Experimental

1. Advantages of Soft versus Hard Constraints in Self-Modelling Curve Resolution Problems. Alternating Least Squares with Multi-way Penalty Function

2. An extension to the Penalty Alternating Least Squares (P-ALS) method, called Multiway Penalty Alternating Least Squares (NWAY P-ALS) has been developed. Optionally hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row wise penalty least squares function. Employment of the soft penalty function resulted in reduced distortion of resolved profiles, fast monotonical convergence, minimisation of active constraints, reduced model lack-of-fit, reduced impact of noise and non-ideal response.

3. Experimental • Three reactions of the pyridine catalysed esterification of acetic anhydride were completed at equimolarity of anhydrous 1-butanol (46.3ml), to acetic anhydride (47.6ml), with different pyridine catalyst concentration, (4ml, 8ml, 2ml), for batches 1-3 respectively. The final batch, batch 4 was completed using a reagent mol ratio of 2:1, Acetic anhydride (47.6ml), anhydrous 1-butanol (23.2ml), and a pyridine catalyst (4ml)

4. A1 A2 A3 m np Row-wise augmentation A3 A2 A1 A1 p A A2 = Ar m n A3 mp n Column-wise augmentation A3 A2 A1 p mn Tube-wise augmentation Example of the three different modes or augmentations of a three-way dataset

5. Column wise augmentation of the NIR batches of the pyridine catalysed esterifcation reaction of 1-butanol

6. Resolved spectral profiles and concentration profiles of acetic anhydride (-),1-butanol (---) and pseudo product (…). Constrained profile (bold line), unconstrained profile (normal line), using the soft MCR-ALS option