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Volume 3 Paper 14


The new principles of the building of equivalent circuits for the modeling of metal-film-corrosive environment systems.

Shagaev A. A.,
Independent researcher, house 17-a Apartment number 6, 660037 Kolomenskaya Str., Krasnoyarsk, Russia, E-Mail Address: or

Abolin O. E.,
Central laboratory, "Chemical-metallurgical plant" Ltd, 30 Matrosova str., Krasnoyarsk, 660079, Russia.

Danilov V. G.,
Laboratory of Catalytic Chemistry of The Coal and Biomass, Institute of Chemistry and Chemical Technology SD RAS, 16 Akademgorodok str., Krasnoyarsk, 660036, Russia.

Abstract

In the paper we propose the main principles of the building of equivalent electric circuits for the modeling of metal-film-corrosive environment systems. At the same time, the authors of this paper took into account the possibility of both electrochemical and ionic chemical processes in such Redox systems. We proceeded from the necessity to take into account all processes in a RedOx (and ionic) system in detail as much as possible. As a result, any chosen element of such equivalent circuit corresponds to its stage of a corresponding RedOx (ionic) process. The requirements for the relative position of all circuit elements were formulated. The proposed principles were applied to the modeling of the behavior of a corroding metal in an arbitrary corrosive environment. The obtained simplest circuit allows to estimate quantitatively the influence of the remainder of the mass of a metal (oxidant and solvent, the electroconductive properties of an electrolyte, the nature of a solvent (and forming products of corrosion), the rate of the physical dissolving of a film) on the total current of corrosion. It was demonstrated that the nature of a corrosion process is determined by the resistances of the transferring of forming corrosion products (ions) in phases contacting with a metal. The corrosion process spreads, mostly, into the phase (contacting with a metal), the electric resistance (of the transferring of forming corrosion products) of which is lesser. The order of the calculation of the resistances of the circuit was proposed. The requirements (for the correct carrying out of a corrosion study) were established. The principles, we propose in this paper can be apply to any RedOx (ionic) systems used in all fields of chemistry (electrochemistry, catalysis, photochemistry etc.).

Keywords: equivalent circuits, corrosion, modeling.

Introduction

Electrode potential is one of the fundamental notions of electrochemistry. It is the key concept when describing the processes of metal corrosion, the functioning of batteries and a number of catalytic processes in chemistry and chemistry interdisciplinary sciences. Number of researchers worked on the problem of the description of electrode potential by means of electric equivalent circuits. It so happened that different researchers used 2 different models to solve this problem:

  1. a corroding metal-oxidant system was considered as a microgalvanic battery, where anodic and cathode areas are located on the heterogeneous surface of a metal in contact with environment. The corrosion of a metal is the result of microgalvanic battery processes. Electrons flow through the metal and ions flow through the electrolyte. This model (let us call it "a heterogeneous surface metal corrosion" or HtSMC) is applied when describing the corrosion of metal and alloys with a heterogeneous composition.
  2. The processes of forming the cations (of the metal) and anions (from the molecules or ions of an oxidant) take place, correspondingly, on the interface of a metal/film and a film/solution in a metal/film/solution system. Electrons flow through the metal and the electronic resistance of the film; cations flow through the cationic resistance of the film. This model (let us call it "a homogeneous surface metal corrosion" or HmSMC) is applied when describing the corrosion of metal and alloys with a homogeneous composition.

Muller [,] was the first who came up with an idea that the electrode potential of the corroding metal (with the a heterogeneous surface) is an intermediate between the potentials of anodic and cathodic electrode areas on its surface. Chupr [] was the first to use equivalent electric circuits for the description of a corroding metal with the help of the Muller theory. In Russia, Akimov and Tomashov [] were the first to study the electrode potentials of a multi phases electrochemical systems. They used HtSMC model. They got the following equation for the metal potential being measured:

(1)

where Ea and Ek are the potentials of the anodic and cathodic areas of the surface of an electrode

ra and rk are the resistances of the anodic and cathodic areas of the whole circuit.

