Steady-state Concentration Gradients Research Articles

Nanoscale Photoelectrochemical Mapping of Two-Dimensional Electrodes

Electron transfer plays a significant role in many chemical processes, especially in the catalytic reactions involved in photoelectrochemical energy conversion and storage. Revealing the electron transfer behavior at the interface of electrode-electrolyte is thus of great importance. Here we fabricate atomically thin semiconductor MX2 (M = Mo, W; X = S, Se) by chemical vapor deposition method and directly map the photoelectrochemical behavior using Atomic Force Microscopy-combined with light-induced Scanning Electrochemical Microscopy (AFM-SECM). AFM-SECM feedback mapping shows a layer-dependent photoelectrocatalytic ability of MX2 to oxidize the redox species Ru2+ back to Ru3+. Moreover, AFM-SECM generation and collection mode shows the potential-dependent edge and basal plane activity for the hydrogen evolution reaction of WSe2. Compared with monolayer and bilayer, few-layer WSe2 shows better stability in an electrochemical environment, faster electron transfer, and higher hydrogen production. Furthermore, finite element method based numerical simulations using MATLAB® and COMSOL Multiphysics® is performed to calculate the electron transfer rate constants k0 and simulate the steady-state concentration gradient. Finally, the photoelectrochemistry at MX2 electrode-electrolyte interfaces are spatially resolved and understanding this behavior will be useful for the future photoelectrochemical devices.

Morphogen gradient formation in partially absorbing media

Morphogen gradients play an essential role in the spatial regulation of cell patterning during early development. The classical mechanism of morphogen gradient formation involves the diffusion of morphogens away from a localized source combined with some form of bulk absorption. Morphogen gradient formation plays a crucial role during early development, whereby a spatially varying concentration of morphogen protein drives a corresponding spatial variation in gene expression during embryogenesis. In most models, the absorption rate is taken to be a constant multiple of the local concentration. In this paper, we explore a more general class of diffusion-based model in which absorption is formulated probabilistically in terms of a stopping time condition. Absorption of each particle occurs when its time spent within the bulk domain (occupation time) exceeds a randomly distributed threshold a; the classical model with a constant rate of absorption is recovered by taking the threshold distribution . We explore how the choice of Ψ(a) affects the steady-state concentration gradient, and the relaxation to steady-state as determined by the accumulation time. In particular, we show that the more general model can generate similar concentration profiles to the classical case, while significantly reducing the accumulation time.

Mechanisms of Enzymatic Transduction in Nanochannel Biosensors.

The immobilization of enzymes in solid-state nanochannels is a new avenue for the design of biosensors with outstanding selectivity and sensitivity. This work reports the first theoretical model of an enzymatic nanochannel biosensor. The model is applied to the system previously experimentally studied by Lin, et al. (Anal. Chem. 2014, 86, 10546): a hourglass nanochannel modified by glucose oxidase for the detection of glucose. Our predictions are in good agreement with experimental observations as a function of the applied potential, pH and glucose concentration. The sensing mechanism results from the combination of three processes: i) the establishment of a steady-state proton concentration gradient due to a reaction-diffusion mechanism, ii) the effect of that gradient on the charge of the adsorbed enzymes and native surface groups, and iii) the effect of the resulting surface charge on the ionic current. Strategies to improve the sensor performance based on this mechanism are identified and discussed.

Modeling of the Electrochemical Motion Sensor Conversion Factor at High Frequencies.

The conversion factor of the electrochemical motion sensors at low frequencies is usually quite high. At the same time, it decreases significantly with the increase in frequency. Thus, increasing the conversion factor for high frequencies is essential for practical use. In this work, the theoretical model that allows establishing the basic laws governing the conversion of high-frequency signals in an electrochemical cell has been suggested. The approach was based on the fact that in the case of high frequencies, the diffusion length is less than the distance between the electrodes and the thickness of the channel and it is enough to consider the transformation of the fluid motion into electrical current only near the cathodes. It was found that the signal output current can be represented as the sum of the term which is proportional to the steady-state concentration gradient along the surface on which the cathode is located, and the term proportional to the concentration gradient normal to the surface. Both first and second terms and the total signal current have been calculated for a particular case of a four-electrode planar system. The practical conclusion is that the high frequency conversion factor increases with the interelectrode distance and the channel width decreases compared to the cathode dimension.

