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David C. Silverman |
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Background on the Potential/pH (Pourbaix) Diagram Potential-pH diagrams are a sometimes overlooked tool that can aid in corrosion prediction and control. Potential-pH diagrams were originally developed by M. Pourbaix, hence their alternative name of Pourbaix diagrams. An atlas of diagrams of pure materials in water is available (M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, NACE International, Houston, TX, 1974). While the diagrams in this atlas were derived using sometimes inaccurate or obsolete thermodynamic free energy data, this reference is an excellent first source of information about these diagrams. The discussion in this reference provides insight on how these diagrams may be related to corrosion. Analyses of several metals have revealed that more recent thermodynamic tabulations sometimes disagree with the original data used by Pourbaix and diagrams calculated from these data. These discrepancies led to modifications for the diagrams for iron, nickel, and chromium (D. C. Silverman, "Presence of Solid Fe(OH)2 in EMF-pH Diagram for Iron", Corrosion, Vol. 38, p. 453 (1982)1 (172k),
D. C. Silverman, "Revised EMF-pH Diagram for Nickel", Corrosion, Vol. 37, p. 546 (1981)1 (162k),
and D. C. Silverman, "Absence of Cr(IV) in EMF-pH Diagram for Chromium", Corrosion, Vol. 39, p. 488 (1983)1 (162k)).
The diagrams were originally calculated and drawn by hand and a simplified method for doing so has been described elsewhere (E. D. Verink, Jr., "Simplified Procedure for Constructing Pourbaix Diagrams", in Uhlig’s Corrosion Handbook, 2nd ed., W. Revie, ed., ch 6, p. 111, 2000). But undertaking such calculations, while being useful from an educational standpoint, is not only tedious but is not necessary. Such diagrams are routinely calculated and plotted using a computer. THERMEXPERT has taken construction of potential-pH diagrams a step further by enabling their calculation to be internet accessible as a web application. The potential-pH diagram is calculated from thermodynamic information. All thermodynamic properties are functions of the state of the material (for example liquid, solid, gas, or ion) and the state of the system in which it resides (for example, the temperature, pressure, concentration, etc.). Changes in thermodynamic properties between initial and final states are not functions of the energy paths followed when moving from the initial state to final the state of the system. In that sense, these properties are called path independent and are only determined by the final equilibrium state of the system. The sign on the change in free energy between initial and final states determines if that final state can occur spontaneously. Free energy is the maximum work that could be obtained theoretically if the energy released during the transformation could be converted to work. A free energy change between initial and final states that is negative implies that the final state is more favorable than the initial state under the defined conditions. In this case work can be done if the process occurs. A free energy change between initial and final states that is positive implies that the final state is less favorable than the initial state under the defined conditions. In this case work must be done to make the process occur. A system always tries to reside in a state in which its total free energy is a minimum. That property is the basis for the calculation of the potential-pH diagram. In a series of reactions involving formation of a group of related compounds, for example, the compound form that has the lowest free energy of formation tends to be the most thermodynamically stable form of that compound. Note that this free energy is actually a change in free energy between elements in well-defined standard states (e.g. 25oC, 1 atm pressure, unit activity, solid, etc.) and the same elements in actual state of the system which normally includes compounds of the elements. The potential-pH diagram is a pictorial representation that shows the state having the lowest free energy of the system as a function of the hydrogen ion activity (as represented by but not necessarily equal to the pH) and electrochemical potential (equilibrium potential) at a given temperature and pressure. The coordinates of pH (assumed to equal the hydrogen ion activity) and potential in which these diagrams are plotted are useful to the corrosion engineer because pH as a measure of acidity and potential as a measure of oxidizing power are important influences on the corrosivity of fluids, especially those containing inorganic and organic ions. These diagrams should be considered as analogous to "road maps" in which the towns and cities might represent the states of the system and the elevation and relative population densities might represent the potential and pH. The diagrams are silent with respect to the kinetics (rate) of moving between system states (between towns), or the reaction pathway (roads or paths between towns) that provide the highest reaction rate (shortest travel time). The potential-pH diagram is a graphical way to show the regions of stability of most stable states of a metal in terms of pH (actually the negative of the Logarithm of the hydrogen ion activity) and potential (actually the equilibrium potential) coordinates. The potential-pH diagram usually reported is actually an overlay of two diagrams. The first shows the forms of the metal that has the lowest free energy in the environment as a function of pH and potential. The second shows the forms of the metal ions in the solution that have the lowest free energy state as a function of pH and potential. These two diagrams are calculated individually by THERMEXPERT and noted as Metal State Diagram for the lowest free energy form of the metal