Relationships Between Different Chromatographic Peak Description ...

Published: Journal of Chromatographic Science, Volume 33, Number 4, April 1995, pp. 194-203.

Relationships Between Different Chromatographic Peak Description Functions and Numerical Solutions of the Mass Balance Equation
Joaquim Olivé and Joan O. Grimalt

Diverse mathematical models for chromatographic peak description—Gaussian, log–normal, gamma, Weibull, Haarhoff and der Van Linde, Littlewood, exponentially modified Gaussian, Gram–Charlier, and Edgeworth–Cramér series—are evaluated by curve fitting to solutions of the differential mass balance equation obtained numerically by an implicit finite differences method. The peak profiles generated from this equation are representative of diverse integration conditions encompassing different adsorption equilibrium isotherms (linear, Langmuir, and Freundlich), injection modes (pulse, exponential, reverse ramp, semiparabolic, and triangular), and axial longitudinal dispersion coefficients. Curve fitting is performed with a generalized least-squares method. The results show a good correspondence between the solutions of the mass balance equation, combined with a linear isotherm, and symmetric injection modes, with the Gaussian function and the functions that may approach Gaussian expressions (exponentially modified Gaussian, Gram–Charlier, Edgeworth–Cramér, log–normal, Haarhoff and der Van Linde). The exponentially modified Gaussian function gives the best fit for the profiles generated with this isotherm and the exponential injection modes. The solution of the mass balance equation, combined with the Langmuir isotherm, shows that the Haarhoff and der Van Linde function is better adapted to this type of profile. Finally, a good correlation between the log–normal function and the solutions of the mass balance equation, combined with the Freundlich isotherm, is observed.

Reproduction of editorial content of this journal is prohibited without publisher’s permission.

This article is available in its entirety by fax for $4.00 per page.
Visa or MasterCard accepted.

To order electronically click here
or call: 847-647-2900 ext. 1323
or fax request to: 847-647-1155.

Please indicate JCS volume and issue along with page numbers.