0765162_Ch01_Roberge 22 9/1/99 2:46 Page 22 Chapter One Practical experience related to boiler corrosion kinetics at different feedwater pH levels is included in Fig 1.5 The kinetic information in Fig 1.5 indicates that high oxygen contents are generally undesirable It should also be noted from Figs 1.5 and 1.6 that active corrosion is possible in acidified untreated boiler water, even in the absence of oxygen Below the hydrogen evolution line, hydrogen evolution is thermodynamically favored as the cathodic half-cell reaction, as indicated Undesirable water acidification can result from contamination by sea salts or from residual cleaning agents Inspection of the kinetic data presented in Fig 1.5 reveals a tendency for localized pitting corrosion at feedwater pH levels between and 10 This pH range represents a situation in between complete surface coverage by protective oxide films and the absence of protective films Localized anodic dissolution is to be expected on a steel surface covered by a discontinuous oxide film, with the oxide film acting as a cathode Another type of localized corrosion, caustic corrosion, can occur when the pH is raised excessively on a localized scale The E-pH diagrams in Figs 1.5 and 1.6 indicate the possibility of corrosion damage at the high end of the pH axis, where the protective oxides are no longer stable Such undesirable pH excursions tend to occur in hightemperature zones, where boiling has led to a localized caustic concentration A further corrosion problem, which can arise in highly alkaline environments, is caustic cracking, a form of stress corrosion cracking Examples in which such microenvironments have been proven include seams, rivets, and boiler tube-to-tube plate joints Hydronic heating of buildings Hydronic (or hot-water) heating is used extensively for central heating systems in buildings Advantages over hot-air systems include the absence of dust circulation and higher heat efficiency (there are no heat losses from large ducts) In very simple terms, a hydronic system could be described as a large hot-water kettle with pipe attachments to circulate the hot water and radiators to dissipate the heat Heating can be accomplished by burning gas or oil or by electricity The water usually leaves the boiler at temperatures of 80 to 90°C Hot water leaving the boiler passes through pipes, which carry it to the radiators for heat dissipation The heated water enters as feed, and the cooled water leaves the radiator Fins may be attached to the radiator to increase the surface area for efficient heat transfer Steel radiators, constructed from welded pressed steel sheets, are widely utilized in hydronic heating systems Previously, much weightier cast iron radiators were used; these are still evident in older buildings The hot-water piping is usually constructed from thin-walled copper tubing or steel pipes The circulation system must be able to cope with the water expansion result- 0765162_Ch01_Roberge 9/1/99 2:46 Page 23 Aqueous Corrosion 23 ing from heating in the boiler An expansion tank is provided for these purposes A return pipe carries the cooled water from the radiators back to the boiler Typically, the temperature of the water in the return pipe is 20°C lower than that of the water leaving the boiler An excellent detailed account of corrosion damage to steel in the hot water flowing through the radiators and pipes has been published.6 Given a pH range for mains water of 6.5 to and the E-pH diagrams in Figs 1.7 (25°C) and 1.8 (85°C), it is apparent that minimal corrosion damage is to be expected if the corrosion potential remains below 0.65 V (SHE) The position of the oxygen reduction line indicates that the cathodic oxygen reduction reaction is thermodynamically very ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; 1.6 ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; B ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; 0.8 ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; Fe(OH) ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; A Fe ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;; ;;;;;;;;;;;;;;; ;;;;; Fe(OH ;;;;;; ;;;;;;;;;;;;;;; );;;;;; ;;;;; ;;;;;;;;;;;;;;; HFeO ;;;;;;;;;;; -0.8 ;;;;;; ;;;;;; Potential (V vs SHE) Thermodynamic driving force for cathodic oxygen reduction Corrosion potential with high oxygen levels 2+ Hydrogen evolution is likely at low pH Lower oxygen - 2 Fe -1.6 10 12 14 pH Figure 1.7 E-pH diagram of iron in water at 25°C, highlighting the corrosion processes in the hydronic pH range 0765162_Ch01_Roberge 24 9/1/99 2:46 Page 24 Chapter One Potential (V vs SHE) favorable From kinetic considerations, the oxygen content will be an important factor in determining corrosion rates The oxygen content of the water is usually minimal, since the solubility of oxygen in water decreases with increasing temperature (Fig 1.9), and any oxygen remaining in the hot water is consumed over time by the cathodic corrosion reaction Typically, oxygen concentrations stabilize at very low levels (around 0.3 ppm), where the cathodic oxygen reduction reaction is stifled and further corrosion is negligible Higher oxygen levels in the system drastically change the situation, potentially reducing radiator lifetimes by a factor of 15 The undesirable oxygen pickup is possible during repairs, from additions of fresh water to compensate for evaporation, or, importantly, through design ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; 1.6 ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; B ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; 0.8 ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; Fe A ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; Fe(OH) ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; ;;;;;;;;;;;;;; ;;;;;;;;;;;;;;Fe(OH) ;;;;;;; ;;;;;;; HFeO -0.8 ;;;;;;; ;;;;;;; ;;;;;;; Fe ;;;;;;; ;;;;;;; -1.6 2+ Hydrogen evolution in low pH microenvironments - 2 10 12 pH Figure 1.8 E-pH diagram of iron in water at 85°C (hydronic system) 14 0765162_Ch01_Roberge 9/1/99 2:46 Page 25 Aqueous Corrosion 25 Oxygen Solubility (ppm) 15 20 40 60 80 o Temperature ( C) Figure 1.9 Solubility of oxygen in water in equilibrium with air at different temperatures faults that lead to continual oxygen pickup from the expansion tank The higher oxygen concentration shifts the corrosion potential to higher values, as shown in Fig 1.7 Since the Fe(OH)3 field comes into play at these high potential values, the accumulation of a red-brown sludge in radiators is evidence of oxygen contamination From the E-pH diagrams in Figs 1.7 and 1.8, it is apparent that for a given corrosion potential, the hydrogen production is thermodynamically more favorable at low pH values The production of hydrogen is, in fact, quite common in microenvironments where the pH can be lowered to very low values, leading to severe corrosion damage even at very low oxygen levels The corrosive microenvironment prevailing under surface deposits is very different from the bulk solution In particular, the pH of such microenvironments tends to be very acidic The formation of acidified microenvironments is related to the hydrolysis of corrosion products and the formation of differential aeration cells between the bulk environment and the region under the deposits (see Crevice Corrosion in Sec 5.2.1) Surface deposits in radiators can result from corrosion products (iron oxides), scale, the settling of suspended solids, or microbiological activity The potential range in which 0765162_Ch01_Roberge 26 9/1/99 2:46 Page 26 Chapter One the hydrogen reduction reaction can participate in corrosion reactions clearly widens toward the low end of the pH scale If such deposits are not removed periodically by cleaning, perforations by localized corrosion can be expected 1.2.2 Filiform corrosion Filiform corrosion is a localized form of corrosion that occurs under a variety of coatings Steel, aluminum, and other alloys can be particularly affected by this form of corrosion, which has been of particular concern in the food packaging industry Readers living in humid coastal areas may have noticed it from time to time on food cans left in storage for long periods It can also affect various components during shipment and storage, given that many warehouses are located near seaports This form of corrosion, which has a “wormlike” visual appearance, can