Calculation of Seawater pH at Polarized Metal Surfaces in the ...

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Calculation of Seawater pH at Polarized Metal Surfaces in the Presence of Surface Films✫ S.C. Dexter and S.H. Lin*

ABSTRACT A model was developed for calculating the pH at a cathodically polarized metal surface. The model accounts for the buffering capacity and ionic strength of seawater, and it is valid in the presence of uniformly distributed calcareous, biological, or corrosion-product-type surface films. The model does not yet account for hydrogen evolution, and it cannot directly handle chemical reactions or the metabolic activities of microorganisms within the film. Calculated pH values are dependent on applied current density, film thickness, and the various diffusion coefficients. A diffusion correction factor is used to modify diffusion coefficients within the film. The model predicts increasing pH with increasing applied current density and film thickness, reaching a maximum of 9.9 at the limiting diffusion current for oxygen under quiescent flow conditions with no hydrogen evolution. Direct measurements of pH by microelectrode techniques were in agreement with model predictions at an applied current of 20 µA/cm2. Measured pH values were higher than calculated at 100 µA/cm2, the difference due to hydrogen evolution. KEY WORDS: pH, cathodic protection, seawater, biofilm, calcareous deposit, mathematical model

INTRODUCTION Cathodic protection has long been recognized as an effective corrosion control method, especially in sea-

✫

Submitted for publication November 1990; in revised form, August 1991. *University of Delaware, College of Marine Studies, Lewes, DE 19958.

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water where conductivity is sufficient for a reasonably uniform current distribution. In addition, the inorganic chemistry of seawater permits the formation of beneficial calcareous deposits on the metal surface during cathodic protection. Many researchers have worked to understand the formation of calcareous deposits.1-5 The major factors that influence calcareous deposition, such as temperature,6-8 velocity of flow,9-12 surface preparation,13 applied potential and current,5,14 and pH4,15 are also well known. The ability of an applied current to change the pH at the metal surface is one of the most important factors in calcareous deposition. Thus, it is not surprising that several models have been developed for calculating the surface pH under cathodic protection conditions. Engell and Forchhammer16 and Wolfson and Hartt7 formulated models to calculate the pH at a bare metal surface based on the rate of cathodic oxygen reduction. In these models, the total amount of OH– ions generated (proportional to applied current) was used to calculate the high pH. However, in seawater, some of the OH– must be used to convert HCO3– to CO3–2 before a dramatic change in pH can occur. The pH values predicted by these models are a full pH unit higher than that of direct measurements.18 Thus, the buffering capacity must be considered when developing an interface pH model to be used in seawater. Sadasivan19 developed a model that predicts the current density during calcareous deposition. In his model, mass balances were set up, and a concentration profile in the diffusion boundary layer was calculated using a finite element technique. However,

0010-9312/92/000015/$3.00/0 National Association of Corrosion Engineers

CORROSION–JANUARY 1992

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the buffering capacity and high ionic strength of seawater and the activities of the chemical species involved still were omitted. In the present work, a model was developed to calculate the pH at the surface of a cathodically protected metal electrode in the presence of surface films (both calcareous and biological), taking into account the buffering capacity and ionic strength of seawater. The model accounts for the physical effects of surface films, but it does not yet account for chemical reactions or metabolic activity of organisms within the film.

INTERFACE pH MODEL Under cathodic protection conditions in seawater, three cathodic reactions occur that cause an increase in pH at the metal surface. These are: Oxygen reduction: O 2 + 2H 2 O + 4e – → 4OH –

(1)

Hydrogen evolution: 2H 2 O + 2e – → H 2 (g) + 2OH – (2) Peroxide production: O2 + 2H2O + 2e– → H2O2 + 2OH–

(3)

In seawater, a change in pH also means a change in the concentrations of all the species in the CO2 system, according to Equations (4) and (5) below.20 CO 2 + H 2O = H+ + HCO –3

K'1 =

(4)

a H [HCO–3 ] [CO2 ]

HCO 3– = H + + CO 3–2 K'2 =

(5)

a H [CO–2 ] 3 [HCO–3 ]

where K’1 and K’2 are the apparent first and second equilibrium constants of carbonic acid, and aH is the activity of hydrogen ions (aH = 10–(pH)). The apparent equilibrium constants for carbonic acid, as calculated from the concentrations of CO2, CO3–2, and HCO3– rather than the activities, were used because of the difficulties in obtaining the activities of the various carbon species required for the true equilibrium constants. The model was developed to be valid under the following set of conditions: (1) oxygen reduction is the major cathodic reaction, and hydrogen evolution is neglected; (2) any surface films are distributed uniformly, and their physical presence provides a diffusion barrier resulting in sharp concentration gradients through the film; (3) transport of oxygen and other chemical

