Showing papers in "The Journal of Physical Chemistry in 1992"
TL;DR: In this article, the activation energy of the A1C02 reaction is 2.5 and 3.9 kcal/mol, respectively, while the experimentally estimated heat of reaction is about 5 kcal/molecular.
Abstract: calculated energy of the 2Z state of A10 is lower by 8.6 kcal/mol than that of the ZII state and in good agreement with the previously calculated valueZo (9.9 kcal/mol). The calculated energy of AIO(ZZ) + CO is 15.4 kcal/mol above that of the trans-type complex. From these values, the reaction A1 + C 0 2 AlO(’Z) + CO is 5.8 kcal/mol endothermic, and this value is consistent with the experimental estimation (4.5 kcal/mol: D(C-0) = 126 kcal/mol, D(A1-O) = 121.5 kcal/mol). The geometries of the transition states of the 22 and the 211 states are similar to each other except for the AlOC angle and the A10 distance. From the transition-state structures, both reactions (2Z and ZII) consequently becomes transition states, which is qualitatively consistant with the Hammond postulate.2’ The ,Z transition state correlates to the C,, complex, and the ZII transition state correlates to trans-type complex. The values of energy barriers of the products are 17.8 and 4.6 kcal/mol for the ZZ and Zll states, respectively. The ZII transition state is lower in energy by 4.6 kcai/mol than the transition state. This is explained by the fact that the 2Z state of A10 at the long A1-O distance from the equilibrium bond distance is higher in energy than the 211 state.19 Thus, both reaction surfaces possibly cross each other in the neighboring region of the transition states. Experimentally determined activation energies’*4 of the A1C02 reaction are 2.5 and 3.9 kcal/mol, while the experimentally estimated heat of reaction is about 5 kcal/mol endothermic. Therefore, the experimental activation energy is considered to be that of the reaction of the AlCO2 complex formation. The calculated activation energy of the complex formation is 2.3 kcal/mol
2,240 citations
TL;DR: A combination of variable-metric second-order update schemes and the DIIS method for both geometry and Hartree-Fock wave function optimization is described and a recursive procedure for updating large Hessians is presented.
Abstract: A combination of variable-metric second-order update schemes and the DIIS method for both geometry and Hartree-Fock wave function optimization is described. A recursive procedure for updating large Hessians is presented. The performances of geometry optimizations with respect to the choice of the coordinate system (symmetry-adapted, internal, and Cartesian coordinates), the initial nuclear Hessian, and the optimization procedure have been investigated by a series of benchmark molecules. Formulas for the generation of initial nuclear Hessians are given
1,864 citations
TL;DR: In this paper, the self-exchange rate of the relays and their density are high, and the flux of electrons through a 1 micrometer thick film of a 3-dimensional macromolecular network can match or exceed the rate of supply of electrons to or from the ensemble of enzyme molecules covalently bound to it.
Abstract: : Electrically insulating proteins can be made redox-conducting through incorporation of a high density of electron relaying redox centers. Electrons diffuse in the resulting redox conductors by self-exchange between identical and electron transfer between different relaying centers. When the self-exchange rate of the relays and their density are high, the flux of electrons through a 1 micrometer thick film of a 3-dimensional macromolecular network can match or exceed the rate of supply of electrons to or from the ensemble of enzyme molecules covalently bound to it. The network now molecularly wires the enzyme molecules to the electrode and the current measures the turnover of the wired enzyme molecules. When the enzyme turnover is substrate-flux, i.e. concentration limited, the current increases with the concentration of the substrate.
715 citations
TL;DR: This article used LDF to calculate the geometry and vibrational frequencies of several molecular transition metal compounds with the calculations being done with polarized double-zeta numerical and gaussian basis sets and the geometries obtained by analytic gradient methods.
Abstract: This paper discusses how LDF is used to calculate the geometry and vibrational frequencies of several molecular transition metal compounds with the calculations being done with polarized double-zeta numerical and gaussian basis sets and the geometries obtained by analytic gradient methods. Most results have good agreement as compared to Hartree-Fock results, but LDF predicting bonds too short. 52 refs., 6 tabs.
690 citations
TL;DR: In this article, the phase behavior and structural properties of a mixture of simple, commercially available, single-tailed cationic and anionic surfactants, such as sodium dodecylbenzenesulfonate (SDBS) and cetyl trimethylammonium tosylate (CTAT), were studied.
