Voltammetry of oxygen in the room-temperature ionic liquids 1-ethyl-3-methylimidazolium bis((trifluoromethyl)sulfonyl)imide and hexyltriethylammonium bis((trifluoromethyl)sulfonyl)imide: One-electron reduction to form superoxide. Steady-state and transient behavior in the same cyclic voltammogram resulting from widely different diffusion coefficients of oxygen and superoxide

The electrochemical reduction of oxygen in two different room-temperature ionic liquids, 1-ethyl-3-methylimidazolium bis((trifluoromethyl)sulfonyl)imide ([EMIM][N(Tf)(2)]) and hexyltriethylammonium bis((trifluoromethyl)sulfonyl)imide ([N-6222][N(Tf)(2)]) was investigated by cyclic voltammetry at a gold microdisk electrode. Chronoamperometric measurements were made to determine the diffusion coefficient, D, and concentration, c, of the electroactive oxygen dissolved in the ionic liquid by fitting experimental transients to the Aoki model. [Aoki, K.; et al. J. Electroanal. Chem. 1981, 122, 19]. A theory and simulation designed for cyclic voltammetry at microdisk electrodes was then employed to determine the diffusion coefficient of the electrogenerated superoxide species, O-2(.-), as well as compute theoretical voltammograms to confirm the values of D and c for neutral oxygen obtained from the transients. As expected, the diffusion coefficient of the superoxide species was found to be smaller than that of the oxygen in both ionic liquids. The diffusion coefficients of O-2 and O-2(.-) in [N-6222][N(Tf)(2)], however, differ by more than a factor of 30 (D-O2 = 1.48 x 10(-10) m(2) s(-1), DO2.- = 4.66 x 10(-12) m(2) s(-1)), whereas they fall within the same order of magnitude in [EMIM][N(Tf)(2)] (D-O2 = 7.3 x 10(-10) m(2) s(-1), DO2.- = 2.7 x 10(-10) m(2) s(-1)). This difference in [N-6222][N(Tf)(2)] causes pronounced asymmetry in the concentration distributions of oxygen and superoxide, resulting in significant differences in the heights of the forward and back peaks in the cyclic voltammograms for the reduction of oxygen. This observation is most likely a result of the higher viscosity of [N-6222][N(Tf)(2)] in comparison to [EMIM][N(Tf)(2)], due to the structural differences in cationic component.

On the steady-state assumption and its application to the rotating disk voltammetry of adsorbed enzymes

Rotating disk voltammetry is routinely used to study electrochemically driven enzyme catalysis because of the assumption that the method produces a steady-state system. This assumption is based on the sigmoidal shape of the voltammograms. We have introduced an electrochemical adaptation of the King-Altman method to simulate voltammograms in which the enzyme catalysis, within an immobilized enzyme layer, is steadystate. This method is readily adaptable to any mechanism and provides a readily programmable means of obtaining closed form analytical equations for a steady-state system. The steady-state simulations are compared to fully implicit finite difference (FIFD) simulations carried out without any steady-state assumptions. On the basis of our simulations, we conclude that, under typical experimental conditions, steady-state enzyme catalysis is unlikely to occur within electrode-immobilized enzyme layers and that typically sigmoidal rotating disk voltammograms merely reflect a mass transfer steady state as opposed to a true steady state of enzyme intermediates at each potential.

Determination of the standard heterogeneous rate constant in polyelectrolyte using steady state microdisk voltammograms

The steady state voltammogram at a microdisk electrode is used to measure the diffusion coefficient and standard heterogeneous rate constant (k(s)) of ferrocene in polyelectrolyte PEG + LiClO4. The k(s) obtained is smaller in polyelectrolyte than in liquid medium. It is proposed that the polymer solvent electron transfer dynamics are affected by the relaxation rates of the ether dipole sites on the polymer chains, which are in turn constrained by the rates of polymer chain segment, or local structure, relaxations. The dependence of k(s) on temperature is observed. The k(s) increases with increasing temperature.

