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19CHEMICAL SCIENCES
THE STATIC AND DYNAMICS MODELING OF ION EXCHANGE IN WATER SOLUTIONS
Kontsevoy A.
Ph.D., assoc. prof., The Department of Technology of Inorganic Substances, Water Purification and General Chemical Technology, Igor Sikorsky Kyiv Polytechnic Institute
Kontsevoy S.
Ph.D., assoc. prof., The Department of Technology of Inorganic Substances, Water Purification and General Chemical Technology, Igor Sikorsky Kyiv Polytechnic Institute
Fedenko Y.
Ph.D., assistant, The Department of Technology of Inorganic Substances, Water Purification and General Chemical Technology, Igor Sikorsky Kyiv Polytechnic Institute
Abstract
The mathematical models for the exchange of double-charged and singly charged ions in statics and dynamics conditions are designed and methods of their solution in Excel (static) and Mathcad (static and dynamics of exchange) are proposed. The coefficients of the known equation for the distribution of ion's initial concentration along the water flow in a filter are calculated. The features of exchange between differently charged ions are studying based on computer experiments. The "method of a characteristic" was adapted for the wave propagation analysis of double-charged ion concentrations in a filter. Convex isotherms of ion exchange lead to "breakfront" of concentrations (their rapid decrease) clearly visible at 2D and 3D figures. The proposed model provides varying technological and design parameters as input data in order to estimate their effect on the exchange process quality.
Keywords: ion exchange, exchange isotherm, ion charge, mathematical model, dynamics of the equilibrium exchange, the front of the concentrations.
Introduction
Ion exchange is one of the typical processes of water purification and one of perspective sorption methods. It is carried out by usage of ion exchange materials. The problem of calculation of filter is conditionally divided on the task of describing static (equilibrium) and modeling of dynamic of ion exchange, including charges of ions, which is capable to exchange. Isotherms of ion exchange determine movement of ions that are absorbed and are part of the mathematic model of ion exchange filters - the main technological equipment of heat and atomic electric stations. The stage of the work cycle of an ion exchange filter is carried out at convex isotherm. Ion exchange at convex isotherm allows increasing the concentration in ion exchanger in comparison with their concentration in solution. Regeneration is realized at concave isotherm. The dynamic model must include the fact, that, at passing of solution through the filter, different concentration points will move with different rates. Depending on the kind of isotherm - convex or concave -«breakage» (the concentration of ion in solution is changed jump-like from c = c0 to c = 0) or «blurred» concentration front can be observed, respectively. Excel and Mathcad had been used in this work for analysis of a mathematic model for ion exchange filters.
The goal was to design the mathematic model of static and dynamic of ion exchange for ions of different charge. For reaching this goal it was necessary to bring out the equation of isotherm of ion exchange, basing on mass action law, to adapt the mathematic apparatus and software solutions for single-charged ions and to give the solution of static and dynamic of ion exchange of ions of different charge. It is also necessary to justify the equation of the initial distribution of the relative
concentration along the filter and find the corresponding coefficients.
Discussion
The classification and principles of working of fuel cells
Fuel cells are an autonomous source of energy independent of fossil fuels. In addition, the lack of combustion of fuel at high temperatures means the environmental purity of such devices. In addition to high productivity and efficiency, the process of producing electricity in a fuel cell is accompanied by a minimal impact on the environment, which is especially important in view of the serious deterioration of the overall environmental situation in the modern world.
Other advantages of fuel cells can be attributed
[5]:
• these are noiseless energy sources (the fuel cell itself doesn't have moving parts);
• the possibility of using different types of fuel;
• a wide range of capacities (from 1 to 10000 kW);
• rapid response to load variables;
• high reliability and safety of low-temperature devices;
• modular design, which allows relatively easy to increase the capacity of already existing power plants with FC.
Most often, FC is classified by the type of electrolyte as a medium for the internal transport of ions. The nature of the electrolyte determines the operating temperature of the FC, from which, in turn, the choice of catalyst and auxiliary materials depends. There are five main types of FC [6], which are discussed below.
