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This paper derives a time-domain analytic expression for chromatographic peak shapes using a stochastic-diffusive model that accounts for axial diffusion, initial spatial variance, and multiple retention mechanisms with varying event durations and rates. The resulting evaluation scheme is significantly faster than existing methods, especially in the single-slow-mechanism case. Fitting the model to literature peaks demonstrates superior accuracy compared to the exponentially modified Gaussian, with further improvements achieved by incorporating multiple slow retention mechanisms.
Achieve orders-of-magnitude faster and more accurate chromatographic peak fitting by modeling multiple retention mechanisms with a novel stochastic-diffusive framework.
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.