In this paper we demonstrate the existence of a total analogy between the potentiostatic and chro... more In this paper we demonstrate the existence of a total analogy between the potentiostatic and chronopotentiometric responses when a constant potential E and a programmed current of the form I(t)sI 0 t u , uGy1/2 , respectively, are applied to planar and spherical electrodes, and also to hemispherical microelectrodes. From the above analogy, we also compare differential pulse voltammetry (DPV) and a new reciprocal derivative chronopotentiometric technique proposed in this paper.
A rigorous and simple analytical solution is reported for the square scheme in single pulse techn... more A rigorous and simple analytical solution is reported for the square scheme in single pulse techniques at (hemi)spherical electrodes when the electron transfers are reversible and the coupled chemical reactions are at equilibrium. The solution presented imposes no restriction to the values of the diffusion coefficients of the different species, and then it fully describes the cases where the coupled chemical processes involve significant changes of diffusivity. Simple criteria are discussed to understand and predict the effects of electrode radius, experiment timescale and chemical thermodynamics on the results obtained in normal pulse voltammetry and derivative voltammetry. Unlike at macroelectrodes and ultramicroelectrodes, the position of the voltammograms (in these and other voltammetric techniques) is time dependent at spherical electrodes of intermediate size when the diffusion coefficients of the species are unequal. An analytical expression for the half-wave potential is given to describe this behaviour and also to assist the quantitative determination of the diffusion coefficients, formal potentials and equilibrium constants with the electrochemical techniques abovementioned. Keywords Unequal diffusion coefficients. Analytical solution. Square scheme. (Hemi)spherical electrodes. Single pulse voltammetry 0 AL/BL E ′ where k 1 ,k 1 ′ and k 2 ,k 2 ′ are the forward and backward rate constants of the different chemical reactions. The solution
The mathematical modelling of heterogeneous charge transfer processes complicated by the reactivi... more The mathematical modelling of heterogeneous charge transfer processes complicated by the reactivity of the redox species in solution is revisited, elaborating on powerful and accurate theoretical approaches and simplifications that can facilitate and speed up the mathematical resolution, the solution implementation, the design of experiments and the calculation and analysis of the electrochemical response. The physicochemical fundamentals and mathematical implications behind such approaches will be discussed for frequent and paradigmatic reaction mechanisms involving homogeneous chemical equilibria and (pseudo)first-order and second-order chemical kinetics. The cases considered will point out how the suitable preliminary examination of the boundary value problem offers profound insights into the electrochemical system that can assist the design of theoretical and experimental studies. This provides criteria for the assessment of complex simulations (for example, by comparison with exact analytical solutions for particular cases) and it can alert about meaningless results derived from blind use of approximations and/or 'brute force' approaches.
Key processes in (bio)electrochemistry involve multiple electron transfers. The study of the stab... more Key processes in (bio)electrochemistry involve multiple electron transfers. The study of the stability of the different oxidation states and the interaction between redox centers is fundamental to understand these processes. In this paper, simple analytical equations are presented for multielectron transfer processes in cyclic voltammetry (CV) and staircase cyclic voltammetry (SCV) at disc electrodes of any size. This provides a simple simulation method for the electrochemical response without demanding computing. The use of CV and SCV, and the corresponding differential techniques, for the characterization of these redox systems is analyzed. Procedures and criteria are given for transient and stationary conditions. The theoretical results are applied to the experimental study of the reduction of anthraquinone-2-sulfonate in water on gold macro-and microdisc electrodes.
A simple theoretical approach is presented to study simple and facilitated ion transfer processes... more A simple theoretical approach is presented to study simple and facilitated ion transfer processes at liquid/liquid microinterfaces of the most common geometries: micropipettes, microholes, micropores and microcapillaries. A general and accurate expression is reported for the current-potential response in any voltammetric technique. The analytical solution describes the effects on the voltammetry of the (very) different mass transport conditions in each phase whatever the size and geometry of the interface and of the values of the diffusion coefficients of the ion. The theory is applied to normal pulse voltammetry and cyclic voltammety, analysing the influence of the geometry on the position and shape of the voltammograms as well as on the attainment of a steady state response. Finally, explicit analytical expressions are derived for the determination of the formal transfer potential of the ion and of the equilibrium constant of the coupled chemical equilibrium from the half-wave potential under steady state conditions.
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
In this chapter, a review is given of the application of the multipulse and sweep techniques Cycl... more In this chapter, a review is given of the application of the multipulse and sweep techniques Cyclic Staircase Voltammetry (SCV) and Cyclic Voltammetry (CV) to the study of more complex electrode processes than single charge transfer reactions (electronic or ionic), which were addressed in Chap. 5.