Electrochemical Generation of Steady-State Linear Concentration Gradients within Microfluidic Channels Perpendicular to the Flow Field.

A new design of microelectrode was introduced to generate electrochemically steady-state linear concentration gradients perpendicular to the flow direction throughout the cross section of microchannels. The shape and geometry of the electrode were established based on operating regimes at microchannel electrodes. Before implementation, optimal conditions were preliminary delineated by numerical simulations according to the flow velocity and microchannel dimensions. To assess experimentally these predictions, a specific microfluidic platform was developed with optimized geometry to simultaneously allow the generation of linear concentration gradients and the mapping of concentration profiles by confocal fluorescence microscopy. As a model, the electrochemical reduction of a quinone in the presence of fluorescein was selected to both generate and monitor a linear proton gradient. A good agreement was observed between theoretical and experimental data, establishing the proof of concept. These results should broaden the performance and applications of electrochemical platforms, particularly in the field of active control of microenvironments in biology, biochemistry, and analytical chemistry.

Dynamic Transport Control of Colloidal Particles by Repeatable Active Switching of Solute Gradients.

Diffusiophoresis (DP) is described as typically being divided into chemiphoresis (CP) and electrophoresis (EP), and the related theory is well-established. However, not only the individual effect of CP and EP but also the size dependency on the resulting DP of colloidal particles has not yet been comprehensively demonstrated in an experimental manner. In this paper, we present a dynamic transport control mechanism for colloidal particles by developing a micro-/nanofluidic DP platform (MNDP). We demonstrate that the MNDP can generate transient and/or steady-state concentration gradients, making it possible to control the direction and rate of transport of colloidal particles through the individual manipulation of CP and EP by simply and rapidly switching solutions. In addition, the MNDP allows the size-dependent separation as well as fractionation of submicron particles through the individual manipulation of CP and EP, thus empirically validating the classic theoretical model for DP under the influence of electrical double layer (EDL) thickness. Furthermore, we provide theoretical analysis and simulation results that will enable the development of a versatile separation and/or fractionation technique for various colloidal particles, including biosamples, according to their size or electrical feature.

Diffusion in an age-structured randomly switching environment

Age-structured processes are well-established in population biology, where birth and death rates often depend on the age of the underlying populations. Recently, however, different examples of age-structured processes have been considered in the context of cell motility or certain types of stochastically gated ion channels, where the state of the system is determined by a switching process with age-dependent transition rates. In this paper we consider the particular problem of diffusion on a finite interval, with randomly switching boundary conditions due to the presence of an age-structured stochastic gate at one end of the interval. When the gate is closed the particles are reflected, whereas when it is open the domain is in contact with a particle bath. We use a moments method to derive a partial differential equation for the expectations of the stochastic concentration, conditioned on the state of the gate. We then use transform methods to eliminate the residence time of the age-structured switching, resulting in non-Markovian equations for the expectations, and determine the effective steady-state concentration gradient. Our analytical results are shown to match those obtained using Monte Carlo simulations.

Multi-Temperaturein SituMagnetic Resonance Imaging of Polarization and Salt Precipitation in Lithium-Ion Battery Electrolytes

Accurate electrochemical modeling of lithium-ion batteries is an important direction in the development of battery management systems in automotive applications, for both real-time performance control and long-term state-of-health monitoring. Measurements of electrolyte-domain transport parameters, under a wide regime of temperature and current conditions, are a crucial aspect of the parametrization and validation of these models. This study constitutes the first exploration of the temperature dependence for the steady-state electrolyte concentration gradient under applied current with spatial resolution via the in situ magnetic resonance imaging (MRI) technique. The use of complementary pure phase-encoding MRI methods was found to provide quantitatively accurate measurements of the concentration gradient, in strong agreement with predictions based on ex situ NMR and electrochemical techniques. Temperature is demonstrated to have a marked influence on the steady-state concentration gradient as well as the...