be explained on the basis of microenvironmental effects and the relevant E-pH diagrams Filiform corrosion is characterized by an advancing head and a tail of corrosion products left behind in the corrosion tracks (or “filaments”), as shown in Fig 1.10 Active corrosion takes place in the head, which is filled with corrosive solution, while the tail is made up of relatively dry corrosion products and is usually considered to be inactive The microenvironments produced by filiform corrosion of steel are illustrated in Fig 1.11.7 Essentially, a differential aeration cell is set up under the coating, with the lowest concentration of oxygen at the head Coated alloy Tail Back of head X Front of head Head Direction of propagation Figure 1.10 Illustration of the filament nature of filiform corrosion 0765162_Ch01_Roberge 9/1/99 2:46 Page 27 Aqueous Corrosion 27 X low oxygen low pH Coating ;;;;;;;;;;; ;;;;;;;;;;; ;;;;;;;;;;; ;;;;;;;;;;; ;;;;;;;;;;; ;;;;;;;;;;; ;;;;;;;;;;; ;;;;;;;;;;; Primary Anode Primary Cathode ;;;;;;; ;;;;;;; ;;;;;;; ;;;;;;; higher oxygen higher pH Oxygen Alloy Stable Corrosion Products “Liquid Cell” Head Tail Figure 1.11 Graphical representation of the microenvironments created by filiform corrosion of the filament The oxygen concentration gradient can be rationalized by oxygen diffusion through the porous tail to the head region A characteristic feature of such a differential aeration cell is the acidification of the electrolyte with low oxygen concentration This leads to the formation of an anodic metal dissolution site at the front of the head of the corrosion filament (Fig 1.11) For iron, pH values at the front of the head of to and a potential of close to 0.44 V (SHE) have been reported In contrast, at the back of the head, where the cathodic reaction dominates, the prevailing pH is around 12 The conditions prevailing at the front and back of the head for steel undergoing filiform corrosion are shown relative to the E-pH diagram in Fig 1.12 The diagram confirms active corrosion at the front, the buildup of ferric hydroxide at the back of the head, and ferric hydroxide filling the tail In filiform corrosion damage to aluminum, an electrochemical potential at the front of the head of 0.73 V (SHE) has been report- 0765162_Ch01_Roberge 28 9/1/99 2:46 Page 28 Chapter One ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; B ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;Fe(OH) ;;;;;;;;;;;;;;;; Fe A ;;;;;;;;;;;;;;;; Back of head ;;;;;;;;;;;;;;;; high pH, cathode ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; Fe(OH ;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; ) ;;;;; HFeO ;;;;; Front of head, ;;;;; low pH, anode Hydrogen evolution ;;;;; 1.6 Potential (V vs SHE) 0.8 2+ 2 -0.8 is not possible Fe -1.6 10 12 14 pH Figure 1.12 E-pH diagram of the iron-water system with an emphasis on the microenvi- ronments produced by filiform corrosion ed, together with a 0.09-V difference between the front and the back of the head.8 Reported acidic pH values close to at the head and higher fluctuating values in excess of 3.5 associated with the tail allow the positions in the E-pH diagram to be determined, as shown in Fig 1.13 Active corrosion at the front and the buildup of corrosion products toward the tail is predicted on the basis of this diagram It should be noted that the front and back of the head positions on the E-pH diagram lie below the hydrogen evolution line It is thus not surprising that hydrogen evolution has been reported in filiform corrosion of aluminum 1.6 Potential (V vs SHE) 0.8 9/1/99 2:46 Page 29 ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; B ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; A ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; Al ;;;;;;;;; ;;;;;;;;; ;;;;;;;;; Aqueous Corrosion Al2O3.3H 2O 0765162_Ch01_Roberge Hydrogen evolution is possible -0.8 Al ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; AlO ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;;;;;;;;;;;; Back of head, higher pH, cathode Front of head, low pH, anode 3+ -1.6 29 10 12 14 pH Figure 1.13 E-pH diagram of the aluminum-water system with an emphasis on the microenvironments