Cottrell Model Research Articles

Influence of Diffusion through a Porous Film under Electrode Surface in Chronoamperometry Problems

In the presented work on chronoamperometry, the Cottrell model has been generalized by taking into account a thin porosity layer covering the surface of the electrode and Tafel kinetics of an electrode reaction. The effective diffusion coefficient inside a porosity layer is calculated by Bruggeman’s law. It is shown that in the quasi-stationary approximation of diffusion inside a thin porous layer, the chronoamperometry problem can be solved analytically. The obtained solution has been compared with the results of direct numerical simulations and a good agreement is shown. Limiting cases of the solution related to low and high porosity are considered.

Relationship between Charge Transfer Diffusion Coefficients and Doping Level for electro generated thin PEDOT films on ITO

Thin films of poly-3,4-ethylene dioxythiophene (PEDOT) were electrodeposited on transparent electrodes of indium tin oxide (ITO) using potentiostatic regime. These films had thicknesses ranging from 15 nm to 60 nm and were studied using UV-vis absorption and chronoamperometric techniques in monomer-free tetrabutylammonium perchlorate/acetonitrile solutions. The charge transfer diffusion coefficient (D) of the films were calculated using Cottrell model for a wide range of potential steps from −1.60 to 1.60 V vs. Ag°/AgNO3. For p-doped films, the highest diffusion coefficients were obtained when a potential of 0.70 V was applied. Moreover, a direct relationship between film thickness and their diffusion coefficients was found for thin PEDOT films showing D values up to 1.4 × 10−9 cm2 s−1 for 60 nm thickness films. These values are remarkably higher than the D of 1.8 × 10−11 cm2 s−1 obtained for spin-coated PEDOT: PSS films of similar thickness.

Physiochemical Properties of Dialkylimidazolium Chloroaluminate Ionic Liquids Under Dynamic Conditions

Aluminum deposition is an industrially important process that is often not optimized in an electrochemical sense. One method of growing thin aluminum films is electrodeposition; this process has been gaining traction in ionic liquids over the last two decades, although details of the process are still under debate. These inconsistencies are largely attributed to widely variable results based on electrolyte purity and a strong dependence on a multitude of parameters including composition, temperature and even experimental set up. This work is targeted to elucidate some of these properties with electrochemical and rheological measurements, alongside NMR and microscopy techniques. Some of the most promising aluminum deposition is done in chloroaluminate ionic liquids. These solutions have high aluminum concentration and low vapor pressure but typically higher viscosity then molecular solvents or aqueous chemistries. 1-ethyl-3-methyl imidazolium chloride (EMIC) and AlCl3 in acidic ratios will readily deposit aluminum. This electrolyte deposits aluminum by the reduction of Al2Cl7 - to aluminum and produces AlCl4 - anions in a relatively complex 3 electron transfer mechanism. The composition of the electrolyte is determined by the ratio of AlCl3 to EMIC and is confirmed by NMR. The varying compositions of the ionic liquid influence both the physical and electrochemical properties. The Walden rule applies well to most ionic liquids and states that the conductivity and viscosity are related, and as a corollary the mobility of ions is dependent as well. We systematically investigate the diffusion parameters that lead to insight of reaction kinetics of the chloroaluminate system. There are methods that have been developed for this type of investigation that do not apply to this system because of a few complications. For example, the Cottrell model indicates a diffusion controlled system, while attempting Koutecky-Levich does not apply because the system cannot reach a diffusion limited regime in the window of the electrolyte. We assert that in a quiescent system the ionic interactions of the electrolyte become quite strong and resistant to cleavage, leading to restricted Al2Cl7 - diffusion. The structuring and interaction of the ionic liquid may be shown in the rheological data, indicating that the solutions are thixotropic. Since the conductivity and diffusivity are dependent on the viscosity, we assert that as the solution is allowed to rest and coordinate in a preferred structure the diffusivity would decrease significantly. This implies that the measured diffusion rates in a quiescent experiment are not relevant in a system that implements convection, which is almost any real system. We apply data derived from the quiescent system experiments to dynamic systems by understanding how the macroscale physical properties change as the system goes from static to dynamic. As mentioned above, the Cottrell equation can measure the diffusion rates of an electrochemically active species, which allows measurement of transport for Al2Cl7 -. Proton pulse field gradient spin echo nuclear magnetic resonance spectroscopy (PGSE NMR) can measure the diffusivity of the cationic species in the system (EMIm+), and the bulk conductivity was used to determine the combined mobility of ions in solution. The anions and cations contribute to the bulk conductivity separately, which necessitates the multiple methods of investigation, as well as the redundancy of using solutions of varying compositions. All of these experiments give results based on a static solution. We apply the viscosity dependence to the data gathered in static solutions to predict properties in dynamic conditions. A close approximation of zero shear viscosity was determined through falling ball experiments. The dynamic viscosity was measured by a rheometer at varying shear rates. The diffusion properties and conductivity are related to viscosity. Composition and temperature variation in the viscosity studies gave insight to the mobility of both the anions and cations under all static or dynamic conditions, and point to complex interaction at the electrode interface for deposition from the Al2Cl7 - in this ionic liquid. Using the diffusivity and composition data gathered from this set of experiments allows for investigation of the reaction kinetics, and optimization of the kinetics to diffusion balance. Increasing the plating rate reduces fabrication times but infringing on the precursor diffusion limits leads to dendritic and poor quality deposits. Adjusting the parameters to give similar kinetic and diffusion properties of the Al2Cl7 - in this electrolyte will give the best deposition properties based on both rate and dense, compact and level morphologies. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Effects of Pore Surface Oxidation on Electrochemical and Mass-Transport Properties of Nanoporous Carbon

