Stochastic Processes in Electrochemistry.

Stochastic behavior becomes an increasingly dominant characteristic of electrochemical systems as we probe them on the smallest scales. Advances in the tools and techniques of nanoelectrochemistry dictate that stochastic phenomena will become more widely manifest in the future. In this Perspective, we outline the conceptual tools that are required to analyze and understand this behavior. We draw on examples from several specific electrochemical systems where important information is encoded in, and can be derived from, apparently random signals. This Perspective attempts to serve as an accessible introduction to understanding stochastic phenomena in electrochemical systems and outlines why they cannot be understood with conventional macroscopic descriptions.

Single-molecule electrochemistry: present status and outlook.

The development of methods for detecting and manipulating matter at the level of individual macromolecules represents one of the key scientific advancements of recent decades. These techniques allow us to get information that is largely unobtainable otherwise, such as the magnitudes of microscopic forces, mechanistic details of catalytic processes, macromolecular population heterogeneities, and time-resolved, step-by-step observation of complex kinetics. Methods based on optical, mechanical, and ionic-conductance signal transduction are particularly developed. However, there is scope for new approaches that can broaden the range of molecular systems that we can study at this ultimate level of sensitivity and for developing new analytical methods relying on single-molecule detection. Approaches based on purely electrical detection are particularly appealing in the latter context, since they can be easily combined with microelectronics or fluidic devices on a single microchip to create large parallel assays at relatively low cost. A form of electrical signal transduction that has so far remained relatively underdeveloped at the single-molecule level is the direct detection of the charge transferred in electrochemical processes. The reason for this is simple: only a few electrons are transferred per molecule in a typical faradaic reaction, a heterogeneous charge-transfer reaction that occurs at the electrode's surface. Detecting this tiny amount of charge is impossible using conventional electrochemical instrumentation. A workaround is to use redox cycling, in which the charge transferred is amplified by repeatedly reducing and oxidizing analyte molecules as they randomly diffuse between a pair of electrodes. For this process to be sufficiently efficient, the electrodes must be positioned within less than 100 nm of each other, and the analyte must remain between the electrodes long enough for the measurement to take place. Early efforts focused on tip-based nanoelectrodes, descended from scanning electrochemical microscopy, to create suitable geometries. However, it has been challenging to apply these technologies broadly. In this Account, we describe our alternative approach based on electrodes embedded in microfabricated nanochannels, so-called nanogap transducers. Microfabrication techniques grant a high level of reproducibility and control over the geometry of the devices, permitting systematic development and characterization. We have employed these devices to demonstrate single-molecule sensitivity. This method shows good agreement with theoretical analysis based on the Brownian motion of discrete molecules, but only once the finite time resolution of the experimental apparatus is taken into account. These results highlight both the random nature of single-molecule signals and the complications that it can introduce in data interpretation. We conclude this Account with a discussion on how scientists can overcome this limitation in the future to create a new experimental platform that can be generally useful for both fundamental studies and analytical applications.

Noise characteristics of nanoscaled redox-cycling sensors: investigations based on random walks.

We investigate noise effects in nanoscaled electrochemical sensors using a three-dimensional simulation based on random walks. The presented approach allows the prediction of time-dependent signals and noise characteristics for redox cycling devices of arbitrary geometry. We demonstrate that the simulation results closely match experimental data as well as theoretical expectations with regard to measured currents and noise power spectra. We further analyze the impact of the sensor design on characteristics of the noise power spectrum. Specific transitions between independent noise sources in the frequency domain are indicative of the sensor-reservoir coupling and can be used to identify stationary design features or time-dependent blocking mechanisms. We disclose the source code of our simulation. Since our approach is highly flexible with regard to the implemented boundary conditions, it opens up the possibility for integrating a variety of surface-specific molecular reactions in arbitrary electrochemical systems. Thus, it may become a useful tool for the investigation of a wide range of noise effects in nanoelectrochemical sensors.

Stochastic sensing of single molecules in a nanofluidic electrochemical device.