produced by filiform corrosion 1.2.3 Corrosion of reinforcing steel in concrete Concrete is the most widely produced material on earth; its production exceeds that of steel by about a factor of 10 in tonnage While concrete has a very high compressive strength, its strength in tension is very low (only a few megapascals) The main purpose of reinforcing steel (rebar) in concrete is to improve the tensile strength and toughness of the material The steel rebars can be considered to be macroscopic fibers in a “fiber-reinforced” composite material The vast majority of reinforcing steel is of the unprotected carbon steel type No significant 0765162_Ch01_Roberge 30 9/1/99 2:46 Page 30 Chapter One alloying additions or protective coatings for corrosion resistance are associated with this steel In simplistic terms, concrete is produced by mixing cement clinker, water, fine aggregate (sand), coarse aggregate (stone), and other chemical additives When mixed with water, the anhydrous cement clinker compounds hydrate to form cement paste It is the cement paste that forms the matrix of the composite concrete material and gives it its strength and rigidity, by means of an interconnected network in which the aggregate particles are embedded The cement paste is porous in nature An important feature of concrete is that the pores are filled with a highly alkaline solution, with a pH between 12.6 and 13.8 at normal humidity levels This highly alkaline pore solution arises from by-products of the cement clinker hydration reactions such as NaOH, KOH, and Ca(OH) The maintenance of a high pH in the concrete pore solution is a fundamental feature of the corrosion resistance of carbon steel reinforcing bars At the high pH levels of the concrete pore solution, without the ingress of corrosive species, reinforcing steel embedded in concrete tends to display completely passive behavior as a result of the formation of a thin protective passive film The corrosion potential of passive reinforcing steel tends to be more positive than about 0.52 V (SHE) according to ASTM guidelines.9 The E-pH diagram in Fig 1.14 confirms the passive nature of steel under these conditions It also indicates that the oxygen reduction reaction is the cathodic half-cell reaction applicable under these highly alkaline conditions One mechanism responsible for severe corrosion damage to reinforcing steel is known as carbonation In this process, carbon dioxide from the atmosphere reacts with calcium hydroxide (and other hydroxides) in the cement paste following reaction (1.6) Ca(OH)2  CO2 → CaCO3  H 2O (1.6) The pore solution is effectively neutralized by this reaction Carbonation damage usually appears as a well-defined “front” parallel to the outside surface Behind the front, where all the calcium hydroxide has reacted, the pH is reduced to around 8, whereas ahead of the front, the pH remains above 12.6 When the carbonation front reaches the reinforcement, the passive film is no longer stable, and active corrosion is initiated Figure 1.14 shows that active corrosion is possible at the reduced pH level Damage to the concrete from carbonationinduced corrosion is manifested in the form of surface spalling, resulting from the buildup of voluminous corrosion products at the concrete-rebar interface (Fig 1.15) A methodology known as re-alkalization has been proposed as a remedial measure for carbonation-induced reinforcing steel corro- 0765162_Ch01_Roberge 9/1/99 2:46 Page 31 Aqueous Corrosion 1.6 Potential (V vs SHE) 0.8 31 ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; B ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; Potential range ;;;;;;;;;;;;;;; Decreasing pH associated ;;;;;;;;;;;;;;; from carbonation with passive ;;;;;;;;;;;;;;; makes shift to Fe A reinforcing steel ;;;;;;;;;;;;;;; active field ;;;;;;;;;;;;;;; possible ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;; Fe O ;;;; HFeO ;;;; Re-alkalization attempts to;;;; Fe 2+ -0.8 re-establish passivity -1.6 10 12 14 pH Figure 1.14 E-pH diagram of the iron-water system with an emphasis on the microenviron- ments produced during corrosion of reinforcing steel in concrete sion The aim of this treatment is to restore