Absolutely the same equation was advanced by Muller for a special case of a passivating metal [, ]. Muller considered the meaning of the values of the equation from the point of view of his passivation theory. Later, Daniel-Bek [] advanced a number of equivalent circuits describing of a above-mentioned equation as well as the functioning of a corroding metal under an external polarization (to explain a negative difference effect). It was following circuits:

Figure. 1. Microelement equivalent circuits put forward by Daniel-Bek. (1) corrosive microelement without an external polarization; (2) corrosive microelement with an anodic external polarization; (3) corrosive microelement with a cathodic external polarization

where a - the arbitrary point of an electric contact with a metal

b - the reference electrode location in the solution

r - the electrolyte resistance between the location of the reference electrode and the corroding metal surface.

ra and rk the anodic and cathodic resistances of the microelement circuit

J external current

R the resistance of the cathodic (anodic) circuit of a connected external cathode (anode).

Fig. 1 (2), to take into account an external polarization some of circuit elements are marked with the sign of " ' ".

Note that the direction of ik in Fig.1.(3) is opposite to the ik direction in Fig.1.(2).

Fig. 1 was considered by Daniel-Bek as applied to a microgalvanic element functioning on the surface of an electrode. So, Daniel-Bek came to the conclusion that the corresponding anodic and cathodic areas of the microgalvanic element circuit were located at the thinnest boundary layer of an electrolyte. Hence, Daniel-Bek drew the conclusion, that the reference electrode was not located in the way of the current, flowing in the electrolytic circuit of the microgalvanic element, which determines the location of the element "r" in the circuit. Fig.1 (2) serves to explain the negative difference effect (the decreasing of the current of metal corrosion due to the anodic polarization of an electrode). Based on the principles of linear dependence of the anodic (Еa) and cathodic (Еk) potentials on the densities of the corresponding currents (ia and ik):

(2)

(3)

where Ea, ba и Ek, bk the corresponding coefficients of the linear dependences. As a result, Daniel-Bek got the following equation for the potential of a corroding metal (anodic polarization):

                   (4)

The equivalent electric circuit (Fig. 1(3)) was proposed by Daniel-Bek to explain the cathodic protection effect (the decreasing of a metal corrosion rate under cathodic polarization).

In the 1990-s Gerasimova [] proposed an equivalent circuit which, at the first approximation, described this electrochemical system quite well quantitatively. The equivalent circuit was based on the HmSMC model.

It was the following scheme:

Figure 2. The Gerasimova equivalent circuit

where Ri and Re the cationic (ions Me+) and electronic resistances of the film of corrosion products on the main electrode. Each of these values (Ri and Re) include phases boundaries resistances.

RV. - the resistance of the voltmeter

φMe/Me(+), φOx/Red, φref.el. the equilibrium electrode potentials of a metal Me1, a reductive-oxidative Red/Ox electrode and a reference electrode, respectively.

The author got the following expression for the potential of an electrode covered with a corrosion product film. This potential was measured with a voltmeter:

(5)

where UV.- voltmeter reading

(6)

(7)

The obtained result shows that, if Ri=0 then UV.=Е1. So, the electrode potential is determined by the Me/Me+ equilibrium, in the case. As Ri increases (or Re decreases) UV. approaches to Е2. Thus, the electrode potential, more and more, is determined by the Red/Ox equilibrium, in the case. This way, the influence of the ratio (Ri/Re) on the measured potential value becomes clear.

The comparison of the approaches of Akimov, Tomashev, Daniel-Bek and Gerasimova, regardless the difference between the corrosion models they use, reveals some similarity when building a metal corrosion circuit:

  1. they used electrode potentials in these circuits
  2. anodic and cathodic electrode potentials were connected back-to-back. In this case, according to the Daniel-Bek and Gerasimova circuits either the cathodic or anodic processes can not supply corresponding ions to the environment. This deprives these circuits of the physical meaning. It brings us to an idea that the potentials must be series-connected and they must be the potentials of processes, not the electrode potentials.

The difference consists in the fact that Gerasimova unlike Daniel-Bek:

  1. didnt take into account the linear dependence of metal (φMe/Me(+) and oxidant (φOx/Red) potentials on the value of the current passing through them (no-current measuring).
  2. used a circuit similar to that of Daniel-Bek (for the polarization).

