Single-molecule junctions sensitive to binary solvent mixtures

Gregor Gurski, Henning Kirchberg, Peter Nalbach, and Michael Thorwart

Phys. Rev. B 106, 075413 – Published 17 August 2022

Abstract

We propose a quantum-mechanical model to calculate the nonlinear differential conductance of a single molecular junction immersed in a solvent, either in pure form or as a binary mixture with varying volume fraction. The solvent mixture is captured by a dielectric continuum model for which the resulting spectral density is determined within the Gladstone-Dale approach. The conductance of the molecular junction is calculated by a real-time diagrammatic technique. We find a strong variation of the conductance maximum for varying volume fraction of the solvent mixture. Importantly, the calculated molecular nonlinear conductance shows a very good agreement with experimentally measured data for common molecular junctions in various polar solvent mixtures.

Received 28 January 2022
Revised 19 June 2022
Accepted 28 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.075413

Physics Subject Headings (PhySH)

Quantum sensing Quantum transport Solvation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Gregor Gurski ¹, Henning Kirchberg ², Peter Nalbach ³, and Michael Thorwart ¹

¹I. Institut für Theoretische Physik, Universität Hamburg, Notkestr. 9, 22607 Hamburg, Germany
²Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
³Fachbereich Wirtschaft & Informationstechnik, Westfälische Hochschule, Münsterstr. 265, 46397 Bocholt, Germany

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Vol. 106, Iss. 7 — 15 August 2022

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Images

Figure 1
Nonlinear differential conductance $G = d I / d V$ as a function of the bias voltage $V$ in the absence of a solvent (gray dashed line) and with various surrounding pure solvents (solid lines) as indicated. $G_{0} = 2 e^{2} / h$ is the conductance quantum. Parameters are $a = 5$ Å, $Δ μ = 5$ D, $T = 0.1 Γ, ɛ_{d} = 1.2 Γ$ , and $Γ = 250$ meV. Inset: Sketch of the model of the molecular junction between two metallic leads and surrounded by a dielectric solvent.
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Figure 2
(a) Spectral density $J (ω)$ normalized to the reorganization energy $η_{NBZ}$ of nitrobenzene as a function of the volume fraction $f$ and the frequency $ω$ (normalized to the cutoff frequency of nitrobenzene $ω_{c}^{NBZ}$ ) for the solvent mixture between nitrobenzene and toluene. (b) Maximum of the spectral density as well as the reorganization energy $η$ , both normalized to $η_{NBZ}$ , for the solvent mixtures toluene-nitrobenzene, chlorobenzene-nitrobenzene, and dimethylformamide-nitrobenzene. The solvent parameters are given in Table S1 of the Supplemental Material [24].
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Figure 3
Maximum of the nonlinear differential conductance as a function of the volume fraction $f$ for the binary mixtures between butanol and ethanol, chlorobenzene and nitrobenzene, as well as toluene and nitrobenzene. The solid lines show the results calculated using the Gladstone-Dale effective dielectric parameters [Eq. (6)] in an effective Debye spectral density. In addition, the circles mark the conductance calculated with a single Debye spectral density of the mixture with the directly measured dielectric parameters taken from Ref. [29]. Parameters are $a = 5$ Å, $Δ μ = 5$ D, $T = 0.1 Γ, ɛ_{d} = 1.2 Γ$ , and $Γ = 250$ meV.
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Figure 4
Full width at half maximum of the nonlinear differential conductance as a function of the volume fraction $f$ for the binary solvent mixtures between nitrobenzene-toluene, nitrobenzene-chlorobenzene, and nitrobenzene-dimethylformamide. The data points have been calculated with an accuracy determined by the voltage step size of $0.02 Γ$ , and we have used a cubic spline interpolation for the final curves (solid lines). Parameters are $a = 5$ Å, $Δ μ = 5$ D, $T = 0.1 Γ, ɛ_{d} = 1.2 Γ$ , and $Γ = 250$ meV.
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Figure 5
Nonlinear differential conductance of a OPE-SMe molecular junction as a function of the volume fraction $f$ for binary solvent mixtures of ACN and TMB (red) as well as of THF and TMB (blue). Parameters are $a = 5$ Å, $Δ μ = 10$ D, $T = 10 Γ, ɛ_{d} = 120 Γ$ , and $Γ = 2.5$ meV. Experimental data are taken from Ref. [11].
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