A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Effects of mobile phone distraction on drivers’ reaction times

Distraction resulting from mobile phone use whilst driving has been shown to increase the reaction times of drivers, thereby increasing the likelihood of a crash. This study compares the effects of mobile phone conversations on reaction times of drivers responding to traffic events that occur at different points in a driver’s field of view. The CARRS-Q Advanced Driving Simulator was used to test a group of young drivers on various simulated driving tasks including a traffic event that occurred within the driver’s central vision—a lead vehicle braking suddenly—and an event that occurred within the driver’s peripheral—a pedestrian entering a zebra crossing from a footpath. Thirty-two licensed drivers drove the simulator in three phone conditions: baseline (no phone conversation), and while engaged in hands-free and handheld phone conversations. The drivers were aged between 21 to 26 years and split evenly by gender. Differences in reaction times for an event in a driver’s central vision were not statistically significant across phone conditions, probably due to a lower speed selection by the distracted drivers. In contrast, the reaction times to detect an event that originated in a distracted driver’s peripheral vision were more than 50% longer compared to the baseline condition. A further statistical analysis revealed that deterioration of reaction times to an event in the peripheral vision was greatest for distracted drivers holding a provisional licence. Many critical events originate in a driver’s periphery, including vehicles, bicyclists, and pedestrians emerging from side streets. A reduction in the ability to detect these events while distracted presents a significant safety concern that must be addressed.

A parametric duration model of the reaction times of drivers distracted by mobile phone conversations

The use of mobile phones while driving is more prevalent among young drivers—a less experienced cohort with elevated crash risk. The objective of this study was to examine and better understand the reaction times of young drivers to a traffic event originating in their peripheral vision whilst engaged in a mobile phone conversation. The CARRS-Q Advanced Driving Simulator was used to test a sample of young drivers on various simulated driving tasks, including an event that originated within the driver’s peripheral vision, whereby a pedestrian enters a zebra crossing from a sidewalk. Thirty-two licensed drivers drove the simulator in three phone conditions: baseline (no phone conversation), hands-free and handheld. In addition to driving the simulator each participant completed questionnaires related to driver demographics, driving history, usage of mobile phones while driving, and general mobile phone usage history. The participants were 21 to 26 years old and split evenly by gender. Drivers’ reaction times to a pedestrian in the zebra crossing were modelled using a parametric accelerated failure time (AFT) duration model with a Weibull distribution. Also tested where two different model specifications to account for the structured heterogeneity arising from the repeated measures experimental design. The Weibull AFT model with gamma heterogeneity was found to be the best fitting model and identified four significant variables influencing the reaction times, including phone condition, driver’s age, license type (Provisional license holder or not), and self-reported frequency of usage of handheld phones while driving. The reaction times of drivers were more than 40% longer in the distracted condition compared to baseline (not distracted). Moreover, the impairment of reaction times due to mobile phone conversations was almost double for provisional compared to open license holders. A reduction in the ability to detect traffic events in the periphery whilst distracted presents a significant and measurable safety concern that will undoubtedly persist unless mitigated.

Fabrication and electrocatalytic properties of polyaniline/Pt nanoparticle composites

Polyaniline (PANI)/Pt nanoparticle composites can be prepared by the spontaneous redox reaction of K2PtCl4 with PANI, to yield thin films that show electrocatalytic properties in both acidic and neutral aqueous media.

Preparation of metal-TCNQ charge-transfer complexes on conducting and insulating surfaces by photocrystallization

A generic method for the synthesis of metal-7,7,8,8-tetracyanoquinodimethane (TCNQ) charge-transfer complexes on both conducting and nonconducting substrates is achieved by photoexcitation of TCNQ in acetonitrile in the presence of a sacrificial electron donor and the relevant metal cation. The photochemical reaction leads to reduction of TCNQ to the TCNQ- monoanion. In the presence of Mx+(MeCN), reaction with TCNQ-(MeCN) leads to deposition of Mx+[TCNQ]x crystals onto a solid substrate with morphologies that are dependent on the metal cation. Thus, CuTCNQ phase I photocrystallizes as uniform microrods, KTCNQ as microrods with a random size distribution, AgTCNQ as very long nanowires up to 30 μm in length and with diameters of less than 180 nm, and Co[TCNQ]2(H2O)2 as nanorods and wires. The described charge-transfer complexes have been characterized by optical and scanning electron microscopy and IR and Raman spectroscopy. The CuTCNQ and AgTCNQ complexes are of particular interest for use in memory storage and switching devices. In principle, this simple technique can be employed to generate all classes of metal−TCNQ complexes and opens up the possibility to pattern them in a controlled manner on any type of substrate.