A new nanoporous (NP) carbon material with a high surface area and a narrow pore size distribution, around 8 Å, has been used to investigate the effects that electrochemical oxidation at positive potentials exerts on the capacitance values and effective diffusion coefficients of ions inside the nanopores. An electroanalytical method, based on the single-particle microelectrode technique with micromanipulator, was applied to calculate the diffusion coefficients of 6 M KOH ions in NP carbon. The results were analyzed for short times using the Cottrell model and for long times using the spherical diffusion model. Using cyclic voltammetry, was found that different stages of oxidation took place between 0 and 0.5 V vs. Hg|HgO. After repeated cycling in the first region of oxidation (0-0.3 V), an activation leading to higher capacitance was observed, but the diffusion coefficients decreased from approximately to cm2 s−1. In the second region of oxidation (0.3-0.5 V), where and evolution can occur, both the capacitance and the diffusion coefficients decreased more dramatically. The effective diffusion coefficients of ions of an activated carbon particle were dependent on the operation potential, decreasing by an order of magnitude when going from −0.3 to +0.3 V. The results are discussed in terms of chemisorption of small oxygen functional groups (‒OH or C=O) and ionic interaction with the pore wall. © 2004 The Electrochemical Society. All rights reserved.

Deformation and fracture of Nb/a-Al2O3composites in compression and bending studied by optical methods

Abstract The fracture behavior of Nb/a-Al2O3 composites was investigated both in compression tests and bending tests using an optical full-field method for the observation of strain fields on the metal surfaces. Joints of polycrystalline materials were prepared by high-vacuum diffusion bonding. The building up of the strain near the interface during the tests, finally leading to the fracture, was studied by examining the strain and displacement fields of the whole metal layer. In compression tests, two types of fracture, fracture of alumina and fracture of interfaces, were detected by cross-examination of the stress–strain curve and the strain maps. The fracture of alumina in compression tests was influenced by the Nb layer thickness and can be rationalized by an extension of Cottrell's model. For four-point bending tests, the results of the strain maps, determined experimentally by means of the optical method, confirmed the strain maps resulting from finite element simulations.

Determination of the effective diffusion coefficient of nanoporous carbon by means of a single particle microelectrode technique

A single particle microelectrode technique with a micromanipulator was applied and adapted for characterisation of mass transport properties of ionic species in a high surface area nanoporous carbon, with uniform pore size of 8 Å. The effective diffusivity of 6 M KOH in this material was determined by means of potential step experiments on nanoporous carbon particles of different sizes. The results were analysed for short times (Cottrell model) and for long times (spherical diffusion model). The average effective diffusion coefficient for short and long times was 1.5×10 −9 and 1.2×10 −9 cm 2 s −1, respectively. The relatively small diffusivity values are discussed in terms of interaction between the ion hydration shell and water molecules adsorbed on the pore wall.

Experimental approach of a crystallographic cleavage criterion in a cast aged duplex stainless steel

The stress state distribution in an aged duplex steel is determined in each phase and is then correlated to local damage mechanisms. The measurements are performed at the grain scale because the studied material contains coarse grains up to one millimetre in size. A single-crystal specific X-ray method is required to determine the stress tensor. During in situ loading, the mechanical state determined in the ferritic crystal is associated with both the plastic flow and the damage mechanism observation. The coupling of the techniques makes it possible to establish that for the studied aged material, the stress normal to a {100} plane value of 465 MPa can be considered as a crystallographic criterion for cleavage propagation. The comparison of this value with the Cottrell's model seems to be good but the number of dislocations in the pile-up must be verified experimentally.

