Polymer particle sizing from Raman spectra by regression of hard model parameters

The particle size of polymer colloids is a key characteristic. It directly affects Raman measurements due to light scattering by particles. This publication exploits the extent to which these spectral changes can be correlated to the particle sizes by using a spectral hard model and data‐driven model. To this end, spectra of aqueous polystyrene nanoparticles are decomposed into pure component spectral models by means of indirect hard modeling (IHM). Each pure component model is characterized by multiple peak‐shaped Voigt profiles. By fitting the model to spectra of polymer colloids, spectral changes due to light scattering by particles are incorporated in the model parameters. The resulting parameter values are used as input for data‐driven partial least squares (PLS) regression to extract particle sizes. The method is applied to Raman spectra of polystyrene nanoparticles of 23–60 nm diameter measured repeatedly at concentrations 0.17–1 wt%. The hybrid model predicts the particle size with R2 = 0.99. In contrast, purely data‐driven PLS regression of the spectral intensities with 3 latent PLS variables results in R2 from 0.78 to 0.83. Resulting PLS scores portray a clear differentiability of Raman scattering and light scattering by particles within IHM model parameters. PLS regression coefficients further allow identification of individual peak parameters that correlate with particle size, which substantiates previous findings on correlation between Raman signal and scattering by polymer colloids. Combining IHM and data‐driven PLS regression demonstrates more accurate prediction of particle size for extended usage of Raman spectroscopy as comprehensive process analytical technology to determine sample concentrations and particle data. Spectral hard models are fitted to Raman spectra of polystyrene nanoparticles. Resulting model parameters are influenced by light scattering by polymer particles. Partial least squares (PLS) regression of model parameters allows more accurate quantification of particle size compared with direct PLS regression of spectra.