IN SITU CHARACTERIZATION OF CORRODING INTERFACES
VIA DIGITAL SIGNAL ANALYSIS
By
JOSEPH WARREN HAGER
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARIIAL FULFIIMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1983
Dedicated to my wife, Jeannie
and to Aric, Kirsten and Anneke.
ACKNOWIDGMENTS
I am indebted to my wife, Jeannie, whose constant encouragement
and personal sacrifice both motivated and, to a large extent, enabled
me to carry this program to its conclusion. The opportunity to use the
excellent and unique facilities of the Solar Energy Research Institute
made my efforts in this area of corrosion research possible. I am
particularly grateful to Steve Pohlman and Pat Russel for coordinating
my stay at SERI and for their many helpful technical discussions. Bob
Fortune developed the software which permits computer control of the
signal analyzer and provides data analysis and graphics. He also con
ceived and designed the optical isolator circuit and provided numerous
helpful technical suggestions. Frank Urban and Ron Bagley acted as
sounding boards for my ideas and also provided numerous helpful
suggestions. Rolf Hunmel's interest, encouragement, and representation
of my work to the rest of my cctmittee was very much appreciated. To
my ccrmittee chairman, Ellis Verink, and committee numbers, John Ambrose
and Gerhard Schmid, I say "thank you" for accommodating an unusual mode
of graduate study. Finally, I acknowledge the financial support of the
U.S. Air Force without which graduate study at this stage in my life
would not have been possible.
TABLE OF CONTENTS
Page
ACKNCLEDGENTS .......................... iii
ABSTRACT. . ..... . .... ... . . ... vi
CHAPTER 1 INTRODUCTION ................... ... 1
CHAPTER 2 THEORETICAL BASIS FOR IMPEDANCE MODELING . . . 9
Electrochemical Interface Models . . . . . . . . 9
Electrochemical Corrosion Monitoring . . . . . . 17
Linear System Theory ...................... 28
Analysis of AC Impedance Data. . . . . . . . ... 36
Recapitulation: StateoftheArt. . . . . . . ... 43
CHAPTER 3 SYSTEM DEVELOPMENT. . . . . . . . . ... 46
System Cmponents... ................... .. .46
Developmental Problems . . . . . . . . . .. 53
Verification of AC System Capabilities . . . . . . 60
Summary of System Development. . . . . . . . ... 73
CHAPTER 4 APPLICATION OF DIGITAL SIGNAL ANALYSIS TO A CORRODING
ELECTRODE ....................... 74
CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE TORK . . 93
Recapitulation: Objectives and Premises . . . . . . 93
Capabilities and Limitations of Digital Signal Analysis. .. .. 96
Recamendations for Future Research. . . . . . . ... 98
APPENDICES
A DIGITAL SIGNAL ANALYSIS TERMINOLOGY . . . ... 106
B OPTICAL COUPLER CIRCUITRY . . . . . .... 119
C SIMULATED ELCTRODE STUDIES . . . . . .... 123
TABLE OF CONTENTS (Continued)
Page
APPENDICES (Continued)
D SYSTEM SOFIFARE .................. 135
BIBLIOGRAPHY ..................... ....... 240
BIOGRAPHICAL SKEIxCH ................... ..... 243
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
IN SITU CHARACTERIZATION OF CORRODING INTERFACES
VIA DIGITAL SIGNAL ANALYSIS
By
Joseph Warren Hager
December 1983
Chairman: Dr. Ellis D. Verink, Jr.
Major Department: Materials Science and Engineering
A technique has been developed for characterizing the dynamic
electrochemical behavior of a corroding interface utilizing an offthe
shelf commercially available digital signal analyzer, a micro computer
and a conventional potentiostat. By treating the corroding electrode
as a relaxed, linear, tineinvariant system, it may be modeled as an
equivalent network of resistors and capacitors. The assemblage of
equipment was successful in experimentally determining the component
values in a threeelement electronic network simulating a simple
electrochemical interface. A white noise voltage signal was applied to
the network while simultaneously monitoring the current response. Both
time domain signals were converted to the frequency domain via the
fast Fourier transform (FET) and manipulated to yield the network
impedance.
Graphical analysis of impedance plots yielded the component values.
The technique was then applied to an evaluation of the corrosion of
430 stainless steel in IN sulfuric acid. The method was successful
in determining ccnponent values of a 5element network used to model
the electrochanical interface in the active, passive, and transpassive
regions of polarization potential and at the corrosion potential.
These findings show that electrode impedance measurements made via
digital signal analysis are sensitive to the character of a corroding
interface. This method, because of its relatively short duration of
measurement, and negligible permanent effect on the electrode may
become an effective means of monitoring corrosion in situ.
CHAPTER I
INTRODUCTION
What probably began as childlike fascination with the look and
feel of metallic lumps in the ashes of an ancient campfire has been
retained by man throughout the entire period of his civilization.
Indeed, the unique properties of metals have rendered them the most
significant class of materials in the technological advancement of man
up to the present day. Even now, as significant advances are made in
the technology of glasses, ceramics, polymers, and sophisticated com
posite materials, metals will continue to be exploited for their unique
properties.
Accompanying the development of the metallurgical technology to
extract and refine metals came the realization that large amounts of
energy are required to convert the ore from its native state to a usable
metallic form. A more startling realization was that the metals which
were won from their ores at such a great expense of energy and effort
seemed most eager to return to their native state and did so whenever
they were left exposed to the terrestrial environment. As various metals
were separated and characterized, they were observed to possess varying
degrees of susceptibility to the environmental degradation we call
corrosion. Despite whatever other unique properties a metal may
possess, its ultimate usefulness and application is very strongly
influenced by its resistance to corrosion.
2
The word "corrosion", although sometimes used to denote the
deterioration of any substance in the environment of its use, generally
connotes the destruction of a metal in the presence of an aqueous
electrolyte or other polar solvent. In the context of the latter
definition, the apparent disappearance of the metal may be attributed
to an electrochemical reaction of the form:
Me Men+ + ne
There are few metals of practical importance for engineering appli
cations which are thermodynamically immune to this anodic reaction in
the environment of their intended use. Accepting this fact, the engineer
is faced with the problem of determining whether the rate at which this
reaction takes place will permit the functional utilization of the
device for its design lifetime. In some cases, if the corrosion rate
is well established and occurs as a uniform attack, one might simply
make the structure thicker than required by strength considerations to
allow for material loss by corrosion. Another tack is to select a
suitable coating which, in effect, separates the metal from the aggres
sive environment. In cases where failure of the metal component would
result in a catastrophic outcome, the solution is often to select a
more expensive, more corrosionresistant material.
The aforementioned design options are logical courses of action
assuming that the rate of the corrosion reaction is known and the
reaction occurs uniformly over the entire surface of exposure. Un
fortunately, the vast majority of corrosion phenomena are not so
straightforward. Some metals, subjected to certain environmental
conditions, are observed to deteriorate very rapidly at some locations
3
while appearing immune at others. Such variations in local behavior
may be attributed to local variations in solution concentrations which
are related to ccmpor4nt configuration, previous cleaning or chemical
treatment or mechanical damage to the part. The local variations in
corrosion rate might also be due to inhomogeneities in the metal itself
introduced during welding or heat treatment; or result from plastic
deformation during fabrication; or be caused by local states of stress
as the part performs its design function. These observations are
particularly disquieting in view of the fact that the local corrosion
rate variations may span many orders of magniturethus rendering an
"average" corrosion rate virtually meaningless.
Another group of metals protect themselves by forming a coherent
protective film of corrosion product which is stable in the aggressive
environment. Local removal of the film results in its immediate reform
ation since the film consists of the corrosion product. But even such
selfprotecting metals are susceptible to local variations in behavior.
Subjected to differing solution concentrations or inhcmogeneities in
the underlying metal, the protective film may allow very rapid local
corrosion (pitting) which may destroy the function of a metal component
without extensive metal loss.
Faced with these observations, the task of making an intelligent
assessment of component durability is formidable to say the least. In
the attempt to address this task, several strategies have evolved. The
first and most straightforward approach is realtime testing of the
component or sample coupon in the actual environment of intended use.
It suffers from the obvious disadvantages that the time of test pre
cludes a priori assessment of component durability in most cases. There
4
is also the nagging question of whether the test environment adequately
represents the range of conditions that will be experienced by the
actual part. A second approach is to expose the component to a more
severe environment in an attempt to effect an accelerated test. Con
sidering the nonlinear character of all deterioration phenomena, this
approach cannot predict absolute durability of a part but may be useful
in comparing alternative materials or processing techniques. The third
approach is the most scientific and is certainly the most rigorous. In
this method, one attempts to determine experimentally and explain
theoretically the electrochemical deterioration of the material over
the entire range of possible local conditions.
Considerable progress has been made in understanding the mechanism
of corrosion processes, via this third approach. For example, in many
corrosion reactions, the rate of consumption of electrons in a number of
possible cathodic reactions has been found to limit the rate at which
the anodic charge transfer step may occur. If the cathodic reaction is
hydrogen evolution, the cathodic charge transfer step may be limited by
the rate at which the diatomic hydrogen molecules are formed. Since the
ultimate goal of corrosion study is to stop or at least inhibit the pro
duction of metal ions from solid metal, the large number of interdepen
dent reactions offer, in principle, a wide range of possible points of
attacking the corrosion process. On the other hand, the sheer number
of possible ratedetermining steps also severely complicates the
unraveling of corrosion mechanisms.
In the absence of a complete understanding of the corrosion
mechanism for a particular metal alloy in a particular environment,
one seeks methods of characterizing and classifying the behavior of
corroding systems on a quantitative experimental basis. The
determination of corrosion rate by the polarization resistance method
represents one such very direct method of characterizing the corroding
interface. Unfortunately, the rendition of a corrosion rate by this
method is not meaningful in metal systems subject to a localized
attack. Such systems often possess passive corrosion product films
which protect the metal surface from the environment initially and then
degrade catastrophically in small areas. In these cases, one seeks a
parameter or combination of parameters which reveals the susceptibility
of the passive film to failure. Since the electrochemical interface
may be modeled as an equivalent electronic network consisting of resis
tive and capacitive impedance terms, a method which quantifies these
terms would provide a more complete characterization of the corroding
interface.
The behavior of an equivalent circuit which contains capacitive
elements is a function of the frequency of the applied signal. A
complete characterization of the circuit therefore requires a scheme
which measures the circuit response to a sequence of singlefrequency
signal applications. An alternate measurement scheme is to apply a
multiplefrequency signal and determine the system transfer function
via the fast Fourier transform (FFT) algorithm. Subsequent graphical
analysis of the system impedance as a function of frequency can yield
quantitative values of electronic components in an assumed network
model. Ifere the complexity of system response precludes a simple
network model, the plots produce a characteristic "fingerprint" of the
corroding interface.
The data collection period of this latter measurement scheme is
obviously shorter than that required for sequential singlefrequency
measurements. In principle, the measurement tire for a multifrequency
analysis is determined by the period of the lowest frequency to be
analyzed; the time required to perform the FFT being considerably less
than one second. In practice, the data precision is improved by
averaging a number of runs which lengthens the measurement period.