Dislocation-associated elastic energy storage in mechanical deformations

The Cottrell model on the mechanical hysteresis of polycrystalline material suggests that elastic energy associated with dislocation activity can be stored and used during reverse loading. A similarity exists, in this respect, with when a model is used and load reversal is applied on a single dislocation segment. With an experimental approach, through the study of the deformation flow curves when load reversal is applied or the hysteresis loop shape in cyclic deformations, this elastically stored energy can be quantitatively assessed. This, in turn, allows one to calculate, approximately, the two major components relating to elastic and frictional resistance towards dislocation movements during uniaxial and cyclic deformations. As the cyclic state is monitored, the change between the average elastic resistance to dislocation movements and the average frictional resistance to dislocation movements appears to be a very sensitive index in predicting changes in cyclic conditions. This method is then explored in relation to persistent slip band formations and fatigue performances generally. It is concluded that the frictional resistance to dislocation movements is more damaging in fatigue than the resistances offered by dislocation interactions resulting in elastic stresses.

Analysis on the critical strain associated with the onset of portevin-Lecatelier effect of substitutional F.C.C. alloys

Flow instability of substitutional f.c.c. alloys, which is a common feature of the Portevin-LeChatelier effect, usually develops after a critical strain is reached. With ∈. and T as the tensile strain rate and deformation temperature, respectively, the Arrhenius equation that ∈. ∝ ∈ c α exp (− Q/ kT) is obeyed in numerous systems. Rationalization of the critical strain exponent, α, based on the conventional Cottrell model is not in agreement with empirical data. A proper modification regards ∈ c as related to some critical mobile dislocation density in which the local vacancy enrichment near dislocation core region is considered. Dislocation interception should also play a role in affecting the average dislocation velocity. The rationalization based on the above concepts reveals a correct grain size dependence.

Effects of the solute concentration on the deformation characteristics of FeMo solid solutions in the power-law creep regime at 1100 K

Creep behaviour at 1100 K has been studied in Fe0.5mol.%Mo alloy (4.0–30 MPa) and Fe1.1mol.%Mo alloy (5.0–45 MPa). Steady state creep characteristics have been analysed together with data reported previously for Fe2.1mol.%Mo alloy and results obtained in conventional tensile tests of these materials. The existence of two transitions in the deformation behaviour becomes evident in b.c.c. FeMo solid solutions as in f.c.c. AlMg alloys. Typical class I behaviour can be observed only under the intermediate stress range. The condition of the upper transition is well described by the Cottrell model for the breakaway of the solute atmosphere as in f.c.c. AlMg alloys. The condition of the lower transition has some common features in FeMo and AlMg alloys, though the creep process in the lower stress range has not been well understood.

Effects of the solute concentration on the deformation characteristics of FeMo solid solutions in the power-law creep regime at 1100 K

Creep behaviour at 1100 K has been studied in Fe0.5mol.%Mo alloy (4.0–30 MPa) and Fe1.1mol.%Mo alloy (5.0–45 MPa). Steady state creep characteristics have been analysed together with data reported previously for Fe2.1mol.%Mo alloy and results obtained in conventional tensile tests of these materials. The existence of two transitions in the deformation behaviour becomes evident in b.c.c. FeMo solid solutions as in f.c.c. AlMg alloys. Typical class I behaviour can be observed only under the intermediate stress range. The condition of the upper transition is well described by the Cottrell model for the breakaway of the solute atmosphere as in f.c.c. AlMg alloys. The condition of the lower transition has some common features in FeMo and AlMg alloys, though the creep process in the lower stress range has not been well understood.

Comments on Cottrell's Long Distance Jasper Trade Hypothesis: In Defense of Renfrew's Trade Models

This paper critically assesses Cottrell's model of prehistoric exchange of jasper said to have been transported through the Mojave Desert to the Tomato Springs site in coastal southern California. We point out numerous conceptual and analytical errors which cast doubt on Cottrell's interpretation of the Tomato Springs site as a control center for the importation, production, and trade of this supposedly nonlocal material. Cottrell has not demonstrated a desert origin for the jasper found at Tomato Springs, and thus has no grounds for testing any of Renfrew's distance-decay models. The presence of local natural sources of jasper better explains the occurrence of this mineral at Tomato Springs and nearby sites.

A statistical approach to upper yield of low carbon steel under non-uniform stress distribution

An experiment was performed to investigate the effect of stress distribution on the upper yield of low carbon steel. Tension, torsion and bending tests were carried out on round bars of low carbon steel and tension tests on notched plates. It was found that the upper yield point rises as the stress concentration or gradient of the specimen increases. A statistical approach is attempted to combine the Cottrell's model of dislocation locking with the weakest link concept.

Community competence: a positive approach to needs assessment.