Multi-Temperature in Situ Magnetic Resonance Imaging of Polarization and Salt Precipitation in Li-Ion Battery Electrolytes

The parameterization and validation of robust electrochemical models for lithium-ion batteries in automotive applications, which are intended to address both the state of charge (SOC) and state of health (SOH) estimation problems, is an important milestone in their widespread deployment. Much effort has been focused on the mass transport characteristics of the electrode domains, but a significant fraction of overall polarization stems from concentration gradients that form in the electrolyte domain and their attendant effect on the mass transport parameters, which have recently been shown by in situ MRI to be quite significant, even within modest operational regimes.1 The effect of temperature on these concentration gradients remains to be explored by in situ MRI. The mass transport in the electrolyte domain is typically modelled as being governed by material balance of a binary salt in a concentrated solution, which can be realized by modifying the Nernst-Planck equation to have non-constant, concentration-dependent coefficients (Equation 1).2 This system has a steady-state concentration gradient (Equation 2) when migration flux driven by the potential and diffusion flux against the concentration gradient are in equilibrium (see Figure 1A). Using in situ MRI, the evolution of this gradient toward the steady-state upon constant-current charging can be monitored (Figure 1B). A surprising outcome of these studies was that at 10°C, an equal parts (v/v) mixture of EC/DEC with 1.00 M LiPF6 exhibited anomalous concentration gradient formation (Figure 2) with a current density corresponding to 6 A·m-2 (or ~C/4), whereas the same mixture and cell construction could be polarized without difficulty at room temperature. On comparing raw MR images from before the polarization and after the relaxation of the disrupted concentration gradient, it is clear that the overall signal intensity is lower whilst the shape of the profile is retained, which is a direct indicator that salt precipitation has occurred. There are two routes by which this salt precipitation phenomenon can be avoided: lowering the salt concentration, so that the absolute concentration at the upper portion of the gradient is decreased proportionately for an equivalent current density, and the selection of an electrolyte with better low-temperature solvation characteristics. Successful polarization and visualization of the electrolyte domain in situ was achieved with a 0.85 M variant of the equal-parts EC/DEC mixture utilized above, at a series of temperatures. This constitutes a means of avoiding the critical concentration at the low temperature where the 1.00 M variant exhibited precipitation, but it would come with a trade-off of reduced ionic conductivity. More significantly, a ‘full-strength’ 1.00 M LiPF6 in EC/PC/DMC, 5:2:3 (v/v) mixture was also successfully polarized at low, room, and elevated temperatures, with the same 6 A·m-2 applied current density. Previous ex situ experiments using the pulsed-field gradient NMR technique, in conjunction with conductivity measurements, had revealed that ion pairing at low temperature was significantly reduced in electrolyte mixtures where the fraction of high-dielectric solvent was maximized.3 A quantitative comparison of the steady-state concentration gradients at a series of inter-electrode distances and temperatures was also conducted with this electrolyte formulation, to assess how the magnitudes of the gradients varied with temperature, and to test the hypothesis inherent in Equation 2 that the inter-electrode spacing does not play a role in determining the magnitude of the steady-state gradient. Within 3σ confidence intervals, the inter-electrode spacing was not found to affect the inter-electrode spacing, which directly confirms that the in situ MRI technique can generate steady-state mass transport parameters which are relevant to real battery modelling efforts. A significant effect of the temperature on the magnitude of the steady-state concentration gradient is also illustrated in these multi-temperature imaging experiments, demonstrating the importance of characterizing the spatial variation and temperature-dependence of electrolyte mass transport characteristics for electrochemical model parameterization and validation. References (1) Krachkovskiy, S. A.; Bazak, J. D.; Werhun, P.; Balcom, B. J.; Halalay, I. C.; Goward, G. R. Visualization of Steady-State Ionic Concentration Profiles Formed in Electrolytes during Li-Ion Battery Operation and Determination of Mass-Transport Properties by in Situ Magnetic Resonance Imaging. J. Am. Chem. Soc. 2016, 138 (25), 7992–7999. (2) Sethurajan, A. K.; Krachkovskiy, S. A.; Halalay, I. C.; Goward, G. R.; Protas, B. Accurate Characterization of Ion Transport Properties in Binary Symmetric Electrolytes Using In Situ NMR Imaging and Inverse Modeling. J. Phys. Chem. B 2015, 119 (37), 12238–12248. (3) Krachkovskiy, S. A.; Bazak, J. D.; Fraser, S.; Halalay, I. C.; Goward, G. R. Determination of Mass Transfer Parameters and Ionic Association of LiPF 6 : Organic Carbonates Solutions. J. Electrochem. Soc. 2017, 164 (4), A912–A916. Figure 1