CORROSION–Vol. 48, No. 1

species to the metal surface is a diffusion-controlled process; and (4) total titration alkalinity is constant. Thus, the model as presently formulated was not meant to account for either the hydrogen evolution expected at very negative potentials or the metabolic activity of the organisms in a biofilm. Suggestions have been made later in the paper as to how such capabilities could be added to the model. Upon cathodically protecting an electrode having a surface film, two distinct diffusion zones can be defined (Figure 1). These are the film itself and the liquid diffusion zone (or boundary layer) between the film surface and the bulk solution. Within the film and diffusion zones, the concentration profiles of the various chemical species follow Fick’s diffusion law, while in the bulk solution, the concentrations are assumed to be constant. An increase in pH at the metal surface (according to Equations [4] and [5]) should result in a high CO3–2 concentration but low HCO3– and CO2 concentrations. Thus, one would expect species CO3–2 and OH–, which are being produced at the interface, to diffuse away from the metal surface, while species CO2 and HCO3– should diffuse toward the metal surface. These expectations are reflected in the directions of the arrows in Figure 1. The concentrations of species X at the metal surface and at the film surface are shown as [X]m and [X] f, while the diffusion fluxes of these species within the film and diffusion zones are shown as J (X)f and J (X)d, respectively. At steady state, the amount of any species diffusing into a zone must equal the amount diffusing out, and the concentration of that species must be continuous across the zone boundaries. The positive direction in this work has been defined as being toward the bulk solution. The model was based on charge and mass balances at the interface between film and diffusion zones. All species are able to diffuse across the film surface; however, only those species involved in the cathodic reaction (Equation [1]) or the CO2 buffering system were considered important for the purposes of this model in calculating the interface pH. Thus, the charge balance can be expressed as: J (OH)f – J (HCO3)d + 2J (CO3)f = 4J (O 2 ) f – J (HCO 3 ) f + J (OH) d + 2J (CO 3 ) d (6) The carbon balance can be expressed as: J (CO3)f – J (HCO3)d – J (CO2)d = – J (HCO 3 ) f – J (CO 2 ) f + J (CO 3 ) d

(7)

where J (X) is the diffusion flux of species X and the subscripts d and f indicate action in the diffusion and film zones, respectively. 51

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The flux, J (X)d, in the diffusion layer follows Fick’s first law: J (X)d = D (X)

{

}

[X]f – [X] d

(8)

where D (X) is the diffusion coefficient of species X, [X] f, and [X] are the concentrations at the film surface and in the bulk solution, respectively, and d is the thickness of the diffusion layer. One might consider including the hydrogen diffusion flux in Equations (6) and (7), but it has been neglected in this edition of the model. To calculate the diffusive fluxes of OH–, HCO3–, CO3–2, CO2, and O2 in the expressions for the charge and carbon balances, the concentrations of these species in the bulk solution and at the metal and film surfaces are needed. These concentrations can be calculated from Equations (9) through (12) using measured values of the pH, temperature, alkalinity, and salinity of the bulk solution.21 -

[OH ] =

[CO2 ] =

a 2H (TA) a H (K 1' ) + (2K '1 ) (K '2

[HCO –3 ] =

[CO–2 ]= 3

(K 'w ) f H aH

a H (K ' 1 ) (TA) a H (K 1' ) + (2K '1 ) (K 2' ) (K ' 1 ) (K '2 ) (TA)

a H (K '1 ) + (2K '1 ) + (K 2' )

(9)

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DOHf{[OH]m – [OH]f} DHCO3d {[HCO3]f – [HCO3]} – f d

(10) +

(11)

+

2DCO3f {[CO3]m – [CO3]f} 4DO2f{[O2]m – [O2]f} + f f

DHCO3f {[HCO3]m – [HCO3]f} DOHd{[OH]f – [OH]} – f d –

(12)

where K’w is the apparent ionization constant of seawater, as defined22 by the product of the concentrations of OH– and H+. TA is the total titration alkalinity, while fH and fOH are the activity coefficients22 of hydrogen and hydroxile ions, respectively, in seawater. The K’ values are as defined by Equations (4) and (5) and are available from the literature20 for given values of temperature and salinity and corrected for the activity coefficients of CO2, HCO3–, and CO3–2. The total titration alkalinities at the metal and film surfaces have been assumed to be equal to those in the bulk solution. The oxygen concentration at the film surface is related to the applied current density, i, by the following equation: i = 4F (DO 2 ) (O 2 – O 2f ) / d

where F is Faraday’s constant, DO2 is the diffusion coefficient of oxygen in the bulk solution, O2 and O2f are the oxygen concentrations in the bulk solution and at the film surface, respectively, and d is as defined previously. The value of d reasonably can be assumed to be 200 µm for a quiescent solution. The oxygen concentration at the metal surface (O2m) can also be calculated from Equation (13), if the appropriate diffusion coefficient for oxygen in the film is known, and the thickness of the film, f, is estimated or measured. The objective of this work was to calculate the pH at the metal surface, and perhaps at the film surface as well, as functions of bulk water chemistry, applied current density, and the properties of the film. This has been done using Equations (4) through (13). First, the diffusion fluxes in Equations (6) and (7) were replaced with their equivalent expressions involving the diffusion coefficients, concentrations, and film thicknesses from Equation (8). For simplicity, the chemical species OH–, O2, CO2, HCO3–, and CO3–2 will be represented by OH, O 2, CO2, HCO3, and CO3, respectively. Doing this yields:

2DCO3d {[CO3]f – [CO3]} =0 d

and DCO3 f {[CO3]m – [CO3] f } f

–

DHCO3d {[HCO3]f – [HCO3]}

+

DHCO3f {[HCO3]m – [HCO3]f }

– (13)

(14)

d

f

DCO3d {[CO3]f – [CO3]} =0 d

(15)


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tion (17) into Equation (16). Writing out the equation, rearranging and regrouping by order of terms, one obtains the following fourth order polynomial equation: C4 (aHm)4 + C3 (aHm)3 + C2 (aHm)2 + C1 (aHm) + C = 0 (18) The H+ activity and hence the pH at the metal surface can be calculated from Equation (18) by an iterative technique provided that the values of the physical, chemical, and electrochemical parameters in the coefficients C to C4 are known or can be measured.