Furthermore, analysis over several frequency ranges provides higher
resolution data at low frequencies. While these practical considera
tions all lengthen the period of measurements, it is still much shorter
(minutes versus hours) than singlefrequency sequential collection over
the same range of frequencies. It is thus possible, in principle, to
completely characterize a corroding interface at reasonably close
intervals of time observing changes in network parameters which may,
among other things, reflect changes in the susceptibility of passive
films to localized breakdown.
Recognizing that a simple electronic network model may not
adequately describe the electrochemical behavior of a corroding metal
interface, it may not always be practical to attempt to quantify and
monitor network parameters. In such cases, one could propose more
elaborate models and support hypothetical mechanisms by fitting data
to these. From the standpoint of corrosion monitoring, however, one
may wish to simply characterize the state of corrosion in an empirical
way. Graphical portrayal of data in a particular format might show that
certain curve forms correlate with "acceptable" corrosion behavior, for
example.
The ultimate purpose of the work described here is to increase
the quality and quantity of information which can be obtained from a
corroding interface in a given period of time. Since the chosen tech
nique is based on the electrochemical nature of the interface, it can
be expected to provide insight into electrochemical reaction mechanisms
present under a given set of conditions. Since the technique employs
alternating current perturbation signals, it can provide information
about the capacitive as well as resistive nature of the corroding
interface. Since it utilizes stateoftheart digital signal analysis
equipment, it is able to interrogate the interface in a shorter period
of time than required by sequential singlefrequency exposure methods.
Individual features of this technique are not unique, having been
investigated by Epelboin (13), Blanc (4), Creason (58), Smith (910),
Lorenz (11) and others (1214). However, there has been no known attempt
to synthesize the wellknown AC electrochemical methods with modern digi
tal signal analysis technology for the specific purpose of investigating
corroding interfaces. The consequence of this effort provides the
technological basis for advanced automated corrosion monitoring systems
and for sophisticated electrochemical interrogation schemes for basic
corrosion research.
The specific objectives of the work described herein were (1) to
assemble an in situ corrosion monitoring system based on digital signal
analysis using offtheshelf ccrmercially available electronic equip
ment and (2) to demonstrate capabilities and limitations of such a
system in characterizing both quantitatively and empirically the
corrosion of 430 stainless steel in IN sulfuric acid subjected to
8
imposed potentials between 0.5 and +1.5 v (SCE). The remainder of
this dissertation outlines the theoretical basis for impedance modeling
and solutions associated with system assembly and generation of the
interface transfer function, and demonstrates system capability on
simulated and real corroding electrodes.
CHAPTER II
THEORETICAL BASIS FOR IMPEDANCE MODELING
The replacement of steel destroyed by electrochemical corrosion in
the terrestrial environment constitutes a significant percentage of the
annual production of steel in the United States. But the rusting of
steel is only one of a large number of metallic deterioration phenomena
which are electrochemical in nature. In fact, all metals are subject
to electrochemical deterioration in some aqueous solvents. Even the
metals which form protective adherent films are susceptible, as the pro
tective nature of the film changes with environmental conditions. Inter
est in corrosion and other electrochemical phenomena has led to intense
study of the interface between a solid surface on which an electrochemical
reaction is taking place and the ionic solution which contacts it.
Electrochemical Interface Models
DoubleLayer Capacitance
The essential feature of an electrochemical interface is the
presence of an enormous electric field (' 107 V/cm) acting over a region
0
roughly 10 A in thickness immediately adjacent to the solid surface (15).
The arrangement of charges and oriented dipoles in this region was termed
the electrical doublelayer by Helmholtz (15) and is further explained
by Bockris (16). They describe the electrified interface as consisting
of two sheets of charge of opposite signone in the solid electrode
surface and the other in solution. This led to the treatment of the
electrified interface as a parallel plate capacitor.
10
Electrocapillarity data, however, do not entirely support the
doublelayer model, and this led Gouy (17) and Chapman (18) to propose
the socalled diffuse doublelayer model which took into account varia
tions in the capacitance with potential. The GouyChapman model
asserted that the charge in the electrolyte solution was scattered in
thermal disarray rather than being ordered in platelike fashion
immediately adjacent to the solid surface. Stern (19) synthesized the
Helmholtz and GouyChapman models stating that some of the charge in the
electrolyte is organized in platelike fashion and some is in thermal
disarray. The precise refinements to the theory of the electrified
interface do not take away the general conclusion that there is a
capacitance associated with the interface.
Faradaic Impedance
In corrosion processes as well as in all other electrochemical
phenanena, electrons are transferred between the solid electrode and
ions on the solution side of the interface. This is the mechanism
by which metal atoms become metal ions and leave the metal surface.
According to Faraday's Law, the rate at which metal atams became metal
ions is directly proportional to the rate at which charge is transferred
across the interface. Since the rate of charge transfer is defined as
current, the corrosion rate is directly proportional to the magnitude
of current flow.
The fundamental equation relating the current density across a
metalsolution interface is attributed to the work of Butler and
Vollmer and is given by:
i = i {e (l)flF/RT )e'F/ (2.1)
o
This equation has the typical form of an Arrhenius rate expression where
i is a concentrationdependent term called the exchange current density,
F is the Faradaic constant, R is the gas constant and 6 is a synmetry
factor. Equation (2.1) shows that the current density is a function of
temperature, T, and the polarization potential, n.
Butler (20) demonstrated that there is a linear relationship
between current density and potential at small values of polarization
potential, i.e.,
i F
RT (2.2)
For 6 = 0.5, io= 1oA/cm2 and T = 250, it can be shown that the error
in making the linear approximation does not exceed 5% if the polariza
tion potential is below 30 mv (16). Obviously other values of the given
parameters determine other ranges of linearity. Using Ohm's Law, the
equivalent electrical impedance to current flow offered by the charge
transfer reaction is thus a function of temperature and concentration
and may be modeled as a resistor. The term "charge transfer resistance"
was coined by Gerischer and Vetter (21).
There are other equivalent electrical impedances in the corrosion
process. As reaction between the various atomic species takes place,
reactants are consumed and products build in concentration. Transport
of reactants to and products from the interface is a diffusion process
which may be accelerated by boundary layer thinning caused by convective
mass transfer. The case of pure diffusion rate control was treated by
Warburg (22) who, after combining the impedances associated with
diffusion of both oxidizing and reducing species, found that the
resultant impedance has both real and imaginary elements. The socalled
"Warburg impedance" is therefore modeled as a resistor and a capacitor
in series.
Chemical reactions may also limit the rate of current flow. The
equivalent electrical impedance of chemical reactions was investigated
by Gerischer (23) who showed that it, too, has real and imaginary ccn
ponents and could also be modeled as a resistor in series with a
capacitor. The diffusion into or release of metal "adatans" from the
ordered metallic lattice of a corroding surface may also impede the
flow of electrons. The term "ad atoms" was coined by Lorenz (24) and is
the word which describes the final state of the metal ion prior to
going into solution. Just as in the case of diffusion and reaction
impedance, this "crystallization impedance" has real and imaginary
parts and is modeled by Vetter (25) as a capacitor in parallel with a
resistor.
Solution Resistance
The final component of the general electronic network model is
the resistance of the solution between the reference electrode and the
thin interface layer where all other components of the network lie. In
electroanalytical studies of redox reactions, one usually adds an
innocuous supporting electrolyte to the solution which eliminates or
minimizes the contribution of this component to the overall impedance.
In corrosion studies, the addition of a highly conductive salt such as
KC1 may prove anything but innocuous, leading to a significant increase
in corrosion rate. Furthermore, if one considers the application of
a general network model to a variety of corrosion monitoring scenarios,
13
there would be great utility in being able to monitor corrosion where
the magniture of the solution resistance is quite large such as in the
corrosion of reinforcing bars in concrete or in the corrosion of metals
in organic solutions with only small concentrations of electrolyte.
Equivalent Circuit Models
The general electronic network model for an electrochemical
interface with all the aforementioned equivalent electrical impedances
is discussed by Vetter (26) and is depicted in Figure 2.1. Grahare (27)
introduced the concept of faradaic impedance to describe the effective
impedance of the seriesconnected upper loop of the general model.
Other investigations have sought to simplify the general model by
neglecting components whose contribution to the total impedance would
be small under particular circumstances. For example, an equivalent
circuit diagram which considers only charge transfer and diffusion
components of the faradaic impedance was introduced by Randles (28)
and is shown in Figure 2.2.
Such simplifying models as those put forth by Randles are justified
in view of the fact that the impedance offered by some components of the
general electronic network model may be orders of magnitude smaller than
others. The simplified models are also less difficult to analyze than
the general model. The method of determining which components to
neglect may not be very straightforward, however. Vetter (29) discusses
the ramifications of this problem at length and describes a variety of
experimental methods useful in electrochemical analysis. For example,
either diffusion or a chemical reaction may be the cause of a limiting
current in a direct current polarization test. One may distinguish
Figure 2.1 General electronic network model for an electrode showing
impedances associated with charge transfer (Rt), diffusion
(R ,C ), chemical reaction (R ,C ), crystallization (R 'C )
ana also considering double layer capacity (CD) and
solution resistance R (after Vetter).
s
Figure 2.2 Pandles circuit model for electrode imnedance, W, Warburg
impedance associated with diffusion; R, charge transfer
resistance; R solution resistance; double layer
capacitance.
15
which of the two provides the dominant resistive component by stirring.
Reaction impedances are not affected by stirring while diffusion
impedances are decreased due to diffusionlayer thinning.
Alternating current measurements may also be used to distinguish
among and to quantify the various impedance components. Since the imped
ance of a capacitive element is a function of frequency, plots represent
ing the dependence of the faradaic impedance (upper half of the circuit
shown in Figure 2.1) on the square root of the reciprocal frequency are
sometimes useful in separating the various contributions to the faradaic
impedance. Such a plot for an interface exhibiting only charge transfer
and diffusion resistance is shown in Figure 2.3. The upper line repre
sents the real part of the impedance and contains only the resistive
elements Rt and Rd while the lower curve is the imaginary part of the
impedance and contains only the capacitive part of the diffusion
impedance. Of course, interfaces exhibiting other contributions to the
faradaic impedance face more difficult interpretation with this method.
Furthermore, experimental techniques of separating the faradaic ccmpon
ent from the doublelayer and solutionresistance components do not
usually work in electrochemical reactions in which the electrode itself
is involved, i.e., corrosion.
Electrochemical Reactions in the
Presence of Passive Films
In addition to the impedance contributions of the electrochemical
interface, the character of corrosion product films is of extreme
importance to the rate and type of corrosion for many metals. Indeed,
the presence of a passive film may protect an otherwise active metal
from electrochemical deterioration.
FO
R RFR+R D
1/' /
Figure 2.3 Dependence of the components of the faradaic impedance
on l/vfor ratecontrol determined by diffusion and
charaetransfer only; Rf, faradaic resistance; Rt,
charge transfer resistance; Rd, diffusion resistance;
1/wCf = l/OCd, capacitive reactance due to diffusion.