We report the electrochemical detection of individual redox-active molecules as they freely diffuse in solution. Our approach is based on microfabricated nanofluidic devices, wherein repeated reduction and oxidation at two closely spaced electrodes yields a giant sensitivity gain. Single molecules entering and leaving the cavity are revealed as anticorrelated steps in the faradaic current measured simultaneously through the two electrodes. Cross-correlation analysis provides unequivocal evidence of single molecule sensitivity. We further find agreement with numerical simulations of the stochastic signals and analytical results for the distribution of residence times. This new detection capability can serve as a powerful alternative when fluorescent labeling is invasive or impossible. It further enables new fundamental (bio)electrochemical experiments, for example, localized detection of neurotransmitter release, studies of enzymes with redox-active products, and single-cell electrochemical assays. Finally, our lithography-based approach renders the devices suitable for integration in highly parallelized, all-electrical analysis systems.

Stochastic amperometric fluctuations as a probe for dynamic adsorption in nanofluidic electrochemical systems.

Adsorption of analyte molecules is ubiquitous in nanofluidic channels due to their large surface-to-volume ratios. It is also difficult to quantify due to the nanometric scale of these channels. We propose a simple method to probe dynamic adsorption at electrodes that are embedded in nanofluidic channels or which enclose nanoscopic volumes. The amperometric method relies on measuring the amplitude of the fluctuations of the redox cycling current that arise when the channel is diffusively coupled to a bulk reservoir. We demonstrate the versatility of this new method by quantifying adsorption for several redox couples, investigating the dependence of adsorption on the electrode potential and studying the effect of functionalizing the electrodes with self-assembled monolayers of organothiol molecules bearing polar end groups. These self-assembled monolayer coatings are shown to significantly reduce the adsorption of the molecules on to the electrodes. The detection method is not limited to electrodes in nanochannels and can be easily extended to redox cycling systems that enclose very small volumes, in particular scanning electrochemical microscopy with nanoelectrodes. It thus opens the way for imaging spatial heterogeneity with respect to adsorption, as well as rational design of interfaces for redox cycling based sensors.

Lithography-based nanoelectrochemistry.

Lithographically fabricated nanostructures appear in an increasingly wide range of scientific fields, and electroanalytical chemistry is no exception. This article introduces lithography methods and provides an overview of the new capabilities and electrochemical phenomena that can emerge in nanostructures.

Fast electron-transfer kinetics probed in nanofluidic channels.

We demonstrate that a 50 nm high solution-filled cavity bounded by two parallel electrodes in which electrochemically active molecules undergo rapid redox cycling can be used to determine very fast electron-transfer kinetics. We illustrate this capability by showing that the heterogeneous rate constant of Fc(MeOH)(2) sensitively depends on the type and concentration of the supporting electrolyte. These solid-state devices are mechanically robust and stable over time and therefore have the potential to become a widespread and versatile tool for electrochemical measurements.

Electrochemical correlation spectroscopy in nanofluidic cavities.

We introduce both theoretically and experimentally a new electrochemical technique based on measuring the fluctuations of the faradaic current during redox cycling. By analogy with fluorescence correlation spectroscopy (FCS), we refer to this technique as electrochemical correlation spectroscopy (ECS). We first derive an analytical expression of the power spectral density for the fluctuations in a thin-layer-cell geometry. We then show agreement with measurements using ferrocenedimethanol, Fc(MeOH)2, in water and in acetonitrile in microfabricated thin-layer cells with a approximately 70 nm electrode spacing. The fluctuation spectra provide detailed information about the adsorption dynamics of Fc(MeOH)2, which cause an apparent slowing of Brownian motion. We furthermore observe high-frequency fluctuations from which we estimate the rates of adsorption and desorption.

(I,0) Mixed-valence state of a diiron complex with pertinence to the [FeFe]-hydrogenase active site: an IR, EPR, and computational study.

Biphenyl-2,2'-dithiolate (bpdt) bridged Fe(2)(bpdt)(CO)(6) (1) undergoes two sequential electrochemically quasi-reversible reductions. The one-electron reduction product 1(-) is unusually stable against irreversible structural changes and could be characterized by IR and EPR spectroscopy supported by computational methods. Reduction to the (I,0) state does not trigger bridging coordination of CO but partial deligation of the dithiolate in 1(-) that ultimately forms a diamagnetic dimerization product.

Redox cycling in nanofluidic channels using interdigitated electrodes.