A procedure was developed for assessing residents' perceptions of community functioning. A questionnaire, derived from Cottrell's work in the area of community competence and elaborated upon by community workers and researchers, was constructed and field tested in five rural communities. In a telephone interview, 433 residents were surveyed. Responses were analyzed to determine which items discriminated among the communities and to what extent they represented Cottrell's original model. Representing six of Cottrell's eight conditions of competence, 14 items were judged to discriminate among the communities (analysis of variance, F-test, maximum p = .008). A factor analysis of the 14 items revealed four factors that were labeled Democratic Participation Style, Crime, Resource Adequacy and Use, and Decision-Making Interactions. The factors are consistent with Cottrell's model and explain 35% of the variance. These findings are discussed in relation to current community research and methodological constraints.

Experimental study on the stress range of class I behaviour in the creep of AlMg alloys

The influence of the solute concentration C on the stress dependence of the creep rates ϵ ̇ S in AlMg alloys (0.5–3.3 mol.% Mg) has been examined at 600 K over the stress range between 2.5 and 85 MPa. The stress exponent n varies with stress as predicted by Yavari and Langdon: n is 3.4 in the intermediate stress region, whereas it is 4.8 in the high and low stress regions. The upper transition stress is almost linearly proportional to C. In the high stress region the solute atmosphere can, at least partly, break away and some segments of dislocations glide in a free-flight-like manner, although the transition stresses are only about one-seventeenth of the maximum stresses predicted from the Cottrell model of the solute atmosphere dragging. The lower transition stress is almost independent of concentration. This independence results from the inverse proportionality of ϵ ̇ S to C in the low stress range as well as in the intermediate stress range where n = 3.4. The necessity of thorough examinations of the creep behaviour of solid solution alloys in the low stress range is suggested.

Stress drops in serrated flow curves of A15Mg

Different types of serrations appear, when the test temperature and the strain rate are varied. Some features of the Portevin-LeChatelier effect are described, for instance the magnitude of the stress drops, Δσ and the time intervals, Δt, between consecutive drops. The activation enthalpy of serrated flow is calculated by means of the conventional method (utilizing the critical strain for the onset of serrations) and by means of a newly developed method (starting from Δσ- and Δt-values). Both methods yield comparable results. However, some details in the analysis disagree with the expectations and discredit the Cottrell model.

Craze initiation in poly(methyl methacrylate) under biaxial stress

AbstractCriteria for craze initiation in poly(methyl methacrylate) have been investigated under various combined loadings including biaxial tension and torsion‐compression at 65°C in air and at room temperature in a crazing agent, kerosene. Environmental crazes are observed even under torsion‐compression loading when air crazing does not occur, and the stress locus for environmental crazing is very different from that for air crazing. A theoretical model analogous to the Cottrell model in crystal plasticity is proposed. Theoretical crazing loci derived from the model are compared with the experimental results.

Serrated flow in Al−5 wt.% Mg alloy

Type B serrations in polycrystalline Al−5 wt.% Mg alloy at 296 K have been examined by a repeated process of strain aging and Lüders band propagation. The magnitude Δσ of the stress drop increases with strain and is proportional to (Dt) 2 3 . This is in agreement with Cottrell's model of strain aging assisted by the enhanced diffusion of magnesium atoms through deformation-induced vacancies. Each stress drop Δσ results in a Lüders band motion with specimen extension Δl ∝( Δσ) 1 − n , where n ≈ 0.3 is the effective stress exponent for Lüders strain in the stress relaxation mechanism proposed by Prewo et al. Higher ductility and work hardening may be explained through the larger travelling distance of Lüders bands associated with the longer aging time.

UKAEA Reactor Group studies of irradiation-induced creep in graphite

A review is presented of the experimental and theoretical studies of fast neutron irradiation creep in reactor graphite carried out by the UKAEA Reactor Group. The studies have covered the effect of varying graphite type, oxidation, stress level and boron doping. The results are shown to accord better with a dislocation pinning-unpinning model of dislocation glide, rather than the Cottrell model often assumed.

The portevin-le chatelier effect in Cu 3Au

Tensile tests were performed on ordered and disordered polycrystalline Cu 3Au over a wide temperature range, and serrated stress-strain curves were observed in both the ordered and disordered material at temperatures from ~300 K to ~550 K. Three distinct types of serration (A, B and C) were identified. For type A serrations, ( m + α) was determined as 2.98 for the ordered material and 2.18 for the disordered material, where m and β are the strain exponents for vacancy creation and dislocation multiplication, respectively. The value of m was estimated as ~1.9 from the onset of type B serrations. The activation energies for the onset of types A and B serrations in disordered Cu 3Au and of type A serrations in ordered Cu 3Au, were close to the appropriate values for vacancy migration. The activation energies for the disappearance of serrated flow were similar to those anticipated for self-diffusion. It is demonstrated that the results are in good agreement with the Cottrell model for dynamic strain ageing.