In a single potential step voltammetric technique, several constant potentials (of increasing amp... more In a single potential step voltammetric technique, several constant potentials (of increasing amplitude) are applied with a time length t 1. When stationary electrodes are used, the time interval between two consecutive potentials must be much greater than t 1, for the initial conditions to be restored (Scheme 2.1). If a Static Mercury Drop Electrode (SMDE) is used, the initial conditions are simply restored by making the drop fall. The measured current at a fixed time value \( t={t}_1 \) is plotted versus the corresponding potential steps discretely [1–3]. The resulting current–potential curve has a sigmoidal shape whose position and slope depend on the reversibility of the electrode process and the wave height is independent of the electron transfer rate. At each fixed potential value, the current–time variation (which has a typical cottrellian behavior for reversible processes at planar electrodes when considering diffusive transport only) can be registered. If the length time is in the range 2–200 ms, the electrochemical technique is called Normal Pulse Voltammetry (NPV), originally known as Normal Pulse Polarography (NPP). This technique was introduced by Barker [5–7] and it was originally designed for the Dropping Mercury Electrode (DME), in which the potential pulse is applied at the end of the life of the drop, with the current being dependent on the relation between the pulse time and the drop lifetime. The main reason for measuring the current at the end of short time intervals is to eliminate the capacitative component (see Sect. 1.9) in order to optimize the sensitivity. Today the DME electrode is scarcely used and most electrochemical techniques are used at stationary electrodes
The general analytical expressions corresponding to the response obtained for a charge transfer p... more The general analytical expressions corresponding to the response obtained for a charge transfer process in cyclic chronopotentiometry are presented. The different geometries considered for the mass transport operator are planar, tubular and spherical. In the case of spherical electrodes (such as the dropping mercury electrode and the static mercury dropping electrode), we have analyzed the following two cases: solution soluble product and electrode soluble product or amalgamation. The solutions deduced here are independent of the method used in solving the differential equations system since we have applied the superposition principle for which we have only used the properties of the linear operators.
... All rights reserved PII: 800134686(96)003568 00131686 97 17.00 + 0.00 Discrimination between ... more ... All rights reserved PII: 800134686(96)003568 00131686 97 17.00 + 0.00 Discrimination between CEC, CE and EC mechanisms by using a sinusoidal currenttime function MariaLuisa Alcaraz,*Angela Molina and Manuela LopezTenes Departamento de Quimica Fisica ...
The study of the reversible reduction/oxidation molecules containing multiple interacting or noni... more The study of the reversible reduction/oxidation molecules containing multiple interacting or noninteracting redox centers has been carried out using the multipotential step technique Differential Staircase Voltammetry (DSCV). Methods to obtain the formal potentials and other characteristic parameters of the process are proposed for any interaction degree between the centers, when using spherical electrodes of any size (from planar to ultramicrospherical electrodes) and, in particular, the advantages of microelectrodes are discussed. The theoretical predictions have been tested with two experimental systems: ethyl viologen in acetonitrile and pyrazine in aqueous acid media, finding an excellent agreement between the theory and experiments. Therefore, the formal potentials for these systems have been evaluated using DSCV.
Este manual se presenta como una “caja de herramientas” donde acudir en busca de recursos y activ... more Este manual se presenta como una “caja de herramientas” donde acudir en busca de recursos y actividades didacticas para elaborar formaciones en diversidad sexual, familiar, corporal y de expresion e identidad de genero, dirigidas a profesionales que trabajan con jovenes. En este sentido, son materiales que se pueden adaptar a las necesidades de cada formacion y a distintos niveles de conocimiento, tanto de los grupos participantes, como de la persona que dinamice las actividades y que son lo suficientemente flexibles para que puedan ser moldeados y utilizados segun los recursos temporales y espaciales que presente cada propuestaformativa. “Somos diversidad” ofrece un total de 44 actividades articuladas en 5 modulos tematicos. Abrazar la diversidad como una oportunidad educativa Transformarse para transformar: afectividad, diferencia y diversidad Sexualidades Corporalidades, identidades y expresiones de genero Diversidad familiar Cada modulo ofrece un indice inicial, una breve bienve...
Square wave voltammetry (SWV) with a solvent polymeric membrane ion sensor has been applied to st... more Square wave voltammetry (SWV) with a solvent polymeric membrane ion sensor has been applied to study the ion transfer of several ionic liquid cations, from water to a poly(vinyl chloride) membrane plasticized with 2-nitrophenyl octyl ether. The study has mainly been focused on dialkylimidazolium and alkylpyridinium cations. The experimental voltammograms obtained are in good agreement with the theoretical predictions. The standard ion transfer potentials of the ionic liquid cations have been obtained and the values found have been used to draw some conclusions on the relationship between structure and lipophilicity. Also, a relationship between the toxicity and the ion transfer potentials of dialkylimidazolium homologues has been found.
