Modeling Methylene Blue Aggregation in Acidic Solution to the Limits of Factor Analysis

Methylene blue (MB+), a common cationic thiazine dye, aggregates in acidic solutions. Absorbance data for equilibrated solutions of the chloride salt were analyzed over a concentration range of 1.0 x 10(-3) to 2.6 x 10(-5) M, in both 0.1 M HCl and 0.1 M HNO3. Factor analyses of the raw absorbance data sets (categorically a better choice than effective absorbance) definitively show there are at least three distinct molecular absorbers regardless of acid type. A model with monomer, dimer, and trimer works well, but extensive testing has resulted in several other good models, some with higher order aggregates and some with chloride anions. Good models were frequently indistinguishable from each other by quality of fit or reasonability of molar absorptivity curves. The modeling of simulated data sets demonstrates the cases and degrees to which signal noise in the original data obscure the true model. In particular, the more mathematically similar (less orthogonal) the molar absorptivity curves of the chemical species in a model are, the less signal noise it takes to obscure the true model from other potentially good models. Unfortunately, the molar absorptivity curves in dye aggregation systems like that of methylene blue tend to be sufficiently similar so as to lead to the obscuration of models even at the noise levels (0.0001 ABS) of typical benchtop spectrophotometers.