and Solution State Diagram for the lowest free energy state of the ion that would be present in solution in conjunction with the sold. The two diagrams are not in equilibrium with each other. In fact, the only place where true equilibrium exists on each diagram is along the lines bordering the regions. The positions of those lines change with concentration, temperature, etc. Within the boundaries the form is the lowest free energy state at that pH, potential, and temperature. If the most stable state of the solid is as an ion, that ion is identical on the two diagrams at the same potential and pH. This figure The region between the parallel dashed lines represents where water is stable. Above the upper line it would be favored to transform to oxygen. Below the lower line it would be favored to transform to hydrogen. Note that pH is actually defined between 0 and 14. But, acidity levels can be at hydrogen ion activities greater than those that define a pH of 0 and alkalinity can be at hydrogen ion activities less than (hydroxyl ion activities greater than) those that define a pH of 14. One would report those measurements in terms of voltage, not pH. For ease of representation, these extensions are shown on the diagrams by extending the pH limits to -2 and 16 which is meant to extend the hydrogen ion activity limits to approximately 10-16 and 100. The usefulness of these diagrams lies in their ability to provide graphical representation of the final state of a system suffering corrosion as a function of the coordinates of pH (acidity) and potential (oxidizing power). If (1) all possible forms of the metal under consideration are included, (2) all additional species important to corrosion are included, and (3) the thermodynamic data validly represent these compounds under system conditions, then the diagrams can show the conditions of hydrogen ion activity (written as -log(H+γ+/- where γ+/- is the mean activity coefficient and assumed to be the pH) and potential under which the metal can remain as a metal, can be oxidized to a solid species, or can to be oxidized to a dissolved species. Note that can does not necessarily mean will. In a way, the diagrams are true negative indicators of corrosion. As long as all components important to corrosion in the system are used in the calculation and the thermodynamic data are valid, these diagrams can predict the conditions of hydrogen ion activity and potential under which corrosion will not occur. In the above figure, that area would be indicated by the region in which bulk nickel metal is stable. Thermodynamics provides no information on corrosion rates. Oxidized product formation at rates of grams per second or micrograms per century would both be shown as oxidized product on the potential-pH diagram as long as that species has the lowest free energy at that pH, potential, and temperature. Note that oxidized solid is not necessarily synonymous with passivity. Experiments are required to determine (1) if thermodynamic predictions of corrosion (ions or oxidized solid) will, indeed, occur over the desired time period and (2) if formation of oxidized products results in passivity or mass loss. One cautionary note is in order. Much of the tabulated thermodynamic data corresponds to bulk properties. Corrosion initiates at the surface. Surface thermodynamics and bulk thermodynamics can be very different because the chemistries at the two locations tend to be very different. Metal/liquid and metal/gas interfaces tend to be much more reactive than the bulk metal. For example, oxygen binds much more strongly to iron immediately at the iron surface than it does to iron in the bulk. One observation showing this point is that fully reduced iron particles when exposed slowly and carefully to air can create an iron oxide crust surrounding metallic iron particles. In the absence of this crust pure iron would oxidize in air catastrophically. This difference between surface and bulk thermodynamics must be kept in mind when relating corrosion phenomena linked to surface reactions to the predictions of these diagrams calculated from bulk thermodynamics. The key to using the potential-pH diagram as a practical aid both in designing appropriate experiments and making better predictions in conjunction with those experiments is to have a way to interface those diagrams with the "real world". In a real situation, the pH of system and corrosion potential are usually fairly easy to measure. Such ease suggests that one way to interface the diagrams with the real world is to place the coordinate (pH, corrosion potential) on the diagram. The measured pH can be related under some circumstances to the hydrogen ion activity through the activity coefficient. A steady state corrosion potential while not being an equilibrium potential does reflect the balance among all of the anodic and cathodic half reactions occurring. This potential would become the equilibrium potential if the anodic and cathodic reactions were themselves at equilibrium. Examples of this approach are provided in the sections Case Study-Titanium/chloride under acidic conditions and Case Study-Complexing Agents-Iron/iminodiacetic acid as well as in D. C. Silverman, "Derivation and Application Of EMF pH Diagrams", in Electrochemical Techniques for Corrosion Engineering, R. Baboian, ed., p. 117, NACE, Houston, 19871 (592k),
D. C. Silverman, "Application of EMF-pH Diagrams to Corrosion Prediction", Corrosion,
Vol. 38, p. 541(1982)1 (558k),
D. C. Silverman and A. L. Silverman, "Potential-pH (Pourbaix) Diagrams as Aids for Screening Corrosion Inhibitors and Sequestering Agents", Paper 07616, CORROSION/2007, Nashville, TN, 20071 (2396k),
and E. D. Verink, Corrosion, Vol. 38, No. 6, 336 (1982).
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David C. Silverman, Ph.D. - Primary Consultant |
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