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Many-Particle Limits in Molecular Solvation


In this paper, the authors study the limit of a sharp interface model for the solvation of charged particles in an implicit solvent as the number of solute particles and the size of the surrounding box tend to infinity. The energy is given by a combination of local terms accounting for the physical presence of the particles in the solvent and a nonlocal electric energy with or without an ionic effect. In the presence of an ionic effect, the authors prove a screening effect in the limit, i.e., the limit is completely localized and hence electric long-range interactions of the particles can be neglected. In the absence of the ionic effect, the authors show that the behavior of the energy depends on the scaling of the number of particles with respect to the size of the surrounding box. All scaling regimes are identified and corresponding limit results proved. In regimes with many solute particles this limit includes electric interactions of \(H^{-1}\)-type between the particles.

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The authors wish to acknowledge the Center for Nonlinear Analysis where this work was carried out.The research of Janusz Ginster was funded by the National Science Foundation under NSF PIRE Grant No. OISE-0967140. The authors are deeply grateful to Irene Fonseca and Giovanni Leoni for bringing the topic to their attention and for many fruitful discussions. The authors would also like to thank the two anonymous referees for their very thorough review of the manuscript and their helpful comments.

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Ginster, J., Gladbach, P. Many-Particle Limits in Molecular Solvation. Arch Rational Mech Anal 235, 793–839 (2020).

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