Abstract: Spontaneous, single-walled, equilibrium vesicles of controlled size and surface charge can be prepared from aqueous mixtures of simple, commercially available, single-tailed cationic and anionic surfactants. We present detailed phase behavior and structural studies of one such mixture, sodium dodecylbenzenesulfonate (SDBS) and cetyl trimethylammonium tosylate (CTAT) in H 2 O, as well as results of less complete surveys of other mixtures
549 citations
TL;DR: In this article, the authors reported calculations of properties of C{sub 60} as a gas and a solid. But, because of the spherical form of the C{ sub 60} molecule, it was treated as a sphere for some calculations.
Abstract: The author reports calculations of properties of C{sub 60} as a gas and a solid. Because of the spherical form of the C{sub 60} molecule, it is treated as a sphere for some calculations. For gas phase molecules the equation of state is derived, from calculations of the second virial coefficient. For solids, compressibility, surface energy, and specific heat are calculated.
531 citations
TL;DR: In this paper, the flat band potential of the nanostructured film and the extinction coefficient of the electrons were derived by sintering 15nm-diameter colloidal anatase particles on a conducting glass support, which indicated the formation of an accumulation layer at the semiconductor/electrolyte interface under negative polarization.
Abstract: Transparent nanostructured TiO 2 films (thickness 4 μms) were prepared by sintering 15-nm-diameter colloidal anatase particles on a conducting glass support. Visible and near-infrared spectra were measured for films biased at potentials between -2.0 and +1.0 V (SCE) and indicate the formation of an accumulation layer at the semiconductor/electrolyte interface under negative polarization. The optical absorbance of the conduction band electrons at 780 nm, measured as a function of the applied potential, has been used to derive the flat band potential of the nanostructured film and the extinction coefficient of the electrons
519 citations
TL;DR: In this article, the Fick-Jacobs diffusion equation is re-derived along with corrections involving the curvature of the tube or channel, and it appears to be quite reliable as long as the curvatures are not too great.
Abstract: Diffusion in a tube or channel of varying cross section has been treated, by Fick and Jacobs, as one-dimensional diffusion past an entropy barrier determined by the tube cross-sectional area or channel width. The Fick-Jacobs diffusion equation is rederived, along with corrections involving the curvature of the tube or channel. On comparison with two exactly solvable examples, the Fick-Jacobs equation appears to be quite reliable as long as the curvature is not too great. 9 refs., 4 figs.
457 citations
TL;DR: The expected attractive van der Waals and repulsive electric double layer forces (the two DLVO forces) between fluid amphiphilic surfaces such as a surfactant micelles, lipid bilayers, and microemulsion droplets in liquids were studied in this article.
Abstract: The forces between fluid amphiphilic surfaces such a surfactant micelles, lipid bilayers, and microemulsion droplets in liquids include the expected attractive van der Waals and repulsive electric double layer forces (the two DLVO forces).
435 citations
TL;DR: In this paper, the bending beam method was introduced to studies of the electrochemistry of polyrrole (PPy) electrodes, where a bipolymer strip made of a PPy layer and a polyethylene layer bound together responds, by bending, to volume changes in the Ppy layer during its electrochemical doping and undoping.
Abstract: We introduce the bending beam method to studies of the electrochemistry of polyrrole (PPy) electrodes, where a bipolymer strip made of a PPy layer and a polyethylene layer bound together responds, by bending, to volume changes in the PPy layer during its electrochemical doping and undoping. A correlation between the local linear strain and the curvature change of the strip is developed. Upon reduction (undoping) in an aqueous solution of LiClO 4 , a tosylate-doped PPy undergoes initial rapid swelling and subsequent rapid skrinking and continuous slow shrinking
382 citations
TL;DR: In this paper, the molecular structures of the surface overlayerers of rhenium(VII) oxide, molybdenum(VI) oxide and titanium(IV) oxide on γ-alumina were determined by in situ Raman spectroscopy under dehydrated conditions.
Abstract: The molecular structures of the surface overlayerers of rhenium(VII) oxide, molybdenum(VI) oxide, tungsten(VI) oxide, chromium(VI) oxide, vanadium(V) oxide, niobium(V) oxide, and titanium(IV) oxide on γ-alumina were determined by in situ Raman spectroscopy under dehydrated conditions. It was found that the dehydrated surface metal oxide structures of all the systems under study, except for supported titanium oxide, are different from those under ambient condition where moisture is present on the surface
TL;DR: In this paper, the properties of aqueous solutions of cetyltrimethylammonium chloride (CTAC) with salicylate (from NaSal) as the binding counterion are presented as a function of counterion concentration.