In solid-polymeric fuel cells (SPFC) electrolyte is a proton exchange polymer membrane. Currently, there
are several different types of polymer membranes - fluorine-containing polymer based on sulfonic acids; membranes based on aromatic polymers (polyether ketones, polysulfones, polyether sulfones); membranes based on polyimides, polyvinyl alcohols. Nafion per-fluorinated electrolyte membranes (Du Pont company) became the most widely used. An important property of such membranes is high proton conductivity in an oiled state, and therefore, for the effective operation of FC, it is necessary to select and adhere to the regime of optimal distribution of moisture (water management). The operating temperature is not higher than 100 °C, fuel is hydrogen, without CO contamination, to prevent poisoning of Pt catalyst. A solid fuel cell electrolyte is much easier to use than a liquid analogue. A thin platinum catalyst chemically activates the reaction on the electrodes. In the past, these devices were very expensive through platinum, but new technologies significantly reduced the thickness of the platinum layer, which allowed, accordingly, to reduce the price.
In alkaline fuel cells (AFC), a concentrated KOH solution immobilized in an asbestos matrix used as an electrolyte. Depending on the alkali content, such FC can operate in the temperature range from 65 °C (3550 % by weight KOH) to 250 °C. (~85 % by weight KOH). The catalyst can be noble metals, Ni, complex oxides. Alkaline FC must be protected from the influence of CO and CO2; the first, as in the previous case, is a catalytic poison, and the second interacts with the electrolyte, changing its composition. Algal fuel cells are widely used in spacecraft. They were developed by NASA for use in the Gemini project and further used on Space Shuttle. AFCs are very effective, release only pure water after the reaction. However, these devices require the purest of hydrogen and oxygen and an electrolyte with KOH, which is very expensive.
In phosphoric acid fuel cells (PAFC), the transfer of protons from the anode to the cathode is carried out in a concentrated solution of phosphoric acid (85-100 % v / v), fixed on a carrier with SiC. The operating temperature of 150-220 °C provides high conductivity of
the electrolyte. The catalyst is platinum. This kind of FC is commercially available, since 1992, PAFC has the potential for use in small, stationary power generation systems. They are known for their reliability, perfect work and high efficiency. They can work on contaminated water spills. The world's largest 11 MW phosphorus works in Tokyo.
In carbonate-fusible fuel cells (CFFC), the electrolyte is a melt of a mixture of alkali metal carbonates in a ceramic matrix with LiAlO2. At a temperature of about 600-700 °C, this melt is a good conductor of CO32- ions. A fairly high working temperature allows the use of fuel in the CFFC directly without any additional preparation, and nickel - as a catalyst. Since CFFCs operate at a temperature of 650 °C, it is more expedient to use them on large stationary installations. They are especially useful in hospitals or in such buildings where there is a constant need for electric and thermal energy (heating or cooling).
In solid oxide fuel cells (SOFC) electrolyte is a dense ceramic membrane with ZrO2. For the appearance of sufficient oxygen-ion conductivity in this phase, it is necessary to heat up to temperatures of 6001000 °C. Oxidation of fuel (H2, CO, CH4) occurs at the anode, which is a metal-ceramic composite Ni / ZrO2 or Co / Z1O2; as a cathode, complex oxides are used, which have an electron (La1-xSrxMnO3-s) or a mixed (La1-xSrxCoO3-s) conductivity. These fuel cells are most suitable for large stationary electric generators that can supply a factory or city with electricity.
The main performance characteristics of FC of different types are summarized in Table 1.
The greatest successes have been achieved in the field of membrane fuel cells (MFC). Currently, one of the most promising fuel cells for wide application are solid-polymer (SPFC), which have a high density of power and have reached the highest technological readiness. The main obstacle to their widespread use is still high cost compared to traditional energy-generating devices.
Table 1.
