Irreversibility in redox molecular conduction: single versus double metal-molecule interfaces

Abstract

In this work we analyze the onset and manifestation of irreversibility phenomena in the charge transport at single and double metal-redox molecule interfaces, with special emphasis on the role of the nuclear system reorganization energy in causing the distortion of cyclic voltammograms in the first case and the occurrence of hysteresis phenomena in the second case. Under physical conditions for which two states of the molecular system come into play, effects of irreversibility increase with the reorganization energy at a single interface, while an opposite trend is seen in the conduction through a molecular junction. The apparent contradiction between these two behaviors, which was raised in a previous work (Migliore, A.; Nitzan, A., J. Am. Chem. Soc. 2013, 135, 9420–32) is here resolved through detailed investigation of the connections between molecule reorganization energy, bias-dependent population of the molecular redox site(s), and threshold voltage scan rate for the onset of irreversible behavior. Moreover, our investigation of the effects of the reorganization energy on the voltammogram peaks proposes a strategy for extracting the value of the reorganization energy of the molecular system from the experimental behavior.

Introduction

Redox molecules have been subject of intensive and extensive experimental investigations in the last few decades, with special focus on electrochemical measurements that are able to detect their properties as systems of biological relevance [1], [2], [3], [4] and of great potential in nano-electronics applications [2], [5], [6], [7], [8], [9]. Properties such as reorganization energy of the redox molecular system and relative alignment between molecular redox levels and metal Fermi levels play a crucial role in a large variety of observed electron transfer (ET) and transport phenomena. For example, the ability of redox molecules to be reversibly oxidized and reduced, in conjunction with the mentioned level alignment, allows for electrochemical gate control of the conductance through single redox molecules, in analogy with the mechanism operating in field effect transistors [6]. Noticeably, technological advance has allowed to track clearly the connection between improvement in junction conductance and metal-molecule level match [9]. As another example, the localization of the transferring charge around the molecular redox center and its stabilization by suitable polarization of the surrounding environment can account for observed behaviors of nonlinear charge transport, such as negative differential resistance (NDR) and hysteresis, that we have recently analyzed [10], [11].

Redox molecular conduction junctions are junctions in which the molecular bridge connecting the metal electrodes can operate in more than one redox state. Such behavior requires that at least two conduction channels coexist: a fast channel that carries most of the observed current and a slow channel whose occupation determines the junction redox state and influences the conduction through the first channel. These junctions are often characterized by irreversible behavior, i.e., at common voltage sweep rates the current response may be decoupled from the voltage change (hence, the current does not follow adiabatically the voltage), thus leading to memory effects (thermodynamic irreversibility) that appear as hysteresis over bias cycles. A similar mechanism underlies irreversibility in cyclic voltammetry of redox molecules under diffusionless [12] conditions. However, studies in the areas of voltammetry and molecular conduction junctions have mostly progressed separately so far. Connections between these two fields of study were proposed in a recent work [11] using a simple two-state molecular model (which corresponds to the slow charge-transport channel in the case of a junction). The analysis in Ref. [11] led us to an apparent contradiction: In cyclic voltammetry the threshold voltage scan rate for the onset of irreversible behavior is lower for larger reorganization energy of the redox molecular bridge. Therefore, given two systems with reorganization energies λ₁ and λ₂, and λ₂ > λ₁, the metal-molecule interface with reorganization energy λ₁ will behave ideally at voltage sweep rates for which the other interface shows already a distorted voltammogram. In general terms, the distortion of the voltammogram at a given scan rate increases with the reorganization energy. In contrast, the irreversibility in the response of a redox junction to a bias cycle, as measured by the maximum width of the hysteresis loop, appears to decrease with increasing reorganization energy of the (solvated) redox molecular bridge. Resolving this apparent contradiction is crucial to the understanding of the common mechanism for irreversibility within the two contexts. The solution of this issue is presented in this work (Section 4), after relating the mechanisms of charge transport through single and double metal-molecule interfaces (see Section 2) and after further investigating (compared to Ref. [11]) the onset of irreversibility in the charge flow through a single metal-molecule interface (Section 3). The reorganization energy of the redox molecular system generally plays a crucial role in determining the conditions for the onset of irreversibility, and the analysis of Section 3 leads to a procedure for estimating the reorganization energy from scan data of irreversible voltammetry.