Impedance data for solid films suggest that a series or parallel
combination of a resistor and capacitor can be used as a model for the
film. Pryor (30), Beck et al. (31, 32), Heine et al. (3335) and
Richardson et al. (36, 37) have conducted numerous studies of the
properties of both airformed and anodic oxide films on aluminum using
AC impedance techniques. In the attempt to isolate the impedance of
the film from the impedance contributions of the electrochemical inter
face, Richardson et al. (37) proposed the equivalent circuit model as
shown in Figure 2.4. Haruyama and Tsuru (38) also considered this
socalled dielectric film model and have contrasted it with charge
transfer and adsorbed oxygen models in predicting the impedance
characteristics of passive iron.
Electrochemical Corrosion Monitoring
In the absence of a general predictive theory for the rate of
metallic deterioration under the wide variety of possible exposure
conditions, engineers rely on empirical corrosion rate data obtained
from systems closely resembling the one of interest. Such data collec
tion methods, using direct analytical methods such as weight loss or
spectroscopic solution analysis, are timeconsuming and, even when
carried out carefully, may not accurately represent the full range of
environmental conditions present in a real system. The direct analytical
methods are also limited to metallic systems which do not form adherent
layers of corrosion product.
Figure 2.4 Richardson, Pbod, Breen model of an electrochemical
interface with a passive film on the surface; CF
capacitance of film; Rf, film resistance; CD, double
layer capacitance; Zf, faradaic imoedance; Rs,
solution resistance.
19
The electrochemical mechanism of metallic deterioration in aqueous
environments has led to the application of electroanalytical methods to
the study of corrosion and to the in situ monitoring of corrosion in
real systems. Electrochemical methods can determine corrosion rates
much more quickly than the direct methods and are reasonably accurate.
However, most electrochemical methods suffer from the disadvantage that
they must perturb the corroding system with an externally applied DC
voltage, a fact which inevitably changes the local surface properties
and perhaps the local corrosion rate from that of the surroundings.
Recognizing the potential adverse consequences of this perturbation,
one seeks a method which obtains information about the corrosion process
as quickly as possible with the smallest possible perturbations.
Two generic types of electrochemical methods have been applied to
the corroding interface: the widelyused direct current polarization
methods and the more recent AC impedance techniques.
DC Methods
The two most popular DC methods are Tafel line extrapolation and
polarization resistance measurements.
Tafel line extrapolation. The method of Tafel line extrapolation
is based on the theories of Wagner and Traud (39) and employs large
polarization amplitudes. By extrapolating the large amplitude cathodic
and anodic polarization curves toward the corrosion potential, one
obtains I and E from the point of intersection. See Figure 2.5.
corr corr
This method is widely used as a laboratory analysis technique, but
because of the large polarization of the corroding electrode, it can
cause irreversible changes during the measurement process. This fact
renders it of only limited value for corrosion monitoring purposes, in
E CORR
*COPR
LOG CURRENT DENSITY
Figure 2.5 Determination of corrosion potential and corrosion
current from Tafel line extrapolation.
21
and of itself, although the determination of Tafel line slopes is
required for corrosion rate computation via the polarization resistance
method. (See discussion of polarization resistance below.)
Lorenz and Mansfeld (11) point out that the corrosion rates
predicted by Tafel line extrapolation for uniform metal corrosion in
acid media are in good agreement with weight loss measurements. However,
in systems where corrosion product layers form on the surface, predictions
of corrosion rate via the Tafel line method may be very inaccurate.
This is not surprising since the imposition of a DC signal may change
the characteristics of the corrosion product film. Furthermore, break
down of the film tends to occur locally rather than uniformly over the
surface. Thus, the "average" corrosion current does not accurately
reflect the destruction of the component. Similar predictive errors
have been observed in the presence of inhibitors (11).
Polarization resistance. Measurement of polarization resistance
is a DC method more suitable for use in corrosion monitoring. Polariza
tion resistance, Rp, is defined as the tangent to a polarization curve
at the corrosion potential. See Figure 2.6. The relationship between
the polarization resistance, R, and corrosion current, icorr was
developed by Stern and Geary (40, 41) and Stern (42). They showed
that for a simple charge transfer controlled system,
8a 8c 1 (2.3)
corr = 2.303 (8 + 8c R
where ir is the corrosion current and Rp is the polarization
corr p
resistance. Since 8 and 8 are the anodic and cathodic Tafel constants,
a c
Ut
C /
CORn
CURRENT DENSITY
Figure 2.6 Determination of Polarization Resistance
Equation (2.1) can be written
i = B
corr (2.4)
p
where
aa c
2.303($a + ic
Thus, the determination of anodic and cathodic Tafel constants and the
slope of the polarization curve yield predictions for i via Equation
corr
(2.4).
Polarization resistance measurements are generally made at applied
potentials within 30 my of the corrosion potential in an attempt to
confine polarization to the linear region. Although R can be measured
with AC or DC perturbations, the majority are made using DC steadystate
techniques. The DC steadystate techniques can be very time consuming
where corrosion rates are very low, a disadvantage for a monitoring
technique. The value of polarization resistance measured by such
a technique also contains a contribution from solution ohmic resistance.
When this socalled "uncompensated resistance" (R,) is large, the error
due to its inclusion is considerable and if not accounted for leads to
underestimation of corrosion rate.
Other sources of error in polarization resistance measurements
are discussed by Lorenz and Mansfeld (11) and reviewed extensively by
Callow et al. (43). Among the many factors mentioned are failure to
achieve steadystate during polarization; timedependence of the
corrosion phenomenon, particularly during early stages; localized
corrosion processes such as pitting or crevice corrosion; hydrogen
absorption and adsorption; adsorption of reaction intermediates; and
inhibitor redox processes.
AC Methods
While the various DC methods all attempt to characterize the
corroding interface in terms of a single resistance value, AC methods
offer, in principle, the possibility of separating solution and faradaic
resistance components and permit simultaneous quantification of the capa
citive component of the complex impedance. Because they are capable of
quantifying both resistive and capacitive impedance components, AC
methods offer much more latitude in establishing the efficacy of the
theoretical models described previously. Numerous investigations have
capitalized on this capability and have used AC methods to measure
polarization impedance, the impedance of anodic films and faradaic
impedance of redox reactions. Excellent reviews of the development of
AC electrochemical methods are given by Grahame (27), SluytersRehbach
and Sluyters (44), and Smith (45).
Because of the capacitive components in the electrochemical
interface network, polarization impedance is frequencydependent (31).
At high frequencies, the capacitive reactance due to the double layer
is low and thus determines the total polarization impedance. Con
versely, at low frequencies the capacitive reactance of the double
layer approaches infinity and the polarization impedance is equal to
the polarization resistance R See Figure 2.7. This realization led
Epelboin et al. (1) to define the polarization resistance, Rp, as the
limit of the faradaic impedance at zero frequency.
Epelboin and coworkers (1, 2) also suggest that a more reliable
correlation with corrosion rates is obtained by using a quantity called
the "charge transfer resistance" (Rt), the limit of the faradaic
LOG FREQUENCY
Figure 2.7 Frequency dependence on an electrochemical
interface inmpedance. Rp is the limit of
faradaic impedance at zero frequency.
impedance at infinite frequency. By performing measurements at high
frequencies, it was reasoned, variations in the surface coverage of
adsorbates would be precluded since diffusion could not keep up with
the changes in polarity. In a study of the inhibition of iron corrosion
by propargyl alcohol in acid solutions, Rt successfully predicted
corrosion rates where measurement of R failed.
p
Lorenz and Mansfeld (11) dispute the general usefulness of this
approach, however, citing its dependence on the assumption that the
doublelayer capacitance can be totally separated from other capacitive
contributions of the electrochemical interface. The treatment of the
double layer as a capacitor in parallel with the polarization resistance
leads to the prediction of a single semicircular loop in the complex
plane plot of the system impedance. As shown in Figure 2.8, the iron
propargyl alcohol systems investigated by Epelboin et al. deviate sub
stantially from this predicted behavior. The presence of inductive loops
in these and other iron systems is a particularly puzzling phenomenon
from the standpoint of correlating with any interface model. One basic
conclusion of Lorenz and Mansfeld's critique seems particularly apropos:
a knowledge of systemspecific corrosion behavior is required before any
electrochemical measurement methods can be used reliably to predict
corrosion rate.
Measuring electrode impedance. The impedance of an electronic
network or of an equivalent circuit which simulates a corroding electrode
is a complex function of frequency possessing both magnitude and phase
information. Having the units of resistance, it may be found by taking
the ratio of the complex current flowing through the circuit to the
complex voltage drop across the network.
jG(a)
200 "j ,I 400
100 so *, 2 200
0 100 200 3C0o 00 soo 500 00 0
S00o 1C0203 I05
(2)
.G(n ..
S 33 25,
p 7050
20 I
%50
,Do
200
200 0 6O 800 100 200
00 00 )
50 100 0i 0 5
1 003
l/fRnn)[6
200 00 00 6800 1 1'1200
.00
2 0", OOIr 15'
0' 0 70oj0 
Figure 2.8 Impedance diagrams for spontaneous corrosion of iron in
aerated H2SO4; (1) LM H2SO4; (2) 0.5 M H2SO4; (3) 0.5 M
H2S04 + 0.1 x 103 M propargylic alcohol; (4) 0.5 M H2S04 +
0.2 x 103 H propargylic alcohol; (5) 0.5 M H2SOa + 0.5 x 103
M propargylic alcohol; (6) 0.5 M H2S04 + 2 x 103 M propar
gylic alcohol; (7) 0.5 M H2SO4 + 5 x 103 M propargylic
alcohol; (8) 0.5 M H2S04 + 20 x 103 M propargylic alcohol.
See Reference (1).
28
This can be done by a number of methods. A simple though tedious
approach is to compare the input voltage perturbation with the output
current response in x and y channels of an oscilloscope. The resulting
Lissajous figure can be used to determine the impedance modulus and
phase shift for a single frequency. The method is timeconsuming since
it must be repeated at each frequency and is not very practical for low
frequencies. Another technique compares input and output signals at a
single frequency and yields direct reading of modulus and phase shift
or, in stme cases, real and imaginary components. The tedium of multiple
sequential frequency measurements is alleviated somewhat by the
availability of progranmable equipment, e.g., Solartron. The only
method capable of simultaneously comparing the perturbation and response
of multiple frequency signals employs equipment which computes the
Fourier transform.
Linear System Theory
Assumptions
When the impedance is evaluated with a digital signal analyzer,
the interface is treated as a "black box" with a single input and
output terminal. The potential drop across the interface is treated
as the output function of the system and is compared with the current
flow through the interface which is treated as the input function of
the system. The algebraic ratio of these two signals expressed as
functions of frequency is the frequency response or sometimes called
the transfer function of the system. Before one attempts to determine
the impedance of a corroding interface by means of digital signal
analysis and to use it to characterize the interface, it is appropriate
29
to consider the inherent assumptions one makes in this process. These
assumptions are relaxedness, linearity, and timeinvariance (46).
