Calculating Electrochemical Activity of Regular-Structure Porous Electrodes with an Immobilized Enzyme

A porous electrode of regular structure with an immobilized enzyme is studied. The electrode carcass, which consists of substrate particles, is a system of two sets of mutually perpendicular planes crossing one another (cellular structure). A monomolecular layer of enzyme molecules is deployed on the inner surface of such a porous substrate. In the center of each cell of the substrate gas pores, which are cylinders of porous grains of a hydrophobizing agent one grain thick, are situated. The rest of the cell space is filled by a solid polymer electrolyte. The ultimate goal of calculations is to estimate the electrochemical activity of such an electrode. The estimation is done for an oxygen electrode with an enzyme whose characteristics are close to those of laccase. The calculation assumes that active centers of enzyme molecules undergo a direct, i.e. without participation of mediators, reduction. It is shown that at an overvoltage of 30 mV, it would be possible to obtain a current density of 0.44 A cm^–2 in an electrode 16 m thick.     

Calculating the Electrochemical Activity of Porous Electrodes of a Filled-up Type with an Immobilized Enzyme

The electrochemical activity of porous electrodes of a filled-up type with an immobilized enzyme is calculated with the aid of computer-aided modeling. The percolation properties of two-component (a mixture of dispersed particles of the substrate and the enzyme) and three-component (a carrier of a gas reactant is added) models of a porous electrode are investigated. Taking into account specific features inherent in the forming macroscopic clusters (collections of particles of one sort or another connected with one another), i.e. an electron cluster and a gas cluster, makes it possible to determine the concentration of an active catalyst which is capable of taking part in the electrochemical process. The calculation of the electrochemical activity is performed in two-component structures, where the process of the current generation is limited by diffusion limitations, and in three-component structures, where the process of the current generation is limited by ohmic limitations. Estimates of the current are performed using an oxygen porous electrode with Nafion and an enzyme as an example. The electrochemical characteristics of this model electrode are close to those obtained on laccase. Introducing a hydrophobizing agent into the active layer of the porous electrode (passing from two-component structures to three-component structures) produces a positive effect. Although the number of active molecules of the enzyme drops in this case by an order of magnitude, the liquidation of diffusion limitations eventually raises the magnitude of the current by approximately threefold. Calculations show that it is quite feasible to obtain currents of 0.2 A cm^–2 on a porous electrode 16 m thick at an overvoltage of 30 mV.     

Gas-Generating Porous Electrodes: Chlorine Generation in DSA at Low and Intermediate Overpotentials

Parameters of gas-generating porous electrodes (GPE) in the range of low overpotentials, where all the pores are filled with electrolyte and the gas generation and transport occur in an internal diffusion mode, are calculated and analyzed. A criterion for estimating critical overpotential values, upon achieving which first gas pores start appearing in GPE, is found. Theoretical critical overpotentials of chlorine generation in DSA satisfactorily agree with experiment. About 20% of porous space takes part in the chlorine generation in DSA of standard thickness (5 m), provided there are no limitations on chlorine transport outside the electrode. The appearance of the low-polarizability part in the anodic branch of polarization curve for DSA is caused by the appearance, in GPE, of a system of gas pores connected with each other and the front electrode surface. This assumption is partially confirmed by theoretical estimation.     

Gas-Generating Porous Electrodes: Calculating Characteristics in the Low-Polarizability Portion

It is shown in the paper how specific features of the structure of the porous space in gas-generating porous electrodes (GGPE) create conditions for the emergence of a low-polarizability portion (LPP) in a polarization curve (PC). A set of equations is derived, which allows one to perform calculation of PC in the initial part of LPP. In the region of small overvoltages and in the initial part of a low-polarizability portion, calculations of basic characteristics of GGPE are performed. The calculations are carried out with the values of constants that are close to those that take place for the process of chlorine generation in dimensionally stable anodes. The shape of PC is established, together with the distribution of the oversaturation of electrolyte solution with gas over the GGPE thickness, the specific liquid surface area at which the electrochemical process of gas generation occurs, the amount of gas in the pores of the porous electrode, the overvoltage dependence of the oversaturation of electrolyte solution with gas at the front surface of GGPE, and the magnitude of the effective penetration depth of the process of gas formation into the porous electrode.     

