Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

Application of static charge transfer within an ionic-liquid force field and its effect on structure and dynamics

The effects of linear scaling of the atomic charges of a reference potential on the structure, dynamics, and energetics of the ionic liquid 1,3-dimethylimidazolium chloride are investigated. Diffusion coefficients that span over four orders of magnitude are observed between the original model and a scaled model in which the ionic charges are +/- 0.5 e. While the three-dimensional structure of the liquid is less affected, the partial radial distribution functions change markedly-with the positive result that for ionic charges of +/- 0.7 e, an excellent agreement is observed with ab initio molecular dynamics data. Cohesive energy densities calculated from these partial-charge models are also in better agreement with those calculated from the ab initio data. We postulate that ionic-liquid models in which the ionic charges are assumed to be +/- 1 e overestimate the intermolecular attractions between ions, which results in overstructuring, slow dynamics, and increased cohesive energy densities. The use of scaled-charge sets may be of benefit in the simulation of these systems-especially when looking at properties beyond liquid structure-thus providing on alternative to computationally expensive polarisable force fields.

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)].

Glucose solvation by the ionic liquid 1,3-dimethylimidazolium chloride: A simulation study

Simulations of beta-glucose in the ionic liquid 1,3-dimethylimidazoliurn chloride have been performed in order to examine the solvation environment of the carbohydrate. Both single molecule and 1:5 glucose:ionic liquid (16.7 wt %) solutions are Studied, and the hydrogen bonding between sugar and solvent is examined. The primary solvation shell around the perimeter of the glucose ring consists predominantly of chloride anions which hydrogen bond to the hydroxyl groups. A small presence of the cation is also found, with the association Occurring through the weakly acidic hydrogen at the 2-position of the imidazolium ring interacting with the oxygen atoms of the sugar secondary hydroxyls. An average chloride coordination number of 4 is found around the glucose for both the single molecule and high concentration Simulations, despite the reduced chloride:glucose ratio in the latter case. In relation to the cation, the glucose molecules occupy positions above and below the plane of the imidazolium ring. Importantly, even at high glucose concentrations, no significant change in the anion-cation interactions and overall liquid structure of the ionic liquid is found, indicating that the glucose is readily accommodated by the solvent at this concentration. Dominant contributions to the sugar-ionic liquid interaction energy come from favorable hydrogen bonding (electrostatic) interactions between hydroxyls and chlorides, although a small favorable van der Waals energy contribution is also seen between the sugar and cations suggesting that the cation could be tailored in order to further improve the dissolution of glucose/cellulose in ionic liquid systems.

Electrochemical studies of gold and chloride in ionic liquids

For the first time, the electrochemistry of gold has been studied in detail in a 'second-generation', non-haloaluminate, ionic liquid. In particular, the electrochemical behaviour of Na[AuCl4] has been investigated in 1-butyl-3-methylimidazolium bis{(tifluoromethyl)sulfonyl} imide, [C(4)mim][NTf2], over gold, platinum and glassy carbon working electrodes. The reduction of [AuCl4](-) initially forms [AuCl2](-) before deposition on the electrode as Au(0). To enable stripping of deposited gold or electrodissolution of bulk gold, the presence of chloride, trichloride or chlorine is required. Specifically trichloride and chlorine have been identified as the active species which preferentially form Au(I) and Au(III), respectively.

A comparative electrochemical study of diffusion in room temperature ionic liquid solvents versus acetonitrile

Measurements on the diffusion coefficient of the neutral molecule N,N,N',N'-tetramethyl-para-phenylenediamine and the radical cation and dication generated by its one- and two-electron oxidation, respectively, are reported over the range 298-348 K in both acetonitrile and four room temperature ionic liquids (RTILs). Data were collected using single and double potential step chronamperometry at a gold disk electrode of micrometer dimension, and analysed via fitting to the appropriate analytical expression or, where necessary, to simulation. The variation of diffusion coefficient with temperature was found to occur in an Arrhenius-type manner for all combinations of solute and solvent. For a given ionic liquid, the diffusional activation energies of each species were not only closely equivalent to each other, but also to the RTIL's activation energy of viscous flow. In acetonitrile supported with 0.1 M tetrabutylammonium perchlorate, the ratio in diffusion coefficients of the radial cation and dication tot he neutral molecule were calculated as 0.89 +/- 0.05 and 0.51 +/- 0.03, respectively. In contrast, amongst the ionic liquids the same ratios were determined to be on average 0.53 +/- 0.04 and 0.33 +/- 0.03. The consequences of this dissimilarity are considered in terms of the modelling of voltammetric data gathered within ionic liquid solvents.

