In chemometrics, two very different classes of mathematical tools, self-modeling curve resolution and hard-modeling (first-principles) methods, have been developed to resolve pure component concentration profiles and spectra from mixture spectra recorded over time during dynamic processes in application areas from overlapped chromatographic peaks to industrial batch processes. This paper presents advantages and disadvantages of each approach via examples, and two novel applications for modeling dissolution, reaction and crystallization process in one comprehensive first-principles model.

In self-modeling curve resolution (SMCR) methods, realistic constraints such as non-negativity of concentration profiles or equality constraints for known pure component spectra are imposed to produce solutions that obey the constraints and Beer’s law. In many cases, SMCR may be the only method available for resolving the pure component profiles; however, it is widely appreciated that in most circumstances, SMCR techniques do not produce unique mathematical solutions, rather a family of feasible solutions that obey boundaries imposed by the constraints. In this presentation, SMCR with a method for computing the range of feasible solutions is illustrated. An algorithm for SMCR that yields improved results by use of soft constraints with penalty functions is also described.

Methods of fitting first-principles multivariate kinetic models are powerful alternatives to SMCR. Such modeling methods do not suffer from ambiguities in the resulting solutions. In process monitoring and control applications, numerical fitting of comprehensive kinetic models use dynamic information to estimate reaction rates, chemical equilibria, process states, end-points, deviations from optimal performance and can provide mechanistic information for process adjustment and optimization.