Mesoscale Simulation of self-diffusiophoretic microrotor

Artificial micro-scale or nano-scale machines that are capable of converting energy to mechanical work, have long been pursued by science and engineering communities for their potential applications in microfluidics, biology and medicine. From a physics point of view, they are also ideal models to investigate fundamental statistical phenomena in non-equilibrium active matters. Inspired by bio-machines and bio-motors like ATP synthase and flagellum motors, we propose a simple design of rotary motors based on pure self-diffusiophoresis effects. The basic design of the rotor consists of three colloidal beads with different surface properties, which leads to different interactions between the beads and solvent molecules. Chemical reactions are imposed on the surface of one of the beads, which creates a source of one of the two solvent molecules and generates a local concentration gradient. The other two beads connected to the catalytic bead have different affinities to the solvent molecules, which leads to asymmetric diffusiophoretic forces on the two non-catalytic beads. A net torque is thus obtained from difference of the diffusiophoretic forces between the two non-catalytic beads. In our simulation, we employ hybrid molecular dynamics (MD) simulations and multi-particle collision dynamics (MPC) to investigate the motion of microrotors. The binary fluid is composed with A-type and B-type solvent particle whose interactions are described by multi-particle collision dynamics while beads-particle interactions are modeled by molecular dynamics. In MPC, all fluid particles execute alternating streaming and collision steps. During streaming steps, the solvents move ballistically. During collision steps, particles are sorted into square cells and only interact with particles in the same cell under a specific stochastic rotation rule. MPC algorithm locally conserves mass, linear momentum, angular momentum and energy, and properly captures thermal fluctuation, mass diffusion, dissipation and hydrodynamic interactions. In our simulation, standard MPC parameters are employed which correspond to a liquid-like behavior of fluid. In MD, beads-solvent interactions are described by Lennard-Jones(LJ) potential with different parameter combinations and the equations of motion is integrated by velocity-Verlet algorithm. To perform hybrid molecular dynamic simulations with multi-particle collision dynamics, between two MPC collision steps, 50 MD steps are implemented for the solvent particles that are in the interaction range of colloidal beads. We first investigate the solvent concentration distribution around static microrotor, and confirm that the catalytic bead generates a steady-state local concentration gradient. Net angular displacements are obtained when the rotor is allowed to rotate freely. The rotational direction and speed of the micorotor are determined by bead-solvent interactions, the rotor geometry, the solvent viscosity and the catalytic reaction ratio. We also study the scenario in which two rotors are placed in close vicinity to each other. We find that the coupling between the concentration fields around the rotors reduces the rotational speed of both rotors.

Electrodiffusion of Molecules in Aqueous Media: A Robust, Discretized Description for Electroporation and Other Transport Phenomena

Electrically driven transport of molecules and ions within aqueous electrolytes is of long-standing interest, with direct relevance to applications that include the delivery/release of biologically active solutes to/from cells and tissues. Examples include iontophoretic and electroporation-mediated drug delivery. Here, we describe a robust method for characterizing electrodiffusive transport in physiologic aqueous media. Specifically, we treat the case of solute present in sufficiently low concentration as to negligibly contribute to the total ionic current within the system. In this limiting case, which applies to many systems of interest, the predominant electrical behavior due to small ions is decoupled from solute transport. Thus, electrical behavior may be characterized using existing methods and treated as known in characterizing electrodiffusive molecular transport. First, we present traditional continuum equations governing electrodiffusion of charged solutes within aqueous electrolytes and then adapt them to discretized systems. Second, we examine the time-dependent and steady-state interfacial concentration gradients that result from the combination of diffusion and electrical drift. Third, we show how interfacial concentration gradients are related to electric field strength and duration. Finally, we examine how discretization size affects the accuracy of these methods. Overall these methods are motivated by and well suited to addressing an outstanding goal: estimation of the net ionic and molecular transport facilitated by electroporation in biological systems.