In this paper we demonstrate the existence of a total analogy between the potentiostatic and chro... more In this paper we demonstrate the existence of a total analogy between the potentiostatic and chronopotentiometric responses when a constant potential E and a programmed current of the form I(t)sI 0 t u , uGy1/2 , respectively, are applied to planar and spherical electrodes, and also to hemispherical microelectrodes. From the above analogy, we also compare differential pulse voltammetry (DPV) and a new reciprocal derivative chronopotentiometric technique proposed in this paper.
A rigorous and simple analytical solution is reported for the square scheme in single pulse techn... more A rigorous and simple analytical solution is reported for the square scheme in single pulse techniques at (hemi)spherical electrodes when the electron transfers are reversible and the coupled chemical reactions are at equilibrium. The solution presented imposes no restriction to the values of the diffusion coefficients of the different species, and then it fully describes the cases where the coupled chemical processes involve significant changes of diffusivity. Simple criteria are discussed to understand and predict the effects of electrode radius, experiment timescale and chemical thermodynamics on the results obtained in normal pulse voltammetry and derivative voltammetry. Unlike at macroelectrodes and ultramicroelectrodes, the position of the voltammograms (in these and other voltammetric techniques) is time dependent at spherical electrodes of intermediate size when the diffusion coefficients of the species are unequal. An analytical expression for the half-wave potential is given to describe this behaviour and also to assist the quantitative determination of the diffusion coefficients, formal potentials and equilibrium constants with the electrochemical techniques abovementioned. Keywords Unequal diffusion coefficients. Analytical solution. Square scheme. (Hemi)spherical electrodes. Single pulse voltammetry 0 AL/BL E ′ where k 1 ,k 1 ′ and k 2 ,k 2 ′ are the forward and backward rate constants of the different chemical reactions. The solution
The mathematical modelling of heterogeneous charge transfer processes complicated by the reactivi... more The mathematical modelling of heterogeneous charge transfer processes complicated by the reactivity of the redox species in solution is revisited, elaborating on powerful and accurate theoretical approaches and simplifications that can facilitate and speed up the mathematical resolution, the solution implementation, the design of experiments and the calculation and analysis of the electrochemical response. The physicochemical fundamentals and mathematical implications behind such approaches will be discussed for frequent and paradigmatic reaction mechanisms involving homogeneous chemical equilibria and (pseudo)first-order and second-order chemical kinetics. The cases considered will point out how the suitable preliminary examination of the boundary value problem offers profound insights into the electrochemical system that can assist the design of theoretical and experimental studies. This provides criteria for the assessment of complex simulations (for example, by comparison with exact analytical solutions for particular cases) and it can alert about meaningless results derived from blind use of approximations and/or 'brute force' approaches.
Key processes in (bio)electrochemistry involve multiple electron transfers. The study of the stab... more Key processes in (bio)electrochemistry involve multiple electron transfers. The study of the stability of the different oxidation states and the interaction between redox centers is fundamental to understand these processes. In this paper, simple analytical equations are presented for multielectron transfer processes in cyclic voltammetry (CV) and staircase cyclic voltammetry (SCV) at disc electrodes of any size. This provides a simple simulation method for the electrochemical response without demanding computing. The use of CV and SCV, and the corresponding differential techniques, for the characterization of these redox systems is analyzed. Procedures and criteria are given for transient and stationary conditions. The theoretical results are applied to the experimental study of the reduction of anthraquinone-2-sulfonate in water on gold macro-and microdisc electrodes.
A simple theoretical approach is presented to study simple and facilitated ion transfer processes... more A simple theoretical approach is presented to study simple and facilitated ion transfer processes at liquid/liquid microinterfaces of the most common geometries: micropipettes, microholes, micropores and microcapillaries. A general and accurate expression is reported for the current-potential response in any voltammetric technique. The analytical solution describes the effects on the voltammetry of the (very) different mass transport conditions in each phase whatever the size and geometry of the interface and of the values of the diffusion coefficients of the ion. The theory is applied to normal pulse voltammetry and cyclic voltammety, analysing the influence of the geometry on the position and shape of the voltammograms as well as on the attainment of a steady state response. Finally, explicit analytical expressions are derived for the determination of the formal transfer potential of the ion and of the equilibrium constant of the coupled chemical equilibrium from the half-wave potential under steady state conditions.
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
In this chapter, a review is given of the application of the multipulse and sweep techniques Cycl... more In this chapter, a review is given of the application of the multipulse and sweep techniques Cyclic Staircase Voltammetry (SCV) and Cyclic Voltammetry (CV) to the study of more complex electrode processes than single charge transfer reactions (electronic or ionic), which were addressed in Chap. 5.