VALUES FOR THE PARAMETERS

FIGURE 1. Schematic diagram of the film and diffusion zones adjacent to a cathodically protected metal surface. The concentrations and diffusion fluxes shown are as defined in the text.

At pH values of 8 and above, typical of seawater, the speciation of the carbonic acid system23 is such that 93% of the total inorganic carbon is present as HCO3–, 6% as CO3–2, and only 1% as CO2. Thus, the two terms in Equation (7) involving diffusion fluxes of CO2 were considered insignificant and have been neglected in Equation (15). Now substituting in Equations (14) and (15) the expressions for the concentrations of the various species in Equations (9) through (13) and rearranging,24 one obtains the following two equations involving the activity of hydrogen ions at the film, aHf, and metal, aHm, surfaces. From Equation (14) one obtains A1 (aHm2 aHf2) + A2 (aHm2aHf ) + A3 (aHmaHf2 ) + A4 (aHmaHf ) + A5 (aHm2 ) + A6 (aHf2 ) + A 7 (a Hm ) + A 8 (a Hf ) = 0

(16)

From Equation (15) one obtains

aHf =

B1 ( aHm ) – B2 B3 ( aHm ) + B4

(17)

where the coefficients A1 to A8 and B1 to B4 are complicated algebraic functions of the applied current density, total alkalinity, and the various equilibrium constants and diffusion coefficients. The activity of H+ at the metal surface now can be calculated by substituting the value for a Hf from Equa-


To calculate the pH at the metal surface from Equation (18), values are needed for: (1) The diffusion coefficients of OH–, HCO3–, -–2 CO3 , CO2, and O2 in the bulk solution and in the film; (2) The first and second equilibrium constants, K’1 and K’2, of carbonic acid as defined in Equations (4) and (5); (3) The ionization constant of seawater, K’w, and the activity coefficients of H+ and OH–; (4) The thicknesses of the film and the diffusion layer; and (5) The pH, total alkalinity, dissolved O2 concentration, temperature, and salinity of the bulk water and the applied current density. Consider each of the above parameters. The tracer diffusion coefficients for OH–, HCO3–, and CO3-–2 in the bulk solution were obtained from Li and Gregory,25 and those for CO2 and O2 from Lerman.26 The diffusion coefficients of these species in the film, however, will vary from those in the bulk solution due to differences in the viscosity, porosity, and tortuosity within the film and interactions between the film and the diffusing species. Several works reported in the literature were helpful in determining the result of such effects. Li and Gregory found that the apparent diffusion coefficients for the ions Cl –, Na+, SO4-–2, and Ca+2 in red clay were 20 to 50% of the free-solution diffusion coefficients in seawater. LaMotta found that the effective diffusivities of glucose within a porous biological slime were 19.5 to 50.5 percent of the molecular diffusivities in water.27 Aller measured the diffusion coefficients of inorganic solutes within organic materials from eight species of marine invertebrates to be 10 to 40 percent of their values in pure water.28 The general consistency of these data from the literature has led us to take the approach of Bungay and coworkers29 and define a diffusion correction factor, , with which to modify the bulk diffusion coefficients for the effect of the film. Thus, the diffusion coefficients 53

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used for the species, OH–, HCO3–, CO3–2, CO2, and O2, in the film were those for the bulk fluid, modified by the correction factor ranging from 0.1 to 0.5. In the results shown in this paper, we have applied a single value of uniformly to all diffusing species. Individual values of for each diffusing species could be used without changing the model if data were available on which to base the choice of the individual values. Values of the diffusion correction factor will be independent of film thickness as long as the film is homogeneous. If, however, the film is layered (e.g., biofilm on top of calcareous deposit) then two film zones would have to be defined, each with its own properties. The values of the first and second equilibrium constants for carbonic acid, K’1 and K’2, were taken from the work of Milero.20 He measured these values directly from seawater of a given temperature and salinity, and he corrected them for the activity coefficients of CO2, HCO3–, and CO3–2. The ionization constant K’w of seawater was defined as the product of the concentrations of OH– and H+. The value of this constant, along with the values of the activity coefficients of H+ and OH– in seawater (fH and fOH, respectively) were taken from the work of Culberson and Pytkowicz.22 The thickness of the film could be measured directly by any one of several methods. For the results shown in this paper, we have used film thicknesses ranging from 20 to 100 µm. The thickness of the boundary diffusion layer has been assumed to be 200 µm for a quiescent solution. Values different from these could be used as needed for other hydrodynamic conditions. The bulk water properties and

FIGURE 2. Calculated pH values at the metal surface of a filmed electrode as a function of applied current density and diffusion correction factor, . Film thickness = 20 µm, and diffusion layer thickness = 200 µm.