A Novel Method to Produce Immobilised Biomolecular Concentration Gradients to Study Cell Activities: Design and Modelling

It is well known that many cell functions are activated by chemical signals with a time and space-dependent profile. To mimic these profiles in vitro, it is necessary to develop a system that is able to generate concentration gradients with a resolution similar to that perceived by cells, which is around nanomolar with a spatial resolution of a few tens of microns. Many devices capable of generating steady-state concentration gradients have been developed using continuous flow micro-fluidic techniques. However, these systems cannot reproduce the immobilised concentration gradients that are present in the extracellular matrix. For this reason, we have developed a new gradient generator to enable precise and reproducible studies on the effects of immobilised concentration gradients on cell behaviour. A well-known gradient of a desired molecule was generated on the bottom surface of a hydrogel, which was then used as a stamp to immobilise the molecule on a functionalised substrate. A concentration gradient was thus obtained using a simple silane-based chemical reaction. To validate the method, image analysis was performed on glass slides printed with fluorescein isothiocyanate (FITC)- collagen and FITC-poly-lysine concentration gradients. Preliminary cell adhesion tests were also carried out by seeding NIH-3T3 and mesencephalic cells on lab-glass slides printed with concentration profiles of collagen and poly-lysine, respectively.

Magnetic field induced concentration gradients in magnetic nanoparticle suspensions: Theory and experiment

An approach for studying steady-state nanoparticle concentration gradients arising in magnetic nanoparticle suspensions in response to strong magnetic field gradient is presented. The experimental approach makes use of microscopic optical absorption measurements of ferrofluid interacting with arrays of patterned magnets. Experimental results are found to be consistent with a simple theoretical description that predicts the local nanoparticle concentration over a wide range of magnetic field conditions and ferrofluid volume fractions.

Frictional Drag and Electrical Manipulation of Recombinant Proteins in Polymer-Supported Membranes

We establish a lipid monolayer supported by a polymer interface that offers advantages over conventional solid-supported membranes for determining the frictional drag at the membrane-protein interface as well as for electric field manipulation of membrane-anchored proteins. Polymer-supported monolayers with functional lipid anchors allow for the specific docking of His-tagged green fluorescent protein variants (His-EGFP and His-DsRed tetramer) onto the membrane surface at a defined surface density. In the first part, we measure the lateral diffusion coefficients of lipids and proteins and calculate the frictional drag at the protein-membrane interface. The second part deals with the electric field-induced accumulation of recombinant proteins on a patterned surface. The mean drift velocity of proteins, which can be obtained analytically from the shape of the steady-state concentration gradient, can be controlled by tuning the interplay of electrophoresis and electroosmosis. The results demonstrate the potential of such molecular constructs for the local functionalization of solid substrates with membrane-associated proteins.

Is Membrane Transport of FFA Mediated by Lipid, Protein, or Both?

![Figure][1] J. Patrick Kampf Torrey Pines Institute for Molecular Studies, San Diego, California ![Figure][1] Alan M. Kleinfeld Torrey Pines Institute for Molecular Studies, San Diego, California akleinfeld{at}tpims.org The mechanism of free fatty acid (FFA)

Neutral reagents in solutions with low content of supporting electrolyte: how to determine the steady-state conditions.

Cyclic voltammograms obtained at ultramicroelectrodes in the electrochemical systems where an uncharged reactant is significantly more concentrated than the supporting electrolyte show an unusual feature. The forward and the backward waves cross over, forming a hysteresis loop. The width of the hysteresis increases with the relative concentration of the reactant, with the electrode size, and with the scan rate. We show that the reason for this hysteresis is the slow transport of supporting electrolyte ions that are necessary to compensate the charge of the reaction product. As a result, the steady-state concentration profile of counterions is reached significantly slower than the steady-state concentration gradient of the reactant, and the counterion transport determines how rapidly the steady state for the whole system is approached. The scan rate yielding near-steady-state voltammograms can differ by more than 1 order of magnitude for systems with high and low concentrations of supporting electrolyte. Experimental evidence for this, supported by digital simulation results, is presented. The appropriate criterion for assessing the steady state in such systems is thus the identity of the forward and backward scans, without hysteresis. If this condition is not fulfilled, the formal potentials and the related parameters determined from the obtained voltammograms may be erroneous.