The Daniel-Bek and Gerasimova equivalent circuits have some disadvantages, such as:

  1. these circuits dont take into account what happens to cations and anions, forming in the course of process of metal corrosion (and in the course of measuring a potential), later on, (their possible interaction in a solution resulting in the formation of ionic compounds (e.g. ion pairs). The energy of the processes must be part of the emf of the total corrosion process and of the electrode potential.
  2. these circuits dont takes into account 3 variants of corrosion process:
    a) the formation of a corrosion products film on the surface of the main electrode only
    b) the dissolving of corrosion products in the solution only
    c) a possibility of a partial dissolving of corrosion products in the solution
  3. these circuits dont takes into account that the corrosion process take place on the reference electrode, as well as, the presence of electroconductive films and other formations with a finite (ionic and electronic) resistance on the surface of the reference electrode.
  4. the Daniel-Bek equivalent circuit takes into account the conductivity of a solution. Neither, Daniel-Beks nor Gerasimovas equivalent circuits take into account the influence of the nature of a solution on Uv and the values of corrosion currents.
  5. Gerasimova didnt take into account the fact, that the processes similar to those taking place on the main electrode can, also, take place at the metal/film and film/solution phase boundaries of the reference electrode. Any oxidation reaction on the reference electrode must correspond to a reduction reaction on the main electrode and vice versa. At the same time, every molecular chemical reaction (or a set of reactions) must be described by a corresponding circuit.
  6. none of this circuits take into account the mass of a metal, oxidant and solvent. It makes this circuits divorced from real life practice.
  7. the reference electrode (Daniel-Bek writes about in his paper) is absent (in form of his potential or the emf) in his circuit. The Daniel-Bek assumption, that the reference electrode is not located in the way of the current flowing in the electrolytic circuit of a microgalvanic element is true only in part. Both the cathodic and anodic areas of a microgalvanic element simply have to form their own electric circuits, respectively, with anodic and cathodic areas on the reference electrode. Thus, the Daniel-Bek equivalent circuit loses its real physical meaning.
  8. The way the anodic and cathodic electrode potentials are connected is such that their emf vectors are in opposite directions. This doesnt allow the cathodic or anodic process to supply the environment with corresponding ions. This deprives these circuits of their physical meaning.

We can neglect the points (2a, b, c) and (4), but the others are very important and cannot be neglected.

Principles of Construction of Equivalent Electric Circuits, Modeling Ionic Chemical Processes 

When building this circuit the authors of this paper took into account the possibility of both electrochemical and chemical corrosion of a metal. We proceeded from the necessity of studying all processes in the metal/environment system in detail as much as possible. At the same time:

1)      any chosen element of an equivalent circuit corresponds to its stage of the process. For example, electrical resistance (ionic, electronic or molecular transfer resistance) corresponds to the process of ions (electrons, molecules) transfer; the emf corresponds to the process of the interaction of particles (molecules, ions and electrons). We can calculate E value using the equation:

(8)

where dG the Gibbs free energy change of the interaction process

n the number of electrons transported in the course of the interaction process (for the solvation process n is equal to the charge of ions)

F the Faraday constant (equal to 96500 C/gram-equivalent)

2)      any chosen phase of the system corresponds to its electric circuit or circuit branch.

3)      every circuit must describe a complete molecular chemical reaction (or a set of complete reactions).

4)      every emf vector of any circuit must describe its separate stage of a molecular reaction of the circuit. The emf vectors direction of the circuit must reflect, correctly, the process, corresponding to the circuit. For example:

if the emf (3) of the circuit (1) describes the solvation process and the emf3 direction coincides with the accepted direction of the path- tracing (for example clockwise) of the whole circuit, then the emf3 direction circuit (2) is opposite to the direction of the path- tracing and, thus, reflects the inverse process(desolvation), and the emf sums of both circuits in the direction of the their path-tracing describe the processes in these circuits correctly.

5)      The initial relative position of all circuit elements must correspond exactly to their actual position in the system we model. However, subsequently, the circuit elements can change their position in according to the electrical laws.