alkalinity around the reinforcing bars of previously carbonated concrete A direct current is applied between the reinforcing steel cathode and external anodes positioned against the external concrete surface and surrounded by electrolyte Sodium carbonate has been used as the electrolyte in this process, which typically requires several days for effectiveness Potential disadvantages of the treatment include reduced bond strength, increased risk of alkali-aggregate reaction, microstructural changes in the concrete, and hydrogen embrittlement of the reinforcing steel It is apparent from Fig 1.14 that hydrogen reduction can occur on the reinforcing steel cathode if its potential drops to highly negative values 0765162_Ch01_Roberge 32 9/1/99 2:46 Page 32 Chapter One Cracking and spalling of the concrete cover ;;;;;; ;;;;;; ;;;;;; Stresses due to corrosion product buildup Reduced pH levels due to carbonation Voluminous corrosion products Reinforcing steel Figure 1.15 Graphical representation of the corrosion of reinforcing steel in concrete leading to cracking and spalling 1.3 Kinetic Principles Thermodynamic principles can help explain a corrosion situation in terms of the stability of chemical species and reactions associated with corrosion processes However, thermodynamic calculations cannot be used to predict corrosion rates When two metals are put in contact, they can produce a voltage, as in a battery or electrochemical cell (see Galvanic Corrosion in Sec 5.2.1) The material lower in what has been called the “galvanic series” will tend to become the anode and corrode, while the material higher in the series will tend to support a cathodic reaction Iron or aluminum, for example, will have a tendency to corrode when connected to graphite or platinum What the series cannot predict is the rate at which these metals corrode Electrode kinetic principles have to be used to estimate these rates 1.3.1 Kinetics at equilibrium: the exchange current concept The exchange current I0 is a fundamental characteristic of electrode behavior that can be defined as the rate of oxidation or reduction at an equilibrium electrode expressed in terms of current The term exchange current, in fact, is a misnomer, since there is no net current flow It is merely a convenient way of representing the rates of oxidation and reduction of a given single electrode at equilibrium, when no loss or gain is experienced by the electrode material For the corrosion of iron, Eq (1.1), for example, this would imply that the exchange cur- 0765162_Ch01_Roberge 9/1/99 2:46 Page 33 Aqueous Corrosion 33 rent is related to the current in each direction of a reversible reaction, i.e., an anodic current Ia representing Eq (1.7) and a cathodic current Ic representing Eq (1.8) Fe → Fe2  2e (1.7) Fe ← Fe2  2e (1.8) Since the net current is zero at equilibrium, this implies that the sum of these two currents is zero, as in Eq (1.9) Since Ia is, by convention, always positive, it follows that, when no external voltage or current is applied to the system, the exchange current is as given by Eq (1.10) Ia  Ic  (1.9) Ia  Ic  I0 (1.10) There is no theoretical way of accurately determining the exchange current for any given system This must be determined experimentally For the characterization of electrochemical processes, it is always preferable to normalize the value of the current by the surface area of the electrode and use the current density, often expressed as a small i, i.e., i  I/surface area The magnitude of exchange current density is a function of the following main variables: Electrode composition Exchange current density depends upon the composition of the electrode and the solution (Table 1.1) For redox reactions, the exchange current density would depend on the composition of the electrode supporting an equilibrium reaction (Table 1.2) TABLE 1.1 Exchange Current Density (i 0) for Mz+/M Equilibrium in Different Acidified Solutions (1M) Electrode Solution log10i0, A/cm2 Antimony Bismuth Copper Iron Lead Nickel Silver Tin Titanium Titanium Zinc Zinc Zinc Chloride Chloride Sulfate Sulfate Perchlorate Sulfate Perchlorate Chloride Perchlorate Sulfate Chloride Perchlorate Sulfate 4.7 1.7 