A novel utilisation of principal component analysis to optimise sorption isotherms and determine diffusion coefficients of five naphthalimide disperse dyes on polyester fibres

Abstract

Experimental data was gathered from more than 700 dyeings of polyester fibres with five naphthalimide disperse dyes. The dyeing process which was the same for all the dyes was carried out separately at five different temperatures, namely: 40°, 60°, 80°, 100° and 120° centigrade. Dye sorption was measured at 10 min time intervals at each temperature until the completion of the dyeing process. Additionally, the raw data was modified by the principal components analysis (PCA) in order to extract the highly informative part of the raw data (i.e. principal components). Such modified data was correlated with the six main sorption models. The results illustrate that unmodified raw data fit a dual combination of sorption models of the Nernst–Freundlich or Nernst–Scatchard type. However, the novel utilisation of PCA‐modified data illustrate that a linear Nernst type sorption model is appropriate, making it less dependent on dye structure and aggregation. The validity of this approach was confirmed by sensitivity analysis, affinity calculations and diffusivity determination. Furthermore, a novel ‘To To’ numerical method worked extremely well in determining diffusion coefficients based on the Hill's approximate solution.