Porous Electrodes with Immobilized Enzymes: The Fractal-Percolation Properties of Supports Manufactured from Particles of Finely Divided Colloidal Graphite

The development of a porous active layer with an immobilized enzyme of a sufficiently large thickness is one of the problems that unavoidably emerge when constructing biofuel cells with high characteristics. Mounting up the thickness can be obstructed not only by the ohmic and diffusion limitations, which have been studied well enough. One more possibility of limitations (supports manufactured from finely divided colloidal graphite, FDCG), namely a “ fractal-percolation effect,” which has recently been discovered experimentally, is discussed in the paper. The essence of the effect consists of that the particles that are constituting a porous support may gather in random fractal clusters, which are connected with one another (the percolation part of the problem) with a probability that is other than unity. As a result, the electrons that are required for performing bioelectrocatalysis are capable of penetrating into a porous support only to a limited depth. Computer simulation of the fractal and percolation processes is performed in this work. As a result, quantitative relationship of the bulk concentration of FDCG in solution with the size of random fractal clusters, with the probability of their contact with one another, and with the degree of providedness of the material of the support by electrons is established. It may happen that all this information can become useful for the development of porous electrodes with an immobilized enzyme of high activity.__________Translated from Elektrokhimiya, Vol. 41, No. 8, 2005, pp. 943–953.Original Russian Text Copyright © 2005 by Chirkov, Rostokin.     

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.     

Computer Simulation of the Structure of Porous Electrodes with an Immobilized Enzyme and Nanosized Support Particles

The efficiency of the operation of a porous electrode with an immobilized enzyme is defined, in particular, by a lucky structure of its active layer, which can contain nanosized particles of the support. The composites of such a kind are prepared with the aid of methods of colloidal chemistry. The aim of this particular investigation is to perform a computer simulation of processes of coagulation of particles of the support and their possible heterocoagulation with molecules of the enzyme. Algorithms of the formation of nanocomposite structures in solution are suggested. Calculations show that the concentration of the enzyme molecules in the nanocomposite structures cannot exceed a certain critical value. On the other hand, at a fixed value of the concentration of the enzyme molecules, the concentration of the support particles must not fall below a certain threshold quantity, which provides for the passing of current through the active layer. In order for all the enzyme molecules, rather than for a fraction of these, in the composite to take part in the process of bioelectrocatalysis, the concentration of support particles must be increased even higher, to an optimum value.__________Translated from Elektrokhimiya, Vol. 41, No. 6, 2005, pp. 738–747.Original Russian Text Copyright © 2005 by Chirkov, Rostokin.     

Fractals and Percolation in the Theory of Porous Electrodes

A computer-aided simulation of the structure of a porous electrode is performed using flat lattices of sites (they are capable of conducting electrons and are randomly distributed in the electrode) as an example. To adequately describe properties of a porous electrode, information about the degree of dispersion of the particles that make up the electrode (fractal dimensionality) must be complemented by that on their clusterization (presence of percolation clusters). These factors impart two properties to a porous electrode, specifically, a developed surface, on which an electrochemical process may proceed, and the possibility of a continuous supply of electrons to this surface. A percolation cluster may be dismembered to a trunk (it provides for the electron transport) and a crown (aggregate of particles that make a major contribution to the electrochemical process). The dismembering was performed via computer flow diagrams proposed by the authors. A computer-aided analysis of characteristics of a porous electrode points to the existence of an optimum structure in which the electrochemical activity is capable of reaching a maximum.     

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.     

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.     