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applied current density (mentioned in [5] above) typically would be measured directly by conventional methods. The values used to generate the results shown in the next section are those typical of fullstrength open-ocean seawater.23

RESULTS FROM THE MODEL Figure 2 shows computer-calculated pH values for a cathodically protected metal surface in seawater of 35 ppt salinity at 25°C as a function of applied current density and diffusion correction factor in the presence of a 20-µm-thick film. The model predicts that interface pH increases with increasing applied current density and with decreasing value. This is reasonable because a decreasing value indicates an increasing resistance of the film to outward diffusion of OH– (i.e., a higher interface pH). The model predicts a maximum pH of about 9.9 even at low and high applied current density. Under these conditions, the oxygen diffusion flux to the surface becomes limiting, and the pH will reach a plateau unless another cathodic reaction occurs. Calculations from the model show little effect of the film until reaches approximately 0.5 and then a substantial effect for values below that as shown in Figure 2. At an average diffusion correction factor of = 0.3, the calculated pH at the metal surface is shown for various film thicknesses and applied current densities in Figure 3. These results reveal that with all other factors held constant, the interface pH increases with film thickness. This agrees with our expectation that a

FIGURE 3. Calculated pH values at the metal surface of a filmed electrode as a function of film thickness and applied current density for = 0.3.


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FIGURE 4. Calculated pH values at the film surface as a function of applied current density and . Film thickness = 20 µm, and diffusion layer thickness = 200 µm.

FIGURE 6. Calculated oxygen concentration profiles near the metal surface at applied current densities of 20, 50, and 100 µA/cm2. Film thickness = 20 µm, diffusion layer thickness = 200 µm, and = 0.3.

FIGURE 7. Calculated OH– concentration profiles near the metal surface at applied current densities of 20, 50, and 100 µA/cm2. Film thickness = 20 µm, diffusion layer thickness = 200 µm, and = 0.3.


FIGURE 5. Calculated pH values at the film surface as a function of film thickness and applied current density for = 0.3.

thick film should retain more of the OH– ions produced than a thin film of the same properties. The data in Figure 3 represent an average value for the diffusion correction factor and cover the general range of film thicknesses and current densities used in cathodic protection. Thus, it should be useful in predicting interface pH values under conditions in which hydrogen evolution is not significant. The model was also used to predict the pH at the film-water interface. These results are shown as a function of applied current density in Figure 4 and film thickness in Figure 5. These data show that the model predicts an increasing film surface pH with increasing applied current density, increasing and decreasing film thickness. Note that the effects of and of film thickness on pH at the film surface are opposite to their effects on pH at the metal surface. The more efficiently OH– ions are retained in the vicinity of the metal surface, the more the pH is changed there, but the less it is changed on the outside of the film. Using the interface pH values predicted from the model, the concentrations of each of the chemical species involved in the charge and carbon balances at the metal and film surfaces could also be calculated. Thus, the concentration profiles vs distance from the metal surface are shown for O2 (Figure 6), OH– (Figure 7), HCO3– (Figure 8), and CO3–2 (Figure 9). In each case, the profiles are shown for applied current densities of 20, 50, and 100 µA/cm2, and the calculations were done for film and diffusion layer thicknesses of 20 and 200 µm and a diffusion correction factor of = 0.3. Note that most of the change in concentration for O2 and OH– takes place within the film, while most of the change for HCO3– and CO3–2 takes place within the liquid diffusion layer. 55

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FIGURE 9. Calculated CO3–2 concentration profiles near the metal surface at applied current densities of 20, 50, and 100 µA/cm2. Film thickness = 20 µm, diffusion layer thickness = 200 µm, and = 0.3. FIGURE 8. Calculated HCO3– concentration profiles near the metal surface at applied current densities of 20, 50, and 100 µA/cm2. Film thickness = 20 µm, diffusion layer thickness = 200 µm, and = 0.3.

COMPARISON TO MEASURED VALUES Several pH measurements near the metal surface were made using microelectrode techniques. A micro pH-sensitive glass electrode of tip diameter 200 µm was made at Montana State University for the authors, and the pH measurements reported in this paper were made at the Center for Interfacial Microbial Process Engineering at Montana State using that electrode. The pH-sensitive glass tip was recessed within an outer sheath of lead glass, which was brought into contact with the metal surface by a micromanipulator. During a measurement, the distance between the metal surface and the curved bulb of the pH-sensitive glass tip was estimated to be between 50 and 100 µm, and the measurement represents an average over the surface of the tip. An electrometer was used to measure the potential difference between the pH-sensitive glass tip and a saturated calomel reference electrode. Measurements were made at five-minute intervals within a period of 30 min. The electrode was calibrated using pH 4 and 7 buffer solutions before the start of each series of six measurements. The amount of recalibration was always below 0.1 pH unit. Thus, each of the pH values reported here is the average of six measurements. The error shown for each measurement was ±0.1 pH unit, corresponding to the largest recalibration increment, rather than to the stan56