Relaxedness. When any physical system is treated as a black box
and one is attempting to abstract key properties of the system from
its response to same excitation, one must be certain that the system
is initially relaxed, i.e., that the system is not still responding to
scae previously applied signal at the instant of test signal applica
tion. For such a relaxed system, the response y(t) may be related to
the input excitation u(t) by the following relationship:
y(t) = h u(t) (2.5)
where h is a function that uniquely specifies the output y(t) in terms
of the input u(t).
Relaxedness is usually a justifiable assumption when evaluating
electrochemical interfaces. From the author's own experience, the re
laxation time of an electrochemical interface from a pulse is typically
less than one second. Thus, if the interface has not been stimulated
for ten seconds or more, the response of the system may be reasonably
assumed to have resulted only from the excitation u(t). Of course, all
electrochemical interfaces exhibit continuous random fluctuations in
potential and current usually known as electrochemical noise (14, 47).
These fluctuations typically have an amplitude on the order of yV, and
the system obviously exhibits continuous response to these excitations.
However, if one makes the amplitude of the excitation signal large
enough, the ratio of input/output signals to system noise is sufficient
to obscure the frequency response due to system noise.
30
Linearity. A relaxed system is considered linear if two
mathematical conditions are satisfied (46): (1) the output due to a
combination of inputs equals the sum of the outputs due to each input
applied individually, i.e.,
h {E ui (t)} = E h ui(t) (2.6)
i i
and (2) the output due to an individual input multiplied by a scalar
equals the output multiplied by that scalar, i.e.,
h {a ui(t) } = ah ui(t) (2.7)
A linear electrochemical system exhibits a linear relationship between
current and potential for all values of frequency. As shown previously
by Equation (2.2), the charge transfer behavior is approximately linear
if the polarization voltage is kept close enough to equilibrium. This
implies that Equation (2.7) is valid only for values of a below same
upper bound. The limit of input signal amplitude can be determined
in practice by the limit of linearity in a DC polarization experiment.
In general, input signal amplitudes less than about 30 mv from
equilibrium satisfy this requirement.
Timeinvariance. A relaxed linear system is timeinvariant if
the characteristics of the system do not change with time. This con
dition is not rigorously valid for the electrochemical interface of a
corroding electrode, particularly when a passive film is present. In
such cases, the gradual growth of the film will have a definite effect
on the values of the network parameters. To get around this limita
tion, one must assume that the corroding electrode exhibits quasisteady
state behavior, i.e., does not change significantly during the period
31
of measurement. Minimizing the period of measurement, besides enhancing
characterization speed, also serves to assure that this condition is
satisfied.
Conclusions. The requirements of relaxedness, linearity and
timeinvariance impose some important constraints on the way electrode
impedances may be measured using digital signal analysis. In order to
neglect the effect of random fluctuations, the excitation signal must
have a significantly larger amplitude than the system noise. To
satisfy linearity requirements, on the other hand, the input signal
should be as small as possible, usually less than about 30 my from
equilibrium. To assume that timeinvariance of the system is adequately
approximated, the period of measurement should be as short as possible.
Domain Transformations
The transformation of time domain signals into the frequency
domain for the purpose of computing electrode impedance is outlined
by Pilla (48). Pilla illustrates how this transformation might be
accomplished in general by the Laplace transformation:
F(s) = / f(t) exp (s)dt (2.8)
0
where s is the Laplace transform variable (49). The quantity s is a
complex number given by s = o + jw in which a is the real and jw the
imaginary part. Due to the properties of F(s), it is possible to
integrate along either or both the real and imaginary axes is the
complex frequency plane which defines F(s). In the imaginary axis
transformation (s = ju), Equation (2.8) may be written:
F(jw) = f (t) exp (jo)dt (2.9)
0
Equation (2.9) is the wellknown singlesided Fourier Transform (48).
For relaxed, linear, timeinvariant systems, the frequency response
function may replace the transfer function with no loss of useful
information (49).
Although sane investigations continued to be made into the utility
of Laplace transformations (50, 51), the development of the "fast Fourier
Transform" algorithm (FFT) (52, 53) made it convenient and practical
to effect the imaginary axis transformation in real time. Creason and
coworkers (58) capitalized on this development, demonstrating that with
an online minicomputer, it is possible to acquire and transform time
domain signals into the frequency domain in less than 3 seconds (6).
Utilizing online ccaputation of the FET, it is possible to
determine the admittance of an electrochemical cell by the expression
A(w) = I (w)/E() (2.10)
where A(w) is the cell admittance, I(J) is the cell current, and E(w)
is the potential across the electrical double layer. For the sake of
convenience of expression, Creason and coworkers (6) chose the
alternative form
A(W) = I(w) E* (w)/E(w)E* (w) (2.11)
where E* () is the complex conjugate of E (c). In this formulation, the
admittance is expressed as the cross power spectrum divided by the
auto power spectrum, a form which produces phase information in
the numerator only. See Appendix A.
33
Although, in principle, this formulation is applicable to any
generalized test signal, Creason and coworkers anticipated that sane
signal waveforms might be more "efficient" than others (68). In
this context, "efficiency" refers to the amount of data dispersion
present after a certain number of replicate measurements. With this
in mind, they undertook a detailed empirical study of measurement
efficiency associated with Fourier transform faradaic admittance
measurements (8). Four waveform classes were used: (1) complex
periodic signals, waveforms composed of discrete coherentlyrelated
sinusoidal components; (2) almost periodic signals, waveforms composed
of discrete noncoherently related sinusoidal components; (3) periodic
transients, signals with continuous welldefined snoothlyvarying phase
and amplitude spectra; and (4) stochastical signals, signals with con
tinuous spectra which have smooth distribution after long times.
The efficiency of the various waveforms was evaluated using the
redox couple Cr(C)3/Cr(CN) 64 in 1 M KCN at 250C on a dropping mercury
working electrode. As is customary for AC polarographic experiments,
the faradaic admittance data is portrayed in plots of magnitude vs a
and cot ) vs . See Figure 2.9. Such plots are linear or nearly so
for the redox couple under consideration, and it was thus possible to
quantitatively assess measurement precision based on the relative
standard deviations of the intercept and slope as determined by the
linear regression technique.
The results of this comparison for 64 replicates on random noise,
pseudorandom noise, pulse and multicaponent sinusoidal arrays of
varying amplitude is quite dramatic. In general, the data precision
34
''
. g
i a ai
0 9' B *
O
4r
0 0. r1
ul^
Iag a
O  a .
C14
*6 \i +
\ * 3 u *
v u a)0)1
35
improved with decreasing signal amplitude presumably in response to
decreases in faradaic nonlinearity. Overall, the best precision was
achieved with a phasevarying 15 component odd harmonic array with a
standard deviation in the intercept of 0.08%. Under a similar set of
measurement conditions, a negative pulse produced an intercept standard
deviation of 6.33%. The random noise and pseudorandcm noise signals
fell between these extremes with standard deviations of 1.39% and 0.56%,
respectively.
Based on these early data, Schwall et al. (12) developed a high
speed synchronous data generation and sampler system for which the
acronym SYDAGES was coined. SYDAGES functions as a programmable signal
generator combined with two data acquisition channels with the capability
of handling signals up to 500 kHz.
Smith (10) has predicted that Fourier transform data processing
on electroanalytical measurements will exceed its influence in the
field of spectroscopy. Despite this predictions, relatively few
investigators have conducted studies utilizing this feature. Blanc et
al. (4) demonstrated how impedance measurements could be made on an
ironsulfuric acid system using a socalled correlator, a device which
determined the Fourier transform. DeLevie and coworkers (13) have
applied the procedure in the study of ionconducting ultrathin membranes.
Smyrl and Pohlman (54) demonstrated that corrosion parameters can
be determined by this method although in their system, the Fourier
Transform was performed batchwise on a CDC 6600 system.
The apparent reticence of the electrochemical community to
embrace this technique may be explained in part by the fact that
electronic system noise becomes a problem when one tries to perturb
an electrochemical interface with small multiple frequency signals.
Unlike the single frequency "lockin amplifier" method, there is no
way to distinguish between electronic system noise and system response
in developing the Fourier spectrum. Fortunately, investigators of
electrochemical noise (3, 14, 47) have also been concerned with this
problem. Recent work by Schideler and Bertocci (47) has resulted in
the development of lownoise potentiostat capable of suppressing
electronic noise to the order of 2.5 x 108v/Hz. They (47) have used
this lownoise potentiostat to measure electrode impedance using both
superimposed and electrochemical noise signals.
Analysis of AC Impedance Data
During the evolution of AC frequency response techniques, a number
of methods of portraying and analyzing data have been proposed and used.
SluytersRehbach and Sluyters (44) provide a review of the possibilities
as they might apply to electrochemical analysis. One of the most
carbon portrayals in the AC literature is the complex plane plot, that
of the imaginary component of the electrode impedance plotted against
the real part.
For a Randles equivalent circuit (see Figure 2.2), the complex
plane plot can provide quantitative information about the various
components of the circuit. Such an equivalent circuit will produce
a complex plane plot of the form shown in Figure 2.10. As can be
seen in Figure 2.10, the plot may be separated into two regions, one
exhibiting semicircular character and the other linear behavior.
This observation is consistent with the analytical determination of
REAL PART OF IMPEDANCE
Analytical prediction of impedance behavior
of Pandles equivalent circuit.
ct
L,
1_
Q_
1_1
0
CE
Figure 2.10
38
SluytersRehbach and Sluyters (44) who showed that the real and
imaginary components of the Warburg impedance can be determined in
the low frequency linear region while the semicircular high frequency
region yields quantitative data on the values of the remaining
components.
If experimental acquisitions of impedance data yields no such
linear low frequency region, which is often the case for corroding
electrodes, the circuit can be modeled as the threeelement networks
shown in Figure 2.11. The impedance of the network shown in Figure
2.11 may be written:
R
Z = R + (2.12)
s l+jmR(Cd
1 + pd
The real part of the impedance is given by
R
P
ZR = R + (2.13)
R +2 2 2
1 + 2 2R
and the imaginary part is given by
R 2
Z = (2.14)
1 + W
By appropriate rearrangement and combination of Equations (2.13) and
(2.14), one finds
zI
S= (2.15)
(ZR Rs )RCD
which upon substitution into Equation (2.13) and the appropriate
rearrangement yields
Zr Rs 2 = 2 (2.16)
RP
Figure 2.11 Simplication of Randles equivalent circuit; valid
where diffusion is not ratelimiting.
OAPEX= P/RPCD
0
C
cZ
a
Figure 2.12 Complex plane evaluation of the threeelement
network shown in Figure 2.11.
This is the equation of a circle in the complex plane with its center
R
on the ZR axis at ZR = R + ? and radius R /2. Intersections of the
circle with the ZR axis occur at Z = R for c = and ZR = Rs R
for a = 0. Only cases where w, (C, R and Rs are positive have physical
significance; so one plots the circle only in the fourth quadrant of the
complex plane. In the literature, this plot is usually rendered as
ZI vs ZR as shown in Figure 2.12. It can also be shown that the fre
quency at ZR = Rs + R/2, i.e., at the apex of the semicircle, can be given
by
1 (2.17)
apex Rp
Given data over a sufficient range of frequency, therefore, one
can determine values for Rs, R and CD from a ccnplex plane plot of
the impedance.
