Fall 2005

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• Fall 2005
• Corrosion Rate

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• Polarization Behavior
• Metallic surfaces can be polarized by the
  application of an external voltage or by the
  spontaneous production of a voltage away from
  equilibrium. This deviation from equilibrium
  potential is called polarization. The magnitude
  of polarization is usually described as an
  overvoltage (h) 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
• E(applied) - Eeq htotal hact hconc iR  
  (see a typical fuel cell polarization curve)
• where
• hact is the activation overpotential, a complex
  function describing the charge transfer kinetics
  of the electrochemical processes. hact is
  predominant at small polarization currents or
  voltages.
• hconc is the concentration overpotential, a
  function describing the mass transport
  limitations associated with electrochemical
  processes. hact is predominant at large
  polarization currents or voltages.
• iR is often called the 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 ... The ohmic drop is
  the simplest of the three polarization terms and
  can be evaluated either directly with a
  conductivity cell or using conductance data.

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• Activation Overpotential
• Both the anodic and cathodic sides of a reaction
  can be studied individually by using some well
  established electrochemical methods where 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
• where
• i is the anodic or cathodic current
• b charge transfer barrier or symmetry
  coefficient for the anodic or cathodic reaction.
  b values are typically close to 0.5
• hact 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 96485 C mol-1

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• THERMODYNAMICS OF CORROSION
• As you learned in Chemistry there is a free
  energy change with reactions. This change in free
  energy must be negative for the reaction to be
  spontaneous.
• There are two reactions involved in the corrosion
  process the total free energy change must be
  negative for corrosion to occur. These reactions
  are an oxidation and a reduction.
• Oxidation occurs at the anode
• Mg Mg2 2e-
• Reduction occurs at the cathode
• 2H 2e- H2
• For a total reaction
• Mg 2H Mg2 H2
• The Free energy can be calculated by
• DG-nFDE
• Where
• n is the number of electons exchanged ( two in
  the above example)
• F is the Faraday Constant (96500
  Coulombs/equivalent)
• E corresponds to the energy change in the
  reaction.

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• Each reaction ( anodic and cathodic) has a
  half-cell potential associated with it given as-
  E
• The sum of the anodic and cathodic half-cell
  potentials is the total potential given as- E
• Further considering concentration effects of the
  hydrogen ion and reaction species concentration
  yields the Nerst Equation
• EEo-(RT)/(nF)lnBb H2Od/AaHm
• Where
• Eo is the defined value for the potential
  referenced to a standard
• R is the gas constant
• T is temperature
• n and F are described above
• The terms of within the natural log are the
  concentrations of the products over the
  reactants.
• That was certainly brief and very cursory but the
  important thing to take away are the types of
  things that can play a role in the corrosion
  reactions. Hopefully you have seen most of this
  in a freshman chemistry course.
• The reference is the standard hydrogen
  electrode (SHE) which is defined as Eo0 Volts.

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• Kinetics of Corrosion
• Thermodynamics are fundamental and show that
  corroison will occur in most environments. It is
  also important to know how fast corrosion will
  occur.
• As shown in the thermodyanmics, the the reactions
  in the corrosive process produce and consume
  electrons. Electron flow can be quantified as
  current Faraday first found the relationship
  between electrons exchanged and mass reacted
• m(Ita)/(nF)
• m mass reacted
• ICurrent
• ttime
• Aatomic weight
• nnuber of equivalents
• F Faraday's Constant (96500 Coulombs/equivalent)
• To find the corrosion rate (and equalize for
  area) divide through by time and Area yielding
• r(ia)/nF
• rcorrosion rate
• i current density
• Each reaction has a characteristic equilibrium
  current density this is termed io
• Electrochemical Polarization is a method used to
  better understand the corrosion behavior of
  various materials by varying the potential above
  or below the equilibrium potential (E). This
  polarization drives the reaction either in the
  noble ( anodic) or active ( cathodic direction).
• While carrying the potential the current produced
  is recorded, as can be seen in the equation above
  the higher the current density, the higher the
  corrosion rate.