6)      We should avoid using, repeatedly the same elements (identical resistances and emfs) in different parts of the circuit. If you fail to do it, it is necessary to check if the sums of the emfs and resistances of all circuits correspond to the reactions in these circuits.

The application of the proposed method to the modeling of the corroding behavior of a metal in arbitrary corrosive environment.

Guided by these principles, the authors of this paper propose an equivalent electric circuit describing a process of metal corrosion. The circuit allows to estimate quantitatively the influence of the remainder of the mass of a metal, oxidant and solvent, the electroconductive properties of an electrolyte, the nature of a solvent and forming products of corrosion on the total current of corrosion (which is equal to the sum of the current of the forming of soluble products of corrosion + the current of the forming of insoluble products of corrosion).

The most simple equivalent electric circuit we propose is the following:

Figure 3. The equivalent circuit proposed in this work.

After simplifying the circuit it is as shown in Fig. 4

Figure 4. The paper authors equivalent circuit after some simplifications.

where Ri and Re - respectively, the sums of the cationic and electronic resistances of metal/film (RiMe/film, ReMe/film) phase boundaries, film (Rifilm, Refilm) and film/solution phase boundaries (Rifilm/s, Refilm/s).

However, unlike the previous authors, the Re value includes the ohmic resistance of a metal (RMe) and, so called, the resistance of transferring the molecules (ions) of an oxidant to the film surface (Rox). Thus, the authors of this paper take into account the mass of a metal and oxidant, as well as, the fact that it is possible to model such processes, the fact, which either wasnt taken into account at all by a number of previous researchers or, for others, was the reason to refuse to consider such processes as electrochemical processes (referring to the diffusive nature of the process of the transferring of an oxidant to a metal) and, consequently, to give up attempting to model such processes by means of electric equivalent circuits.  It should be taken into account that the corresponding values of resistances are functions of time, currents flowing through them (including the current of the physical dissolving of a film), the mass of a metal (and an oxidant), the initial characteristics of a film and the whole set of external and internal conditions (temperature, illumination, dynamic recrystallization processes and so on). For more detailed information about the Ri and Re values see Appendix 2.

RSc1 and RSa1 respectively, the cationic (for main electrode cations) and anionic (for anions forming) resistances of the layers of an electrolyte (the layers, taking part in a corrosion products dissolving process). This values depends from time, currents, initial and current electrolyte parameters, external and internal condition influencing by them. For more information about the RSc1 and RSa1 values see Appendix 2.

RaS and RkS the resistance of the transferring of the molecules of a solvent to the anodic and cathodic areas of a corrosive element on the surface of the film/solution phase boundary for solvation of forming ions. For details see Appendix 2.

RMc and RMа the cationic and anionic resistance of cation and anion migration on the surface of a film on the electrode from the areas, where they form (anions) or the areas of their way out (cations) on the surface of the film/solution phase boundary to the areas, where they interact, which results in the forming of a crystal lattice. For more information about this values see Appendix 2.

EMe/Me(+) and ERed/Ox emf (potentials) values, corresponding to the following processes:

(9)

           (10)

these values are calculated by means of the Gibbs equation for change of energies of the corresponding processes.

Esc and Esa - the values of the emfs of solvation processes (cation and anion). These values are calculated by means of the Gibbs equation for change of energies of the corresponding processes. For more information about this values see Appendix 1.

ESinter. the emf of the process of the interaction of solvated cations and anions in a solution. For more information about this value see Appendix 1.

Ecr. the emf of the process of the crystallization of a corrosion product. For more information about this value see Appendix 1

The circuit (which includes the area from the metal to the film/solution phase boundary) describes the process of the forming of a film on the metal. The circuit (which includes the area from the metal to the solution) describes the process of the forming of soluble corrosion products. The circuit (which includes the area from the film/solution phase boundary to the solution) describes the process of the physical dissolving of a film in the solution. When there is no film on the metal, the branch of the circuit with Еcr. is excluded from the circuit and instead of the Riме/film, Reме/film, Rifilm, Refilm, Rifilm/s, Refilm/s values we put the cationic and electronic resistances of the metal/film phase boundary (Riме/s and Reме/s). Thus, we have a simple chemical corrosion case. The circuit we got in this case is the simplest and is not considered in this paper because of the simplicity of the calculation of its current.