Other methods of graphical analysis have been suggested in the
literature (54). Linear plots are useful because it is difficult to
curvefit a semicircle when there is data scatter. By combining
Equations (2.13) and (2.14), two linear equations are derived:
ZR R + Rp RpCD W z (2.18)
zI
Z = R + C (2.19)
Plotting ZR vs Z *f yields a straight line with a slope of 2r RpCD
and an intercept of Rs + Rp. A plot of ZR vs Zi/f provides an inter
cept of R See Figure 2.14.
IMAGINARY*FREGUENCY
 IlMAG INARY/FREQUENCY
Figure 2.13 PohlmanSmyrl technique of analyzing the impedance
of the threeelement network given in Figure 2.11.
FREQUENCY (HZ)
FREQUENCY (HZ)
Figure 2.14 Bode plot of frequency response for the threeelement
network shown in Figure 2.11. m. and f are com
plicated functions of CD and R .
,s P
' P v R
r
A third camon method of data portrayal is done with plots of
log I Z and phase angle, $, vs log of frequency, f, commonly known as
Bode plots. The values of and Rs may be obtained from the former
plot as shown in Figure 2.14 and in combination with the latter plot
yields C. The Bode plots have several advantages over the other
graphical portrayals: (1) since the log frequency scale is used, data
from lower frequencies are not obscured; (2) the network component values
may be computed using higher frequency data than with the other methods.
This is fortunate since the low frequency data require much more time
to gather and are more susceptible to significant dispersion.
Recapitulation: StateoftheArt
The characterization of electrochemical interfaces has been
attempted with a variety of methods. DC techniques result in the
depiction of the interface as a single polarization resistance term,
which includes the resistance of the electrolyte solution. AC techniques
offer the possibility of separating solution resistance from faradaic
resistance components while quantifying capacitive components at the
same time. In Figure 2.15, schematic diagrams of electrochemical cells
contrast the interface model using DC polarization with one possible
model using an AC technique. AC impedance may be measured by a variety
of methods, the majority of which require the sequential application of
a series of single frequency sinusoidal signals.
The tedium and timeconsumption of such processes is eliminated in
principle by fast Fourier transform technology. Using the FFT algorithm
in an online minicomputer, one can simultaneously investigate a
continuum of frequency by converting time domain input perturbation
(A)
(B)
Figure 2.15 Schematic diagrams of electrochemical cells. The
interface model is represented as shown in (A) by
the DC polarization technique. The threeelement
model including double layer capacitance as shown
(B) or other more complicated models may be depicted
using AC techniques. R polarization resistance;
Rs, solution resistance, CDL, double layer capaci
tance; C, counter electrode; R, reference electrode,
W, working electrode.
45
and output response signals into the frequency domain and computing the
electrode impedance. Graphical methods applied to the resultant cam
plex plane plots result in the determination of equivalent circuit
parameters.
The primary difficulties encountered with FFT electrode impedance
measurements have been associated with selection of the "most efficient"
signal type and signal amplitude. In general, pseudorandom noise
effects less data dispersion than white noise, while transient signals
such as pulse, ramp, and step tend to be the least efficient. With
regard to signal amplitude, one must select a signal large enough to
negate the effects of electronic equipment and electrochemical system
noise while not introducing faradaic nonlinearities with too large a
signal amplitude. The development of lownoise potentiostats should be
helpful in permitting this to be done.
CHAPTER III
SYSTEM DEVELOPMENT
System Components
The assemblage of equipment referred to here as the "AC system"
was built around a HewlettPackard (HP) 5420 digital signal analyzer.
The analyzer continuously monitors and digitizes timevarying analog
signals corresponding to the perturbation and response of the system
under investigation. Having gathered an ensemble of digitized data
representing the time domain, the analyzer performs a transformation
to the frequency domain via the fast Fourier transform algorithm (FFT).
A variety of algebraic manipulations may then be performed on the
resultant arrays to yield both time and frequency domain functional
relationships which describe the frequency response of the system. (See
Appendix A for a more thorough discussion of the capabilities of a digi
tal signal analyzer.)
The signal analyzer capability of primary interest in this study
is the rendition of the transfer function. In its general definition,
the transfer function of a system is a frequency domain correspondence
between perturbation and response signals. Since it is a complex
function, it provides both magnitude and phase information at each fre
quency. In this study, the pertubation, E(t), is a bandwidth limited
white noise (BLWN) voltage signal applied between the reference and
working electrode of a threeelectrode electrochemical cell. The
response, I(t), is a timevarying voltage signal directly proportional
to the current passing between the counter and working electrodes. The
transfer function, H(f), is therefore a measure of the corroding
electrode admittance, Y(f).
H(f) = Y(f) = output I(f)
input (f) (3.1)
By mathematically inverting the ratio of response to perturbation or by
reversing the voltage/current leads to the analyzer, one obtains the
electrode inpedance, Z(f).
1 E(f)
Z(f) =f (3.2)
A schematic diagram illustrating this analyzer function is shown in
Figure 3.1.
As mentioned in the previous chapter, the BLNN signal is not the
most "efficient" for electrochemical interface perturbation (8). The
BMN source was used because of its availability, being an integral part
of the HP5420. Other signal sources should provide data less susceptible
to scatter.
As shown schematically in Figure 3.2, the BLW signal is injected
into the Princeton Applied Research (PAR) 173 potentiostat at the summing
junction of the control amplifier. Here it adds to any DC set potential
dialed on the potenticmeter. The resultant combination of AC and DC
voltage components is then maintained between the reference and working
electrodes. This combined signal is sensed by the potentiostat electro
meter circuit and is fed to one of the two analogtodigital converter
(ADC) channels of the HP5420. The flow of current between the counter
electrode and the working electrode in response to the voltage perturba
tion is sensed by a zeroresistance amneter which produces a voltage
S0
40 )
S "I
Si ri
r4 p
n1~,
4J U r
n c n ,.. 3 En H
4 m0 CJ o
 43 4 u*4
4) O 4o ce 0
a ,4 4 ~ 4.,) H tJ Q
01 q 4
W H 0 4
 0 O
o 4o
a ro 
4 .8 r
l C *
~01 *S4u
* QH
*r4J d 0
0 Y Z r ?C,
*^ c~ ra~ o o
proportional to the measured current. This latter voltage is fed to
the second ADC channel of the HP5420.
Since the PAR 173 was designed for DC work, there was initially
some concern about the capability of the potentiostat to reliably trans
mit the higher frequency components of the AC signal. To test the fre
quency response of the potentiostat, a 1 volt pp sinusoidal signal was
applied at the summing junction of the control amplifier. The voltage
drop across a resistor connected between the reference and working
electrode leads was monitored and compared to the input signal on a dual
trace oscilloscope as the signal frequency was increased. There was no
perceptible attenuation or phase lag across the resistor until about
30 kHz; above the 25.6 kHz maximum bandwidth range of the HP5420. This
procedure demonstrates that the potentiostat is adequate for the range
of frequencies which will be analyzed with this technique.
The third major component of the AC system is the 187K byte, HP9845
minicaputer with integral dotmatrix thermal printer and two integral
tape drives. To permit even faster retrieval from mass storage, the com
puter was also equipped with two eightinch floppy disk drives. The
computer carried out a variety of tasks including control of the HP5420,
storage of impedance data from individual runs, tying data from sequen
tial runs, mathematical manipulation of data and graphical portrayal of the
data on the HP9845 CRT, thermal printer or remote, fourcolor plotter.
A schematic diagram illustrating the interconnection of the various
components is given in Figure 3.3. The HP9845 is connected to the HP5420
via an HP interface bus (HPIB); all other signalcarrying connections
being made with coaxial cable.
Figure 3.3 Schematic illustrating the interconnection of the
electrochemical cell, PAR 173 potentiostat, HP 5420A
signal analyzer and HP 9845 computer. The computer
controls the operation of the analyzer and receives
impedance data from it. in the form of real, imaginary,
frequency triples of data. Following data manipulation,
the computer delivers graphical portrayals of the
impedance data.
It would have, of course, been possible to control the setup and
execution of an analysis run by means of manual key strokes on the
HP5420 console. However, the versatility of the HP5420 renders the
number of keystrokes required to establish a desired setup state rather
largetypically 1520. By creating ccmnand sequences in the software
of the HP9845, tediuminduced operator error in the execution of an
analysis run can be eliminated. The time required for a set of sequen
tial analysis runs on the same electrode is thus minimized and the runs
are reproducible. Furthermore, the HP5420 is incapable by itself of
connecting sequentially gathered sets of data, a task necessitated by
developmental problems discussed in the next section.
Mathematical manipulation of data includes such tasks as multiplying
and dividing the imaginary part of the impedance data by frequency for
portrayal in plots of real versus imaginary x frequency and versus
imaginary/frequency. The computer also determines the magnitude of the
impedance from real and imaginary parts, computes log magnitude versus
log frequency plots and scales the data by the value of the resistor
across which the current is determined. A linear regression routine
may be performed on any selected section of plot yielding the equation
of the straight line fit and correlation coefficient. A datasmoothing
routine may also be performed on data sets.
Once the desired mathematical manipulations have been performed
on the data, they may be portrayed graphically in any of the standard
formats described in Chapter II or in any other desired format.
Graphical analysis of the standard formats presumes the data fit the
53
threecomponent equivalent circuit model described previously, yielding
two values of resistance and one of capacitance. One may also generate
a theoretical data set for a threecomponent network with arbitrary values
of Rs, Rp and CD and plot the theoretical set against the real data.
The numerous capabilities of the computer are all controlled from
a single main program written in BASIC. The main program is read into
the random access mnomry from tape or floppy disk. Once the user selects
the desired computer function from the menu displayed on the CRT, other
sections of code required to perform the specified task are read in
from floppy disk at the direction of the main program. The main program
is interactive with the user thus permitting operation by persons not
highly trained in computer technology. As previously mentioned, the user
may also create command files of frequentlyrepeated operations which may
be stored or reexecuted. Appendix D contains a thorough description of
both the main program and same frequentlyused command files.
Developmental Problems
Equipment Integration
At the outset of the project, it was anticipated that equipment
integration would be a relatively simple task. During attempts to
interface the HP5420 and its integral random noise source to the PAR 173,
however, offset voltages were encountered, presumably the result of dis
similar ground loop currents. These offset potentials were troublesome
because they changed the DC component of the applied signal. As a con
sequence, the set potential of the potentiostat was observed to change
by as much as 30 mv. In addition, the DC components of the perturbation
and response signals were part of the input to the ADC channels while
only the AC components are of interest front the standpoint of analysis.
The choice of AC coupling in the setup of the HP5420 is supposed
to solve the latter difficulty by eliminating the DC component of the
signal. However, in practice, the choice of AC coupling did not
eliminate the offset potential; in fact, it seemed to exacerbate the
problem. Thus, the use of the analyzer's most sensitive 100 mv range
was precluded since the combination of the AC signal with DC offset
caused the ADC to overflow.