Time-dependent interface stability during directional solidification of a single phase alloy(Ⅰ) Theoritical

The initial transient solute redistribution during directional solidification is systematically investigated by carefully comparing the current theoreltical models with experimental results. It is shown that at the transient front solute redistribution generally meets an exponential profile no matter whether there exi sts liquid convection or pure diffusion in front of the liquid/solid interface.The profile can be described by a unified formula. Based on this, a general time-dependent linear dynamic analysis of the morphological instability of a solidifying planar interface during directional solidification is carried out. It is found that the timedependent instability solution has the same form as the steadystate solution described by Mullins and Sekerka, but the timedependent concentration gradient GtC, interface velocity Vi and diffusion length l should replace the corresponding steadystate concentration gradi ent GC，interface velocity V，diffusion length DL/V in Mulli ns and Sekerka solution.

Comparison of Emission Models With Computational Fluid Dynamic Simulation and a Proposed Improved Model

Understanding source behavior is important in controlling exposure to airborne contaminants. Industrial hygienists are often asked to infer emission information from room concentration data. This is not easily done, but models that make simplifying assumptions regarding contaminant transport are frequently used. The errors resulting from these assumptions are not yet well understood. This study compares emission estimates from the single-zone completely mixed (CM-1), two-zone completely mixed (CM-2), and uniform diffusivity (UD) models with the emissions set as boundary conditions in computational fluid dynamic (CFD) simulations of a workplace. The room airflow and concentration fields were computed using Fluent 4. These numerical experiments were factorial combinations of three source locations, five receptor locations, three dilution airflow rates, and two generation rate profiles, constant and time-varying. The aim was to compute plausible concentration fields, not to simulate exactly the processes in a real workroom. Thus, error is defined here as the difference between model and CFD predictions. For the steady-state case the UD model had the lowest error. When the source near-field contained the breathing zone receptor, the CM-2 model was applied. Then, in decreasing agreement with CFD were UD, CM-2, and CM-1. Averaging over all source and receptor locations (CM-2 applied for only one), in decreasing order of agreement with CFD were UD, CM-1, and CM-2. Source and receptor location had large effects on emission estimates using the CM-1 model and some effect using the UD model. A location-specific mixing factor (location factor) derived from steady-state concentration gradients was used to build a more accurate time-dependent emission model, CM-L. Total mass emitted from a time-varying source was modeled most accurately by CM-L, followed by CM-1 and CM-2.

Thermally perturbed barodiffusion in a binary liquid mixture

In a binary liquid, the existence of a gravity-induced concentration gradient (the barodiffusion gradient) is a requirement for the system to be in equilibrium. In order to study the effect of forces which could drive such a system from equilibrium, we observe the long-time evolution of gravity-induced concentration gradients in the presence of small perturbing horizontal temperature gradients (\ensuremath{\leqslant} 85 mK/cm) in a system of aniline and cyclohexane near its critical point. These measurements are unique since previous studies of gravity-induced concentration gradients in binary liquids have focused only on fast developing gradients created by sedimentation or on the measurement of equilibrium barodiffusion. Our results reveal large variations in the steady state concentration gradients even in the absence of applied temperature gradients, suggesting that very small temperature gradients may cause significant fluctuations in a binary liquid system. Additionally, as the applied temperature gradient increases, the growth of the concentration gradients slows and fluctuations on time scales much shorter than the expected diffusion time appear.

Micropatterning fluid lipid bilayers on solid supports.

Lithographically patterned grids of photoresist, aluminum oxide, or gold on oxidized silicon substrates were used to partition supported lipid bilayers into micrometer-scale arrays of isolated fluid membrane corrals. Fluorescently labeled lipids were observed to diffuse freely within each membrane corral but were confined by the micropatterned barriers. The concentrations of fluorescent probe molecules in individual corrals were altered by selective photobleaching to create arrays of fluid membrane patches with differing compositions. Application of an electric field parallel to the surface induced steady-state concentration gradients of charged membrane components in the corrals. In addition to producing patches of membrane with continuously varying composition, these gradients provide an intrinsically parallel means of acquiring information about molecular properties such as the diffusion coefficient in individual corrals.