Premonolayer oxidation of nanostructured gold : an important factor influencing electrocatalytic activity

The study of the electrodeposition of polycrystalline gold in aqueous solution is important from the viewpoint that in electrocatalysis applications ill-defined micro- and nanostructured surfaces are often employed. In this work, the morphology of gold was controlled by the electrodeposition potential and the introduction of Pb(CH3COO)2•3H2O into the plating solution to give either smooth or nanostructured gold crystallites or large dendritic structures which have been characterized by scanning electron microscopy (SEM). The latter structures were achieved through a novel in situ galvanic replacement of lead with AuCl4−(aq) during the course of gold electrodeposition. The electrochemical behavior of electrodeposited gold in the double layer region was studied in acidic and alkaline media and related to electrocatalytic performance for the oxidation of hydrogen peroxide and methanol. It was found that electrodeposited gold is a significantly better electrocatalyst than a polished gold electrode; however, performance is highly dependent on the chosen deposition parameters. The fabrication of a deposit with highly active surface states, comparable to those achieved at severely disrupted metal surfaces through thermal and electrochemical methods, does not result in the most effective electrocatalyst. This is due to significant premonolayer oxidation that occurs in the double layer region of the electrodeposited gold. In particular, in alkaline solution, where gold usually shows the most electrocatalytic activity, these active surface states may be overoxidized and inhibit the electrocatalytic reaction. However, the activity and morphology of an electrodeposited film can be tailored whereby electrodeposited gold that exhibits nanostructure within the crystallites on the surface demonstrated enhanced electrocatalytic activity compared to smaller smooth gold crystallites and larger dendritic structures in potential regions well within the double layer region.

Galvanic replacement mediated synthesis of hollow Pt nanocatalysts : significance of residual Ag for the H2 evolution reaction

With the increasing popularity of the galvanic replacement approach towards the development of bimetallic nanocatalysts, special emphasis has been focused on minimizing the use of expensive metal (e.g. Pt), in the finally formed nanomaterials (e.g. Ag/Pt system as a possible catalyst for fuel cells). However, the complete removal of the less active sacrificial template is generally not achieved during galvanic replacement, and its residual presence may significantly impact on the electrocatalytic properties of the final material. Here, we investigate the hydrogen evolution reaction (HER) activity of Ag nanocubes replaced with different amounts of Pt, and demonstrate how the bimetallic composition significantly affects the activity of the alloyed nanomaterial.

Galvanic replacement mediated transformation of Ag nanospheres into dendritic Au--Ag nanostructures in the ionic liquid [BMIM][BF4]

We demonstrate an unusual shape transformation of Ag nanospheres into {111}-oriented Au–Ag dendritic nanostructures by a galvanic replacement reaction in the ionic liquid (IL) 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]).

Morphology changes and mechanistic aspects of the electrochemically-induced reversible solid-solid transformation of microcrystalline TCNQ into Co TCNQ 2-based materials (TCNQ= 7, 7, 8, 8-Tetracyanoquinodimethane)

The chemically reversible solid−solid phase transformation of a TCNQ-modified glassy carbon, indium tin oxide, or metal electrode into Co\[TCNQ]2(H2O)2 material in the presence of Co2+(aq) containing electrolytes has been induced and monitored electrochemically. Voltammetric data reveal that the TCNQ/Co\[TCNQ]2(H2O)2 interconversion process is independent of electrode material and identity of cobalt electrolyte anion. However, a marked dependence on electrolyte concentration, scan rate, and method of electrode modification (drop casting or mechanical attachment) is found. Cyclic voltammetric and double potential step chronoamperometric measurements confirm that formation of Co\[TCNQ]2(H2O)2 occurs through a rate-determining nucleation and growth process that initially involves incorporation of Co2+(aq) ions into the reduced TCNQ crystal lattice at the TCNQ|electrode|electrolyte interface. Similarly, the reverse (oxidation) process, which involves transformation of solid Co\[TCNQ]2(H2O)2 back to parent TCNQ crystals, also is controlled by nucleation−growth kinetics. The overall chemically reversible process that represents this transformation is described by the reaction:  2TCNQ0(s) + 2e- + Co2+(aq) + 2H2O \[Co(TCNQ)2(H2O)2](s). Ex situ SEM images illustrated that this reversible TCNQ/Co\[TCNQ]2(H2O)2 conversion process is accompanied by drastic size and morphology changes in the parent solid TCNQ. In addition, different sizes of needle-shaped nanorod/nanowire crystals of Co\[TCNQ]2(H2O)2 are formed depending on the method of surface immobilization.