Three grounds were considered in determining the origin of the
offset potentials: earth ground, power ground and circuit or virtual
ground. Although one normally assumes earth and power ground to be
identical, a several hundred millivolt difference was found in our
laboratory. Several virtual grounds were also found to be dissimilar.
For example, merely connecting the virtual ground on the potentiostat
to the virtual ground of the ADC caused the ADC to overflow on its most
sensitive 100 mv range. Since the corroding interface is maintained at
the virtual ground of the potentiostat, it is clear that ground loop
currents and the associated offset potentials are a logical consequence
of these disparate ground potentials.
Conventional isolation techniques were not successful in eliminating
the voltage offsets or were accompanied by unacceptable side effects.
Cacmon point grounding, for example, reduced the offset potentials only
slightly. Because of the impedance associated with capacitors and in
ductors, both capacitor and transformer coupling would have introduced
artifact over some range of frequency.
55
Optical isolation proved to offer a novel yet practical solution
to this dilemma. An optical isolation circuit was designed and built.
When used between the noise source and input to the potentiostat, offset
potentials were eliminated. The circuit design and operation of the
optical coupler is described in Appendix B.
Frequency Resolution
A second major area of difficulty in creating the AC impedance
system based on digital signal analysis was caused by a limitation of
the signal analyzer itself. When operated in the transfer function mode,
the HP5420 creates ensenbles of digitized data from the analog signals
injected into its two ADC channels. Each ensemble of data is transformed
into 256element array in frequency domain via the FFT algorithm.
Dividing the array coming from channel 2 by the array coming from
channel 1 yields the transfer function which in the case of these ex
periments is the electrode impedance. Once impedance data have been
collected for a particular range of frequency, they may either be stored
on tape as real, imaginary, frequency triples of data, used directly for
display in a variety of common graphical formats on the integral CRT of
the HP5420, or be transferred to the HP9845 for storage on floppy disk.
One limitation of the analyzer in the study of electrode impedance
is a consequence of frequency resolution. Once a range of frequency
analysis has been selected, the analyzer divides the range into N = 256
equally spaced frequency intervals. The width of a single interval thus
defines the uncertainty in frequency, Af, for that range, and Af is
always 1/256th of the full scale value of frequency. Although at the
upper value of frequency in the range the percent error given by
56
100xAf/f is approximately + 0.4%, it becomes + 4% one decade below
the top and + 40% two decades below the top. In the limit, the lowest
frequency interval contains all frequencies between 0 and 1/256th of the
fullscale frequency.
Since the percent error of a frequency measurement is thus inversely
proportional to the frequency at which the measurement is made, it is
called 1/f error in the technical literature. The upper decade of fre
quency contains approximately 225 of the 256 frequency intervals which
is another illustration of why lower frequencies are resolved so poorly.
Figure 3.4 shows how the frequency resolution changes as a function of
frequency for various ranges of analysis.
Work with simulated electrodes suggests that three decades of
frequency are useful in characterizing electrodes, and for real electro
chemical interfaces, at least five decades are needed if the appropriate
range of analysis is not known initially. Since only error less than
+ 4% was considered acceptable, it was decided to analyze over consecu
tive decades of bandwidth to improve the low frequency resolution. The
shaded region of Figure 3.4 depicts the error envelope when data from
five successivelymeasured ranges are tied together discarding low
resolution overlapping data.
Since it is not possible to either store or display a connected set
of data from sequential runs on the HP5420, the HP9845 performs this
function on sets of data previously stored on floppy disk. A schematic
illustration of this datatying exercise is shown in Figure 3.5. The
sequences of ccmmands necessary to set up the HP5420, make a run for a
particular frequency range, store the data for that run and to repeat
4N
, 5
=
o
lU
10
H 4
s ^i I
ORH
S.1
t
o
s 1
_1 II I_ ~ I
the sequence for four subsequent decades of frequency were written as
command files which could be executed by the HP9845. The final step in
command files of this type is a datatying step which consolidates the
five individual data sets, discarding low resolution overlapping data.
This large data set which consists of greater than 1130 individual points
is then stored on floppy disk for subsequent manipulation or graphical
portrayal. The ccrmand file CCOMEL, which controls the HP5420 in the
acquisition and tying of data, and other ccamand files are described in
more detail in Appendix D.
ADC ResolutionAmplitude Quantization Error
The HP5420 digitizes the analog voltage signals with twelvebit
analogtodigitizer converters. Since one bit is used to indicate
polarity, the converter is able to resolve a fullscale voltage reading
into 211 or 2048 discrete voltage levels. Since the most sensitive
range of the HP5420 is 100 my fullscale, the best that the HP5420 can
resolve is about 50 yv.
Although investigators of anodic films have used AC signals of
50 my pp (23), the general consensus of electrochemists seems to be
that one should not perturb an electrochemical interface with a signal
greater than 5 mv pp if nonlinear effects are to be totally avoided.
The HP5420 would digitize such a signal by dividing positive and negative
voltage excursions of 2.5 mv into 50 discrete voltage levels, respec
tively. Such resolution is not very good for measurements which must be
used in mathematical analysis. Since the FET is a linear operation,
the percent error associated with a time domain signal is carried over
into the frequency domain as an equivalent percent error in magnitude.
60
There are a number of possible ways of dealing with this amplitude
quantization error of the HP5420. The first is to accept the resultant
penalty in data quality. Gross approximation of voltage values will,
of course, result in frequency domain data scatter but will not necess
arily destroy the character of graphical portrayals. The second
possibility is to use a higher amplitude signal, accepting the risk of
nonlinear behavior. The third possibility is to amplify the signal
before injecting it into the ADC, accepting the deterioration in signal
tonoise ratio brought about by the additional amplifier stage. To
satisfy such a requirement, the optical isolators were equipped to
provide a gain of 10X, if desired.
All of the above techniques were tried. In the investigations of
real electrochanical systems described in the next chapter, it was
possible to use signals of higher amplitude without apparent illeffect.
In real systems, however, the electrode impedance changes by orders of
magnitude during the formation or dissolution of adherent corrosion
product films. Thus, for a given amplitude of voltage perturbation,
the current response could vary by orders of magnituderequiring
appropriate ranging of the currenttovoltage converters. To assure
that the current monitoring ADC was not subjected to either overflow or
underflow conditions, one had to monitor current levels prior to each
run and set the range of the currenttovoltage converters accordingly.
Verification of AC System Capabilities
To lend credibility to the assertion that the AC system described
herein can be used to reliably characterize an electrochemical inter
face, experiments were first run on simulated electrodes consisting of
61
two resistors and one capacitor. Since the doublelayer capacitance
for an electrochemical interface is widely reported to be on the order
of 20 MF/n 2, an available capacitor with 9.94 PF capacitance was
considered representative of the double layer and was used in each of
the simulated electrodes. Two values of polarization resistance were
used: 9960 and 49.72, simulating high and low values of polarization
resistance, respectively.
To examine the capability of the system to render values for this
equivalent polarization resistance, R and the equivalent doublelayer
capacitance, C, when the solution resistance, R varies over a wide
range, calculations were first performed to determine what a reasonable
upper value for Rs would be in an electrochemical cell with a low
conductivity electrolyte. As described in the next chapter, electro
chemical experiments were performed in the PARC K47 Corrosion Cell using
both cylindrical specimens and the flat specimen holder. If one uses
the Luggin Probe tip diameter which is 2.5 nm and the flat corroding
sample diameter of 10.7 nm, and if the separation of Luggin probe and
sample is 1 am, one determines the cell constant, K, to be 204 cm.
Given the equation
A = K o (3.3)
where A is conductivity, K is the cell constant and a is the specific
conductivity, the resistance Rs is given by
Rs = 1/K a (3.4)
Thus, if a low conductivity solution with = 10 cnm were put
into this cell, it can be shown that R = 4900q. Accordingly, discrete
values of resistance between 9.97 and 9990.Q were chosen to represent
an appropriate range of Rs in the simulated electrodes.
A listing of the component values of the various simulated
electrodes is given in Table 31. As can be seen from the table, the
simulated electrodes fall into two groups, one in which R is 9960 and
P
R varies between 9.97 and 99990, and the second in which R is 49.7M
s p
and R varies as above. The simulated electrode experiments were first
s
run by applying the BLWN voltage signal directly across the three
component network and measuring the current response as the voltage drops
across R rather than through the potentiostat. See Figure 3.6. The
s
reason for this procedure was to demonstrate the best capability of the
signal analyzer without the potentially complicating influences of the
potentiostat. Experiments with a single simulated electrode comparing
operation of the AC system with and without the potentiostat and optical
isolators and as a function of signal amplitude are described in
Appendix C. These experiments demonstrate that the signaltonoise
ratio is adversely affected by the presence of the potentiostat but that
the character of the data plots is not changed.
Typical data illustrating all five graphical formats are shown in
Figures 3.7 3.9 for simulated electrode "G". Theoretical curves, as
depicted by the solid lines, are determined by using the calibrated
component values for simulated electrode G to solve Equations (2.13)
and (2.14) for the real and imaginary components of impedance. In each
of the five plots of Figures 3.7 3.9, one observes deviation of the
experimental data points from the theoretical curve at low values of
frequency. Data scatter at low frequencies is attributed to 1/f error
as discussed earlier. However, one also observes an apparent systematic
deviation from the predicted behavior at low frequencies.
Figure 3.6 Schematic illustration of threeelement network connections
to the ACsystem.
Table 31 Component Values of Simulated Electrodes
Identifier R s() R (0) CD(pF) Rs/R
D 9.97 996 9.94 10.0 x 103
E 49.7 996 9.94 49.9 x 103
F 100.8 996 9.94 101 x 103
G 474.0 996 9.94 476 x 10 
H 989.0 996 9.94 992 x 10
I 4520.0 996 9.94 4.54
J 9990.0 996 9.94 10.0
N 9.97 49.7 9.94 201 x 103
0 49.6 49.7 9.94 998 x 10
P 100.8 49.7 9.94 2.03
Q 474.0 49.7 9.94 9.54
R 991.0 49.7 9.94 19.3
S 4520.0 49.7 9.94 90.9
T 9990.0 49.7 9.94 201
R =996n
COMPLEX PLANE ANALYSIS
(B) 0.81
0.54
0.27
S n
Figure 3.7 (A) Simulated electrochemical interface consisting
of discrete electronic components with the values
shown. (B) Complex plane plot of the impedance of
the network shown in (A). Points represent values at
discrete frequencies as determined by the FFT; solid
line depicts analytically predicted relationship.
EAL (Koas)
1.6
1.3
1.0
0.7
0.4
POHLMANS;IYRL TECHNIQUE
20 40
II G/F (OHMS/HZ)
Figure 3.8 PohlmanSmyrl portrayal of the data obtained from
the simulated electrode of Figure 3.6 (A). Points
represent values at discrete values of frequency;
solid lines depict analytically predicted relation
ships.
I'AG.F (ChM.HZ)
102
1 i n 2 ao in
101 1 10 1 1d 4 1iD
FFFIENCY (HZ)
BODE ANALYSIS
5
15
25
MIN FIN
35 I
101 1 10 102 103 i4 15
FREQUENCY (HZ)
Figure 3.9 Bode portrayal of impedance data for the
network of Figure 2.6 (A).