The main performance characteristics of FC of different types [7]
FC type SPFC L PAFC CFFC SOFC
Temperature, °C 80-100 65-250 150-220 600-1000 600-1000
Material of anode Pt/C, Pt-Ru/C Pt/C, Pt-Co/C Pt/C, Pt-Ru/C Ni-Al, Ni-Cr Ni, NiO
Material of cathode Pt/C Pd/C Ni (Pt) Pt/C, Pt-WO3/C NiO, LiFeO2 LaSrMnO3
Electrolyte Polymer membrane (ionomer) KOH/ NaOH on the career H3PO4 on the career LiKCO3, LiN-aCO3 on the career ZrO2, CeO2, Y2O3
The range of optimal capacities, kW 0,01-100 kW ~ 100 kW ~100 kW > 1 MW > 1 MW
Resource, h until 2-104 until 104 until 5-104 until 2-104 until 6-104
The main components of the fuel cell are anode, cathode and electrolyte. Anod provides fuel in the form of combustible gas (hydrogen, hydrocarbon compounds, CO etc.), where the catalyst dissociates fuel molecules into cations. At the same time, an oxidizing gas (oxygen, air) is fed to the cathode. At the cathode is the reaction of oxygen recovery, while it is ionized.
Anions of oxygen pass through a dense ceramic electrolyte to the anode. At an anode there is a reaction of oxidation of fuel, which involves cations of fuel and oxygen anions. As a result of the reaction, electrons and heat energy are released. Also, the reaction products are water vapor (using pure hydrogen) or water vapor and carbon dioxide (with hydrocarbon fuels) [8].
Total reaction: 2H2 + 02 2^0 + Q + E
Figure 1. The principle of work on the example of a ceramic fuel cell [8].
The catalytic layer is one of the main components of fuel cells. It is a thin (5-20 microns) gas-permeable layer containing a fine-dispersed catalyst with a developed surface. On the one hand, the catalytic layer adjoins the proton conductive membrane, and on the other hand - to the gas diffusion layer.
Platinum and metals of platinum group (MPGs) are commonly used to catalyze the oxidation of hydrogen, as well as the recovery of oxygen occurring in fuel cells.
The high cost and scarcity of metals make, however, the use of pure metal catalysts unprofitable and require a reduction in their number with the maximum effectiveness of their use. This is achieved by the use and development of new catalysts on carriers. The carrier should be cheap, have electrical conductivity and sufficient chemical and electrochemical stability. In addition, the catalytic bed should have good gas permeability and provide good contact with the proton exchange membrane. The specified requirements are satisfied with carbon materials.
Generators of hydrogen based on sodium borohy-dride. The usage of hydrogen generators allows you to obtain H2 directly at the site of its use, eliminating the problems of its storage, storage and transportation. Physical methods of hydrogen storage in the form of cryogenic liquid or compressed gas in most cases are ineffective (low volume density, high energy consumption, the ability to evaporate), and also insufficiently comfortable and safe (explosive gas under high pressure), therefore storage of hydrogen in the state of chemical compounds (hydrocarbons, water, hydrides) is an interesting and promising alternative [9].
At creation of such sources of hydrogen for mobile power installations on the basis of fuel elements in recent times special attention is paid to binary and complex hydrides as a compact form of storage of hydrogen [10,11].
The reasons for the use of hydrides as a hydrogen source are the high-volume density of hydrogen in hydrides and the relative ease of its production from these compounds. Among hydrides, sodium borohydride (NaBH4) has a special place due to the high content of H2 (10.8 % by weight), an acceptable price and stability of its alkaline solutions. The process of catalytic hydrolysis of sodium borohydride is a promising way of
obtaining high-purity hydrogen, with half of hydrogen released from water [12,13]:
kat
NaBH4 + 2H2O NaBO2 + 4H2. (1.4)
The usage of catalysts ensures hydrogen production in the temperature range from - 40 °C to + 85 °C, accelerates the process of generation of H2, prevents the formation of by-products, and also makes it easy to control the process of hydrogen generation, stop it and start it at the consumer's request.
At present, an important task is to create new cat-alytically active materials for use in portable hydrogen generators based on sodium borohydride. In the proposed generators, expensive catalysts based on platinum group metals are used [14-17]. For this reason, the most relevant are studies aimed at reducing their content in catalysts or replacements for transition metals.
