Solvent Effects on Structure and Screening in Confined Electrolytes

Jie Yang, Svyatoslav Kondrat, Cheng Lian, Honglai Liu, Alexander Schlaich, and Christian Holm

Phys. Rev. Lett. 131, 118201 – Published 11 September 2023

Abstract

Using classical density functional theory, we investigate the influence of solvent on the structure and ionic screening of electrolytes under slit confinement and in contact with a reservoir. We consider a symmetric electrolyte with implicit and explicit solvent models and find that spatially resolving solvent molecules is essential for the ion structure at confining walls, excess ion adsorption, and the pressure exerted on the walls. Despite this, we observe only moderate differences in the period of oscillations of the pressure with the slit width and virtually coinciding decay lengths as functions of the scaling variable $σ_{ion} / λ_{D}$ , where $σ_{ion}$ is the ion diameter and $λ_{D}$ the Debye length. Moreover, in the electrostatic-dominated regime, this scaling behavior is practically independent of the relative permittivity and its dependence on the ion concentration. In contrast, the crossover to the hard-core-dominated regime depends sensitively on all three factors.

Received 28 February 2023
Revised 4 July 2023
Accepted 15 August 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.118201

Physics Subject Headings (PhySH)

Classical fluids Ionic fluids

Coarse graining Density functional calculations

Condensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Authors & Affiliations

Jie Yang^1,2, Svyatoslav Kondrat ^1,3,*, Cheng Lian ^2,†, Honglai Liu², Alexander Schlaich ^1,4,‡, and Christian Holm ^1,§

¹Institute for Computational Physics, University of Stuttgart, 70569 Stuttgart, Germany
²School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
³Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
⁴Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, 70569 Stuttgart, Germany

^*svyatoslav.kondrat@gmail.com; skondrat@ichf.edu.pl
^†liancheng@ecust.edu.cn
^‡schlaich@icp.uni-stuttgart.de
^§holm@icp.uni-stuttgart.de

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Vol. 131, Iss. 11 — 15 September 2023

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Images

Figure 1
Implicit and explicit solvent models and density profiles of confined electrolytes. (a) Schematics of two charged plates confining an electrolyte with implicit (top) and explicit (bottom) solvent models. Cations and anions have the same diameter $σ_{ion}$ and the solvent consists of two touching oppositely charged beads of the same diameter $σ_{s}$ . $x$ denotes the coordinate perpendicular to two plates separated by distance $H$ . (b) Density profiles of cations (top), anions (middle), and solvent beads (bottom) for bulk ion density $ρ_{b} = 4 M$ (salt concentration 2M) and $H / σ_{ion} = 6$ . The gray rectangles show the areas excluded to the center of ions (top and middle) and solvent beads (bottom). (c) Excess adsorption $Δ Γ_{ion} = Γ_{ion} - 2 Q / e$ [Eq. (3)] for the ions (top) and $Γ_{s}$ for the solvent (bottom) as functions of the plate-plate separation $H$ at $ρ_{b} = 4 M$ . Ion diameter $σ_{ion} = 0.5 nm$ , surface charge $Q = 0.5 e / {nm}^{2}$ , and temperature $T = 293 K$ . For the implicit solvent calculations, we have chosen $ε_{r} = 9.8$ , as estimated by a dielectric capacitor model for the explicit solvent (see the main text).
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Figure 2
Implicit vs explicit solvent models: Pressure and screening behavior. (a) Relative pressure difference $Δ P / P_{b}$ (where $Δ P = P - P_{b}$ and $P_{b}$ is the bulk pressure) as a function of slit width $H$ for the bulk ion density $ρ_{b} = 4 M$ (salt concentration $ρ_{salt} = 2 M$ ). The gray area shows separations $H < σ_{ion}$ , where $σ_{ion}$ is the ion diameter. (b) Period of oscillations $Λ$ and (c) decay length $ξ$ as functions of the scaling variable $σ_{ion} / λ_{D}$ obtained from fitting the numerical DFT results for the pressure by Eq. (4). The red symbols in panels (b) and (c) denote the salt concentration 2M used in panel (a). The parameters are the same as in Fig. 1.
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Figure 3
Effect of the relative permittivity of the solvent. (a) Screening lengths $ξ$ expressed in terms of the Debye length $λ_{D}$ as functions of $σ_{ion} / λ_{D}$ for several values of the dielectric constant $ε_{r}$ , assumed ion concentration independent. The green dashed line indicates the scaling power law $ξ / λ_{D} \propto (σ_{ion} / λ_{D})^{1.5}$ . (b) Screening lengths in aqueous electrolytes for a constant dielectric permittivity $ε_{r} = 78$ [as in panel (a)] and when $ε_{r}$ depends on the ion concentration (see the main text for the equation). The orange lines and symbols show the screening lengths obtained for large slit width ( $H / σ_{ion} \geq 16$ ) from the decay of the total ion density ( $ξ_{ρ}$ ) and charge density ( $ξ_{c}$ ) with the distance from the wall for $ε_{r} = 78$ [panel (a)] and $ε_{r} (ρ_{b})$ [panel (b)]. The parameters are the same as in Fig. 1.
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