  CORROSION  THEORY ## Mixed potential theory Resistance Polarization             Back to Material Science ## Electrochemical Data for  Aqueous Corrosion

Electrochemical Principle

When a steel structure is in contact with an open aqueous environment or in underground soil , an electrochemical cell is formed with following anodic and cathodic reactions.

Fe = Fe++  + 2e        …….. ……..1.1           Ea  - Half cell potential [O] + H2O  + 2e = 2OH-   ……… 1.2         Ec - Half Cell potential

The cell potential E = Ea – Ec  ……….. 1.3

The free energy change associated with it

DG = -nFE , ………………1.4

where n is the no of charge e or electron involved and  F is Faraday. The half cell potentials Ea and  Ec are related to activities and standard potential by Nernst equation as follows.

Ea = Ea0  - RT/nF ln (a Fe++  )  ………….1.5

Ec= Ec0  - RT/nF ln ( OH-)2/(O)     ……….1.6

( Assuming the solution behave ideally and activity equals to concentration )

If the resistance of the aqueous electrolyte path in between the anode and cathode be R ( Fig.1.1 ), then electrochemical corrosion current I0 can be written as

I0 = (Ea - Ec)/ R  …………….1.7

Thus corrosion of steel depends on electrode potential Ea and Ec , which in turn are related to concentration Fe++ and OH- ions (pH) , dissolved oxygen concentration , temperature and resistivity of the electrolyte.  It has been illustrated how on a same steel piece some regions act as anodic sites and others as cathodic sites. This is a case of inseparable electrodes. The equivalent electrical circuit shows a cell  and current  flowing through the resistance offered by the electrolyte. Unlike the normal electrical circuit , here the current is the carrier of the charge through the electrolyte. Electron flows from anodic sites to cathodic site through steel which also acts as external conductor.If a second metal M with electrode potential EM is present in the system , it  ionizes as follows

M = M++ + 2e  ………… 1.8

Depending on its position in the EMF series , it may suppress or aggravate corrosion reaction 1.1. In this case  , two electrochemical cells will be  formed and from the sign and magnitude of free energy change eqn. 1.4 , one can find out which metal will preferentially corrode For example for iron corroding in neutral aerated water , the cell potential is determined from  under standard half cell electrode potential

E =  (0.82)/2 – (-0.440) = 0.85 volt

From equation 1.4

DG = -2´ 23061´ 0.85 = -39203.70 cals

( F= 96500 coulombs converted to 23061 cal/g equivalent/volt)

With Zn into the system  DG = -2´ 23061´ ((0.82)/2 – (-0.763))     = -54101.106 cals

Higher negative free energy value for Zn indicates that zinc will preferentially corrode , protecting steel

Cathodic reaction 1.2  generates OH- ions and so region in the vicinity of steel surface becomes alkaline with increase in pH. If If the electrolyte here is stagnant, such as in under ground soil, soon a different cathodic reaction takes place as follows with higher electrode potential .

2H2O  + 2e = H2 + 2OH-      …… 1.9  Ec = -0.828 volt

The evolution of hydrogen in the above reaction leads to embitterment of steel hydrogen. The free energy change DG calculated for the cell using this cathodic reaction will have higher negative value.

The corrosion product of reactions  1.1 and 1.2 is hydrated ferrous oxide which is not thermodynamically stable and in presence of aerated aqueous media is converted to ferric form.

2Fe + 2H2O + O2 = 2Fe(OH)2  ---------   1.10

4Fe(OH)2 + 2H2O + O2 = 4Fe(OH)3 ……1.11

So another electrochemical reaction  with ahalf cell potential becomes active into the system.

Fe2+  = Fe3+  +e  ……….   1.12     Ea= -0.771 volt

Instead of water or soil , if corrosion takes place in acid the cathodic reaction will be of hydrogen evolution reaction as follows.

2H+  +  2e = H2   …… 1.13       Ea= -0.000 volt

From above discussion it is clear that depending on  constituents , concentration and temperature of environment, various electrochemical cells may be formed with different free energy changes and accordingly corrosion of steel would take place

E-PH Diagram

It is seen from Nernst equation that electrode potential of steel in aqueous media are influenced by  concentration of reacting ions associated with electrochemical reaction. Depending on the type of environment acidic, neutral, alkaline , oxidizing or reducing, various ions viz.  Fe2+ , Fe3+, OH- , H+ as well oxides may be present. A graphical representation of electrode potential of a metal at different pH values  with or without presence of these ions is called a E-PH diagram or Pourbaix diagram after M. Pourbaix* who first obtained for different metal-water systems. Detail E-PH diagram of iron with various reactions can be found in any corrosion text. Only utility of the diagram as far as corrosion control is concerned is discussed with a simplified form of it in fig. 1.2 Various environmental conditions such as acidic, alkaline , oxidizing and reducing are indicated by arrows. So for a highly acidic and oxidizing aqueous environment, one has to concentrate near top left portion of the diagram The diagram maps three major zones of corrosion, passivity and immunity with respective ions or compounds present. Corrosion of steel would take place  into the corrosion zones in the acidic regions  with formation of Fe3+ or Fe2+ ions as well under alkaline condition with formation of hypoferrite ion  ( caustic embrittlement of steel). Steel corroding neutral aerated water is indicated by  black circle as shown in fig. 1.2