4.4; 1.7 8.0; 8.5 3.1 8.7; 6.0 0.0 2.7 3.0 8.7 3.5; 0.16 7.5 4.5 0765162_Ch01_Roberge 34 9/1/99 2:46 Page 34 Chapter One TABLE 1.2 Exchange Current Density (i 0) at 25°C for Some Redox Reactions System Cr3/Cr2 Ce4/Ce3 Fe3/Fe2 H/H2 O2 reduction Electrode Material Solution Mercury Platinum Platinum Rhodium Iridium Palladium Gold Lead Mercury Nickel Tungsten Platinum Platinum 10%–Rhodium Rhodium Iridium KCl H2SO4 H2SO4 H2SO4 H2SO4 H2SO4 H2SO4 H2SO4 H2SO4 H2SO4 H2SO4 Perchloric acid Perchloric acid Perchloric acid Perchloric acid log10i0, A/cm2 6.0 4.4 2.6 7.8 2.8 2.2 3.6 11.3 12.1 5.2 5.9 9.0 9.0 8.2 10.2 TABLE 1.3 Approximate Exchange Current Density (i 0) for the Hydrogen Oxidation Reaction on Different Metals at 25°C Metal log10i0, A/cm2 Pb, Hg Zn Sn, Al, Be Ni, Ag, Cu, Cd Fe, Au, Mo W, Co, Ta Pd, Rh Pt 13 11 10 7 6 5 4 2 Table 1.3 contains the approximate exchange current density for the reduction of hydrogen ions on a range of materials Note that the value for the exchange current density of hydrogen evolution on platinum is approximately 102 A/cm2, whereas that on mercury is 1013 A/cm2 Surface roughness Exchange current density is usually expressed in terms of projected or geometric surface area and depends upon the surface roughness The higher exchange current density for the H/H2 system equilibrium on platinized platinum (102 A/cm2) compared to that on bright platinum (103 A/cm2) is a result of the larger specific surface area of the former Soluble species concentration The exchange current is also a complex function of the concentration of both the reactants and the products involved in the specific reaction described by the exchange current This function is particularly dependent on the shape of the charge transfer barrier  across the electrochemical interface 0765162_Ch01_Roberge 9/1/99 2:46 Page 35 Aqueous Corrosion 35 Surface impurities Impurities adsorbed on the electrode surface usually affect its exchange current density Exchange current density for the H/H2 system is markedly reduced by the presence of trace impurities like arsenic, sulfur, and antimony 1.3.2 Kinetics under polarization When two complementary processes such as those illustrated in Fig 1.1 occur over a single metallic surface, the potential of the material will no longer be at an equilibrium value This deviation from equilibrium potential is called polarization Electrodes can also be polarized by the application of an external voltage or by the spontaneous production of a voltage away from equilibrium The magnitude of polarization is usually measured in terms of overvoltage , which is a measure of polarization with respect to the equilibrium potential Eeq of an electrode This polarization is said to be either anodic, when the anodic processes on the electrode are accelerated by changing the specimen potential in the positive (noble) direction, or cathodic, when the cathodic processes are accelerated by moving the potential in the negative (active) direction There are three distinct types of polarization in any electrochemical cell, the total polarization across an electrochemical cell being the summation of the individual elements as expressed in Eq (1.11): total  act  conc  iR (1.11) where act  activation overpotential, a complex function describing the charge transfer kinetics of the electrochemical processes act is predominant at small polarization currents or voltages conc  concentration overpotential, a function describing the mass transport limitations associated with electrochemical processes conc is predominant at large polarization currents or voltages iR  ohmic drop iR follows Ohm’s law and describes the polarization that occurs when a current passes through an electrolyte or through any other interface, such as surface film, connectors, etc Activation polarization When some steps in a corrosion reaction con- trol the rate of charge or electron flow, the reaction is said to be under activation or charge-transfer control The kinetics associated with apparently simple processes rarely occur in a single step The overall anodic reaction expressed in Eq (1.1) would indicate that metal atoms 0765162_Ch01_Roberge 36 9/1/99 2:46 Page 36 Chapter One