dard deviation of the measurements themselves, which was smaller. Values of pH near the surface of both bare and filmed metal electrodes were measured under cathodic protection conditions. The measurements were made in a NaCl/NaHCO3 solution, prepared to have the same ionic strength and buffering capacity as seawater, but without the microorganisms to prevent biofilm formation during the measurement and without calcium and magnesium ions to prevent calcareous deposition. The solution was open to the atmosphere during the pH measurements but was not actively stirred or aerated. The specific metal surface used was that of the nickel-based superalloy C-276, which forms a stable passive film and is not susceptible to localized corrosion initiation in Cl– containing media. Filmed electrodes were prepared by mixing a culture of the marine bacterium, Vibrio harveyi, with 2% marine agar in 3% NaCl and brushing this mixture onto the C-276 electrode surface. The density of the stock bacterial culture was 109 cells per mL of solution, and this was diluted six times in making the agar mixture. Thus, the density of bacterial cells in the agar film was in the 108 cells per mL range. Measurement of pH on a given electrode was always finished within three hours of the time the bacteria were mixed with the agar. The thickness of the film was estimated to be about 4000 µm by measuring the distance between the outer part of the film and the metal surface using a micromanipulator. Measurements of pH were taken at galvanostatically applied current densities of 20 and 100 µA/cm2. The results of the pH measurements are shown in Table 1. With no applied current, there was no mea-


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surable pH difference between the filmed and bare electrodes under these conditions, and the free corrosion potentials of the two electrodes were similar (within normal scatter). Note that these were shortterm laboratory measurements. Thus, the authors do not believe that the result should be used to imply anything about the ability of natural population organisms to change the pH at a metal surface exposed in the field for longer times. The data show that the measured interfacial pH increased with applied current density on both the bare and filmed electrodes. The increase in pH was higher on the filmed than on the bare electrodes at each of the applied current density levels. The rate of pH increase was higher for all electrodes at the low current density level. The potential of each electrode was monitored during these experiments, and these data also are shown in Table 1. At each current density level, the shift in potential was greater on the filmed than on the bare electrodes. At the two most negative potentials, corresponding to a current density of 100 µA/cm2, gas bubbles were observed to form at the metal surface and were trapped within the agar on the filmed electrode. It is presumed that the gas formed was hydrogen, although this was not directly confirmed. Figure 10 shows the data from Table 1 plotted along with predictions from the model for: (1) a bare metal surface, (2) a surface covered with a 100-µm thick biofilm with = 0.5, and (3) a surface covered with a 50-µm-thick calcareous deposit with = 0.1. For an applied current density of 20 µA/cm2, the measured values of pH for both the bare (solid circle) and biofilmed (solid triangle) surfaces are in general agreement with the model predictions. At the high applied current density, however, the measured values are considerably more basic than those predicted by the model.

DISCUSSION The significance of this model in comparison to its predecessors is that it accounts for the buffering capacity and ionic strength of seawater, and it is valid in the presence of surface films rather than just at the bare metal surface. Consider the limitations of the model based on the conditions stated earlier under which it was formulated. The first condition was that oxygen reduction was the major cathodic reaction. This is probably valid under aerated seawater conditions at low applied cathodic current density, where the oxygen diffusion flux can keep up with demand, and the electrode potential is more positive than approximately –0.7 V SCE (the value below which hydrogen evolution is thermodynamically possible at pH 8). At more negative (active) potentials and higher


current densities, oxygen transport to the cathodic surface gradually becomes diffusion limited. If the applied current is able to polarize the electrode to a potential more active than about –1.0 V SCE, a significant amount of hydrogen evolution is likely to occur. This was observed in the present work on the filmed electrode at a current density of 100 µA/cm2. Thus, as shown in Figure 10, the model, which does not account for hydrogen evolution, underestimated the metal surface pH at the high current density. This deficiency in the model could be corrected by adding an additional diffusion flux corresponding to the amount of OH– generated by hydrogen evolution to the charge balance in Equation (6). The formation of hydrogen gas bubbles within the film may give rise to two other effects that are not accounted for in the model. First, the bubbles may physically block the diffusion pathway for chemical species migrating both to and from the metal surface. Second, the formation of hydrogen gas at the cathodic surface can disrupt the formation of the calcareous deposit layer.30-32 Both of these effects would invalidate the results of the model if bubble formation was extensive. The second condition was that any films present would be uniformly distributed over the metal surface and that they would act as a diffusion barrier. The condition of uniform coverage is approached on surfaces with mature biofilms or well-developed calcareous deposits. On surfaces where the film provides spotty coverage, the model will give only an average value for the interface pH. That average pH value may or may not be meaningful. Any film will act as a diffusion barrier for that portion of the surface it covers. A complication, which the model cannot yet directly handle, arises when the film becomes an active source or sink for any of the chemical species in Equations (6) and (7). Thus, the model does not yet have the capability to account for the metabolic production or use of species such as oxygen or CO2 by microorganisms within the biofilm. For most bacteria, growth is seriously TABLE 1 Interface pH and Potential as Measured on Bare and Agar-Filmed Electrodes Galvanostatically Protected at Current Densities of 20 and 100 µA/cm2 Current Density