Abstract: Artifact-free electron micrographs and rheological properties of aqueous solutions of cetyltrimethylammonium chloride (CTAC) with salicylate (from NaSal) as the binding counterion, are presented as a function of counterion concentration.
TL;DR: In this paper, the coordination and nature of V sites in V-silicalite samples prepared by hydrothermal synthesis are characterized, and four vanadium species were detected: (1) a polynuclear vanadium oxide species containing reduced vanadium, (2) a nearly octahedral vanadyl (VO{sup 2+}) species in the zeolitic channels which interacts with Bronsted sites, (3) a V{sup 5+} species in sites characterized by a nearly symetric tetrahedral environment, and (4) after reduction a V
Abstract: The coordination and nature of V sites in V-silicalite samples prepared by hydrothermal synthesis are characterized. Four vanadium species were detected: (1) a polynuclear vanadium oxide species containing reduced vanadium species, (2) a nearly octahedral vanadyl (VO{sup 2+}) species in the zeolitic channels which interacts with Bronsted sites, (3) a V{sup 5+} species in sites characterized by a nearly symetric tetrahedral environment, and (4) after reduction a V{sup 4+} species in a nearly tetrahedral environment. The polynuclear vanadium oxide species can be removed from the zeolite by an ammonium acetate extraction and is derived from excess vanadium present in the preparation of V-silicalite. The excess vanadium remains as an amorphous oxide in pores or in external positions, as indicated by XPS. The tetrahedral V{sup 5+} species can be attributed to atomically dispersed V species anchored to the silicalite framework, probably as a framework satellite, and localized inside the pore structure, as indicated by FT-IR and XPS. The UV-visible DR spectrum of this species differs from that of other tetrahedral compounds, suggesting the presence of a short V-O bond. The FT-IR spectroscopy data obtained in the characterization of surface acidity show the presence of strong Lewis acid sites associated with Vmore » only, inside the zeolitic channels. Only weak silanol groups are present on the external surface. The nearly octahedral VO{sup 2+} species interacts with the OH groups associated with tetrahedral V{sup 5+} species. The model of the possible localization of V{sup 5+} sites in the zeolitic structure is also given. 79 refs., 11 figs., 3 tabs.« less
TL;DR: In this article, the adsorption of NO onto copper loaded ion-exchanged zeolites was studied by means of infrared spectroscopy coupled with isotopic techniques, and the binding sites which would bind NO were identified.
Abstract: The authors have studied the adsorption of NO onto copper loaded ion-exchanged zeolites by means of infrared spectroscopy coupled with isotopic techniques. Such zeolites have been reported to be catalytically active for the decomposition of NO, and the development of such catalysts for exhaust gas treatments is a major factor behind this work. The authors studied the molecular form that NO took when it was adsorbed, and the nature of the sites which would bind NO. They found bound forms of the nature, NO{sup {delta}+}, NO{sup {delta}{minus}}, and (NO){sub 2}{sup {delta}{minus}}. They also observed the formation of N{sub 2} and N{sub 2}O.
TL;DR: A bichromophoric molecule consisting of two coumarins linked by a pentakis spacer can efficiently bind Pb 2+ ions in acetonitrile and in propylene carbonate as mentioned in this paper.
Abstract: A bichromophoric molecule consisting of two coumarins linked by a pentakis(ethylene oxide) spacer can efficiently bind Pb 2+ ions in acetonitrile and in propylene carbonate. The resulting changes in photophysical properties are reported with special attention to photoinduced electronic energy transfer. Steady-state data allow one to determine the transfer efficiency and stoichiometry of the complex, whereas subpicosecond time-resolved experiments by the excite-and-probe technique provide information on the transfer kinetics. The stoichiometry of the complex is 1:1 in acetonitrile and 1:3 (ligand:metal) in propylene carbonate
TL;DR: In this article, the excited-state dipole moments of aminobenzonitriles have been determined in cyclohexane, benzene, and 1,4-dioxane using time-resolved microwave conductivity (TRMC) and fluorescence spectroscopy techniques.