According to the literature, the most promising are catalysts based on amorphous cobalt borides [18,19]. However, because of the applied nature of most works, the results obtained are not systematized, the reasons for most of the revealed patterns remain unpublished. The results obtained by different authors are incorrectly compared because of the difference in the conditions of experiments.
Therefore, there is an active search for catalysts of the hydrolysis process of sodium borohydride. The catalytic activity of acids [20], noble [21,22] and transition metals [22,23] is shown.
Hydrogen peroxide as the oxidizer for FC
Fuel cells designed for use in non-atmospheric air, for example in space or at the bottom of reservoirs, require liquid or compressed O2 as a cathode oxidizer.
The O2 transport tank significantly reduces oxygen density and safety standards for fuel cell systems. As these indicators are critical for fuel cells used as space or underwater energy sources, alternative oxidants other than O2, such as H2O2, have been investigated.
Several types of fuel cells using H2O2 as an oxidizer have been developed in recent years, including methanol fuel cells with hydrogen peroxide [24-26], hydrogen peroxide borohydride fuel elements [27-29] and fuel cells with transition metals and hydrogen peroxide [30-35].
The productivity of the cathode essentially depends on the nature of the cathode catalysts. Several types of catalysts for the H2O2 electrical conducting reaction, including noble metals (Pt, Pd, Ir, Au, Ag and a combination of these metals) [27-31,36], macrocyclic complexes of transition metals (complexes of porphyrin Fe and Co, complexes of Cu triazine) [37] and other types such as PbSO4 and Co3O4 [35,38]. Among these types of electrical catalysts are the most active and stable catalysts of noble metals. However, precious metals, other than expensive, also catalyze the chemical decomposition of H2O2 to O2. Therefore, it is necessary to look for electrical catalysts with low cost and greater resistance to the decomposition of H2O2.
A preliminary literature review [35] shows that Co3O4 nanoparticles have good activity and resistance to electro-catalytic reduction of H2O2 in alkaline solution.
Electrical catalytic activity of cobalt-containing catalysts. Texas specialists suggest the use of platinum alloy with cobalt and copper. The new catalyst is an alloy of particles, the metal content of which varies from surface to nucleus: the surface of particles is enriched with platinum, and the core consists predominantly of copper and cobalt. The first tests of this catalyst showed an efficiency that exceeds a similar indicator of modern catalysts for fuel cells in 4-5 times. In addition, the nano-catalyst was significantly cheaper [39].
For the production of a catalyst, deposited on a graphite electrode, metal particles were placed in an acid solution and subjected to cyclic effects of alternating voltage. Less noble metals, especially copper, dissolved from the surface, leaving it enriched with platinum. The core had the same composition as the original alloy.
Moreover, formed as a result of electrochemical etching of copper and cobalt, voids on the surface of the particles resulted not only in the enrichment of the surface with platinum, but also in a significant increase in the surface area of the catalyst. However, the increase of the catalyst's efficiency by 4-5 times compared to pure platinum catalyst, according to Strasseur, cannot be explained solely by an increase in surface area.
Computer calculations have shown that the distance between the platinum atoms in the enriched shell
is shorter compared with the same distance in pure platinum. Such "compressed" state is fixed with the help of enriched cobalt and copper core. The shortened interatomic distance platinum platinum promotes a more readily adsorption of oxygen. This, apparently, changes the electronic structure of the shell so that the process of transferring an electron to the formation of a negatively charged molecule of oxygen becomes much simplified [39].
A new material based on graphene has been developed at Brown University (Rhode Island), which is capable of serving as an almost effective catalyst of the oxygen-reducing reaction, as well as platinum, but at the same time it is more stable. This material is a graphene sheet coated with cobalt nanoparticles and its oxide [40].
A number of scientists have succeeded in reducing the content of platinum in catalysts, but at the very least to abandon its use has still not succeeded.
The cobalt catalyst described in the article for the online edition of Angewandte Chemie was the first alternative solution that does not contain precious metals. Cobalt is a fairly widespread metal and costs many times cheaper than platinum.