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• The curve above shows slightly different
  behavior. This is called passivity an increased
  corrosion resistance in oxidizing conditions due
  to a thin barrier film formed in these conditions
  or at anodic potentials. Passivity can be seen by
  the lowering of the current density as the
  potential is increased. A good example of this is
  stainless steel. The reason that stainless steel
  does resist corrosion so well is that a thin
  chromium oxide film naturally forms on the
  surface preventing an anodic reaction form
  occurring on the surface of the steel. It is
  desirable to stay in the passive region ( above
  the critical point) because of the reduced
  current density which correlates to a reduced
  dissolution rate. The passive region shows a
  rather steady current density for a wide range of
  potential values, until the passive film breaks
  down, causing an increase in the current density.
  This is occurs at relatively high potential and
  is usually called trans-passive breakdown.

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• Summary of Electrochemical Theory
• Electrochemical Reactions
• An electrochemical reaction is a reaction
  involving the transfer of charge as a part of a
  chemical reaction. Typical electrochemical
  reactions in corrosion are metal dissolution and
  oxygen reduction
• In contrast a chemical reaction, such as the
  precipitation of a metal hydroxide, does not
  involve a transfer of charge
• Faraday's Law
• Faraday's Law relates the amount of charge
  involved in an electrochemical reaction with the
  number of moles of reactant reacting and the
  number of electrons required for the reaction.
• In addition to Faradaic processes that obey
  Faraday's Law, non-Faradaic processes may also
  occur. Typically these are processes such as
  adsorption that do not involve a complete
  transfer of charge from the solution to the
  metal.

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• Electrochemical Half Cells
• A half cell is an electrochemical reaction that
  results in a net surplus or deficit of electrons,
  and it corresponds to the smallest complete
  reaction sequence (while it may proceed as a
  sequence of simpler reactions, the intermediate
  stages are not stable).
• Oxidation or anodic reactions are those that
  result in a surplus of electrons, and for
  corrosion these typically correspond to the
  various metal dissolution reactions, such as
• Reduction or cathodic reactions result in the
  consumption of electrons, and for corrosion these
  typically correspond to the oxygen reduction or
  hydrogen evolution reactions
• Note that the above reactions have been shown
  going in one direction only. While the reverse
  reactions are perfectly possible, they reverse of
  an anodic reaction is a cathodic reaction and
  vice versa.

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• Reversibility of Electrochemical Reactions
• A reaction is said to be reversible if it can
  proceed easily in either direction as conditions
  change (typically as the electrochemical
  potential is changed). There are several aspects
  of reversibility.
• Chemical reversibility relates to the chemical
  feasibility of the reaction, with a chemically
  irreversible reaction being one in which the
  reverse reaction is prevented by the occurrence
  of competing reactions,
• A thermodynamically reversible reaction is a
  chemically reversible reaction for which the
  reaction will change direction as a result of an
  infinitesimal change in potential. 
• A practically reversible reaction is a
  thermodynamically reversible reaction that occurs
  at a significant rate with small overpotentials.

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• Electrochemical Equilibria
• Thermodynamically reversible reactions will adopt
  an equilibrium potential which is described by
  the Nernst equation
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• Example of an Electrochemical Equilibrium
• If we consider copper in equilibrium with copper
  ions in solution
• Consequently the equilibrium potential will go up
  as the concentration of copper ions in solution
  goes up

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• Reference Electrodes
• Reference electrodes are needed to convert from
  the charge carriers in the metal (electrons) to
  the charge carriers in solution (ions) in a
  reproducible fashion. They must be practically
  reversible.
• The Normal Hydrogen Electrode (NHE) is used as
  the (arbitrary) standard. This consists of
  hydrogen at unit activity (i.e. solution in
  equilibrium with hydrogen gas at 1 atmosphere) in
  equilibrium with unit activity of hydrogen ions
  in solution (1.19 M HCl solution). The
  equilibrium potential is detected with a platinum
  electrode that is coated with platinum black
  (finely divided platinum) to enlarge the
  effective surface area.
• The NHE is inconvenient for general-purpose use,
  and a range of secondary reference electrodes
  have been developed (Table 1).