Investigation of mediated oxidation of ascorbic acid by ferrocenemethanol using large-amplitude fourier transformed ac voltammetry under quasi-reversible electron-transfer conditions at an indium tin oxide electrode

The ability of the technique of large-amplitude Fourier transformed (FT) ac voltammetry to facilitate the quantitative evaluation of electrode processes involving electron transfer and catalytically coupled chemical reactions has been evaluated. Predictions derived on the basis of detailed simulations imply that the rate of electron transfer is crucial, as confirmed by studies on the ferrocenemethanol (FcMeOH)-mediated electrocatalytic oxidation of ascorbic acid. Thus, at glassy carbon, gold, and boron-doped diamond electrodes, the introduction of the coupled electrocatalytic reaction, while producing significantly enhanced dc currents, does not affect the ac harmonics. This outcome is as expected if the FcMeOH (0/+) process remains fully reversible in the presence of ascorbic acid. In contrast, the ac harmonic components available from FT-ac voltammetry are predicted to be highly sensitive to the homogeneous kinetics when an electrocatalytic reaction is coupled to a quasi-reversible electron-transfer process. The required quasi-reversible scenario is available at an indium tin oxide electrode. Consequently, reversible potential, heterogeneous charge-transfer rate constant, and charge-transfer coefficient values of 0.19 V vs Ag/AgCl, 0.006 cm s (-1) and 0.55, respectively, along with a second-order homogeneous chemical rate constant of 2500 M (-1) s (-1) for the rate-determining step in the catalytic reaction were determined by comparison of simulated responses and experimental voltammograms derived from the dc and first to fourth ac harmonic components generated at an indium tin oxide electrode. The theoretical concepts derived for large-amplitude FT ac voltammetry are believed to be applicable to a wide range of important solution-based mediated electrocatalytic reactions.

Rapid synthesis of porous honeycomb Cu/Pd through a hydrogen-bubble templating method

A rapid electrochemical method based on using a clean hydrogen-bubble template to form a bimetallic porous honeycomb Cu/Pd structure has been investigated. The addition of palladium salt to a copper-plating bath under conditions of vigorous hydrogen evolution was found to influence the pore size and bulk concentration of copper and palladium in the honeycomb bimetallic structure. The surface was characterised by X-ray photoelectron spectroscopy, which revealed that the surface of honeycomb Cu/Pd was found to be rich with a Cu/Pd alloy. The inclusion of palladium in the bimetallic structure not only influenced the pore size, but also modified the dendritic nature of the internal wall structure of the parent copper material into small nanometre-sized crystallites. The chemical composition of the bimetallic structure and substantial morphology changes were found to significantly influence the surface-enhanced Raman spectroscopic response for immobilised rhodamine B and the hydrogen-evolution reaction. The ability to create free-standing films of this honeycomb material may also have many advantages in the areas of gas- and liquid-phase heterogeneous catalysis.

Large amplitude Fourier transformed AC voltammetric investigation of the active state electrochemistry of a copper/aqueous base interface and implications for electrocatalysis

The higher harmonic components available from large-amplitude Fourier-transformed alternating current (FT-ac) voltammetry enable the surface active state of a copper electrode in basic media to be probed in much more detail than possible with previously used dc methods. In particular, the absence of capacitance background current allows low-level Faradaic current contributions of fast electron-transfer processes to be detected; these are usually completely undetectable under conditions of dc cyclic voltammetry. Under high harmonic FT-ac voltammetric conditions, copper electrodes exhibit well-defined and reversible premonolayer oxidation responses at potentials within the double layer region in basic 1.0 M NaOH media. This process is attributed to oxidation of copper adatoms (Cu*) of low bulk metal lattice coordination numbers to surface-bonded, reactive hydrated oxide species. Of further interest is the observation that cathodic polarization in 1.0 M NaOH significantly enhances the current detected in each of the fundamental to sixth FT-ac harmonic components in the Cu*/Cu hydrous oxide electron-transfer process which enables the underlying electron transfer processes in the higher harmonics to be studied under conditions where the dc capacitance response is suppressed; the results support the incipient hydrous oxide adatom mediator (IHOAM) model of electrocatalysis. The underlying quasi-reversible interfacial Cu*/Cu hydrous oxide process present under these conditions is shown to mediate the reduction of nitrate at a copper electrode, while the mediator for the hydrazine oxidation reaction appears to involve a different mediator or active state redox couple. Use of FT-ac voltammetry offers prospects for new insights into the nature of active sites and electrocatalysis at the electrode/solution interface of Group 11 metals in aqueous media.