Calculation of Effective Electroconductivity of Porous Electrodes with Pores Partially Filled by a Conductive Liquid

A method for calculating the effective electroconductivity of porous media filled in part by a conductive liquid is suggested. Its principal advantage is the possibility to automate calculations with the aid of a personal computer. Porous electrodes are simulated by a simple cubic lattice of links. A calculation of the dependence of the effective electroconductivity of such structures on the share of conductive links (with each link having a unit resistance) is performed. The calculation stages are as follows. (1) Links of percolation clusters are divided into dead-end links that make no contribution to electroconduction and through links. (2) A percolation cluster is freed of dead-end links and there remains a trunk that consist of through links. (3) A trunk is viewed as a bulk equivalent electric circuit, for which a computer performs the recording of all the Kirchhoff equations. (4) A computer-aided calculation of a set of Kirchhoff equations is performed, which permits the determination of the distribution of potential and current over the thickness of a porous electrode and, in particular, the magnitude of the effective electroconductivity of the porous electrode.     

Self-accelerating chlorine evolution on porous anodes of finite thickness

Operation of a finite-thickness porous electrode under the chlorine evolution conditions is analyzed in the framework of the convective diffusion model. According to calculations, the gas evolution in the anode’s porous coating is a necessary but insufficient condition for the self-acceleration of the electrode process. Despite the gas evolution process in the anode pores, the anodic process on the low-activity electrodes decelerates, which is externally manifested in an increased Tafel slope of the polarization curve as compared with that for a smooth electrode. Self-acceleration of the anodic chlorine evolution takes place only on electrodes with true exchange currents in excess of 10^-4 A cm^-2. Externally, the self-acceleration effect manifests itself in the emergence of a low-polarizability portion in the high-current region of the polarization curve. Such a different effect of the gas evolution process on the chlorine reaction kinetics at porous electrodes of different catalytic activity is due to an altered balance between the diffusive and convective current constituents in the overall process rate following a change in the exchange current for either electrode.     

Computer-aided Modeling of Porous Electrodes with an Immobilized Enzyme: Substrates with a Partially Regular Structure

In porous electrodes with an immobilized enzyme the substrate must have a high specific surface area, which must be accessible to landing onto it a maximum number of enzyme molecules. These demands are not easy to meet. Conceivable are limiting versions as follows: a stochastic substrate, where substrate particles (SP) are distributed in the volume randomly, and a regular substrate, where SP are distributed strictly regularly. Both versions of the organization of SP have advantages and disadvantages; therefore, in the paper studied is a third, intermediate, version, specifically, substrates with a partially regular structure. Shown is that there exists an optimum of values of fractal dimensionality for a regular base of a substrate, where, by somewhat sacrificing the amount of active enzymes, one can attain a considerable ease of the process of landing enzymes on the surface of a porous substrate. Calculations also show that of practical interest may be a porous substrate with a purely regular structure.     

Gas-generating porous electrodes at low overvoltages: Allowance for the outside-electrode limitations

Characteristics of gas-generating porous electrodes (GPE) are calculated and analyzed at low over-voltages, when all the electrode pores are still filled with electrolyte. The calculations assume the existence of limitations outside the electrode, specifically, the diffusion of gas molecules dissolved in electrolyte and their conglomeration into bubbles. Separate solutions are found and then sewn for GPE and the electrolyte chamber outside it, where the generated gas is collected. An important parameter is revealed, namely, the ratio of a characteristic gas-generation current inside GPE to a characteristic gas-removal current inside the outside-electrode region. The parameter determines both the net current density in GPE and the depth of the electrochemical process penetration into the electrode’s porous space. The two limiting cases studied are the hydrogen-generating water electrolysis on a porous platinum electrode and the chlorine generation on dimensionally stable anodes (DSA). A way to estimate all quantities that characterize the gas removal into the outside-electrode region is shown. It is established that only a narrow (no greater than a micrometer) region adjacent to the front surface of GPE takes part in the chlorine generation process on DSA of standard thickness (5 μm).     