If you cant understand the nature of the RSc, RSa, RMc и RMa values see Appendix 2.

The calculation based on the second Kirchhoff's law for our equivalent circuit, results in the following expressions:

The corrosion current (If.i.s.), when only a surface film forms:

(11)

The corrosion current (If.s.s.), when only soluble corrosion products form:

(12)

The total corrosion current (Icor) equal to the sum of the If.i.s. and If.s.s.currents:

      (13)

The expressions (11)-(13) we got have a clear thermodynamic meaning.

The (Ecr.+ERed/Ox+ EMe/Me(+) value, included in the If.i.s. corresponds to the Gibbs energy change of the forming of insoluble corrosion products. The (Esc+Esa+ESinter.- Ecr.) value corresponds to the dissolving of corrosion products. Thus, a metal corrosion current (when an insoluble film forms on the surface of an electrode) is proportionate to the difference of the Gibbs energy changes of the reactions of the forming and dissolving of a film.

(Esc+Esa+ESinter.+ERed/Ox+ EMe/Me(+)) value, included in the If.s.s. is proportionate to the Gibbs energy changes of the reaction of the forming of soluble corrosion products. The (Esc+Esa+ESinter.- Ecr.) value is already known to us. Thus, the metal corrosion current, when soluble corrosion products form, is proportionate to the sum of the Gibbs energy changes of the reactions of the dissolving of a metal and film.

It is obvious that both expressions (11) and (12) include the same term, but with different signs:

(14)

This term is the electrical current analogue of the rate of the physical dissolving of a film.

The Iк value of the total metal corrosion current is proportionate to the difference of the Gibbs energy changes of the reactions of the forming of corrosion products film and soluble corrosion products.

The extreme cases of the functioning of the equivalent circuit are the following:

I - The Sum of the Resistances of the Migration of Ions on the Surface of a Film is Much  Larger than the Sum of the Ionic Resistances of the Solution.

 

In the case, total corrosion current is equal to:

(15)

So, when the sum of the resistances of the migration of ions (formed as a result of a corrosion process) on the surface of a film is much larger than the sum of the resistances of ions in a solution the process of the dissolving of corrosion products starts and the film stops to grow. Only the process of the dissolving of a metal in a solution runs.

II - The Sum of the Ionic Resistances of the Solution is Much  Greater than the Sum of the Resistances of the Migration of Ions on the Surface of a Film.

In this case the current, is given by:

(16)

i.e., when the sum of the resistances of ions in a solution is much larger than the sum the of the resistances of the migration of ions (formed as a result of a corrosion process) on the surface, a corrosion process (when insoluble corrosion products form on the surface of a metal) starts.

An example of this kind of corrosion is metal corrosion in gases or nonconductive environments where a conductor between a metal and oxidant is the film itself. The sum of the resistances of the migration of ions on the surface of a film is less than the sum of the ion resistances of gasiform or other corrosive nonconductive environments.

These two extreme cases show that an electrochemical system: metal - conductive (or nonconductive film) oxidant is a self-switching circuit (SSC). Its behavior is determined entirely by the resistances of the phases (or more exactly currents, flowing through these phases) to which the products of metal corrosion can be transferred. Corrosion products (ions) are transferred, mostly, to the phases having the least electrical resistances to this transferring (or when the currents, flowing through these phases are maximum). The circuit, proposed by the authors, is the simplest and serves to illustrate an approach to the modeling of redox processes by means of equivalent electric circuit. To model more complex redox systems, more complex equivalent circuits (taking into account all possible processes in the system) will be needed. However, the principles of circuit construction remain the same, as stated above.