Laboratory tests have shown that the new catalyst is slightly inferior to platinum at the initiation rate of the reaction, but during its course it restores oxygen at a faster pace than platinum. Graphene-cobalt material has also shown better resistance to degradation. After 17 hours of operation, it retained 70 % of initial efficiency, compared with 60 % for platinum over the same period of time.
Scientists have used the self-assembly method to produce material, which provides the best control of the size, shape and location of nanoparticles. To do this, they prepared two separate solutions for cobalt and graphene nanoparticles, and then carefully mixed them with the use of sound waves. Graphene material with uniform cobalt inlaid was deposited from a solution in a centrifuge and dried. In the open atmosphere, the outer layers of atomic cobalt oxidized, forming on each nanoparticle a shell protecting the cobalt core (see Fig. 2) [40].
Figure 2. Graphene with inlaid metal cobalt [40].
The thickness of the shell was controlled by varying the residence time of the material in a state heated to 70 °C. Experimentally it was found that in the best
way the catalytic properties of the material are detected with a shell thickness of 1 nm [40].
The catalyst that was created in this way brought out fuel cells from the laboratory phase in their widespread commercial distribution.
Usage of cobalt as electrical catalyst of FC. Cathodes containing cobalt and used in solid oxide fuel cells (SOFCs) are known for their ability to operate at high temperatures.
The Cathode Oxygen Reaction (ORR) is important for a Microbial Fuel Cell (MFC). A carbon-based catalyst, doped with nitrogen and cobalt (CoNC), was synthesized to initiate ORR in MFC. CoNC, prepared at 900 °C (CoNC-900), demonstrated high catalytic activity and excellent resistance (5.5 % reduction after 10000 cycles). Long-term performance tests have shown that the CoNC-900 MFC is very stable [41].
A platinum-free catalyst for Oxygen Reaction (ORR) and hydrogen oxidation reactions (HOR) was developed for a fuel cell with a proton exchange membrane (PEMFC). The synthesized catalyst is two-functional and consists of cobalt with palladium and nitrogen. Palladium-cobalt nanoparticles of bimetallic alloy are scattered over graphite carbon nitride (Pd-Co / gCN), and they serve as an effective anode and cathode catalyst in a fuel cell with a proton-exchange membrane. The inclusion of cobalt with palladium in the material changes the bond strength of the palladium-hydrogen (Pd-H) complex and promotes the initiation of HOR, which leads to a significant improvement in the super-potential at the anode, while cobalt, coordinated with nitrogen, mainly increases the activity of the ORR on the cathode in an acidic medium [42].
Another type of catalyst - a catalyst for cobalt hydroxide oxide (CoOOH-PPy-BP), modified polypyr-role - was obtained by chemical impregnation and used as a cathode catalyst in hydrocarbon fuel cells. CoOH surface oxygen vacancies provide favorable sites for O2 uptake, accelerating the activation of O2. And electronic holes created due to vacancies of oxygen on CoOOH capture electrons from the anode, forming excited cationic states [Co3+ + e-] [43].
The efficiency of the fuel element with borohy-dride (DBFC) depends both on the activity of the anode catalyst and on the hydrolysis of borohydride. Anode Co3O4 catalysts from different sources of cobalt were investigated and it was shown that the catalytic activity of Co3O4 was related to its microstructure, which was based on the precursor. The maximum power was 40, 62 and 28 mWcm-2 DBFC with an anode of CoCl2 and a CosO4 catalyst (denoted DBFC-A), Co (NOs)2 (denoted DBFC-B) and Co(CHsCOO)2 (denoted DBFC-C), respectively. DBFC-A showed good voltage stability with a specific capacity of 720 mA / g and the highest amount of electron transfer [44].
A new three-dimensional (3D) porous nickel-cobalt film (Ni-Co) is successfully applied to nickel foam and is further used as an effective anode for a fuel cell containing urea and hydrogen peroxide (DUHPFC). Schematic principle of this fuel cell is shown in Fig. 3. By changing the ratio of moles of cobalt / nickel, an anode of polypropylene Ni-Co / Ni was obtained with a ratio of 80 % in terms of the best efficiency [45].