Abstract: Singlet excited-state dipole moments of a number of aminobenzonitriles have been determined in cyclohexane, benzene, and 1,4-dioxane, using time-resolved microwave conductivity (TRMC) and fluorescence spectroscopy techniques. For the 4-(dialkylamino)benzonitriles (methyl, ethyl, propyl, and decyl) intramolecular charge transfer (ICT) occurs in the excited singlet state even in the nonpolar solvent cyclohexane
TL;DR: In this paper, pressure-temperature profiles for the hydrate-ice-gas and hydrate liquid water-gas equilibria were measured for methane and propane hydrates in 70-Angstrom-radius silica gel pores.
Abstract: The pressure-temperature profiles for the hydrate-ice-gas and hydrate-liquid water-gas equilibria were measured for methane and propane hydrates in 70-{Angstrom}-radius silica gel pores In both cases, the equilibrium pressures were 20-100% higher than those for the bulk hydrates The dissociation characteristics of the gas hydrates in pores were also studied calorimetrically by heating the hydrates under about zero pressure from 100 K to room temperature It was found that after the initial dissociation into ice and gas the hydrate became totally encapsulated among the pore walls and the ice caps formed at the pore openings The hydrate thus trapped in the interior of the pore remained stable up to the melting point of pore ice These results are similar to those obtained in previous studies on the bulk hydrates which are also stabilized by a shielding layer of ice However, the apparent increase in the stability of the pore hydrates was found to be much larger than that of the bulk hydrates The composition of methane hydrate in 70-{Angstrom} pores was determined to be CH{sub 4}{center_dot}594H{sub 2}O, and its heat of dissociation into pore water and gas, obtained calorimetrically, was 4592 kJ mol{sup {minus}1}; The corresponding values in the bulk phasemore » are 600 and 5419 kJ mol{sup {minus}1}, respectively 30 refs, 4 figs, 2 tabs« less
TL;DR: In this article, an improved kinetic model for the high-temperature oxidation of toluene has been developed using previously established reaction mechanisms for benzene, and a linear sensitivity analysis indicated that the reaction mechanism was most sensitive to the rate constant of C{sub 6}H{sub 5}CH{sub 3} + O{sub 2} {r_arrow}
Abstract: An improved kinetic model for the high-temperature oxidation of toluene has been developed using previously established reaction mechanisms for benzene and toluene. The model is compared to benzene and toluene flow reactor experiments near 1100 and 1200 K, respectively. Fuel decay rates and many intermediate species profiles are reproduced successfully for both lean and rich equivalence ratios. A linear sensitivity analysis indicated that the reaction mechanism was most sensitive to the rate constant of C{sub 6}H{sub 5}CH{sub 3} + O{sub 2} {r_arrow} C{sub 6}H{sub 5}CH{sub 2} + HO{sub 2} (71). A value of k{sub 71} = 3.0 x 10{sup 14} exp(-20700/T) cm/mol/s was found to fit the experimental data best. The model revealed that the presence of resonantly stable radical such as benzyl and phenoxy can inhibit the reaction rate of the fuel by removing H atoms from the system. Specific shortcomings of the model are also discussed. 70 refs., 10 figs., 4 tabs.
TL;DR: In this paper, the authors examined the effects of solvation on chromophores using a simple self-consistent reaction field (SCRF) model, in which a SCRF selfconsistent field calculation is followed by configuration interaction to generate excited states in the presence of a dielectric continuum.
Abstract: We examine the effects of solvation on chromophores using a simple self-consistent reaction field (SCRF) model. In this model a SCRF self-consistent field calculation is followed by configuration interaction to generate excited states in the presence of a dielectric continuum. The absorption process is considered instantaneous, and only the electron polarization of the solvent is allowed to respond to the excited-state charge distribution. This model is then applied to a variety of molecules in «solution» using the intermediate neglect of differential overlap (INDO/S) model Hamiltonian. The model reproduces very well the shifts observed in aprotic solvents
TL;DR: In this article, the infrared spectra of the hydroxyl region and that of surface chemisorbed CO 2 species for Re 2 O 7 /Al 2 O 3, CrO 3/Al 2O 3, MoO 3 /Al2 O 3, V 2 O 5 /Al O 3 ), TiO 2 /Al 3, and Nb 2 O 6 /Al 1 O 3 catalytic systems were investigated.
Abstract: The infrared spectra of the hydroxyl region and that of surface chemisorbed CO 2 species for Re 2 O 7 /Al 2 O 3 , CrO 3 /Al 2 O 3 , MoO 3 /Al 2 O 3 , V 2 O 5 /Al 2 O 3 , TiO 2 /Al 2 O 3 , and Nb 2 O 5 /Al 2 O 3 catalytic systems have been investigated. A sequential consumption of the alumina OH groups upon deposition of the supported metal oxide has been found for all the investigated catalytic systems. A possible relationship between BrOnsted acidity and a new low-frequency band in the hydroxyl region observed at high loadings of the supported metal oxide systems is postulated
TL;DR: In this article, it is proposed that these structures may be giant fullerenes which have grown by direct insertion into the graphitic network of smaller carbon species accreted from the vapor phase.