Study on ferrocene derivatives diffusion dynamics in polymer electrolyte by solid-state voltammetry

The diffusion rates of seven ferrocene derivatives have been estimated in polyelectrolyte PEG . LiClO4 by using non-steady-state chronoamperometry. The D-app of ferrocene derivatives increases with temperature, and the dependency of D-app on temperature obeys the Arrhenius equation. The D-app of ferrocene derivatives decreases with increasing size of electroactive species. The Delta D-app values of D-T>Tm and D-T T-m in the polyelectrolyte. On the other hand, the diffusion behaviour of ferrocene derivatives is qualitatively analyzed by using cyclic voltammetry. Copyright (C) 1996 Elsevier Science Ltd

A study of the dependence of ferrocene diffusion on electrolyte concentration and size in a polymer medium using non-steady-state chronoamperometry

This article describes a quantitative study of the diffusion rate of ferrocene(Fc) dissolved in ploy(ethylene glycol)(PEG) medium containing MClO(4)(M = Li+, Na+, Bu(4)N(+), Hx(4)N(+)). The apparent diffusion coefficient D-app and the active concentration c(a) of Fc were simultaneously measured by using non-steady-state chronoamperometry. The D-app and c(a) of Fc have been estimated in PEG containing different concentrations and sizes of supporting electrolyte, and the dependence of D-app on ferrocene concentrations has been observed. The values of D-app decrease with increasing concentrations of Fc, increasing concentrations of LiClO4 or the ratio (O:Li) and also with 4 decreasing cation radius of the electrolyte. The temperature dependencies conform to a simple free volume model. The concentration and size of the counterion dependencies of the diffusion rate are similar to the behavior of their dependencies of ionic conductivity in polyelectrolyte.

THEORY OF STEADY-STATE CURRENT AT MULTIPLE MICROCYLINDER ELECTRODES COUPLED WITH A PARALLEL PLANAR ELECTRODE

A novel device of multiple cylinder microelectrodes coupled with a parallel planar electrode was proposed. The feedback diffusion current at this device was studied using bilinear transformation of coordinates in the diffusion space, where lines of mass flux and equiconcentration are represented by orthogonal circular functions. The derived expression for the steady-state current shows that as the gap between cylindrical microelectrodes and planar electrode diminishes, greatly enhanced currents can be obtained with high signal-to-noise ratio. Other important geometrical parameters such as distance between adjacent microcylinders, cylinder radius, and number of microcylinders were also discussed in detail.

APPLICATION OF ULTRAMICROELECTRODES IN STUDIES OF HOMOGENEOUS CATALYTIC REACTIONS .3. THE CONDITION FOR QUASI-1ST AND 2ND-ORDER HOMOGENEOUS CATALYTIC REACTIONS AT ULTRAMICRODISK ELECTRODES IN THE STEADY-STATE

The conditions for quasi-first and second order homogeneous catalytic reactions and their variation with each other at an ultramicrodisk electrode in the steady state are discussed in this paper. The order of reaction can be controlled by changing the dimension of the ultramicroelectrode: the second order reaction can be changed to quasi-first by decreasing the dimension of the ultramicroelectrode. An example of this is given. The main factor effect on the reaction order is the dimension of the ultramicroelectrode. The K4Fe(CN)6-aminopyrine system is selected to confirm the theory, the experiments showing that the system is a second order reaction at a 432 mum microelectrode, and a quasi-first order reaction at a 19 mum ultramicroelectrode. The kinetic constant of the system can be determined by applying the previous theory of homogeneous catalytic reaction.

Extraction of electrode kinetic parameters from microdisc voltammetric data measured under transport conditions intermediate between steady-state convergent and transient linear diffusion as typically applies to room temperature ionic liquids

The extraction of electrode kinetic parameters for electrochemical couples in room-temperature ionic liquids (RTILs) is currently an area of considerable interest. Electrochemists typically measure electrode kinetics in the limits of either transient planar or steady-state convergent diffusion for which the voltammetic response is well understood. In this paper we develop a general method allowing the extraction of this kinetic data in the region where the diffusion is intermediate between the planar and convergent limits, such as is often encountered in RTILs using microelectrode voltammetry. A general working surface is derived, allowing the inference of Butler-Volmer standard electrochemical rate constants for the peak-to-peak potential separation in a cyclic voltammogram as a function of voltage scan rate. The method is applied to the case of the ferrocene/ferrocenium couple in [C(2)mim][N(Tf)(2)] and [C(4)mim][N(Tf)(2)].