两种功能化纳米金粒子固酶电极的催化性能

以合成的4-巯基苯甲酸功能化纳米金粒子和聚乙烯基吡啶包覆纳米金粒子分别作为固酶载体,制备了2种新型固酶电极,在此基础上组装了2种酶燃料电池。采用电化学方法结合紫外可见分光光度法、透射电镜技术等手段研究了固酶载体的形貌,酶-载体间相互作用对电极表面固定酶分子的光谱学性质,酶-电极间直接电子迁移能力和催化底物反应性能的影响,进一步评估和比较了两种酶燃料电池的能量输出性能。实验结果表明：4-巯基苯甲酸功能化纳米金粒子固酶基电极可以实现酶-电极间的直接电子迁移而且对葡萄糖和氧气具有良好的催化性能(催化反应起始电位分别为-0.03和0.96 V,底物转化频率分别是1.3和0.5 s^-1),其催化性能的重现性、长期使用性能、酸碱耐受性和热稳定性良好,随着自组装固酶层数的增加,催化性能随之增强直至达到极限催化电流;电池性能测试结果表明4-巯基苯甲酸功能化纳米金粒子固酶基燃料电池的开路电压为0.88 V,最大输出能量密度：864.0 μW·cm^-2,长期使用性能优异(储存3 周后仍可达到最佳能量输出的80%以上)。     

两种功能化纳米金粒子固酶电极的催化性能

以合成的4-巯基苯甲酸功能化纳米金粒子和聚乙烯基吡啶包覆纳米金粒子分别作为固酶载体, 制备了2种新型固酶电极, 在此基础上组装了2种酶燃料电池。采用电化学方法结合紫外可见分光光度法、透射电镜技术等手段研究了固酶载体的形貌, 酶-载体间相互作用对电极表面固定酶分子的光谱学性质, 酶-电极间直接电子迁移能力和催化底物反应性能的影响, 进一步评估和比较了两种酶燃料电池的能量输出性能。实验结果表明:4-巯基苯甲酸功能化纳米金粒子固酶基电极可以实现酶-电极间的直接电子迁移而且对葡萄糖和氧气具有良好的催化性能(催化反应起始电位分别为-0.03和0.96 V, 底物转化频率分别是1.3和0.5 s^-1), 其催化性能的重现性、长期使用性能、酸碱耐受性和热稳定性良好, 随着自组装固酶层数的增加, 催化性能随之增强直至达到极限催化电流;电池性能测试结果表明4-巯基苯甲酸功能化纳米金粒子固酶基燃料电池的开路电压为0.88 V, 最大输出能量密度:864.0 μW·cm^-2, 长期使用性能优异(储存3 周后仍可达到最佳能量输出的80%以上)。     

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.     

硝酸还原酶在巯基自组装膜上的电化学性质

应用自组装技术将硝酸还原酶 (NR)构筑在硫醇自组装单分子膜上 ,研究了Au/半胱胺 /NR和Au/半胱胺 /NR/卵磷脂两种酶电极在磷酸缓冲液中的直接电化学行为     

Computer-Aided Simulation of Porous Electrodes of a Filled-up Type

In the paper, computer-aided simulation of porous electrodes of a filled-up type is done using two-dimensional lattices as an example. The attention is mainly focused on the simulation of porous electron-conducting substrates that are required to put the catalyst particles on. The principal parameter of the system is the share of the electron-conducting particles of the substrate. Calculated are the share of the electron-conducting particles of the substrate (a conducting cluster), the distribution of this quantity over the electrode thickness, and the number of exits made by a conducting cluster onto the rear surface of the electrode. The notion of transparency is introduced. The perimeter of a conducting cluster is determined. The number of active particles of a catalyst is found out. Two versions of the electrode functioning are investigated for catalysts-enzymes. In one version the electrochemical process proceeds no matter the position of the enzyme molecules. In the other, the electrochemical process takes place provided certain conditions of contact between enzyme molecules and a conducting cluster are ensured. Established is the region of optimum concentrations of components at which the electrochemical activity of the electrode is maximum.     