In a single potential step voltammetric technique, several constant potentials (of increasing amp... more In a single potential step voltammetric technique, several constant potentials (of increasing amplitude) are applied with a time length t 1. When stationary electrodes are used, the time interval between two consecutive potentials must be much greater than t 1, for the initial conditions to be restored (Scheme 2.1). If a Static Mercury Drop Electrode (SMDE) is used, the initial conditions are simply restored by making the drop fall. The measured current at a fixed time value \( t={t}_1 \) is plotted versus the corresponding potential steps discretely [1–3]. The resulting current–potential curve has a sigmoidal shape whose position and slope depend on the reversibility of the electrode process and the wave height is independent of the electron transfer rate. At each fixed potential value, the current–time variation (which has a typical cottrellian behavior for reversible processes at planar electrodes when considering diffusive transport only) can be registered. If the length time is in the range 2–200 ms, the electrochemical technique is called Normal Pulse Voltammetry (NPV), originally known as Normal Pulse Polarography (NPP). This technique was introduced by Barker [5–7] and it was originally designed for the Dropping Mercury Electrode (DME), in which the potential pulse is applied at the end of the life of the drop, with the current being dependent on the relation between the pulse time and the drop lifetime. The main reason for measuring the current at the end of short time intervals is to eliminate the capacitative component (see Sect. 1.9) in order to optimize the sensitivity. Today the DME electrode is scarcely used and most electrochemical techniques are used at stationary electrodes
The general analytical expressions corresponding to the response obtained for a charge transfer p... more The general analytical expressions corresponding to the response obtained for a charge transfer process in cyclic chronopotentiometry are presented. The different geometries considered for the mass transport operator are planar, tubular and spherical. In the case of spherical electrodes (such as the dropping mercury electrode and the static mercury dropping electrode), we have analyzed the following two cases: solution soluble product and electrode soluble product or amalgamation. The solutions deduced here are independent of the method used in solving the differential equations system since we have applied the superposition principle for which we have only used the properties of the linear operators.
... All rights reserved PII: 800134686(96)003568 00131686 97 17.00 + 0.00 Discrimination between ... more ... All rights reserved PII: 800134686(96)003568 00131686 97 17.00 + 0.00 Discrimination between CEC, CE and EC mechanisms by using a sinusoidal currenttime function MariaLuisa Alcaraz,*Angela Molina and Manuela LopezTenes Departamento de Quimica Fisica ...
The study of the reversible reduction/oxidation molecules containing multiple interacting or noni... more The study of the reversible reduction/oxidation molecules containing multiple interacting or noninteracting redox centers has been carried out using the multipotential step technique Differential Staircase Voltammetry (DSCV). Methods to obtain the formal potentials and other characteristic parameters of the process are proposed for any interaction degree between the centers, when using spherical electrodes of any size (from planar to ultramicrospherical electrodes) and, in particular, the advantages of microelectrodes are discussed. The theoretical predictions have been tested with two experimental systems: ethyl viologen in acetonitrile and pyrazine in aqueous acid media, finding an excellent agreement between the theory and experiments. Therefore, the formal potentials for these systems have been evaluated using DSCV.
Este manual se presenta como una “caja de herramientas” donde acudir en busca de recursos y activ... more Este manual se presenta como una “caja de herramientas” donde acudir en busca de recursos y actividades didacticas para elaborar formaciones en diversidad sexual, familiar, corporal y de expresion e identidad de genero, dirigidas a profesionales que trabajan con jovenes. En este sentido, son materiales que se pueden adaptar a las necesidades de cada formacion y a distintos niveles de conocimiento, tanto de los grupos participantes, como de la persona que dinamice las actividades y que son lo suficientemente flexibles para que puedan ser moldeados y utilizados segun los recursos temporales y espaciales que presente cada propuestaformativa. “Somos diversidad” ofrece un total de 44 actividades articuladas en 5 modulos tematicos. Abrazar la diversidad como una oportunidad educativa Transformarse para transformar: afectividad, diferencia y diversidad Sexualidades Corporalidades, identidades y expresiones de genero Diversidad familiar Cada modulo ofrece un indice inicial, una breve bienve...
Square wave voltammetry (SWV) with a solvent polymeric membrane ion sensor has been applied to st... more Square wave voltammetry (SWV) with a solvent polymeric membrane ion sensor has been applied to study the ion transfer of several ionic liquid cations, from water to a poly(vinyl chloride) membrane plasticized with 2-nitrophenyl octyl ether. The study has mainly been focused on dialkylimidazolium and alkylpyridinium cations. The experimental voltammograms obtained are in good agreement with the theoretical predictions. The standard ion transfer potentials of the ionic liquid cations have been obtained and the values found have been used to draw some conclusions on the relationship between structure and lipophilicity. Also, a relationship between the toxicity and the ion transfer potentials of dialkylimidazolium homologues has been found.
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