Chromatographic Peak Shape from a Stochastic-Diffusive Model with Multiple Retention Mechanisms: Analytic Time-Domain Expression and Derivatives

TL;DR

This paper derives an efficient analytical model for chromatographic peak shapes within a stochastic-diffusive framework, incorporating multiple retention mechanisms, and demonstrates its superior fitting accuracy over traditional models.

Contribution

It introduces a novel, computationally efficient analytic expression for complex chromatographic peak shapes with multiple retention mechanisms, including derivatives for parameter optimization.

Findings

The model is 2-4 orders faster than previous methods.

It achieves lower RMSE than the exponentially modified Gaussian in literature.

Allowing multiple slow mechanisms improves fit significantly for some peaks.

Abstract

A time-domain analytic expression for chromatographic peak shapes is derived within a stochastic-diffusive framework that incorporates axial diffusion (molecular and multipath/Eddy), finite initial spatial variance, a retention mechanism characterized by a high rate of short-duration events, and an arbitrary number of independent slow retention mechanisms, each characterized by its own rate of infrequent, long-duration events. A highly efficient evaluation scheme is derived for this expression. In the single-slow-mechanism case, it is two to four orders of magnitude faster than the previously available analytic route. Analytical derivatives with respect to all model parameters are also obtained, and each can be evaluated at computational cost comparable to that of the peak-shape expression. Illustrative fits to three literature peaks yielded full-profile RMSE values lower than those of the exponentially modified Gaussian in all tested cases, with minima ranging from 0.03 to 0.14 percent of peak height, compared with 0.43 to 5.57 percent for the reference model. Relative to the one-slow-mechanism formulation, allowing more than one slow mechanism produced a data-dependent improvement that exceeded one order of magnitude for one of the peaks.