In the complex plane plot, this deviation is manifested with
experimentally determined points having lower absolute values of real
and imaginary components than theoretically predicted. Even more
striking is the fact that the experinentallydetermined impedance takes
on positive imaginary values at low frequencies thus exhibiting the
characteristics of a network containing inductance, which this circuit
does not contain.
If we now consider the complex plane plots of other dummy cells
(Figures 3.10 and 3.11), we can observe the behavior of this apparent
systematic error as the values of the network resistances are changed.
The series of plots in Figure 3.10 exhibits the effect of increasing
the series resistance, Rs, from 9.970 to 99900 while Rp and C are
held at 9960 and 9.94 uF, respectively. In the series of Figure 3.11,
Rs is again varied from 9.970 to 99900 while CD is maintained at
9.94 i1F and R is held at 49.7n. Since the diameter of the semi
P
circle is determined only by R it remains constant throughout the
series. The frequency at the apex of the semicircle is shown by
Equation (2.17) to be a function only of Rp and CD and therefore also
remains constant throughout the series. The only supposed effect of
changing Rs is to shift the constant diameter semicircle along the real
axis. In these series, this is accomplished by selecting the appropriate
range of the abscissa without changing the scale.
To explain the behavior of the ccrplex plane plot series in Figure
3.10, one must be aware that CD acts as a short circuit bypassing Rp
at high frequencies and as an open circuit at low frequencies. At high
(A)
4.35E02
O :.0G
a. aoce 0.aac2 a .ee 02 *I.20Ee2
REPL (OHMS)
(C)
IMPEDaNCE
6.53E02
2. :402
.aaca2 z.B0E *2 i .oE. a i. E *
RESL 'OHMS)
(E)
IMPEDRNCE
6.E3E02
2.35E02
2.aE.a 1 I a, ,
4 .Eca; .4.90cE3 5.2cE3 s. aca3
PEPL c OHMSi
(B)
IMPEDRNCE
+s.53E*2
+4.35E*ee 
e.aBeCa i .aaEa i. aca; 1.2BEa
REFL.OHMS)
(D)
IMPEDPNCE
4.5 
REPL (OHMS
(F)
IMPEDRNCE
4.53E:M
n.c5Ea2 Z
i.:acaz 7
a.9Ea02
9.30CE0 i.3cEa4 I.a'ca" i. IE04
RERL 'OHMS)
Figure 3.10 Ccnplex plane plots of simulated electrode imnedance, R = 996Q
(A) Duimy Cell D (B) Dumny Cell E (C) Dummy Cell G
(D) Dunny Cell H (E) Dummy Cell I (F) Dunmy Cell J
(A)
.3.aeca, 
i.3cel
.a.aecee .3 Ec 1 4i.aecal 9. aaEa
PERL rCHMS1
(B)
:MPEDANCE
. 33E' 1 ,
3 .Ec3l
5 in.cElal
g a.aaoa
,.J
i
I
*I
1..3E..4I ,
3.00Bscl C.0BECI I .sac.I *L.20Eac2
RElL (OHMS)
(C)
IMPEDPNCE
i .cel 
!.53C<81 
.9. 0BC.+1 l.2926E2 *1.5 2 I.38EB2
REFL (OHMS)
:.4rFrOpIE
1.S3CE 01 
I. nc;al
**.sEc*a02 .QEc*.2 *S.10Ece2 *5.4ec*a2
RElL (OHMSI
(E)
.33CE.1 
I*3al 
1.aaE1a
IMPEDNrCE
I.S3E* a
9.7eca2 lie.0eC03 i.aEc*3 *i. Ea3
RESL (OHMS)
(F)
TIPEDRNCE
3.6E01
i.n3C*el] 
r c.aaE a '.
ircal
*4. 52C*a *4.53C.83 c.56EC03 .59aC8*3
RERL 'OHMS,
Figure 3.11 Ccnplex plane plots of simulated electrode impedance, R = 9.9'R
(A) Dunny Cell N (B) Durry Cell O (C) Dmuny Cel P
(D) Durmy Cell Q (E) Dunry Cell R (F) Dumnmy Cell S
frequencies, therefore, the only impedance in the circuit is due to
R Since the rms voltage drop across the circuit is set at a level
s
which minimizes the amplitude quantization error, the quantization
error in the current measurement is also minimized. The high frequency
data are therefore least susceptible to data scatter due to this error
source. At low frequencies, the voltage drop across the network is
divided between R and R hen R is small with respect to R the
voltage drop across Rs (used to measure current flow through the net
work) is small and subject to amplitude quantization error. This
explains why the data scatter increases as a function of frequency when
R Rp is small.
The apparent systematic error present at low frequencies in Figure
3.7 may, in fact, be a manifestation of the low frequency quantization
error described in the previous paragraph. When viewed as part of the
plot series of Figure 3.10, it can be seen that this error disappears
when Rs/R becomes greater than 1. There is definitely a systematic
error at low frequencies in the plot series of Figure 3.11, however.
The apparent inductive character of the network as evidenced by the
positivegoing loop is also apparently affected by the ratio of R/Rp.
In the absence of a more plausible explanation for its occurrence, the
loop is presently considered an anomalous characteristic of the 49.7s
resistor. However, its presence indicates that there is evidence, even
in dummy cells, for the socalled "mysterious inductive loops" mentioned
by Mansfeld which occur in many electrochemical interfaces.
The magnitude of Rs has another effect on the results. As shown
in Figure 3.6, the voltage drop across Rs is used to determine the
current flow through the network which is used in turn to determine
the transfer function. The magnitude of the transfer function deter
mined by the analyzer is thus smaller than the impedance by a factor of
the resistance, R Since the transfer function has to be scaled by the
s
values of R to determine the impedance, any scatter in the transfer
s
function data is also scaled by the same factor. This amplification
of scatter as a function of scaling factor (magnitude of R ) is evident
5
in both plot series.
Another striking feature of both Figures 3.10 and 3.11 is the
discontinuity in the semicircular character present in the data at fre
quencies immediately below 256 Hz. This gap is attributed to instru
mental artifact due to the characteristic of a lowpass filter. As
described in Appendix A, low pass filters are used to condition the
analog signal to prevent aliasingg" with the sampling signal. In the
HP5420A, either one of two filters is used depending on the selected
bandwidth of analysis. The filter handling the lower frequency analysis
ranges is employed when the range of analysis goes to 256 Hz or below.
Further credibility is given to this argument when one observes that the
semicircular character is restored at frequencies well below 256 Hz.
Rather than being a fault of the individual instrument, this behavior
was also observed in independent measurements made on dumny cells at
Dow Chemical Caopany (55).
Figures 3.8 and 3.9 are portrayals of the data of Figure 3.7
in the PohlmanSmyrl and Bode formats, respectively. In the Pohlman
Smyrl plots, one observes scatter of both the high and low frequency
data in the real versus imaginary frequency portrayal. (Note horizontal
and vertical scatter of data points in Figure 3.8A.) This phenomenon
is due to the fact that the imaginary component beccres zero at both
high and low frequencies. Since the data are quantized, zero is never
actually reached, and amplification of these nearzero values by the
frequency leads to this scatter. This argument is substantiated by
Figure 3.8 in which one observes no scatter in the high frequency data
(in which quantization error has been attenuated by dividing by fre
quency); however, the quantization error of the low frequency data has
been amplified by dividing by frequencies less than 1.
The Bode analysis of Figure 3.9 shows conclusively that the low
frequency data suffer from a systematic rather than a random error.
The cause of this deviation of the experimental data from theoretical
predictions is assured to be due to the actual low frequency behavior
of the individual components.
Summary of System Developrent
This chapter has dealt with the creation of an AC impedance
measurement system based on digital signal analysis. Chief develop
mental problems involved equipment interfacing and coping with two
types of error associated with digital signal processing, namely 1/f
error and amplitude quantization error. Tests of the digital signal
analyzer and associated equipment on three component simulated electrode
networks as described her and in Appendix C verify that the signal
analysis approach combined with appropriate analysis techniques can
return the values of the network components with acceptable levels of
accuracy. These tests also reveal various ways 1/f and amplitude
quantization errors can manifest themselves.
CHAPTER IV
APPLICATION OF DIGITAL SIGNAL ANALYSIS TO A CORRODING ELECTRDE
As a demonstration that the electrode impedances, as determined
by digital signal analysis techniques, can be used to characterize
corroding interfaces, a series of experiments was conducted on 430
stainless steel in 1N sulfuric acid. This alloy/environment combin
ation was chosen because it is familiar to corrosion researchers, has
been thoroughly characterized with DC polarization methods and exhibits
active, passive and transpassive behavior depending on the polarization
potential.
The system of 430 stainless steel in IN sulfuric acid has been
selected by the ASTM to be used in Standard Recrrrended Practice (SRP)
G 572 (56) as a means of checking technique and instrumentation for
potentiostatic and potentiodynamic anodic polarization measurements.
When subjected to either potentiostatic or potentiodynamic anodic
polarization, the resultant potential versus log current plots exhibit
the behavior shown in Figure 4.1. Being so well characterized, this
system offers the opportunity to illustrate the sensitivity of the AC
technique in distinguishing among the various interface conditions.
The experimental apparatus outlined in SRP G 572 for performing
potentiostatic or potentiodynamic scans was used with a few exceptions.
A Princeton Applied Research (PAR) K47 Corrosion Cell System was used
for both the potentiodynamic scan and for the AC impedance measurements.
10
10 3 10" 10s 10 10 7
CURRENT (A)
Standard potentiodvnamic anodic polarization plot for type
430 stainless steel in N H2S04 at 300C with a potentio
dynamic scan rate of 0.6 volts/hour. After ASTM SRP G572
1. 4
.6 F
 fi L
,Figure 4.1
....~.I ......I ~,....I
76
The PAR cell system consists of a 1 liter flask equipped with ground
glass ports for the test specimen, purge gas vent and entry, salt
brindge/reference electrode and two high density graphite rods for
counter electrodes.
The test specimen was a cylinder with a length of 0.5 in. and a
diameter of 0.30 in. resulting in a total exposed surface area of 5.17 cm
Electrical contact to the specimen is made through a threaded steel rod
within a glass tube which is compression sealed against the upper surface
of the cylindrical sample. A PAR Model K77 Saturated Calamel Electrode
was inserted into the salt bridge tube. Both the reference electrode
and tube are terminated with a Vycor R frit, permitting ionic continuity
while minimizing ionic exchange. During this operation, the bridge tube
was filled with saturated KC1 solution. The reference electrode was
connected to the high impedance electroneter of the potentiostat.
The electrolyte was purged with nitrogen gas for at least 15
minutes prior to the insertion of the sample and purging was continued
throughout the potentiodynamic run and the conduction of AC tests. The
nitrogen gas was the exhaust from a 4000 SCF liquid nitrogen vessel
with a purity specified at 99.99%. Since the major impurity in the
liquid nitrogen is H20, there is no significant contribution to contamin
ation. Because of the low heat capacity of nitrogen, there was no
detectable change in solution temperature as a result of contact with
the cold nitrogen gas. The cell solution was stirred constantly using
a magnetic stirrer.