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Table 1 Practical Reference Electrodes
Note that zinc in seawater is a useful practical
reference electrode, although it has no
theoretical basis for the reference potential.
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• Electrochemical Kinetics
• The Electrochemical Double Layer
• There is a tendency for charged species to be
  attracted to or repelled from the metal-solution
  interface. This gives rise to a separation of
  charge, and the layer of solution with different
  composition from the bulk solution is known as
  the electrochemical double layer. There are a
  number of theoretical descriptions of the
  structure of this layer, including the Helmholtz
  model, the GouyChapman model and the
  GouyChapmanStern model.
•  
• As a result of the variation of the charge
  separation with the applied potential, the
  electrochemical double layer has an apparent
  capacitance (known as the double layer
  capacitance).

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Kinetics of a Single Electrochemical Reaction
Activation control An activation controlled
reaction is one for which the rate of reaction is
controlled solely by the rate of the
electrochemical charge transfer process, which is
in turn an activation-controlled process. This
gives rise to kinetics that are described by the
ButlerVolmer equation
While the Butler-Volmer equation is valid over
the full potential range, we can obtain simpler
approximate solutions over more restricted ranges
of potential Large overpotentials - the Tafel
equations are obtained (only applicable for
irreversible reactions)
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or, in terms of the anodic and cathodic Tafel
slopes, ba and bc,
(note that bc above is taken to be positive, as
this is commonly assumed however, bc is strictly
negative, and the divisor in the Stern-Geary
equation should be 2.303(ba - bc) RCT
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Mass transport control This implies fast
kinetics, hence the surface reaction is
reversible and the potential is given by the
Nernst equation applied to the surface
concentrations
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The Kinetics of Multiple Reactions When multiple
reactions are possible, the resultant kinetics
are described by the mixed potential theory. This
simply says that the total current in an external
circuit is the sum of all of the currents due to
the individual reactions (with anodic currents
being positive and cathodic current negative). In
free corrosion conditions this implies that the
sum of the negative currents is equal to the sum
of the positive currents. When there are only two
reactions of any significance (one anodic and one
cathodic), the theory is analogous to that for a
single reaction. The behaviour can be summarized
diagrammatically with the Evans and E-log i
diagrams.
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The mixed potential theory leads to the concepts
of the corrosion potential, Ecorr, and the
corrosion current density, icorr. Ecorr is simply
that potential at which the sum of the anodic and
cathodic currents is zero, and it is therefore
that potential that the specimen will adopt in
free corrosion. icorr is, in some ways, a more
important parameter, as it describes the rates of
the anodic and cathodic reactions. Providing all
of the anodic reactions lead to the oxidation of
metal, then icorr is the corrosion rate of the
metal (with the current being related to the rate
of loss of metal through Faraday's Law).
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• The Rate Determining Step
• Real electrochemical reactions tend to occur as a
  sequence of very simple steps. For example, even
  a very simple reaction such as hydrogen evolution
  occurs as two steps, with two alternatives for
  the second step
• The rate of the overall reaction is controlled by
  the rate of the slowest reaction, and this is
  known as the rate controlling step. This may be
  an electrochemical reaction (such as Step 1
  above) or a chemical reaction (such as Step 2a).
  Different rate controlling steps will typically
  give a different Tafel slope for the reaction and
  a different reaction order (dependence on
  concentration of reactants). Electrochemical
  measurements may be used to help to determine the
  reaction mechanism and the rate-controlling step.

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