Simulation of Electrochemical Process for Glucose Oxidase Immobilized Conducting Polymer Electrodes

Abstract

Computer simulation of electrochemical processes that govern the operation of conducting polymer modified electrodes (CPME) have been reported in this paper. Comparison of the behaviour of a biocatalyst (GOX) in free solution and in the immobilized phase in conducting polymer modified electrodes (CPME) has been provided The output has been obtained using the Runga Kutta numerical method solved by programming in FORTRAN 77. The results point out that the catalytic current generated by an immobilized enzyme in layer is larger as compared to that for the enzyme in solution, and that it varies with the thickness of the diffusion layer.     

Calculating Electrochemical Activity of Porous Electrodes of a Filled-up Type with an Immobilized Enzyme and Regular Gas Pores

A model for a porous electrode of a filled-up type with an immobilized enzyme, in which a system of regular gas pores is formed, is studied. The system of regular gas pores is in fact a collection of equidistant cylinders whose thicknesses are equal to one grain of the hydrophobizing agent. Usually, the gas reactant passes into a porous electrode via a number of chains that comprise porous grains of the hydrophobizing agent. The latter is distributed in the electrode bulk in a random fashion. In this case, channels for supplying gas are formed at high concentrations of the hydrophobizing agent. As a result, the number of molecules of a catalyst in a porous electrode, and along with it the current, are not great. Should we pass to electrodes with regular gas pores, the required amount of a hydrophobizing agent would decrease. As a result, the number of molecules of the enzyme in the electrode and the current would increase. The calculation of the last quantity is the subject matter to which the paper pays a major attention. The calculation is performed for two versions of distribution of a hydrophobizing agent over the electrode bulk, specifically, a random distribution and a regular distribution. Concrete calculations are carried out for an oxygen porous electrode with an enzyme whose electrochemical characteristics are close to those obtained on laccase. It was assumed in the calculations that the enzyme operates without mediators. It is established that a porous electrode with a quasi-regular structure has a considerable advantage. With an electrode thickness of 13 m one can manage to obtain currents of nearly 0.74 A cm^–2 as early as at an overvoltage of about 30 mV.     

Interaction of Enzyme with Polymer Matrix in Immobilized Enzymes

Thermolysin was immobilized by radiation polymerization of hydroxyalkyl acrylate and tetradecaethylene glycol dimethacrylate monomers at low temperatures in the presence of the enzyme, and the degree of interaction of the enzyme with the polymer matrix was studied by measuring the thermal stability of the immobilized enzyme. The thermal stability was affected by the molecular structure of the monomer; the thermal stability of the immobilized enzyme from hydrophilic monofunctional monomers in the wet state was higher than that from hydrophobic bifunctional monomers. The thermal stability in polymers formed from hydroxy-alkyl acrylates decreased with an increase in the number of methylene units in the monomer, owing to a change of the state of the enzyme trapped in the porous polymer matrix. The enzyme molecule trapped in a hydrophilic porous polymer matrix appeared to be stabilized by interaction with the polymer chains.     

Gas-Generating Porous Electrodes: Effect of the Porous Space Structure on Polarization Curves

The operation of gas-generating porous electrodes (GGPE) is studied qualitatively and quantitatively in the entire range of overvoltages. The range comprises a low-overvoltage region, a transition region, and a low-polarizability region. The first region extends to the instance when first gas pores form at the rear surface of GGPE. In the second region, the formation of a gas channel begins. This is the channel through which gas is removed from GGPE by filtration. The formation of the gas channel is completed when first gas pores emerge at the front surface of GGPE. In the third, gas is removed by a powerful process, specifically, by gas filtration in gas pores. The current in the last region increases very rapidly. The presented theory reveals basic parameters that determine the nature and principal features of polarization curves (PC). In all the regions, PC are calculated with constants close to those typical for chlorine generation in DSA. It is shown how the porous space structure (pore types, distribution of pores by size in the presence of micropores and macropores, maximum and minimum pore radii) and parameters that characterize outer-diffusion limitations (processes that occur in the electrolyte chamber) define all characteristics of GGPE and, which is more, define the shape of PC. Using results of this mathematical modeling of gas generation and removal in porous electrodes and electrolyte chamber, one can start looking for ways to purposefully alter the porous space structure of GGPE (in particular, DSA) in order to subsequently optimize characteristics of DSA and GGPE of other types.     