A potentiodynamic scan made a 1 mv/s with a PAR 350 Corrosion
Measuremrent System is shown in Figure 4.2. The corrosion potential was
2.5
U 2
U
0 1. 5
i
> .5
1 I I II I #
l34 105 10B 107 10
CURRENT
Figure 4.2 Eperimentally determined potentiodynamic anodic polarization
plot for type 430 stainless steel in N H2S04 at 220C with
N2 purge gas and a scan rate of 1 mV/s.
78
determined to be 0.571 V vs SCE with the scan being made from 0.621 V
to +1.600 V. Solution resistance was determined to be 0.29n and polar
ization resistance of 1.1i. The potentiodynamic behavior of Figure 4.2
exhibits score differences from the reference plot of Figure 4.1. These
are attributed to the differences in scan rate and the fact that
nitrogen rather than hydrogen purge gas was used. Since the purpose
of the AC experiments is to illustrate impedance characterization of
the metal electrode under conditions of active, passive and transpassive
behavior, the minor differences between Figures 4.1 and 4.2 are of no
consequence.
Upon completion of the potentiodynamic scan, the specimen was
repolished and placed into fresh solution. A PAR 173 potentiostat was
used to set DC potentials in increments of 200 mV anodic to the corrosion
potential. A BLWN signal of approximately 40 mv pp was fed to the
summing junction while the respective DC potential was maintained by
the potentiostat. See the wiring schematic of Figure 4.3. The figures
which follow are the complex plane plots of the impedance behavior at
the respective values of anodic potential.
At the corrosion potential (Figure 4.4), the complex plane plot
resembles the semicircular form of the threeelement network model at
intermediate frequencies but exhibits a second semicircular lobe at
lower frequencies. One notes that the real axis intercept occurs at
about 0.3 ohms while the uncampensated resistance measurement in the
DC polarization run (Figure 4.2) listed as 0.29 ohms. Since the
Luggin probe was moved between the potentiodynamic scan and the AC
run, this should be regarded as good agreement for solution resistance.
Figure 4.3 Schematic illustration of wiring for AC inpedance
experiments on 430 stainless steel.
.099
.066
.033 
0 
S33 28
.28
.34
.46
REAL (Ohms)
Figure 4.4 Ccaplex plane plot of electrode inpedance of 430 stainless
steel in N H2 SO at the corrosion potential.
I I
81
If one fits a semicircle to the first lobe of Figure 4.4, the value
for R in a threeelement network model is found to be about .09 S,
P
more than an order of magnitude below the polarization resistance
determined by the DC polarization method.
Although the complex plane method cannot determine the value of
CD exactly unless the frequency at the apex of the semicircle is known,
its value can be bracketed by viewing the range of frequency over which
data were gathered. Using this method it can be shown that the value
of C lies between 104 and 105 pF. Fittings this range of CD values to
the plot of phase angle vs frequency (see Figure 4.5) gives a good
match when C is 105 F.
To evaluate twolobe behavior a more complicated model than the
threeelement network is necessary. Since a passive film is expected
on this material at higher polarization potentials, it was reasoned
that an extremely thin film might also exist at the corrosion potential.
A network model similar to that proposed by Richardson, Wood and Breen (37)
was therefore considered. See Figure 4.6. Although more complicated
than the threeelement network, the impedance of this model can also
be evaluated analytically as a function of frequency and element values.
A BASIC computer program, GRAFIT, was written to accept any value of
Rp, R, R, CF and to plot the resultant impedance over a range of
frequency from 0.25 to 25000 Hz. See Appendix D. By using the values
for Rs, CD, and Rp already determined, and experimenting with various
values of CF and RF, the fit of Figures 4.7 was achieved. Although not
a perfect fit over all ranges of frequency, one may be confident that
all element values are within the right order of magnitude.
~
.46
.34 .4
REAL (Ohms)
1B0 101 102
FREQUENCY
10(
Complex plane plot, (A) and phase angle vs. frequency
plot, (B) of electrode impedance of 430 stainless steel
maintained at the corrosion potential. Solid lines
depict fit of an assured threeelement network where
R = .295', R = .088M, and C = 0.1 F.
s p
(A) 099
c
S. 0
o .066
'I
.033
0
.033
.28
'Figure 4.5
I L
CD CF
R
R R
Rp F
Figure 4.6 Five element network model representing the corrosion of
430 stainless steel in N H2SO 4
84
E
0 Q33
z
Z
(A)
.26
.33
.4
.47
.54
.34
REAL
FREQUENCY
.46
(Ohms)
'Figure 4.7 Complex plane plot, (A) and Bode plots (B) and (C) of
electrode impedance of 430 stainless steel in N HVSO4
at the corrosion potential. Solid lines depict fit of
fiveelement network nodel of Figure 4.6 where Rg = .295n,
R = 0.088R, R = 0.070, CD = 0.1 F and C = 3 F.
. 099
LU
4 C
C
WI
lug5 C.
(C)
(Hz)
r8
The magnitudes of the element values are startling in view of
both the findings of the DC polarization experiment and of accepted
values of doublelayer capacitance. Rationalization of these findings
is deferred until after the consideration of electrode impedance at
other values of DC polarization potential. Another puzzling aspect of
the complex plan plot is the appearance of a positive imaginary at
high frequencies. This feature of the experimental data is attributed
to artifact frcm the optical coupling circuits as discussed in the
previous chapter. Consideration of the high frequency tail in Figure
4.7 (C) also lends credibility to this explanation. The apparent data
mismatch at the high frequency real axis intercept is believed to be
caused by the low pass filter in the vicinity of 256 Hz, an artefact
also discussed previously.
The impedance of the stainless steel in the active region is
considered next. The complex plane impedance plot shown in Figure 4.8
was made at a polarization potential of about 300mv vs SCE. It can be
seen that this plot is similar to the one made at the corrosion potential
except that there is much more scatter in the low frequency data which
defines the second semicircular lobe. The scatter in this case is
attributed to the instability of what has been modeled as a thin passive
film. A reasonably good match of experiment and model is obtained with
element values shown in Figure 4.9. The decrease in R is to be
P
expected in the active corrosion region.
In the passive region, the behavior changes drastically as
illustrated by Figure 4.10. However, the behavior can still be
predicted with the same model. As shown in Figure 4.11, a reasonably
.099
/I
0 .066
.
S033
. 033  
S .28 .34 .4 .46
REAL (Ohms)
Figure 4.8 Complex plane plot of electrode impedance of 430 stainless
steel in N H2S04 polarized into the active corrosion region
at a polarization potential of 300 mV vs. SCE.
.099
.066
.033
. 33.
.28
.26
.33
.4
. 47
I i I
.34 .4
REAL (Ohms)
.46
54 I I i " .... I.
101 10a 102 10 103 10B I
(B) FREQUENCY (H=)
Figure 4.9 Ccmplex plane plot (A) and Bode plots (B) and (C) of
electrode impedance of 430 stainless steel in N H2S04
at 300 mV vs. SCE. Solid lines depict fit of five
element network model of Figure 4.6 where R = 0.2950,
Pp = 0.10, RF = 0.07n, CD = 0.1 F, and CF = 3 F.
0 m
T)
<./
2
1i
4
6 L
I
(L
I
75
88
15
.IC
v 10
>I
Z :
<
0 7 14 21
REAL (Ohms)
'Figure 4.10 Complex plane plot of electrode impedance of 430 stain
less steel in N H2S04 polarized into the passive region
at a polarization potential of +450 mV vs. SCE.
15
z
H 5
I
0
0 7
SI I
0 * 90
D 1 
C
10 1 100 10 1 102 20 4 1 
() FREQUENCY CHm ) (C)
Figure 4.11 Comolex plane plot (A) and Bode plots (B) and (C) of
electrode impedance of 430 stainless steel in N H2S04
at +450 mV vs. SCE. Solid lines depict fit of five
element network where CD = 1000lF, CF = 100VF, Rp = 0.62,
Rf = 200P, and R,= 0.3,0.
90
good match is obtained by increasing Rp slightly, increasing RH
dramatically and decreasing both C and CF.
Figures 4.12 and 4.13 illustrate how the model can also be used
to describe transpassive behavior. Here one notes a dramatic decrease
in the values of Rf indicating film breakdown.
The difference in the impedance descriptions of a corroding metal
electrode at the corrosion potential (as contrasted with the active,
passive and transpassive potentials) illustrates the sensitivity of the
AC impedance method to changes in the surface conditions of the inter
face and especially to changes in the protective character of a passive
film. While the changes in the resistance of a film are intuitive and
may be surmised from DC polarization data, the capacitive character of
the interface cannot be determined by direct current methods.
The data on capacitance provide additional descriptive information
about the nature of the electrochemical interface at a particular
instant in time. The fact that capacitance values of a corroding electrode
exhibit drastic variations depending on polarization potential and the
fact that they differ from accepted values of doublelayer capacitance
bf wellbehaved systems on dropping mercury electrodes should be
considered as further evidence of the sensitivity of this method to
the condition of surface.
4. 4
/\
(0
E
C) 3.3
0 2.2
z
steel in N H24 polarized into the transpassive region
Zat a polarization potential of 1.300 V vs. SCE.
CD ..... ......
< ." "" :
I ."
0 2 4 6
REAL (Ohms)
SFigure 4.12 Ccnplex plane plot of electrode impedance of 430 stainless
steel in N H2S04 polarized into the transpassive region
at a polarization potential of 1.300 V vs. SCE.
4.4
3.3
2.2
1. 1
0
1
0g 101 102 103
FREQUENCY CHz)
Complex plane plot (A) and Bode plots (B) and (C) of
electrode impedance of 430 stainless steel in N 2SO4
at a polarization potential of 1.300 v vs. SCE.
REAL (Ohms)
Figure 4.13
m
Z
V
15 Li
_J
Z
LJ
U)
<
I
0
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH
Recapitulation: Objectives and Premises
The specific objectives of this work as stated in Chapter I
were (1) to assemble an in situ corrosion monitoring system based
on digital signal analysis using offtheshelf ocrmercially available
electronic equipment; and (2) to demonstrate the capabilities and
limitations of such a system in characterizing the corrosion of
430 stainless steel in lN sulfuric acid. This attempt is based on
the premise that a corroding interface, whether active, passive or
transpassive, behaves as a relaxed, linear timeinvariant system
with respect to dynamic response to voltage perturbations.
The extent to which these assumptions are valid was considered
in sane detail. Relaxedness is probably a reasonable assumption if
the perturbation signal amplitude is kept above the level of random
system noise. Although no electrochemical system is truly linear
over an extremely broad range of voltage, behavior over small enough
voltage excursions can be considered linear. Time invariance is also
not rigorously valid for a corroding interface since passive films
may grow slowly or change their character over time. However, if
the period of measurement is short, on the order of minutes, the
assumption of time invariance is also reasonable.
In comparing the proposed corrosion monitoring system based on
digital signal analysis with the more familiar DC polarization
_~~