Immunity is the zone where corrosion never occurs. Thermodynamically corrosion is not favorable here and DG comes out positive. In the passivity zone, on the other hand, corrosion does take place initially, but soon adherent, compact hydrated oxide layer forms over the surface. This oxide layer is passive to corrosive media and acts as a barrier between the metal surface and electrolyte. So the rate corrosion becomes negligibly small. So in this zone corrosion is thermodynamically favorable but not kinetically.  To control corrosion of steel from, one can either move into passivity region shown by arrow from black circle (fig.1.2) by oxidizing the system that is dragging electron from the steel, known as Anodic protection or into the immunity region by reducing it that is pumping electron into the steel known as cathodic protection to be covered in later chapters.

The rate of any chemical reaction r is amount reacted in unit time per unit area . So  the amount reacted w on surface area s in t time can be represented as

r= Dw/st      1.14

From above equation unit of  rate of corrosion is expressed in mdd ,which in mg per dm2 per day. But often change in weight is not a true representation   of  degree of representation. For example if  very small holes develops into the hull of ship, the amount degraded is not much, but it may lean to entry of sea water into the hull , making it

accident prone.  So it is felt thickness of penetration per unit time is more appropriate and unit of corrosion is also expressed in mils per year in short mpy. One mil is thousand of an inch.

Since corrosion is an electrochemical reaction with consumption or production of electrons, the rate of corrosion is a measure of rate of electron flow or current I. By Faraday’s law I can be related with the amount reacted w on surface area s in t time.

w= Ita/nF                             1.15

Where a is the atomic weight

r =w/s= (a/nF).(I/s)

Or    r = (a/nF). i                1.16

where i is current density that is current per unit area.

Now all the terms within bracket in equation 1.15 is constant for a particular corrosion reaction , the current density i is  proportional to the rate of corrosion. It  is expressed in mA/dm2  or mA/cm2. Electrochemical determination of corrosion rate by i is more accurate and precious than by weight change method mdd or thickness measurement mpy, since very small current in terms of fraction of  mA can be measured. Corrosion rate i can be converted to mpy , knowing density and atomic weight of the metal from the equation

mpy = 0.129 ai/nd                1.17       ( i is in mA/cm2, d gm/cc)

It is seen from equation 1.7 that the electrochemical current I0  flowing through the cell is proportional to  (Ea - Ec). But as soon as current flows, the electrodes get polarized. Anode potential no more remains at Ea but increases in the positive direction as EP,a  and cathode potential  Ec shifts in the negative direction to EP,c  as shown in fig.1.3.  This phenomenon of shifting of electrode potentials from equilibrium values to polarized potentials is known as Polarization and magnitude of change is called overvoltage, designated by h.

After polarization electrode potentials of anode and cathode come to very close to each other (within about 1-2 mV) and a much smaller current I indicated by following equation 1.14 flows.  I =( EP,c  - EP,a  ) / R                 1.18

Where resistive part R consists of electrolyte resistance Rel and  external resistance Rext which is conductive resistance from cathode to anode outside electrolyte so that equation can written as

I Rel + I Rext =( EP,c  - EP,a  )                  1.19

If the two electrodes are externally short circuited which is the case for inseparable electrodes , Rext =0. then,

I Rel =( EP,c  - EP,a  )                          1.20

If the electrolyte is of high conductivity such as acid or sea water , Rel will be negligibly small and may be approximated to very close to zero. Then right hand part of the above equation is close to zero.

0        @( EP,c  - EP,a

or  EP,c  @ EP,a   =  Ecorr                        1.21

Under such conditions cathode potential becomes equal to anode potential and both of them are equal to corrosion potential Ecorr.    At corrosion potential anodic reaction takes place with rate Ia known as anodic current which is equal and opposite in direction to Ic cathodic and both of them are equal to Icorr , corrosion current or rate of corrosion.  This is illustrated  in fig.1.4., with an example of iron corroding in acid. At Ecorr and Icorr, dissolution of iron takes place in acid at a rate which is equal to the rate of reduction of hydrogen ions so that there is no net accumulation of electron.

Ecorr is the mixed potential of the two electrode potential. It will be seen later that both Ecorr and Icorr have huge implication   in combating corrosion of materials

Why does polarization takes place ?

Before reactants start reacting, they need to achieve the activation energy to surmount to activated state. This energy requirement is proportional to the change in the electrode potential  or overvoltage.