Amperometric detection is ideally suited for integration into micro- and nanofluidic systems as it directly yields an electrical signal and does not necessitate optical components. However, the range of systems to which it can be applied is constrained by the limited sensitivity and specificity of the method. These limitations can be partially alleviated through the use of redox cycling, in which multiple electrodes are employed to repeatedly reduce and oxidize analyte molecules and thereby amplify the detected signal. We have developed an interdigitated electrode device that is encased in a nanofluidic channel to provide a hundred-fold amplification of the amperometric signal from paracetamol. Due to the nanochannel design, the sensor is resistant to interference from molecules undergoing irreversible redox reactions. We demonstrate this selectivity by detecting paracetamol in the presence of excess ascorbic acid.

Study of the electrochemical reduction of dioxygen in acetonitrile in the presence of weak acids.

The electrochemical reduction of dioxygen has been studied in acetonitrile at glassy-carbon electrodes. The initial step is the reversible one-electron reduction to form superoxide. In the presence of hydrogen-bond donors (water, methanol, 2-propanol), the superoxide forms a complex with the donor resulting in a positive shift in the potential that can be analyzed to obtain formation constants for these complexes. Stronger acids result in protonation of the superoxide followed by reduction to produce HO2-. In the absence of hydrogen-bond donors, the reduction of superoxide occurs at very negative potentials, and this second reduction peak is very much drawn-out along the potential axis, indicating a small value of the transfer coefficient, alpha. The addition of hydrogen-bond donors, HA, brings about a positive shift in this peak, without a noticeable change in shape. The reaction occurring at the second peak is a concerted proton and electron transfer (CPET) in which the electron is transferred to superoxide and a proton is transferred from HA to the superoxide, forming HO2- and A- in a concerted process. An estimation of the standard potential for this reaction shows that the second reduction always occurs at a high driving force, which explains the small value of alpha that is observed. Consistent with a CPET, a kinetic isotope effect, HA versus DA, was detected for the three hydrogen-bond donors. The increasing positive shift of the second peak with increasing water concentration has been interpreted as being a consequence of the change in the formal potential, as water is both a reactant in the process and a participant through the hydrogen-bond stabilization of the anions.

Stochasticity in single-molecule nanoelectrochemistry: origins, consequences, and solutions.

Electrochemical detection of single molecules is being actively pursued as an enabler of new fundamental experiments and sensitive analytical capabilities. Most attempts to date have relied on redox cycling in a nanogap, which consists of two parallel electrodes separated by a nanoscale distance. While these initial experiments have demonstrated single-molecule detection at the proof-of-concept level, several fundamental obstacles need to be overcome to transform the technique into a realistic detection tool suitable for use in more complex settings (e.g., studying enzyme dynamics at single catalytic event level, probing neuronal exocytosis, etc.). In particular, it has become clearer that stochasticity--the hallmark of most single-molecule measurements--can become the key limiting factor on the quality of the information that can be obtained from single-molecule electrochemical assays. Here we employ random-walk simulations to show that this stochasticity is a universal feature of all single-molecule experiments in the diffusively coupled regime and emerges due to the inherent properties of brownian motion. We further investigate the intrinsic coupling between stochasticity and detection capability, paying particular attention to the role of the geometry of the detection device and the finite time resolution of measurement systems. We suggest concrete, realizable experimental modifications and approaches to mitigate these limitations. Overall, our theoretical analyses offer a roadmap for optimizing single-molecule electrochemical experiments, which is not only desirable but also indispensable for their wider employment as experimental tools for electrochemical research and as realistic sensing or detection systems.

Electrochemical approach to concerted proton and electron transfers. Reduction of the water-superoxide ion complex.

Concerted proton and electron transfers (CPET) currently attract considerable theoretical and experimental attention, notably in view of their likely involvement in many enzymatic reactions. Electrochemistry, through techniques such as cyclic voltammetry, can provide a quite effective access to CPET in terms of diagnosis and quantitative kinetic characterization. The relationships expressing the rate constant of an electrochemical CPET are given. Besides the CPET standard potential, it depends on two main factors. One is the reorganization energy, which appears as the sum of an intramolecular contribution and two solvent reorganization energies corresponding to proton and electron transfers, respectively. The other is the pre-exponential factor that mainly depends on proton tunneling through the activation barrier. Procedures for estimating these various factors as well as the H/D kinetic isotope effect are described. Application of the theory is illustrated by the experimental results obtained for the cyclic voltammetric reduction of the water-superoxide ion complex in dimethylformamide and acetonitrile.