in the metal lattice are in equilibrium with an aqueous solution containing Fe2 cations The reality is much more complex, and one would need to use at least two intermediate species to describe this process, i.e., Felattice → Fesurface Fesurface → Fe2 surface Fe2 → Fe2 surface solution In addition, one would have to consider other parallel processes, such as the hydrolysis of the Fe 2 cations to produce a precipitate or some other complex form of iron cations Similarly, the equilibrium between protons and hydrogen gas [Eq (1.2)] can be explained only by invoking at least three steps, i.e., H  → Hads Hads  Hads → H2 (molecule) H2 (molecule) → H2 (gas) The anodic and cathodic sides of a reaction can be studied individually by using some well-established electrochemical methods in which the response of a system to an applied polarization, current or voltage, is studied A general representation of the polarization of an electrode supporting one redox system is given in the Butler-Volmer equation (1.12): ireaction  i0 exp  exp    (1   reaction reaction  nF reaction  RT nF ) reaction RT  (1.12) where i reaction  anodic or cathodic current  reaction  charge transfer barrier or symmetry coefficient for the anodic or cathodic reaction, close to 0.5 reaction  Eapplied  Eeq, i.e., positive for anodic polarization and negative for cathodic polarization n  number of participating electrons R  gas constant T  absolute temperature F  Faraday 0765162_Ch01_Roberge 9/1/99 2:46 Page 37 Aqueous Corrosion 37 When reaction is anodic (i.e., positive), the second term in the ButlerVolmer equation becomes negligible and ia can be more simply expressed by Eq (1.13) and its logarithm, Eq (1.14):   nF ia  i0 exp a a RT  (1.13)   i a  ba log10 a i0 (1.14) where ba is the Tafel coefficient that can be obtained from the slope of a plot of against log i, with the intercept yielding a value for i0 RT ba  2.303 nF (1.15) Similarly, when reaction is cathodic (i.e., negative), the first term in the Butler-Volmer equation becomes negligible and ic can be more simply expressed by Eq (1.16) and its logarithm, Eq (1.17), with bc obtained by plotting versus log i [Eq (1.18)]: ic  i0 nF   exp (1   ) RT   i  b log   i c c c c 10 c (1.16) (1.17) RT bc  2.303 nF (1.18) Concentration polarization When the cathodic reagent at the corroding surface is in short supply, the mass transport of this reagent could become rate controlling A frequent case of this type of control occurs when the cathodic processes depend on the reduction of dissolved oxygen Table 1.4 contains some data related to the solubility of oxygen in air-saturated water at different temperatures, and Table 1.5 contains some data on the solubility of oxygen in seawater of different salinity and chlorinity.10 Because the rate of the cathodic reaction is proportional to the surface concentration of the reagent, the reaction rate will be limited by a drop in the surface concentration For a sufficiently fast charge transfer, the surface concentration will fall to zero, and the corrosion process will be totally controlled by mass transport As indicated in Fig 1.16, mass transport to a surface is governed by three forces: dif- 0765162_Ch01_Roberge 38 9/1/99 2:46 Page 38 Chapter One TABLE 1.4 Solubility of Oxygen in Air-Saturated Water Temperature, °C Volume, cm3* Concentration, ppm Concentration (M), mol/L 10 15 20 25 30 10.2 8.9 7.9 7.0 6.4 5.8 5.3 14.58 12.72 11.29 10.00 9.15 8.29 7.57 455.5 397.4 352.8 312.6 285.8 259.0 236.7 *cm3 per kg of water at 0°C TABLE 1.5 Oxygen Dissolved in Seawater in Equilibrium with a Normal Atmosphere Chlorinity,* % 10 15 20 Salinity,† % 9.06 18.08 27.11 36.11 11.89 10.49 9.37 8.46 7.77 7.04 6.41 11.00 9.74 8.72 7.92 7.23 6.57 5.37 Temperature, °C 10 15 20 25 30 ppm 14.58 12.79 11.32 10.16 9.19 8.39 7.67 13.70 12.02 10.66 9.67 8.70 7.93 7.25 12.78 11.24 10.01 9.02 8.21 7.48 6.80 *Chlorinity refers to the total halogen ion content as titrated by the addition of silver nitrate, expressed in parts per thousand (%) †Salinity refers to the total proportion of salts in seawater, often estimated empirically as chlorinity 1.80655, also expressed in parts per thousand (%) fusion, migration, and