Dynamic Monte Carlo self-modeling curve resolution method for multicomponent mixtures

A new algorithm for performing self-modeling curve resolution (SMCR) on second-order bilinear data sets is described. The new method, called Dynamic Monte Carlo SMCR (DMC-SMCR), seeks to define boundaries of allowable pure component profiles (spectra, concentrations, etc.) in mixture analysis. The algorithm employs a directed Monte Carlo approach to search for valid solutions with high efficiency. The parameters for the search (direction, step size) are set through bootstrap estimates of the geometry of the solution space. Step sizes are also continuously adjusted to provide a success rate of 50%, ensuring that boundary regions are fully explored. The algorithm employs the usual non-negativity assumptions, but adapts to problems arising from measurement noise by accepting as valid some solutions which may exist slightly outside the principal components subspace. The DMC-SMCR algorithm was successfully applied to four different data sets: (1) UV–VIS spectra from the oxidation of oxalic acid by permanganate (three components), (2) infrared spectra from nitric acid aerosols (three components), (3) fluorescence spectra from a mixture of four polycyclic aromatic hydrocarbons (PAHs), and (4) a simulated six-component mixture. In all cases, the algorithm produced boundaries in good agreement with the known or estimated pure component profiles and calculation times were typically under 5 min on a standard laboratory computer.