A new combination of previously established molecular-thermodynamic methods was offered in conjunction with the Cubic Plus Association (CPA) equation of state (EoS) for the assessment of the second critical micelle concentration (SCMC), and curvature parameters in aqueous solutions of non-ionic surfactants encompassing Tween 80, Tween 60, Span 80, and Span 60. This combination will yield a quantifiable examination that adheres to creating the micelles resembling worms, enabling the optimization of critical curvature parameters, as well as the prediction of the SCMC. This previously well-known model is reliant upon theoretical components, including chain conformation, headgroup-steric effects, and interfacial tension pertaining to the energy of micelle-free systems. So, the optimized curvature parameters obtained because of these forces can be used as the input of CPA EoS to independently count the association interactions and predict the SCMC for the first time. For the aforementioned surfactants, the first critical micelle concentration (FCMC) data was previously used to modify five pure parameters of the CPA EoS. Consequently, applying the adjusted parameters, the SCMC of noted aqueous solutions has been predicted reasonably using CPA EoS.

中文翻译：

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通过 CPA EoS 预测吐温和司盘水溶液的第二临界胶束浓度：定量理论在蠕虫状胶束生长中的应用

先前建立的分子热力学方法的新组合与立方加协会（CPA）状态方程（EoS）一起提供，用于评估第二临界胶束浓度（SCMC）和非水溶液中的曲率参数离子表面活性剂包括 Tween 80、Tween 60、Span 80 和 Span 60。这种组合将产生可量化的测试，坚持创建类似蠕虫的胶束，从而能够优化临界曲率参数以及 SCMC 的预测。这个先前众所周知的模型依赖于理论成分，包括链构象、头基空间效应以及与无胶束系统能量相关的界面张力。因此，由于这些力而获得的优化曲率参数可以用作 CPA EoS 的输入，以独立计算关联相互作用并首次预测 SCMC。对于上述表面活性剂，第一临界胶束浓度 (FCMC) 数据先前用于修改 CPA EoS 的五个纯参数。因此，应用调整后的参数，使用 CPA EoS 合理地预测了所示水溶液的 SCMC。