Engineering Schemes

Peak Shape Models

For an ideal separation the peaks in the chromato-gram are usually considered to be Gaussian. This is a convenient, if not always accurate, model and peak asymmetry can arise from a variety of instrumental and chromatographic sources. The most common types of peak distortion are skewness (the peak front is sharper than the rear) and tailing (the rear of the peak is elongated compared to the front). Although instrumental sources of peak asymmetry should, of course, be minimized, chromatographic sources cannot always be avoided. Curve fitting by computer offers the possibility of deconvoluting chromato-graphic peak profiles into their individual contributions. The exponentially modified Gaussian function, obtained by the combination of a Gaussian function with an exponential decay function (that provides for the asymmetry in the peak profile), is often an acceptable description of chromatographic peaks in analytical applications.

Chromatographic sources of peak asymmetry result from mechanical effects, for example the formation of voids in the stationary-phase bed and excessive extra-column volumes, and from isotherm characteristics. Most of the theory of analytical chromatographic separations is based on a linear isotherm model where the compositions in the stationary and mobile phases are proportional and characterized by a distribution constant that is independent of sample size and composition (Figure 5). The peaks resulting from a linear chromatography model are symmetrical and can be characterized by a normal distribution. The width of the chromatographic zone is proportional to retention and can be obtained directly from peak shape considerations. The extent to which the properties of the chromatographic system contribute to zone broadening (peak widths) is given by the number of theoretical plates, N. For a normal distribution this is equivalent to (tRJot)2 , where tR is the retention time and ot is the peak standard deviation in time units. Simple algebraic manipulation of this formula permits calculation of N from the peak width at base or half-height, etc. For column comparison purposes the height equivalent to a theoretical plate, H, equivalent to the column length divided by N, is generally used.

Nonlinear isotherms (nonlinear chromatography) result in the production of asymmetric peaks. Lang-muir isotherms are frequently observed for adsorption interactions on surfaces with an energetically heterogeneous distribution of adsorption sites with incompatible association/dissociation rate constants. For sorbents with monolayer coverage, Langmuir-type isotherms result when solute-stationary phase interactions are strong compared with solute-solute interactions. Because the interactions between solutes are comparatively weak, the extent of sorption decreases following monolayer formation, even though the concentration in the mobile phase is increasing. In this case the concentration of the component in the stationary phase at equilibrium is no longer proportional to its concentration in the mobile phase and the peak shape and retention time will depend on the sample composition and amount. Anti-Langmuir type isotherms are more common in partition systems when solute-stationary phase interactions are relatively weak compared with solute-solute interactions, or where column overload results from the introduction of large sample amounts. Such conditions are common in preparative chromatography, where economic considerations dictate that separations are optimized for production rate and to minimize mobile phase consumption and operating costs.