A model for polybutadiene coatings on porous silica

Summary Non-wetting viscous liquids such as oligobutadiene prefer active sites such as pores during the process of physisorption. Thus, polybutadiene (PBD) coatings on porous silica do not result in a homogeneous polymer film but in an inhomogeneous loading where the bulk polymer is mainly sited in the pores of the silica. An increasing polymer loading leads to increasingly filled pores instead of a thicker polymer film. We cannot exclude the possibility that most of the surface is covered at least with a thin polymer film since the chromatographic behaviour is relatively good for polypeptides, which are highly susceptible to the silanol groups of silica.     

Computer Simulation of Porous Electrodes with Immobilized Enzymes: The Percolation Properties of Multicomponent Structures

The percolation characteristics of porous electrodes with immobilized enzymes are calculated. It is presumed that active centers of the enzymes undergo direct oxidation or reduction on the electrode. Two versions of a three-dimensional electrode structure consisting of particles of identical size are studied. In one, the frame of the porous electrode (PE) comprises only those parts of the support that conduct electrons. In the other, the electrode is a two-component structure capable of ensuring the supply of two participants of the electrochemical process to the enzymes. Calculated are: the fraction of the support parts that conduct electrons (taken as a whole, they form an electron cluster); the electron cluster's transparency; and the number of exits the electron cluster has onto the rear surface of PE. The character of distribution of enzymes that are in contact with one or two macroscopic clusters, which comprise conductive particles, over the PE thickness is established. In doing so, it is assumed that the two clusters can be supplied either from one side (parallel clusters) or from two opposite sides (collision clusters) of PE. The electron cluster surface accessible to contact with enzymes and the number of enzymes in contact with such an electron cluster are determined. Two possibilities of the PE functioning are examined. In one, the electrochemical process proceeds at any contact of the enzyme with the support particles. In the other, a certain type of enzyme immobilization on the support is required. The region of optimum concentrations of components that make PE is established. Within this region the electrochemical activity may reach a maximum.     

Gas-Generating Porous Electrodes: Large Ohmic Resistances

It is shown how it becomes possible, in gas-generating porous electrodes (GGPE), to construct polarization curves (PC) that encompass also the region of high ohmic resistances up to an ultimate possible overvoltage that is reached at practically complete expulsion of the electrolyte out of the electrode pores near the front surface of the electrode, without restricting oneself, while taking into account ohmic limitations, by not-too-high values of overvoltages. As the true appearance of the dependence of the magnitude of an effective specific ionic electroconductivity of GGPE on the specific features of the structure of its porous space and the degree of occupation of its porous space by the electrolyte and gas is unknown, an attempt is undertaken to evaluate possible values of limiting ohmic limitations, specifically, to take into account the presence of both maximum and minimum ohmic losses. Calculations of PC and some other characteristics of GGPE are conducted using the constants that are close to the constants that take place for the process of formation of chlorine in dimensionally stable anodes. It is discovered that, if one selects a nonoptimum structure of the porous space of the electrode (this means that, with the emergence of gas pores in the electrode, ohmic losses would rapidly increase), then one fails to realize the values of the electrochemical activity of the electrode in excess of a few A cm^–2.     

The nature of permeability anisotropy and catalytic activity

The phenomena of permeability anisotropy and an increase in the rates of catalytic reactions in porous membranes modified with highly dispersed catalytic systems were analyzed. A model of stochastic gas motions was proposed; this model is based on the hypothesis of the specific interaction of molecules with the inner surface of pores resulting in a nonisotropic distribution of molecules over traveling directions. The effects of asymmetric gas transfer in porous and gradient-porous membranes were considered to explain differences in the rates of heterogeneous catalytic reactions in a nanoporous membrane reactor under changes in the direction of supplying a reaction mixture. From the model proposed, it follows that the transversal diffusion of gas molecules is most probable in the porous medium of a ceramic membrane with a pore-size distribution gradient from large to small pores along the flow direction. This diffusion results in an increase in the frequency of molecular collisions with the wall of a microchannel and, correspondingly, in an increase in the contact time. The model proposed explains the intensification of a number of heterogeneous catalytic reactions performed in the porous media of catalytic porous membranes.     