The following consequences, important for corrosion study, ensue from the results obtained:

1)      To obtain really comparable experimental results, experiments with the corrosion resistance of test piece should be carried out:

a)     with test pieces of the same size and prehistory (the same composition of their surface film)

b)     using an electrolyte of the same composition and contained in ampoules of the same volume and shape, to observe the current concentrations equality of cations and anions in solutions at any instant of time and in any place

c)      using the same number of test pieces of a metal and with the same relative positions in every capsule, containing an oxidant medium. This condition is, also, necessary to observe the current concentrations equality of cations and anions in solutions at any instant of time and in any place

d)     under the same conditions (temperature, light and so on), which can influence the values of the resistances and solubility of corrosion products

e)     points (b) and (c) may be ignored if the calculation of a specific corrosion rate is made (specific rate = corrosion rate/(the volume of an electrolyte * the sum of the surfaces of test pieces)).

f)       When making calculations it is necessary to take into account the change of the mass of test pieces (a pure metal and pure film mass), as well as, the change of the concentrations of cations and anions forming in a solution.

The authors of this paper believe that this method of modeling can easily be applied to interpreting impedance measurements in electrochemistry.

Conclusions

Based on the results obtained, the following conclusions were drawn:

1)      it was demonstrated that the nature of a corrosion process (running on the surface of a metal in any oxidizing medium) is determined by the resistances of the transferring of forming corrosion products in phases (already existing or forming in the course of corrosion) contacting with a metal (taking into account the contribution of the resistances of the transferring of an oxidant, solvent, ohmic resistance of a metal and the resistances of phase boundaries). The corrosion process spreads, mostly, into the phase (contacting with a metal), the electric resistance (of the transferring of forming corrosion products) of which is lesser.

2)      Requirements (for the correct carrying out of a corrosion study) were established.

Appendix 1.

The physical meaning of the Еsc, Еsa and ЕSinter. values and the order of their calculation.

The physical meaning of these values is obvious. These values mean the potentials of the corresponding processes, calculated on the basis of Gibbs equation. The "n" value (for solvation processes) is the valency of an ion, and the product of the valencies of ions (for interaction processes). The authors realize that, in fact, several different solvation and ions interaction processes can run in a solution. To simplify the description we take into consideration only some of them.

Appendix 2. 

The physical meaning of the RSc, RSa, RMc, RMa, Ri, Re values and the order of their calculation.

The physical meaning of the Ri and Re values is obvious. They are the electronic and cationic resistances of a corrosion products film (on a metal) and phase boundaries (metal/film and film/electrolyte).

Based on the Ohm and electrolysis laws the authors got the following expression for the Ri =Rifilm(t) value:

(17)

where S film surface area

Pifilm the specific cationic resistance of a film

Rifilm(t), Rifilm(0) the ionic resistances of a film for instants of time t and t=0.

dfilm film density

EqMen+, EqAn- - the masses of 1 gram-equivalent of a metal ion and an anion.

t time

We can get the similar equation for the Re =Re(t) value:

(18)

where Refilm electronic specific resistance of a film

Refilm(0) = Refilm(t) for an instant of time t=0

However, as noted above, the paper authors regard the Re(t) value as the electronic resistance of a film (Re(t)), the ohmic resistance of a metal (RMe(t)) in a corrosive microelement and the resistance of the transferring of the ions (molecules) of an oxidant to the surface of a film (Rox(t)), i.e. Re(t) =Re(t) + RMe(t) + Rox(t).

Based on the Ohm and electrolysis laws and if the metal test piece we use is rectangular and if the thickness of this metal test piece decreases, at the same time, its length and the width are constant in the course of corrosion process, we can get the following expression for the RMe(t) value:

(19)

where PMe the specific resistance of a metal

        (20)

lab the effective distance between the anodic and cathodic areas of a corrosive microelement on the metal/film phase boundary (the metal side)

Sab(t) the cross-section area through which the corrosion current flows in the given microelement.

MMe(t), MMe(0) the mass of a metal at the instances of time t and 0

This equation shows that at the instance of time when the metal has been consumed completely (MMe(t)=0), the ohmic metal resistance of the microelement will be equal to infinity, and as RMe(t) and Re(t) are series-connected, the circuit will open, the corrosion process will stop running.

