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Published February 12, 2021 | Supplemental Material + Published
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Like dissolves like: A first-principles theory for predicting liquid miscibility and mixture dielectric constant


Liquid mixtures are ubiquitous. Miscibility and dielectric constant are fundamental properties that govern the applications of liquid mixtures. However, despite their importance, miscibility is usually predicted qualitatively based on the vaguely defined polarity of the liquids, and the dielectric constant of the mixture is modeled by introducing mixing rules. Here, we develop a first-principles theory for polar liquid mixtures using a statistical field approach, without resorting to mixing rules. With this theory, we obtain simple expressions for the mixture's dielectric constant and free energy of mixing. The dielectric constant predicted by this theory agrees well with measured data for simple binary mixtures. On the basis of the derived free energy of mixing, we can construct a miscibility map in the parameter space of the dielectric constant and molar volume for each liquid. The predicted miscibility shows remarkable agreement with known data, thus providing a quantitative basis for the empirical "like-dissolves-like" rule.

Additional Information

© 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY). Submitted 11 September 2020; Accepted 24 December 2020; Published 12 February 2021. We thank D. Tirrell, I. Nakamura, R. Wang, K. Shen, P. Zhang, N. Alsaifi, and J. Jiang for helpful discussions throughout this work. We also thank the anonymous reviewers whose comments have helped to improve this work. Funding: This work was supported by the Yale-NUS College Start-Up Grant and the Yale-NUS College Summer Research Programme. Acknowledgement is also made to the donors of the American Chemical Society Petroleum Research Fund (53404-ND5) for partial support of this research. Author contributions: B.Z. and Z.-G.W. conceived the research. B.Z. formulated the theory. B.Z., G.R., and Z.Y.K. performed the numerical calculations and analyzed the data. B.Z. and Z.-G.W. wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

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