Abstract: Recently 3-1 50-nm-diameter carbon fibers have been discovered which appear to grow spontaneously by deposition from carbon vapor. It is proposed that these structures may be giant fullerenes which have grown by direct insertion into the graphitic network of smaller carbon species (atoms, ‘linear” chains, monocyclic rings, or even smaller fullerenes) accreted from the vapor phase.
TL;DR: In this article, a model equation for the excess Gibbs energy and solvent and solute activity efficients (given previously for symmetrical salt systems) for mixtures containing an indefinite number of ions of arbitrary charge, over the entire concentration range, was developed for unsymmetrical mixing.
Abstract: Model equation for the excess Gibbs energy and solvent and solute activity efficients (given previously for symmetrical salt systems) are here developed for mixtures containing an indefinite number of ions of arbitrary charge, over the entire concentration range. The equations are expressed on a mole fraction basis and comprise a Debye-Huckel term extended to include the effects of unsymmetrical mixing, and a Margules expansion carried out to the fow suffix level
TL;DR: In this paper, the electron transfer kinetics of betaine-30 and the related compound tert-butylbetaine were reported, and the experimental data were in excellent agreement with a new theoretical model which is an extension of the approach given by Sumi and Marcus.
Abstract: This paper reports new kinetic data on the electron-transfer kinetics of betaine-30 and the related compound tert-butylbetaine. The experimental data are in excellent agreement with a new theoretical model which is an extension of the approach given by Sumi and Marcus (Sumi, H; Marcus, R. A. J. Chem. Phys. 1986, 84, 4894). Most of the parameters required for the kinetic predictions can be obtained in a straightforward fashion by fitting the static absorption spectra of the charge-transfer band
TL;DR: In this article, the structure and wetting properties of self-assembled monolayers (SAMs) on gold derived from two different mixtures of n-alkanethiols (C12SH and CI3SH; Cr2SH and C22SH) were characterized and correlated.
Abstract: We have characterized and correlated the structure and wetting properties of self-assembled monolayers (SAMs) on gold derived from two different mixtures of n-alkanethiols (C12SH and CI3SH; Cr2SH and C22SH); in each of these SAMs, one thiol had a perdeuterated alkyl chain and one a perprotonated chain to allow the two alkanethiols to be distinguished in the SAM by polarized infrared external reflectance spectroscopy (PIERS). The hydrocarbon parts of the SAMs consist of well-defined regions exhibiting structural characteristics reminiscent of those formed in crystalline and liquidlike states. In each SAM, both the shorter alkanethiolate and the section of the longer alkanethiolate closest to the gold contain very low densities of gauche conformations (and presumably are ordered) over all compositions of the SAM. The terminal portion of the longer alkanethiolate-that which extends beyond the terminus of the shorter alkanethiolate-is disordered. The density of gauche conformers present in this mmponent decreases as its concentration in the SAM is increased. The advancing and receding contact angles (0" and d,, respectively) of water and hexadecane (HD) respond differently to the disordered region: for hexadecane, 0.(HD) and d,(HD) reach minima when the interface is present in the disordered, liquidlike state; for water, d"(H2O) and 0,(H2O) appear insensitive to the presentr of this disorder. The IR spectra of these mixed SAMs are consistent with previous inferences from wetting that the components of the SAMs, as prepared here (adsorption of 1 mM thiol from ethanolic solutions over 24-48 h at -25 oC), do not phase segregate into macroscopic islands. The larger interpretation which follows from the data, however, is that this result reflects a structural architecture derived from a kinetically controlled growth process. Under suitable conditions, phase segregation is important as might be expected from consideration of elementary thermodynamics. The importance of kinetic and thermodynamic factors in the structural characteristics of multicomponent SAMs is discussed.
TL;DR: In this article, the structural properties of silicalites depend upon the preparation procedure and are characterized by the presence of internal atomic dimension defects (nanodefects and microcavities).