Bare

Agar and V. harveyi filmed

0

8.2 ± 0.1 –250

8.2 ± 0.1 –290

20

9.0 ± 0.1 –650

9.4 ± 0.1 –820

100

10.2 ± 0.1 –970

10.4 ± 0.1 –1030

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FIGURE 10. Values of pH calculated from the model as compared to measured pH values (solid points). Bare Surface

Diff. layer thickness (µm) Film thickness (µm) Diff. correction factor

200 1 1.0

BioCalcareous Filmed Filmed

200 100 0.5

200 50 0.1

limited33 at pH values above 9. Data from the model for an average diffusion correction factor of = 0.3 (Figure 3) indicate that pH 9.5 at the metal interface is achieved at a film thickness of 60 µm for an applied current of 20 µA/cm–2 and less than 10 µm at 100 µA/ cm–2. Thus, for applied current densities above 20 µA/ cm–2, including most practical cathodic protection currents, bacterial metabolism should not be a serious problem. For current densities below 20 µA/cm–2, corresponding to those sometimes used for protecting stainless alloys from pitting, bacterial metabolism may influence the interface pH in ways not accounted for by the model. Evidence that bacterial activity can influence cathodic protection at low applied current densities is found in the works of Johnsen and Bardal34 and Dexter and Lin.35 Johnsen and Bardal found that the current density for maintaining stainless alloys in the 300 to 500 mV SCE range increased dramatically in natural seawater, and they attributed this to the action of a biofilm on the metal surface. Dexter and Lin found that an applied current density of 20 µA/ cm2 was unable to maintain the potential of a stainless alloy in the protected range once a biofilm had formed. Low applied current conditions may also be experienced in regions of restricted geometries such as in crevices and under disbonded coatings. The model is not expected to give valid results in such locations, especially in the presence of large populations of microorganisms. 58

The third condition was that transport of oxygen is diffusion controlled. Two sets of conditions can occur under which this is not valid. The first involves nonsteady-state flow conditions in which the thickness of the diffusion boundary layer is changing with flow velocity or is under the influence of localized turbulence. The other condition occurs when the film becomes an active source or sink for one of the chemical species in the charge or carbon balance equations. For example, an actively metabolizing biofilm may either consume or produce oxygen. Such effects are not currently accounted for in the model. Conceivably, production or consumption of oxygen by the microorganisms in the film could be modeled as an effect on the oxygen diffusion coefficient. Thus, it could be included in the value of the diffusion correction factor for oxygen. However, this would require another level of complexity in the model, as separate values of would have to be used for each diffusing species, rather than the overall value that is currently used. The final condition was that the total titration alkalinity remains constant. Two effects need to be considered here. First is the ability of microorganisms in the film to use or produce CO2, and second is the removal of CO3–2 in the calcareous deposition process. Generation or consumption of CO2 gas by the organisms within the biofilm is not expected to change the total alkalinity21,31 because that process is separate from the carbonic acid buffering system of the water. However, the removal of CO3–2 in the calcareous deposition process (or by bacteria) will change the alkalinity. Thus, the model would have to be modified in order to be valid under conditions in which a calcareous deposit is actively forming. In some cases, it may be possible to estimate the diffusion correction factor in more detail than has been done so far in this work. Li and Gregory found that the diffusion coefficients of various chemical species inside deep sea sediments, Dsed, could be related to their values in the bulk water, D, by a dimensionless correction factor, ’.25 Thus, Dsed = ’D, where ’ = [ / 2 (1+)]

(19)

In Equation (19), is the ratio of the viscosity of the bulk solution to the average viscosity of the solution in the pore waters of the sediment. It is a function of both porosity and salt content. is the tortuosity, which is the ratio of the length of the actual tortuous diffusion path of ions around the particles in a sediment (or in a film) to the equivalent straight-line distance. is the distribution coefficient, which represents the excess percentage of ions absorbed in a unit volume of sediment. Theoretically, Equation (19) could be used to estimate values of to use for each diffusing species in


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the model. could be used to account for the increase in viscosity within a film composed of microorganisms, exopolymer, corrosion product, and calcareous deposit. An increase in viscosity of the film would decrease , consequently causing a decrease in . This would represent an average value of the viscosity within a heterogeneous film that could have considerable variations from point to point along the metal surface. The value of the tortuosity, , would be nearly one (thus, negligible) for a purely agar or gelatinous type film. The incorporation of microorganisms, corrosion products, inorganic debris, and calcareous deposits into the film, however, would cause an increase in the tortuosity of the diffusion path and a decrease in the value of . The distribution coefficient, , could be used to account for the injection or removal of species such as O2 or CO3–2 within the film, as discussed above. Such detailed corrections to the diffusion coefficients could only be done meaningfully in a carefully controlled model system in which the film had uniform properties in both the lateral and thickness directions. Any real film, of course, would be highly viable, especially in the lateral direction parallel to the metal surface. Under such conditions, it would only be possible to define an average correction factor for the macroscopic surface. Figure 10 shows that the predictions from the model were in reasonable agreement with actual measurements of the interface pH at an applied current density of 20 µA/cm2 but not at 100 µA/cm2. Comparison of the measured and calculated points is most meaningful for the bare metal surface at the low current density. In this case, calculations from the model were done for minimal values of the film thickness (1 µm) and (1.0). One would expect the micro-pH electrode to underestimate the true interface pH due to its distance from the surface, as already explained above. In contrast, the model calculates the pH right at the surface. Thus, it is reasonable for the measured data near the bare surface to fall below the line calculated from the model as shown in Figure 10. It is more difficult to make a direct comparison between the measured and calculated values of pH for the filmed surface. The measured data were taken, as described previously, under a 4000-µm-thick agar film to which marine bacteria had been added. The calculated curve represents an idealized biofilm with a uniform thickness of 100 µm, an estimated value of 0.5, and a diffusion layer thickness of 200 µm. Using = 0.5 and d = 200 µm at an applied current density of 20 µA/cm2, the model can now be used to predict the biofilm thickness at which the pH reaches a maximum (corresponding to oxygen diffusion limited conditions). Doing this the model predicts that the interface pH