Accelerated computation of cyclic steady state for simulated-moving-bed processes

Industrial applications of the simulated-moving-bed (SMB) chromatographic technology have brought an emergent demand to improve the SMB process operation for higher efficiency and better robustness. Improved process modelling and more-efficient model computation will pave a path to meet this demand. However, the SMB unit operation exhibits complex dynamics, leading to challenges in SMB process modelling and model computation. One of the significant problems is how to quickly obtain the steady state of an SMB process model, as process metrics at the steady state are critical for process design and real-time control. The conventional computation method, which solves the process model cycle by cycle and takes the solution only when a cyclic steady state is reached after a certain number of switching, is computationally expensive. Adopting the concept of quasi-envelope (QE), this work treats the SMB operation as a pseudo-oscillatory process because of its large number of continuous switching. Then, an innovative QE computation scheme is developed to quickly obtain the steady state solution of an SMB model for any arbitrary initial condition. The QE computation scheme allows larger steps to be taken for predicting the slow change of the starting state within each switching. Incorporating with the wavelet-based technique, this scheme is demonstrated to be effective and efficient for an SMB sugar separation process. Moreover, investigations are also carried out on when the computation scheme should be activated and how the convergence of the scheme is affected by a variable stepsize.

Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

Volatile properties of particles emitted by compressed natural gas and diesel buses during steady state and transient driving modes

Volatile properties of particle emissions from four compressed natural gas (CNG) and four diesel buses were investigated under steady state and transient driving modes on a chassis dynamometer. The exhaust was diluted utilising a full-flow continuous volume sampling system and passed through a thermodenuder at controlled temperature. Particle number concentration and size distribution were measured with a condensation particle counter and a scanning mobility particle sizer, respectively. We show that, while almost all the particles emitted by the CNG buses were in the nanoparticle size range, at least 85% and 98% were removed at 100ºC and 250ºC, respectively. Closer analysis of the volatility of particles emitted during transient cycles showed that volatilisation began at around 40°C with the majority occurring by 80°C. Particles produced during hard acceleration from rest exhibited lower volatility than that produced during other times of the cycle. Based on our results and the observation of ash deposits on the walls of the tailpipes, we suggest that these non-volatile particles were composed mostly of ash from lubricating oil. Heating the diesel bus emissions to 100ºC removed ultrafine particle numbers by 69% to 82% when a nucleation mode was present and just 18% when it was not.

How long does it take for aquifer recharge or aquifer discharge processes to reach steady state?

Groundwater flow models are usually characterized as being either transient flow models or steady state flow models. Given that steady state groundwater flow conditions arise as a long time asymptotic limit of a particular transient response, it is natural for us to seek a finite estimate of the amount of time required for a particular transient flow problem to effectively reach steady state. Here, we introduce the concept of mean action time (MAT) to address a fundamental question: How long does it take for a groundwater recharge process or discharge processes to effectively reach steady state? This concept relies on identifying a cumulative distribution function, $F(t;x)$, which varies from $F(0;x)=0$ to $F(t;x) \to \infty$ as $t\to \infty$, thereby providing us with a measurement of the progress of the system towards steady state. The MAT corresponds to the mean of the associated probability density function $f(t;x) = \dfrac{dF}{dt}$, and we demonstrate that this framework provides useful analytical insight by explicitly showing how the MAT depends on the parameters in the model and the geometry of the problem. Additional theoretical results relating to the variance of $f(t;x)$, known as the variance of action time (VAT), are also presented. To test our theoretical predictions we include measurements from a laboratory–scale experiment describing flow through a homogeneous porous medium. The laboratory data confirms that the theoretical MAT predictions are in good agreement with measurements from the physical model.

Volatile properties of CNG and Diesel bus emissions produced during steady state and transient driving modes

An analysis of the emissions from 14 CNG and 5 Diesel buses was conducted during April & May, 2006. Studies were conducted at both steady state and transient driving modes on a vehicle dynamometer utilising a CVS dilution system. This article will focus on the volatile properties of particles from 4 CNG and 4 Diesel vehicles from within this group with a priority given to the previously un-investigated CNG emissions produced at transient loads. Particle number concentration data was collected by three CPC’s (TSI 3022, 3010 & 3782WCPC) having D50 cut-offs set to 5nm, 10nm & 20nm respectively. Size distribution data was collected using a TSI 3080 SMPS with a 3025 CPC during the steady state driving modes. During transient cycles mono-disperse “slices” of between 5nm & 25nm were measured. The volatility of these particles was determined by placing a thermodenuder before the 3022 and the SMPS and measuring the reduction in particle number concentration as the temperature in the thermodenuder was increased. This was then normalised against the total particle count given by the 3010 CPC to provide high resolution information on the reduction in particle concentration with respect to temperature.