Abstract: In paper 1 we have shown that the structural properties of silicalites depend upon the preparation procedure. In particular Na- and Al-free sample (S) prepared following a specifically designed method is characterized by the presence of internal atomic-dimension defects (nanodefects and microcavities). On the basis of spectroscopic data and computer graphic simulations, it is shown that the microcavities derive from one or more missing [SiO 4 ] units and can contain up to four OH groups per missing tetrahedron
TL;DR: In this article, the effects of solvent viscosity and dielectric strength, concentration of excess cadmium ions, temperature, and stirring upon the colloids' absorption spectra have been examined.
Abstract: Q-sized CdS semiconductors have been synthesized in several nonaqueous solvents without the use of added stabilizers. The effects of solvent viscosity and dielectric strength, concentration of excess cadmium ions, temperature, and stirring upon the colloids' absorption spectra have been examined. In addition, efficiency of photoinitiation of polymerization of several vinylic monomers has been examined using both bulk and quantum-sized CdS, ZnO, and TiO_2. The Q-sized semiconductors demonstrated significantly higher quantum yields for photopolymerization than their bulk-sized counterparts. A correlation between the reactivity of a monomer toward polymerization and its Alfrey and Price Q and e values was observed. Hole scavenging by the solvent was necessary for efficient polymerization to occur. A correlation between the semiconductor photoinitation efficiency, and the reduction potential of its conduction band electrons was also found. On the basis of these observations, a mechanism of an anionic initiation step followed by free radical chain propagation steps has been proposed.
TL;DR: In this paper, a colloidal CdS-ZnO system in a photoelectrochemical cell has been demonstrated by modifying the surface of an optically transparent electrode with ZnO and cdS colloids.
Abstract: Picosecond laser flash photolysis and photoelectrochemical studies have been carried out to elucidate the charge-transfer processes in CdS-ZnO coupled semiconductor systems. Charge injection from excited CdS into ZnO occurs within the laser pulse duration of 18 ps. Long-lived trapped charge carriers demonstrate the improved charge separation in CdS-ZnO coupled semiconductor systems. The feasibility of employing a colloidal CdS-ZnO system in a photoelectrochemical cell has been demonstrated by modifying the surface of an optically transparent electrode with ZnO and CdS colloids. Charge injection from excited CdS into ZnO particle on the electrode with ZnO and CdS colloids. Charge injection from excited CdS into ZnO particle on the electrode surface is confirmed by recording the photocurrent action spectra. An incident photon-to-photocurrent conversion efficiency of 15% has been observed for OTE/ZnO/CdS at 420 nm. 26 refs., 11 figs.
TL;DR: In this paper, the vibrational modes associated with free (isolated) silanol groups on an aerosil silica and a precipitated silica which have been activated in vacuum in the temperature range from 450 to 800 o C.
Abstract: Infrared spectroscopy has been used to study the vibrational modes associated with free (isolated) silanol groups on an aerosil silica and a precipitated silica which have been activated in vacuum in the temperature range from 450 to 800 o C. Both silicas exhibit two Si-O-H angle deformation modes at 760 and 840 cm -1 , indicative of two types of isolated silanol species, called type I and II, respectively
TL;DR: In this paper, self-assembled monolayers of ω-hydroxy thiols on Au electrodes are investigated as electron tunneling barriers allowing the measurement of heterogeneous electron kinetics of solution species over a wide range of electrode potentials without mass transport limitations.
Abstract: Self-assembled monolayers of ω-hydroxy thiols on Au electrodes are investigated as electron tunneling barriers allowing the measurement of heterogeneous electron kinetics of solution species over a wide range of electrode potentials without mass transport limitations. From the dependence of the electron-transfer rate of a series of redox couples on the thickness of the monolayer film, a more precise tunneling coefficient, β, of 1.08±0.20 per methylene unit in the ω-hydroxy thiol was measured independent of the redox couple and was found to be nearly independent of the electrode potential
TL;DR: In this article, the authors extended the theory of the feedback mode of the scanning electrochemical microscope (SECM) to include the cases of both finite heterogeneous electron-transfer (et) kinetics at the substrate and arbitrary substrate sizes.
Abstract: The theory of the feedback mode of the scanning electrochemical microscope (SECM) is extended to include the cases of both finite heterogeneous electron-transfer (et) kinetics at the substrate and arbitrary substrate sizes. Theoretical treatments are developed using two independent approaches: (i) the formulation and numerical solution of multidimensional integral equations and (ii) the alternating direction implicit finite-difference method. Working curves and tabulated data are presented for both quasi-reversible and irreversible et reactions on the substrate