Soluble and miscible states are two important thermodynamic states in academic research and practical applications but their quantitative distinctions are still fuzzy. In this study, for the first time, the mathematical formulations of the quantitative criteria for distinguishing the thermodynamic soluble and miscible states are analytically developed by means of the Flory–Huggins solution theory and solubility parameter. The quantitative bottom and upper solubility limits for a total of 13 binary and ternary mixtures are calculated at different conditions. Moreover, the composition, temperature and pore radius are specifically studied to evaluate their effects on the soluble and miscible states. On the basis of the work from this study, the insoluble, soluble but immiscible, and miscible states are definitively quantified and clearly distinguished for the first time.

中文翻译：

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热力学可溶和可混溶态的定量区分

可溶和可混溶状态是学术研究和实际应用中的两个重要的热力学状态，但其定量区别仍然模糊。在本研究中，这是首次借助Flory-Huggins溶液理论和溶解度参数对区分热力学可溶和可混溶状态的定量标准的数学公式进行了分析。在不同条件下计算了总共13种二元和三元混合物的定量溶解度下限和溶解度上限。此外，专门研究了组成，温度和孔半径，以评估它们对可溶和可混溶状态的影响。根据这项研究的成果，不溶，可溶但不互溶的