Assessment of Solubility\nBehavior of a Copolymer in\nSupercritical CO<sub>2</sub> and Organic Solvents: Neural Network\nPrediction and Statistical Analysis

In the industrial sector, understanding the behavior\nof block copolymers\nin supercritical solvents is crucial. While qualitative agreement\nwith polymer solubility curves has been evaluated using complex theoretical\nmodels in many cases, quantitative predictions remain challenging.\nThis study aimed to create a rapid and accurate artificial neural\nnetwork (ANN) model to predict the lower critical solubility and upper\ncritical solubility space of an atypical block copolymer, poly(styrene-<i>co</i>-octafluoropentyl methacrylate) (PSOM), in different supercritical\nsolvent systems over a wide range of temperatures (51.75–182.05\n°C) and high pressure (3.28–200.86 MPa). The experimental\ndata set used in this study included one copolymer, five supercritical\nsolvents, one cosolvent, and one initiator. It consisted of seven\nunique copolymer–solvent combinations (252 cloud point pressures)\nused to predict the model quantitatively and qualitatively. To predict\nthe PSOM–solvent interactions, the study considered two different\ninput systems: a six-variable system, a five-variable system, and\none target output. Initially, we used a three-layer feed-forward neural\nnetwork to select the best learning algorithm (Levenberg–Marquardt)\nfrom 14 different algorithms, considering one sample PSOM–solvent\nsystem. Then, the network topology was optimized by varying hidden\nneuron numbers from 2 to 80 for all seven PSOM–solvent combination\nsystems. The predicted cloud point pressures were in excellent agreement\nwith the experimental cloud point pressures, confirming the model’s\naccuracy. It is clear from the results of a minimum mean square error\n(≤1.90 × 10<sup>–27</sup>) and maximum linear regression <i>R</i><sup>2</sup> (≥0.99) during training, validation,\nand testing of all the data sets. Further, the ANN model accuracy\nwas tested by statistical analysis, confirming the model’s\nability to accurately capture the miscibility regions of polymers,\nenabling efficient processing of various polymer materials. This data-driven\napproach facilitates the prediction of coexistence curves for other\npolymers and complex macromolecular systems.