ΔGa#  = nFha         1.22      and

ΔGc#  = nFhc            1.23

Where  ΔGa#   and    ΔGc#   are the activation energies for anodic and Cathodic electrode reactions respectively with corresponding  overvoltages ha   and       hc

For a solid iron surface to react with liquid acid containing H+ ions following steps need to occur.

i.                     H+ ions must be available in the vicinity of solid surface

ii.                   Formation of hydrogen atom by H+ + e = H

v.                   Formation of gas bubble and its detachment .

vi.                 Availability of iron surface in contact with acid

vii.                 Ionization Fe= Fe+2 + 2e

Of all steps of Cathodic reduction reaction ( i- iv), one which will need maximum energy will control the electrode reaction rate and contribute for activation polarization. In general reaction (ii ) and (vii) account for activation polarization for cathodic and anodic reactions respectively.

The activation polarization or overvoltage h  is related to current density ia or  ic  by Tafel ‘s equation.

ha   =  +ba log(ia/i0)           1.24

hc   =  -bc log(ic/i0)            1.25

where i0 is the exchange current density.

For any single electrode at equilibrium say Fe/Fe2+ , rate of forward reaction Rf  is equal to the rate of  backward reaction Rb.

Fe2+ + 2e ® Fe      Rf       1.26

Fe= Fe2+ + 2e         Rb         1.27

Rf = Rb = i0 a/nF                   1.28 The exchange current is related to rate of forward reaction and backward reaction by the equation 1.28. Though the rate of forward 1.26 and backward reaction  1.27 are equal, there is no net accumulation Fe2+ or Fe , still there is a rate which is represented by i0

Consider iron two electrodes iron and platinum dipped in acid as shown in fig.1.6.  At anode iron ionizes releasing electrons that pass through the external conductor to other electrode platinum and these electrons discharge hydrogen ions, when they are available in the vicinity of the platinum electrode surface. Once hydrogen ions adjacent to the platinum electrode have been consumed by electron , ions from the bulk of the solution need to diffuse through the solution towards the electrode surface for further reaction. Now the speed of  electron movement through the external conductor from anode to cathode is much faster than the diffusional ionic speed of  ions through the bulk solution towards the cathode surface. There is concentration deficiency of H+ ions near cathode surface and build up of negative charge electron, when the electrode potential of the cathode decreases or moves in the negative direction. This phenomenon is known as concentration polarization or  Diffusion polarization. At times situation may arises, no  H+ ions are available near cathode surface, no cathodic reaction takes place and overvoltage

approaches to negative infinity( see Fig.1.7). The rate at which it occurs is called limiting current density iL. The concentration overvoltage can be given by the equation.

hcon = 2.3RT/nF log ( 1- i/iL)            1.29

iL = DnFC/d                                    1.30

where is the diffusivity of the reaction ion of concentration C, d is the thickness of the concentration gradient. Thus iL  increases (fig.1.7) with higher concentration, higher temperature and solution agitation due to increase in D.

The total polarization h is the combined effect of activation and concentration polarization. Concentration polarization is normally absent at anode , since there is unlimited supply of the metal for ionization at anode , Thus total polarization for cathode and anode can be written as ;

ha   =  +ba log(ia/i0)                                           1.31

hc   =  -bc log(ic/i0)  +  2.3RT/nF log ( 1- ic/iL)       1.32

From the above equations , it is seen that for a particular system of a metal corroding in an environment, the parameters ba, bc , i0 and iL define the system and rate of corrosion is decided by them.            In practice there may be more  than one anodic reactions and cathodic reactions and each of the equation must follow either of the above two equation

This polarization arises in cases where electrolyte resistance is very high. For example if an insulating coating which separates anodic and cathodic areas, is applied to steel structure. In this case the anodic line and cathodic line  instead of intersecting , is separated by resistance polarization IR (fig.1.9). Mixed potential theory

According to Mixed potential theory, the total rate of oxidation or sum of anodic currents must be equal to total rate of cathodic current or the sum of cathodic currents and this would occur at the potential, Ecorr and current, icorr         Activation polarization normally occurs  in the initial stage of any reaction that is when current or rate is not very high, whereas concentration polarization generally occurs when at a later stage when the current is high. For most cases the point Ecorr and icorr in the region of activation polarization. Hence concentration polarization is normally not considered for determination of corrosion rate. However for corrosion of steel in aerated aqueous media or soil represented by following equations , concentration

Cathodic     O2 + 2H2O  + 4e = 4OH-              1.33

Anodic            Fe = Fe 2+  + 2e 1.34  Polarization occurs at very early stage. Since the cathodic reduction reaction is controlled by concentration of dissolved oxygen and rate controlling step is the diffusion of dissolved oxygen. So the point of Ecorr and icorr  is on the concentration polarization line of cathodic reaction (fig. 1.8). Corrosion current icorr approaches limiting current density iL

Prepared by S Paul