Similarly (for the resistance of the transferring of an oxidant to the surface of a film on a metal (Pox(t))) if the specific resistance of the transferring of the ions (molecules) of an oxidant to the surface of a film on a metal (Pox(t)) is (at the first approximation) in inverse proportion to the molar concentration of an oxidant in a solution:

                                                                  (21)

where K2 proportionality coefficient

VS the volume of a solution

μox the gram-molecular weight of an oxidant 

         MOx(t) current mass of an oxidant

if we apply the electrolysis low to the calculation of the current mass of a metal, we get the following equation for the resistance of the transferring of an oxidant to the surface of a film:

                   (22)

where

(23)

MOx(0), MOx(t)- the initial and current mass of an oxidant

This equation shows that at the instance of time when Mox(t)=0 the resistance (of the transferring of the ions (molecules) of an oxidant to the surface of a film on the metal of a microelement) will be equal to infinity. So, at this instance of time, the circuit will open, because Rox(t) is series-connected with Re(t). The corrosion process will stop.

We got a similar equation for the resistance of the transferring of the molecules of a solvent to the anodic (cathodic) areas on the surface of the film/solution phase boundary Rs(t):

(24)

where Ms(0) solvent mass at instant of time t=0

EqSk, EqSk - the masses of the 1 gram-equivalent of the forming ion of a metal and an anion in the course of solvation reactions.

μs the gram-molecular weight of a solvent

           Ks the coefficient of proportionality similar to that in the case of an oxidant.

This equation shows that at the instance of time when the mass of a solvent =0, the resistance (of the transferring of the molecules of a solvent to the surface of a film on the metal of a microelement) will be equal to infinity. So, at this instance of time, the solvation process (of the corrosion products) will stop completely, because Rs(t) is in the circuit of dissolving.

Thus, we get the following equation for the Rfilm value we use for the further calculations (see this Appendix below):

(25)

One can suppose, that at the start time of the corrosion experiment we can neglect the RMe(t) value, because it is insignificant (small). A similar assumption, as we believe, can be made for the Rox(t) value under the same conditions. This simplification permits us to can get a simpler equation for the sum (25):

(26)

On the basis of the initial data of the corrosion experiment and the equation (26) we can calculate the (Rifilm(0)+Refilm(0)) and (Pifilm(0) + Pefilm(0)) values, that we will need later on. Having at our disposal (Rifilm(0)+Refilm(0)) and (Pifilm(0) + Pefilm(0)) values and using a more exact equation for the sum (25), we can calculate the Кох and Кме values.

The physical meaning of the RSc, RSа, values is clear enough when we see Fig. 3 and Fig. 4. These are the following sums: RSc = RSc1 + Ras; RSа =RSа1 + Rcs. Where RSc1 and RSа1 are effective electric (ionic) resistance of the electrolyte (or any other medium), contacting with the film covering the metal.

It is clear, that the trajectories of the transferring of the forming ions (in the solution), to the areas where the ionic products form, can be different (even for the same ions). However, we believe that there are some averaged trajectories of the cations and anions under standard experiment conditions. So, there are some averaged effective ionic resistances of a solution (or another medium).

The same reasoning is for the migration of forming ions on the surface of a film to the areas where the ions are built to the lattice.

We think that we can illustrate the similar figure and reasoning case.

Ras and Rcs - the resistances of the transferring of the molecules of a solvent to the areas of the exit (and the forming) of cations (and anion), for their (ions) solvation.

It is clear, that we can not measure the RSc and RSа values directly, but we can calculate these values. The calculation should be made on the basis of the method we proposed in this paper, the processing of the data of the corrosion experiment and using the equations we deduce in the paper. It is clear, that values of the given resistances arent constant (even for the same experiment). As the process of the dissolving of corrosion products (or a simple physical film dissolving) is observed (in the system), the values of these resistances are functions of time, the concentration of cations and anions in a solution, masses of a metal, oxidant and solvent, the currents flowing through them as well as a number of internal and external conditions influencing the processes of the dissolving of a film and the transferring of charges in it. The authors of the paper propose the following method of the calculation of the Ri, Re ,RSc, RSa, RMc и RMa values:

On the basis of the following corrosion experimental data:

  1. the increase (or decrease) in weight of a metal test piece (with a film) within the current 1 sec - (dMt.spec.)