convection In the absence of an electric field, the migration term is negligible, and the convection force disappears in stagnant conditions For purely diffusion-controlled mass transport, the flux of a species O to a surface from the bulk is described with Fick’s first law (1.19), CO JO  DO x   (1.19) where JO  flux of species O, mol  s1  cm2 DO  diffusion coefficient of species O, cm2  s1 CO  concentration gradient of species O across the interface, x mol  cm4 The diffusion coefficient of an ionic species at infinite dilution can be estimated with the help of the Nernst-Einstein equation (1.20), which relates DO to the conductivity of the species (O): 0765162_Ch01_Roberge 9/1/99 2:46 Page 39 Aqueous Corrosion 39 Fe2+ Fe2+ 2e- e- e- H+ diffusion H+ Mass transport migration convection H+ H+ exchange current density (i ) Charge transfer Tafel slope (b) activation barrier () Figure 1.16 Graphical representation of the processes occurring at an electrochemical interface RTO DO  |zO|2F (1.20) where zO  the valency of species O R  gas constant, i.e., 8.314 J  mol1  K1 T  absolute temperature, K F  Faraday’s constant, i.e., 96,487 C  mol1 Table 1.6 contains values for DO and O of some common ions For more practical situations, the diffusion coefficient can be approximated with the help of Eq (1.21), which relates DO to the viscosity of the solution  and absolute temperature: TA DO  (1.21)  where A is a constant for the system 0765162_Ch01_Roberge 40 Conductivity and Diffusion Coefficients of Selected Ions at Infinite Dilution in Water at 25°C |z| , S  cm2  mol1 H 349.8 Li 38.7 Na K 1 50.1 73.5 D 105, cm2  s1 Anion |z| , S  cm2  mol1 D 105, cm2  s1 9.30 OH 197.6 5.25 1.03 F 55.4 1.47 1.33 Cl 76.3 2.03 1.95 NO3 71.4 1.90  Ca2 119.0 0.79 ClO4 67.3 1.79 Cu2 107.2 0.71 SO42 160.0 1.06 Zn2 105.6 0.70 CO32 138.6 0.92 2.26 HSO4 50.0 1.33 2.44 HCO31 41.5 1.11 O2 H2O — — — — Page 40 Cation 9/1/99 2:46 TABLE 1.6 0765162_Ch01_Roberge 9/1/99 2:46 Page 41 Aqueous Corrosion 41 The region near the metallic surface where the concentration gradient occurs is also called the diffusion layer Since the concentration gradient CO/x is greatest when the surface concentration of species O is completely depleted at the surface (i.e., CO  0), it follows that the cathodic current is limited in that condition, as expressed by Eq (1.22): CO,,bulk ic  iL  nFDO (1.22) For intermediate cases, conc can be evaluated using an expression [Eq (1.23)] derived from the Nernst equation:  2.303RT i conc  log10  nF iL  (1.23) where 2.303RT/F  0.059 V when T  298.16 K Ohmic drop The ohmic resistance of a cell can be measured with a milliohmmeter by using a high-frequency signal with a four-point technique Table 1.7 lists some typical values of water conductivity.10 While the ohmic drop is an important parameter to consider when designing cathodic and anodic protection systems, it can be minimized, when carrying out electrochemical tests, by bringing the reference electrode into close proximity with the surface being monitored For naturally occurring corrosion, the ohmic drop will limit the influence of an anodic or a cathodic site on adjacent metal areas to a certain distance depending on the conductivity of the environment For naturally occurring corrosion, the anodic and cathodic sites often are adjacent grains or microconstituents and the distances involved are very small TABLE 1.7 Resistivity of Waters Water Pure water Distilled water Rainwater Tap water River water (brackish) Seawater (coastal) Seawater (open sea) ,   cm 20,000,000 500,000 20,000 1000–5000 200 30 20–25 ... Filiform corrosion Filiform corrosion is a localized form of corrosion that occurs under a variety of coatings Steel, aluminum, and other alloys can be particularly affected by this form of corrosion, ... lowest concentration of oxygen at the head Coated alloy Tail Back of head X Front of head Head Direction of propagation Figure 1.10 Illustration of the filament nature of filiform corrosion 0765162_Ch01_Roberge... the head of the corrosion filament (Fig 1.11) For iron, pH values at the front of the head of to and a potential of close to 0.44 V (SHE) have been reported In contrast, at the back of the head,