol-water, it would be possible to choose a lower solvent strength mixture (e.g. 25% methanol-water) and then increase the methanol content (say to 75%) over a given period of time. This would have the effect of increasing the k values for the early peaks and decreasing the k values for the later peaks, the object being to get all peaks in the optimum region, where k is between 1 and 10. Modern computer-controlled liquid chrom-atographs have the facility to use isocratic periods and linear and nonlinear gradient programs with multiple ramps to give better control over k values.

The retention equation also indicates that a similar effect could be achieved using the analogous technique of flow programming and changing the mobilephase flow rate. Having optimized the retention factors by gradient elution, it may still be necessary to alter the selectivity of the system in order to achieve a complete separation. Using the solvent strength parameters, solvents can be classified into eight groups according to their proton acceptor, proton donor and dipole properties and a triangular graph constructed. Solvents are selected from the different classes in order to maximize differences in their properties (bearing in mind the need for solvent compata-bility, e.g. miscibility).

For the solvent polarity parameter the value of P' for a binary mixture (AB) is given by:

where and are volume fractions of A and B.

From this relationship it is possible to calculate mixtures of solvents having the same solvent strengths, e.g. 45% methanol-water, 52% acetonit-rile-water, 37% tetrahydrofuran-water all have the same solvent strength and would give the same retention factors (k), but because of their different proton acceptor/donor and dipole properties they would give different selectivities (a values).

A satisfactory separation is achieved when all three terms in the Purnell equation are optimized.

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