reaches a maximum value of 9.9 for biofilm thicknesses of 425 µm and above. Thus, the model indicates that the pH under the 4000-µm-thick experimental biofilm should have been at least 9.9. Compared to this value, the micro-pH electrode again underestimates the interface pH. Note from Figure 10 that the model also predicts a considerably higher interface pH at the same current density under a film that is predominantly calcareous in character with an estimated value of 0.1. The discrepancy between the predicted and measured values at the high current density in Figure 10 points to one of the main limitations of the model as currently configured. The electrochemical potentials of the bare and filmed electrodes at the high current density were –0.97 and –1.03 V SCE, respectively (Table 1). Both of these potentials are negative enough that appreciable hydrogen evolution would be expected at the cathode surface. Indeed, gas bubbles suspected of being hydrogen were observed to form on the filmed electrode during the measurement. Thus, it seems reasonable that oxygen reduction at the cathode was diffusion limited under these conditions and hydrogen evolution contributed significantly to the overall generation of OH– at the electrode surface. This is in agreement with the model predictions, especially as shown in Figure 3, where the curve for the high current density reaches a plateau at a film thickness of 50 to 60 µm, indicating that the oxygen reaction is diffusion limited. Thus, this version of the model, which does not account for hydrogen evolution, underestimates the interface pH under any conditions in which oxygen diffusion becomes the limiting factor. In other words, the model underestimates the interface pH as soon as conditions at the metal surface become anaerobic.

SUMMARY AND CONCLUSIONS A model has been constructed to calculate the pH at a cathodically polarized metal surface in saline waters in the presence of both calcareous deposits and biofilms. The model takes into account the buffering capacity and ionic strength of the electrolyte but does not include hydrogen evolution. Formulation of the model was based on charge and carbon balances at the metal and film surfaces using the chemical species involved in the cathodic oxygen reduction reaction and the seawater buffering system. The final equation is a fourth order polynomial, which is solved by computer using an iterative technique. The model is valid for waters of all salinities and temperatures and for all applied current densities below the point at which oxygen diffusion to the metal surface becomes rate limiting. Values of pH calculated from the model will not be accurate under conditions in 59

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which (1) hydrogen evolution is the dominant cathodic reaction; (2) microorganisms in the film are acting as an active source or sink for the chemical species in Equations (6) and (7); (3) surface films are macroscopically nonuniform or spotty; or (4) CO3–2 is being consumed during calcareous deposition. Conceivably, the relationship in Equation (19) could be used to account for the effects of either bacterial metabolism or the depletion of carbonate during calcareous deposition. Calculated values of pH may also not be accurate at applied current densities less than 20 µA/cm2 if a biofilm is present due to the metabolic activity of the organisms. Data needed as input to the model are the bulk seawater properties, diffusion coefficients, and equilibrium constants, along with the film and diffusion layer thicknesses. These values were either measured or estimated from the literature. Definition of a “diffusion correction factor” allowed the bulk diffusion coefficients to be modified for use within the film region. Published data from the literature on seawater chemistry and geochemistry showed that the correction factor will usually have values from 0.1 to 0.5. In this edition of the model, a single value of the diffusion correction factor was applied to all diffusing species. Predictions from the model were compared to interface pH measurements made by a micro-pH electrode near the surfaces of both bare and filmed electrodes at applied current densities of 0, 20, and 100 µA/cm2. The measured and calculated pH values agreed well at 20 µA/cm2, the calculated values right at the metal surface being more basic than the measured values as expected due to the distance from the electrode tip to the surface. Agreement was not as good at 100 µA/cm2. The calculated values were too low because the model does not account for hydrogen evolution. The model predicts that the maximum surface pH obtainable with oxygen reduction as the sole cathodic reaction is 9.9. A corollary to that conclusion would be that it requires hydrogen evolution to get an interface pH value greater than 10.

ACKNOWLEDGMENTS The authors wish to thank Drs. Characklis and Lewandowski of Montana State University for their help in making the micro-pH electrode and for the use of their laboratory facilities. We also thank Dr. W. Ullman for helpful discussions on the model. Support for this work was provided by NOAA Office of Sea Grant, Department of Commerce, under Grant No. NA86AA-D-SG-040. The U.S. government is authorized to produce and distribute reprints for government purposes not withstanding any copyright notation that may appear hereon.

