Additivity of statistical moments in the exponentially modified Gaussian model of chromatography

A homologous series of saturated fatty acids ranging from C₁₀ to C₂₂ was separated by reversed-phase capillary liquid chromatography. The resultant zone profiles were found to be fit best by an exponentially modified Gaussian (EMG) function. To compare the EMG function and statistical moments for the analysis of the experimental zone profiles, a series of simulated profiles was generated by using fixed values for retention time and different values for the symmetrical (σ) and asymmetrical (τ) contributions to the variance. The simulated profiles were modified with respect to the integration limits, the number of points, and the signal-to-noise ratio. After modification, each profile was analyzed by using statistical moments and an iteratively fit EMG equation. These data indicate that the statistical moment method is much more susceptible to error when the degree of asymmetry is large, when the integration limits are inappropriately chosen, when the number of points is small, and when the signal-to-noise ratio is small. The experimental zone profiles were then analyzed by using the statistical moment and EMG methods. Although care was taken to minimize the sources of error discussed above, significant differences were found between the two methods. The differences in the second moment suggest that the symmetrical and asymmetrical contributions to broadening in the experimental zone profiles are not independent. As a consequence, the second moment is not equal to the sum of σ² and τ², as is commonly assumed. This observation has important implications for the elucidation of thermodynamic and kinetic information from chromatographic zone profiles.