Galvanic Replacement of Semiconductor Phase I CuTCNQ Microrods with KAuBr4 to Fabricate CuTCNQ/Au Nanocomposites with Photocatalytic Properties

In this study, the reaction of semiconductor microrods of phase I copper 7,7,8,8-tetracyanoquinodimethane (CuTCNQ) with KAuBr4 in acetonitrile is reported. It was found that the reaction is redox in nature and proceeds via a galvanic replacement mechanism in which the surface of CuTCNQ is replaced with metallic gold nanoparticles. Given the slight solubility of CuTCNQ in acetonitrile, two competing reactions, namely CuTCNQ dissolution and the redox reaction with KAuBr4, were found to operate in parallel. An increase in the surface coverage of CuTCNQ microrods with gold nanoparticles occurred with an increased KAuBr4 concentration in acetonitrile, which also inhibited CuTCNQ dissolution. The reaction progress with time was monitored using UV−visible, FT-IR, and Raman spectroscopy as well as XRD and EDX analysis, and SEM imaging. The CuTCNQ/Au nanocomposites were investigated for their photocatalytic properties, wherein the destruction of Congo red, an organic dye, by simulated solar light was found dependent on the surface coverage of gold nanoparticles on the CuTCNQ microrods. This method of decorating CuTCNQ may open the possibility of modifying this and other metal-TCNQ charge transfer complexes with a host of other metals which may have significant applications.

Synthesis of CuTCNQ/Au microrods by galvanic replacement of semiconducting phase I CuTCNQ with KAuBr4 in aqueous medium

The spontaneous reaction between microrods of an organic semiconductor molecule, copper 7,7,8,8-tetracyanoquinodimethane (CuTCNQ) with [AuBr4]− ions in an aqueous environment is reported. The reaction is found to be redox in nature which proceeds via a complex galvanic replacement mechanism, wherein the surface of the CuTCNQ microrods is replaced with metallic gold nanoparticles. Unlike previous reactions reported in acetonitrile, the galvanic replacement reaction in aqueous solution proceeds via an entirely different reaction mechanism, wherein a cyclical reaction mechanism involving continuous regeneration of CuTCNQ consumed during the galvanic replacement reaction occurs in parallel with the galvanic replacement reaction. This results in the driving force of the galvanic replacement reaction in aqueous medium being largely dependent on the availability of [AuBr4]− ions during the reaction. Therefore, this study highlights the importance of the choice of an appropriate solvent during galvanic replacement reactions, which can significantly impact upon the reaction mechanism. The reaction progress with respect to different gold salt concentration was monitored using Fourier transform infrared (FT-IR), Raman, and X-ray photoelectron spectroscopy (XPS), as well as XRD and EDX analysis, and SEM imaging. The CuTCNQ/Au nanocomposites were also investigated for their potential photocatalytic properties, wherein the destruction of the organic dye, Congo red, in a simulated solar light environment was found to be largely dependent on the degree of gold nanoparticle surface coverage. The approach reported here opens up new possibilities of decorating metal–organic charge transfer complexes with a host of metals, leading to potentially novel applications in catalysis and sensing.

A facile chemical screening method for the detection of stress corrosion cracking in 9 carat gold alloys

Stress corrosion cracking (SCC) is a well known form of environmental attack in low carat gold jewellery. It is desirable to have a quick, easy and cost effective way to detect SCC in alloys and prevent them from being used and later failing in their application. A facile chemical method to investigate SCC of 9 carat gold alloys is demonstrated. It involves a simple application of tensile stress to a wire sample in a corrosive environment such as 1–10 % FeCl3 which induces failure in less than 5 minutes. In this study three quaternary (Au, Ag, Cu and Zn) 9 carat gold alloy compositions were investigated for their resistance to SCC and the relationship between time to failure and processing conditions is studied. It is envisaged that the use of such a rapid and facile screening procedure at the production stage may readily identify alloy treatments that produce jewellery that will be susceptible to SCC in its lifetime.