Figure 3. Schematic representation of the fuel cell [45].
Electrodeposition of cobalt on ferrite stainless steel plays an important role in reducing chromium poisoning on the cathode side of solid oxide fuel cells (SOFCs). The electrochemical activity between La0.6Sr0.4Co0.8Fe0.2O3 (LSCF) and stainless steel with cobalt coating in the atmosphere at 700 °C was investigated. Thus, the formed Co3O4 layer blocks the chromium migration [46].
Investigation of Co as anode for Li-ion batteries. The main cathode material of lithium ion batteries is lithium cobalt oxide (or lithium cobaltate), lithium manganese oxide (also known as spinel or lithium man-ganate), lithium phosphate lithium, and lithium nickel manganese-cobalt (NMC) and lithium-nickel cobalt alumina (NCA) [47]. Various materials, including sili-
con-based alloys, are also used as anode. Nano-struc-tured lithium titanate, as an anode additive, shows a promising life cycle, excellent low temperature characteristics and excellent safety [47].
In order for the battery voltage to be sufficiently large, Japanese researchers used as active material a positive electrode of cobalt oxides. Cobalt oxide has a potential of about 4 V relative to the lithium electrode, so the operating voltage of the Li-ion battery has a characteristic value of 3 V and above [48].
Lithium-ion battery design with high energy storage and high efficiency is a subject of enhanced research interest, which is of key importance for large-scale applications and further commercialization.
Conventional lithium-ion batteries are expensive and have stability problems that restrict their practical
use. In search of cheaper and more secure Li-ion batteries, the concentration gradient method is used to obtain LiNi0.9Co0.i-xTixO2 (0,02 < x < 0,05) cathode materials enriched on the surface of Co and Ti, which demonstrate a decrease in oxygen loss and improvement of structural stability. The material with the best characteristics (x = 0.04) shows a discharge capacity of 214 mAh / h in the range of charge voltage / discharge 3.0-4.3 V (versus Li / Li+), and perfectly stores up to 98.7 % capacities after 50 cycles [49].
Organic-inorganic hybrids increase the choice of materials for Li-ion batteries due to the versatility of organic ligands. As an alternative to carboxylate-based ligands, Fe and Co methylenediphosphonate was successfully synthesized and tested as negative electrodes based on diphosphonates for Li-ion batteries [50].
Highly active Co / Mn-1,4,5,8-naphthalene tetra-carboxylate (Co-NTC or Mn-NTC) was synthesized using a simple rheological phase method with NTCDA. This complex of Co-NTC or Mn-NTC can be spontaneously burned in ambient air to produce nanosized metal oxide. The cyclic leveling of the charge showed that the Co-NTC or Mn-NTC combustion product (used as anode for lithium ion batteries) provides high discharge and charge output power and provides excellent battery stability [51].
A promising anode material for high-performance lithium-ion batteries (LIBs) may also be silicon (Si), but it is rapidly erased due to strong volumetric expansion during the introduction / removal of Li. To mitigate structural deterioration Si was doped with various metal sources, but the resulting materials showed low electrical conductivity. To solve this contradictory problem a new nanocomposite of graphene oxide (rGO) Si / Co-CoSi2 / rGO has been developed by mechanical mixing of Si nanoparticles, Co3O4 microparti-cles and rGO nanowires with subsequent carbon-forming restoration. The proposed nanocomposites demonstrated a high specific capacity of 952 mAh / h with a preservation of 79.3 % of the capacity after 80 cycles of charge / discharge at a current density of 100 mA / g [52].
The analysis of literary sources shows that progress in the development of electrochemical energy is largely determined by the successes in the development of active and stable nanomaterials for cathodes and anodes of fuel cells. However, the high cost and scarcity of metals make the use of pure metal catalysts unprofitable and require a reduction in their number with the maximum effectiveness of their use. This is achieved by the use and development of new catalysts on carriers.
Consequently, the necessity to create inexpensive, stable and efficient electrocatalysts is an urgent task of today, the solution of which will be of considerable interest in the theoretical and practical aspects.
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