软粒子力学性能的模拟研究

运用弹性膜理论结合三角网格动力学模型模拟研究了平行板压缩软粒子的过程, 仔细考察了压缩过程中软粒子的形状变化、应力响应、力学松弛和粘弹行为. 模拟结果与已有的实验基本一致.     

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.     

荷电膜渗透传质过程的计算机模拟:一价离子的传递

The transport of monovalent ions through a charged membrane was investigated by percolation approach. Based on percolation concept and theory, the theoretical simulation was conducted for two-dimension (2D) and three-dimension (3D). The results showed that for 2D lattices there has a obviously skip or percolation threshold with charged components from 0.4 to 0.6, and for 3D lattices, such value is between 0.1-0.2. The simulative results were well conformed to those by Monto Carlo simulation for a random system. A practical charged membrane which prepared from the blends of sulphonated polyphenylene sulfide (SPPS)/poly(ether sulfone) (PES) can be considered as a 3D lattices. The experimental conductivity was related with a 3D simulation and the result showed the membrane has a transition from insulator to conductor at the ratio of charged components SPPS about 0.144. Obviously, this value falls in the range of a theoretical simulation for a 3D lattices.     

Coarse-grained Dynamics Simulation in Polymer Systems: from Structures to Material Properties

Polymers are widely used in our daily life and industry because of their intrinsic characteristics, such as multi-functionality, low cost, light mass, ease of processability, and excellent chemical stability. Polymers have multiscale space-time properties, which are mainly reflected in the fact that the properties of polymer systems depend not only on chemical structure and molecular properties, but also to a large extent on the aggregation state of molecules, that is, phase structure and condensed state structure. Thanks to the continuous development of simulation methods and the rapid improvement of scientific computation, computer simulation has played an increasingly important role in investigating the structure and properties of polymer systems. Among them, coarse-grained dynamics simulations provide a powerful tool for studying the self-assembly structure and dynamic behavior of polymers, such as glass transition and entanglement dynamics. This review summarizes the coarse-grained models and methods in the dynamic simulations for polymers and their composite systems based on graphics processing unit(GPU) algorithms, and discusses the characteristics, applications, and advantages of different simulation methods. Based on recent studies in our group, the main progress of coarse-grained simulation methods in studying the structure, properties and physical mechanism of polymer materials is reviewed. It is anticipated to provide a reference for further development of coarse-grained simulation methods and software suitable for polymer research.     

Record Atomistic Simulation of Crystalline Silicon: Bridging Microscale Structures and Macroscale Properties

Based on the molecular dynamics software package CovalentMD 2.0, the fastest molecular dynamics simulation for covalent crystalline silicon with bond-order potentials has been implemented on the third highest performance supercomputer “Sunway TaihuLight” in the world (before June 2019), and already obtained 16.0 Pflops (10¹⁵ floating point operation per second) in double precision for the simulation of crystalline silicon, which is recordly high for rigorous atomistic simulation of covalent materials. The simulations used up to 160,768 64-core processors, totally nearly 10.3 million cores, to simulate more than 137 billion silicon atoms, where the parallel efficiency is over 80% on the whole machine. The running performance on a single processor reached 15.1% of its theoretical peak at highest. The longitudinal dimension of the simulated system is far beyond the range with scale-dependent properties, while the lateral dimension significantly exceeds the experimentally measurable range. Our simulation enables virtual experiments on real-world nanostructured materials and devices for predicting macroscale properties and behaviors from microscale structures directly, bringing about many exciting new possibilities in nanotechnology, information technology, electronics and renewable energies, etc. © 2019 Wiley Periodicals, Inc.