Acid Red 138, as a weak acid azo dye with a long alkyl chain, is widely used for protein fiber dyeing while it cannot dissolve in supercritical carbon dioxide. The objective of this study is to investigate the solubility of Acid Red 138 with water at the temperatures of 353.15, 363.15, 373.15, 393.15 and 413.15 K and over a pressure range of 20 to 26 MPa. The test results revealed that the phase equilibrium of water and Acid Red 138 was affected by the competition between pressure and density of supercritical carbon dioxide. Furthermore, the experimental solubilities were correlated by three types of density-based model. Good agreement with less than 3.36% of average absolute relative deviation between the calculated and the experimental data of water was achieved. In addition, the Chrastil model, Mendez-Santiago–Teja model and Sung–Shim model exhibited excellent correlation results for Acid Red 138 solubilities with the AARD values of 8.58%, 6.06% and 5.19%. Better understanding of the solubility behavior of Acid Red 138 in supercritical carbon dioxide displays potential for developing a microemulsion system for the eco-friendly dyeing of natural fibers.

中文翻译：

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用水助溶剂预测酸性红 138 在超临界 CO2 中的溶解度†

酸性红138是一种具有长烷基链的弱酸性偶氮染料，广泛用于蛋白质纤维染色，但不溶于超临界二氧化碳。本研究的目的是研究酸性红 138 在 353.15、363.15、373.15、393.15 和 413.15 K 的温度和 20 至 26 MPa 的压力范围内与水的溶解度。测试结果表明，水和酸性红138的相平衡受到超临界二氧化碳压力和密度竞争的影响。此外，实验溶解度与三种基于密度的模型相关。水的计算和实验数据之间的平均绝对相对偏差小于3.36%，达到了良好的一致性。此外，Chrastil 型号，Mendez-Santiago-Teja 模型和 Sung-Shim 模型对酸性红 138 溶解度的相关性结果非常好，AARD 值为 8.58%、6.06% 和 5.19%。更好地了解酸性红 138 在超临界二氧化碳中的溶解行为，显示了开发用于天然纤维环保染色的微乳液系统的潜力。