  (27)

  1. the increase (or decrease) in weight of the corrosion products in the solution, conditioned by a pure physical dissolving of a film, only, (i.e. without taking into account the mass of the corrosion products transferred by the current of the forming of soluble products) within the current 1 sec - (dMf.s.);

  (28)

  1. the increase in weight of the soluble products in the solution within 1 sec - (dMs.sub.), conditioned by the process of metal corrosion only.

  (29)

  1. the increase (or decrease) in weight of the insoluble products formed in the course of the interaction, covering the metal surface in form of a film within the current 1 sec (dMi.sub.) and conditioned by the process of metal corrosion only

     (30)

where:

                                               (31)

                                                                  (32)

                                 (33)

             (34)

                  (35)

            (36)

the authors got the following expressions for two types of corrosion processes (corrosion in liquid mediums with the formation of soluble and insoluble products) for the Rfilm, RS, RM values:

Table 1. The equations for determining the parameters of corrosion processes (standard experiment conditions).

The formation of soluble corrosion products

Rfilm

RM

RS

The formation of insoluble corrosion products

Rfilm

Rм

RS

where Eqме, Eqan and Eqfilm weight of the 1 gram-equivalent of a metal, anion and film.

The Rfilm, RM and RS values are obtained under the same experimental conditions (test pieces of the same size, the same number of test pieces in every ampoule with the same volume of the solution, the same temperature, light etc.). If the conditions of the experiments are different, then, instead of the dMt.spec, dMf.s., dМs.sub. values, we must use their specific values (dMt.spec./(S*V), dMf.s./(S*V), dМs.sub./(S*V)) (where S the total area of the surface of the test pieces of a metal in one ampoule with a solution of some volume =V) [7]. We can use these specific values (dMt.spec./(S*V), dMf.s./(S*V), dМs.sub./(S*V)) to compare the corrosive activities (with respect to the metal) of different mediums.

Table 2. The equations for determining the parameters of corrosion (non-standard experiment conditions).

The formation of soluble corrosion products

Rfilm

RM

RS

The formation of insoluble corrosion products

Rfilm

RM

RS

We have not yet managed to determining the Ri, Re, RSc, RSa, RMc and RMa values, but we demonstrated the possibility of determining the Rfilm., RM and RS values.

We also believe that this circuit can be used for gas corrosion (when only one product (a film) forms), but in the case the physical meaning of the Esc , Esa, RSc, RSa and ЕS.inter. values is different. The meaning is:

Esc и Esa the emf processes of cations (anions) - gas molecules interaction. In theory, the products of cations (anions) - gas molecules interaction can form.

RSc и RSa the electric resistances of the transferring of the products of ions (cations or anions) -gas molecules interaction from the surface of a metal to the area where they interact (forming an uncharged product, as a result). These values are large and can reduce the current in the corresponding branches to 0 (which is observed in fact).

ESinter.- the emf of the process of the interaction of the products of ions (cations or anions) -gas molecules interaction (forming an uncharged product, as a result).

The method of the calculation of the Rfilm, RM и RS values is the same as aforesaid.

Acknowledgments

Special thanks to Prof Finkelshtein A.V. the Siberian Techonological university, Krasnoyrsk, (for his advices and significant remarks concerning the material of this paper) and to Panov E. E. (for the important assistance in the translation of this paper).

References

. Muller W.J., Monatsch. Chem., 52, 53, 1929.

. Muller W.J., Korrosion u. Metal., 14, 63, 1938.

. Chupr V., Z. Elektrochem., 45, 297, 1939.

. Akimov G.V., Tomashov N.D., Physical chemistry journal, 8, 623, 1936.

. Daniel-Bek V.S. "To the metals corrosion theory ", Physical chemistry journal 15, number 3, 383-400, 1941.

. Gerasimova L.K., Kedrinskiy I..A., Oleynikov S.L. "The potential of a lithium electrode in aprotic dipolar solvents " - the report at the anniversary regional conference conference 17-21 April 1989 Krasnoyarsk.- p. 6.

. Shagaev A.A. " About the correctness of corrosion research " poster report at the 11th All-Union lithium power sources conference, Saratov (in Russian; available from the author).