Abstract The removal of toxic dyes from contaminated waters by ultrafiltration can be enhanced by the addition of water-soluble binding polymers. Herein, we report results of the complexation-ultrafiltration process applied to remove the anionic dye (Acid-Orange 7, AO7) from aqueous solutions using polyethyleneimine (PEI) as a chelating agent. Factors influencing the process were pH of feed solution, the polymer-to-dye ratio (r), and initial dye concentration (C0). A central-composite design of experiments was employed to investigate the effects of factors on the rejection efficiency and permeate flux. In this respect, we used commercial membranes (ultrafiltration discs, Ultracel® 10kDa) made of regenerated cellulose. The data-driven modeling and optimization of polymer assisted ultrafiltration process was performed with the aid of multiple regression analysis and genetic algorithms, respectively. The single-objective optimization (SOO) disclosed the conditions (pH 5.69, r = 2.46, C0 = 83 mg/L) that yielded a high rejection efficiency (99.02%). Instead, the multi-objective optimization (MOO) revealed the Pareto front. This suggested a feasible domain of factors (pH: 4.00–5.67, r: 1.55–2.49, C0: 50–83 mg/L) that provided an acceptable compromise between the rejection efficiency and permeate flux. In addition, a composite membrane (made of polysulfone and nanoclay) was tested under optimal conditions, unveiling superior rejection efficiency equal to 99.62%. Moreover, insights about molecular interactions (between AO7, PEI, and polysulfone) were unraveled by automatic docking simulations.

中文翻译：

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聚合物辅助从水溶液中超滤 AO7 阴离子染料：实验设计、多变量优化和分子对接洞察

摘要 添加水溶性粘合聚合物可以增强超滤从污染水中去除有毒染料的能力。在此，我们报告了使用聚乙烯亚胺 (PEI) 作为螯合剂从水溶液中去除阴离子染料 (Acid-Orange 7, AO7) 的复合超滤过程的结果。影响该过程的因素是进料溶液的 pH 值、聚合物与染料的比率 (r) 和初始染料浓度 (CO)。采用实验的中心复合设计来研究因素对截留效率和渗透通量的影响。在这方面，我们使用了由再生纤维素制成的商业膜（超滤盘，Ultracel® 10kDa）。分别借助多元回归分析和遗传算法对聚合物辅助超滤过程进行数据驱动建模和优化。单目标优化 (SOO) 公开了产生高排斥效率 (99.02%) 的条件 (pH 5.69, r = 2.46, C0 = 83 mg/L)。相反，多目标优化 (MOO) 揭示了帕累托前沿。这表明一个可行的因素域（pH：4.00–5.67，r：1.55–2.49，C0：50–83 mg/L）在截留效率和渗透通量之间提供了可接受的折衷。此外，复合膜（由聚砜和纳米粘土制成）在最佳条件下进行了测试，展示了高达 99.62% 的优异截留率。此外，关于分子相互作用（AO7、PEI、