Double potential step chronoamperometry at microdisk electrodes: simulating the case of unequal diffusion coefficients

An efficient approach to the simulation of the double potential step chronoamperometry at a microdisk electrode based on an exponentially expanding time grid and conformal mapping of the space is presented. The dimensionless second potential step flux data are included as a function of the first potential step duration and the ratio of the diffusion coefficients of the reacting species allowing instant analysis of the experimental double potential step chronoamperograms without a need for simulation. The values of the diffusion coefficients are determined for several test systems and found to be in good agreement with existing literature data. (C) 2004 Elsevier B.V. All rights reserved.

Electroanalytical determination of trace chloride in room-temperature ionic liquids

The electroanalytical quantification of chloride in [C(4)mim][BF4], [C(4)mim][NTf2] and [C(4)mim][PF6] ionic liquids has been explored using linear sweep and square wave voltammetry. Cathodic stripping voltammetry at a silver disk electrode is found to be the most sensitive. The methodology is based on first holding the potential of the electrode at +2.0 V (vs Ag wire), to accumulate silver chloride at the electrode. On applying a cathodic scan, a stripping wave is observed corresponding to the reduction of the silver chloride. This stripping protocol was found to detect ppb levels of chloride in [C(4)mim][BF4], [C(4)mim][NTf2], and [C(4)mim][PF6]. Although other methods for chloride have been reported for [BF4](-)- and [PF6](-)-based ionic liquids, no methods have been reported for [NTf2](-) ionic liquids.

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.

Chloride determination in ionic liquids

The determination of chloride impurities in water miscible and water immiscible ionic liquids has been explored using ion chromatography (IC) and cathodic stripping voltammetry (CSV). This paper shows the first quantification of chloride in [NTf2](-) based ILs. The parameters investigated include sample preparation, solvent effect, sample stability, and limit of quantification (LOQ).

Plasma chloriding of thin-film silver - A novel process in silver-silver chloride reference electrode fabrication

Silver thin films were modified using a novel plasma modification process for the development of thin-film silver-silver chloride reference electrodes. The surface, physical, and electrochemical properties of these electrodes were investigated by atomic force microscopy, thickness and resistivity measurement techniques, as well as impedance spectroscopy and potentiometry. After plasma treatment, thin-film growth was observed and the electrodes, in general, exhibited low interface impedance and a roughened surface. Evidence of a complex surface reorganization was found. Correlating plasma conditions with film properties suggested that increasing pressure and exposure duration increased species availability, therefore governing the reaction rates, while input power appeared to influence the type of surface chemical reactions. Results also indicated that Ar/Cl-2 mixtures should be employed rather than pure chlorine plasmas. (C) 2002 The Electrochemical Society.

Full-Scale Marine Exposure Tests on Treated and Untreated Concretes Initial 7-Year Results

An extensive chloride profiling program was undertaken on concrete pier stems erected in the vicinity of the Dornoch Bridge located at the Dornoch Firth in Northeast Scotland. The pier stems were 2 m (6.562 ft) high and octagonal in plan with 0.66 m (2.165 ft) wide faces. The piers were constructed in sets of three with the lowest of each set in the tidal zone and the highest in the atmospheric zone. The pier stems were placed in such a way that they would represent the exposure conditions of the actual bridge piers of the Dornoch Bridge. In all, six of the pier stems were made using plain ordinary portland cement (OPC) concrete (with three of these having the surface treated with silane); the remaining three pier stems had a concrete containing caltite as an additive. Three exposurezones were studied: the tidal zone, the splash zone, and the atmospheric zone. The tidal zone was further subdivided into two levels defined as low-level and high-level. Chloride profiles were obtained from the different regimes over a period of 7 years for all nine pier stems. This paper describes the nature of chloride ingress and the usefulness of diffusion parameters in classifying each exposure regimes. Furthermore, the effectiveness of silane and caltite in protecting concrete from chloride ingress in different exposure zones was studied.