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REFERENCES 1. P. Gartland, E. Bardal, R. Anderson, R. Johnson, Corrosion 40, 3(1984): p. 127. 2. W. Hartt, C. Culberson, S. Smith, “Calcareous Deposits on Metal Surfaces in Seawater–A Critical Review,” CORROSION/83, paper no. 59 (Houston, TX: NACE, 1983). 3. W. Hartt, M. Kunjapur, S. Smith, “Influence of Temperature and Exposure Time upon Calcareous Deposits,” CORROSION/86, paper no. 291 (Houston, TX: NACE, 1986). 4. C. Culberson, “Effect of Seawater Chemistry on the Formation of Calcareous Deposits,” CORROSION/83, paper no. 61 (Houston, TX: NACE, 1983). 5. H. Humble, Corrosion 4(1948): p. 358. 6. S.-H. Lin, S.C. Dexter, Corrosion 44, 9(1988): p. 615. 7. M. Guillen, S. Feliu, Rev. Metal. CENIM, 2(1966): p. 519. 8. M. Kunjapur, W. Hartt, S. Smith, “Influence of Temperature on Calcareous Deposition on Cathodically Polarized Steel in Seawater,” CORROSION/85, paper no. 316 (Houston, TX: NACE, 1985). 9. H. Hack, R. Guanti, Materials Performance 28, 3 (1989): p. 29. 10. Z. Foroulis, H. Uhlig, J. Electrochem. Soc. 111, 1(1964) : p. 13. 11. R. Lee, J. Ambrose, “A Hydrodynamical, Morphological and Chemical Study of Calcareous Deposits,” CORROSION/86, paper no. 292 (Houston, TX: NACE, 1986). 12. R. Andresen, “Cathodically Protected Steel in Seawater; Polarization Curves and Cathodic Reactions,” SINTEF report JN-7034, Trondheim, Norway, 1981. 13. J. Ambrose, A. Yaniv, R. Lee, “Nucleation, Growth and Morphology of Calcareous Deposits on Steel in Seawater,” CORROSION/83, paper no. 60 (Houston, TX: NACE, 1983). 14. R. Korlipara, R. Zatorski, H. Herman, MTS J. 17, 4 (1983): p. 19. 15. R. Lee, J. Ambrose, “Influence of Cathodic Protection Parameters on Calcareous Deposit Formation,” CORROSION/86, paper no. 191 (Houston, TX: NACE, 1986). 16. H. Engell, P. Forchhammer, Corrosion Science 5(1965): p. 479. 17. S. Wolfon, W. Hartt, Corrosion 37, 2 (1981): p. 70. 18. Z. Lewandowski, W. Lee, W. Characklis, B. Little, Corrosion 45, 2(1989): p. 92. 19. G. Sadasivan, “Computer Simulation of Calcareous Deposition,” Master’s Thesis, Florida Atlantic University, Boca Raton, FL (1989). 20. F. Millero, Geochimica et Cosmochimica Acta 43 (1979): p. 1651. 21. J. Gieskes, “The Alkalinity-Total Carbon Dioxide System in Seawater,” in The Sea, vol. 5 (New York, NY: John Wiley, 1974), p. 123. 22. C. Culberson, R. Pytkowicz, Marine Chemistry 1 (1973): p. 309. 23. S. Dexter, C. Culberson, MP 19, 9(1980): p. 16. 24. S. Lin, “Interaction Between Biofilm Formation and Calcareous Deposition Under Cathodic Protection Conditions,” PhD Dissertation, University of Delaware, Lewes, DE, (1989). 25. Y. Li, Y. Gregory, Geochimica et. Cosmochimica Acta 38 (1974): p. 703. 26. A. Lerman, Geochemical Processes: Water and Sediments (New York, NY: John Wiley and Son, 1979), p. 94. 27. E. Lamotta, Env. Sci. and Technol. 10, 8 (1976): p. 765. 28. R. Aller, J. Marine Res. 41(1983): p. 299. 29. H. Bungay, W. Whalen, W. Sanders, Biotech. and Bioeng. XI (1969): p. 765. 30. W. Hartt, N. Lin, “An Evaluation of Calcareous Deposits as Affected by Seawater Movements,” Proc. 6th Intl. Offshore Mechanics and Arctic Engr. Symp. vol. III, (New York, NY: ASME, 1987) p. 425. 31. W. Mao, W. Hartt, “Growth Rate of Calcareous Deposits Upon Cathodically Polarized Steel in Seawater,” CORROSION/85, paper no. 317 (Houston, TX: NACE, 1985). 32. R. Kole, “An Investigation of the Calcareous Scale Deposited on Steel, Aluminum and Galvanized Iron While Under Cathodic Protection,” Master’s Thesis, University of Miami, Miami, FL (1973). 33. T.A. Langworthy, “Microbial Life at Extreme pH Values,” Microbial Life in Extreme Environments, D.J. Kushner, ed. (New York, NY: Academic Press, 1978) p. 279. 34. R. Johnsen, E. Bardal, Corrosion 41, 5(1985): p. 296. 35. S. Dexter, S. Lin, Materials Performance, 30, 4(1991): p. 16.