Preparation of Collagen‐Glycosaminoglycan Sponges with Open Surface Porous Structures Using Ice Particulate Template Method

Funnel‐like sponges of collagen incorporated with glycosaminoglycan (GAG) were prepared by freeze‐drying using ice particulates as templates. The funnel‐like collagen‐GAG sponges showed similar porous structures to those of funnel‐like collagen sponges. The funnel‐like collagen‐GAG and collagen sponges have one top surface layer and one bulk porous layer. The large, top surface pores were determined by ice particulates that were used as templates, and the inner bulk pores were determined by freezing temperature. The funnel‐like pore structures facilitated homogenous cell distribution, improved cell viability, and resulted in homogenous tissue formation. Incorporation of GAG increased the mechanical property and cell viability of collagen sponges.

     

Gas-Generating Porous Electrodes: The Nature of the Low-Polarizability Portion in the Polarization Curves

The phenomenon of a low-polarizability portion (LPP) is discussed in the paper. The phenomenon is responsible for the possible rapid increase in the current in polarization curves (PC) for the gas generation in gas-generating porous electrodes (GGPE). A fresh viewpoint on the nature of LPP is propounded. The inflection in PC, which follows the linear Tafel portion, owes its inception to the emergence, in the electrode pores, of a network of gas pores that are freed of electrolyte and are connected with each other. The effective diffusion coefficient for gas molecules in gas pores filled with water vapor is larger than the effective diffusion coefficient for the same gas molecules in liquid pores filled with an electrolyte solution by several orders of magnitude. The emergence of a gas phase in a GGPE leads to a rapid increase in the effective diffusion coefficient. This circumstance in turn is capable of rapidly intensifying processes of the formation and removal of gas, which leads to a considerable increase in the overall current. A method for obtaining an approximate solution of the problem (the notion on ideal porous electrode) is suggested. A system of equations is derived, which can sufficiently accurately, qualitatively and quantitatively describe the character of variations in a polarization curve in the initial part of a low-polarizability portion. Theoretical and experimental polarization curves for the chlorine evolution on a dimensionally stable anode are compared quantitatively.     

Peculiarities of metal electrodeposition inside a flow-through porous electrode with low initial conductivity in oxidant containing solution

The earlier developed dynamic model of a flow-through electrode is used for studying how the variations in initial conductivity of a porous matrix κ_s,ini and a metal deposit affect the rate of metal deposition from an oxidant-containing solution for the direct-flow operation mode of the porous electrode. It is found that in contrast to an oxidant-free solution in which the decrease of κ_s,ini improves the uniformity of deposit distribution inside the porous cathode and increases the deposit final mass m _f, the opposite situation is observed in the presence of an oxidant, namely, a decrease in κ_s,ini, under otherwise similar conditions reduces the deposit mass and leads to its specific spatial distribution. The final metal deposit is divided into two separate fragments (rear and front) with a region of low conductivity of the initial porous matrix in between. Dynamics of the current and metal redistribution within the porous electrode, the reasons for the formation and stabilization of the rear fragment of coating, the correlation between the metal deposition rate and changes in the anodic zone position and intensity are discussed. It is shown that with the appearance of a specific profile of deposit distribution, the dependence of m _f on the metal conductivity develops a limit that differs considerably from the deposit final mass for an equipotential porous electrode.     

Porous Electrodes with Immobilized Enzymes: The Problem of Development of Nanocomposites with High Concentrations of Molecules of Active Enzymes

The currents that are generated in a porous electrode with an immobilized enzyme increase with increasing concentration of molecules of an electrochemically active enzyme. However, a finely divided composite, which is manufactured from colloidal particles of a support that have nanodimensions and molecules of the enzyme with the aid of methods of colloid chemistry, has a peculiar structure: it consists of a set of fractal clusters, which are capable of adsorbing only a limited number of enzyme molecules. The paper is devoted to computer simulation of all the stages of immobilization of the enzyme, specifically, producing random fractal clusters of required dimensions and deploying molecules of the enzyme on them. An analysis of the link of the concentration of molecules of an active enzyme with the structure and characteristics of a porous composite makes it possible to give an interpretation to experimental facts obtained by other authors for an oxygen electrode consisting of finely divided colloidal graphite and laccase.     

The properties of the interfacial boundary in one model of a porous body

Summary The role of a change in the radius of the pores along the length of the pores in capillary equilibrium it a porous body has been investigated. In a model cn non-intersecting pores consisting of successively arranged units with random values of the length and radius, the distribution of the length of the gas part of the pores has, at least at high pressures, an exponential character.I thank V.G. Levich, Yu.A. Chizmadzhev, and A.A. Chernenko for interest in the work and discussion.     

Gas-generating Porous Electrodes: Effect of the Catalyst Activity on the Polarization Curves

Effect of the activity of the catalyst in gas-generating porous electrodes (GPE) of the DSA type on the anodic branch of polarization curves is studied. The structure of the GPE porous space and the electrode kinetics are assumed to remain invariant. The quantities that are varied are the electrode thickness and the exchange current j ₀. Characteristics of GPE electrodes of high, medium, and low activity (j ₀ of 1.2 × 10^–2,1.2 × 10^–4, and 1.2 × 10^–6 A cm^–2, respectively) are compared. The standard thicknesses, calculated for these electrodes, are 1, 5, and 20 m. In GPE of high and medium activity, after the emergence of first gas pores, the gas generation region, which before this was localized in a narrow region near the front surface of GPE, can rapidly expand by tens of times, so can the overall current. With a further overvoltage increase, ohmic restrictions again press the gas generation region to the front surface of GPE. In the low-activity GPE, the expansion of the gas generation region and the increase in the overall current are insignificant. It is shown that the medium-activity GPE commonly used in the chlorine electrolysis may be viewed as optimal. However, this by no means implies that the DSA operation mechanism is ideal. Perfecting the porous-space structure of DSA even further gives one a chance to considerably better its electrochemical characteristics.     

Considering vibrations in the thermodynamic functions of a solid adsorbate in slit-like pores

Problems that arise in refining calculations of the equilibrium thermodynamic functions of an adsorbate located near an adsorbent’s surface or inside slit-like pores when its collective vibrational motions are considered are discussed. A technique is proposed for calculating collective vibrations for a small number of vacancies in a defective heterogeneous adsorbate from changes in the number of degrees of freedom and the local frequencies in the frequency distribution function in an ideal bulk crystal.     

Contact angles, pore condensation, and hysteresis: insights from a simple molecular model

We discuss the thermodynamics of adsorption of fluids in pores when the solid-fluid interactions lead to partial wetting of the pore walls, a situation encountered, for example, in water adsorption in porous carbons. Our discussion is based on calculations for a lattice gas model of a fluid in a slit pore treated via mean field density functional theory (MFDFT). We calculate contact angles for pore walls as a function of solid-fluid interaction parameter, alpha, in the model, using Young's equation and the interfacial tensions calculated in MFDFT. We consider adsorption and desorption in both infinite pores and in finite length pores in contact with the bulk. In the latter case, contact with the bulk can promote evaporation or condensation, thereby dramatically reducing the width of hysteresis loops. We show how the observed behavior changes with alpha. By using a value of alpha that yields a contact angle of about 85 degrees and maintaining the bulk fluid in a supersaturated vapor state on adsorption, we find an adsorption/desorption isotherm qualitatively similar to those for graphitized carbon black where pore condensation occurs at supersaturated bulk vapor states in the spaces between the primary particles of the adsorbent.