Title: In situ characterization of corroding interfaces via digital signal analysis
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Title: In situ characterization of corroding interfaces via digital signal analysis
Physical Description: vii, 244 leaves : ill. ; 28 cm.
Language: English
Creator: Hager, Joseph Warren, 1946-
Copyright Date: 1983
 Subjects
Subject: Corrosion and anti-corrosives   ( lcsh )
Electrochemical analysis   ( lcsh )
Electronic data processing -- Corrosion and anti-corrosives   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Joseph Warren Hager.
Thesis: Thesis (Ph. D.)--University of Florida, 1983.
Bibliography: Bibliography: leaves 240-242.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00099353
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000473783
oclc - 11665522
notis - ACN8992

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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: State-of-the-Art. . . . . . . ... 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 off-the-

shelf commercially available digital signal analyzer, a micro computer

and a conventional potentiostat. By treating the corroding electrode

as a relaxed, linear, tine-invariant 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 three-element 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 5-element 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 child-like 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 corrosion-resistant 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 magniture-thus 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

self-protecting 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 real-time 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 non-linear 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 rate-determining 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 single-frequency

signal applications. An alternate measurement scheme is to apply a

multiple-frequency 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 single-frequency

measurements. In principle, the measurement tire for a multi-frequency

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 single-frequency 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 state-of-the-art digital signal analysis

equipment, it is able to interrogate the interface in a shorter period

of time than required by sequential single-frequency exposure methods.

Individual features of this technique are not unique, having been

investigated by Epelboin (1-3), Blanc (4), Creason (5-8), Smith (9-10),

Lorenz (11) and others (12-14). However, there has been no known attempt

to synthesize the well-known 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 off-the-shelf 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

Double-Layer 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 double-layer by Helmholtz (15) and is further explained

by Bockris (16). They describe the electrified interface as consisting

of two sheets of charge of opposite sign--one 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

double-layer model, and this led Gouy (17) and Chapman (18) to propose

the so-called diffuse double-layer model which took into account varia-

tions in the capacitance with potential. The Gouy-Chapman model

asserted that the charge in the electrolyte solution was scattered in

thermal disarray rather than being ordered in plate-like fashion

immediately adjacent to the solid surface. Stern (19) synthesized the

Helmholtz and Gouy-Chapman models stating that some of the charge in the

electrolyte is organized in plate-like 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

metal-solution 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 concentration-dependent 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 so-called

"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 "ad-atans" 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 series-connected 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 diffusion-layer 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 double-layer and solution-resistance 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/v-for rate-control determined by diffusion and
charae-transfer 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. (33-35) and

Richardson et al. (36, 37) have conducted numerous studies of the

properties of both air-formed 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

so-called 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 time-consuming 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 widely-used 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 steady-state

techniques. The DC steady-state 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 so-called "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 steady-state during polarization; time-dependence 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), Sluyters-Rehbach

and Sluyters (44), and Smith (45).

Because of the capacitive components in the electrochemical

interface network, polarization impedance is frequency-dependent (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

double-layer 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 system-specific 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 70-50



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 10-3 M propargylic alcohol; (4) 0.5 M H2S04 +
0.2 x 10-3 H propargylic alcohol; (5) 0.5 M H2SOa + 0.5 x 10-3
M propargylic alcohol; (6) 0.5 M H2S04 + 2 x 10-3 M propar-
gylic alcohol; (7) 0.5 M H2SO4 + 5 x 10-3 M propargylic
alcohol; (8) 0.5 M H2S04 + 20 x 10-3 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 time-consuming 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 time-invariance (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.

Time-invariance. A relaxed linear system is time-invariant 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 quasi-steady

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

time-invariance 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 time-invariance 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 well-known single-sided Fourier Transform (48).

For relaxed, linear, time-invariant 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 (5-8) capitalized on this development, demonstrating that with

an on-line minicomputer, it is possible to acquire and transform time

domain signals into the frequency domain in less than 3 seconds (6).

Utilizing on-line 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 (6-8). 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 coherently-related

sinusoidal components; (2) almost periodic signals, waveforms composed

of discrete non-coherently related sinusoidal components; (3) periodic

transients, signals with continuous well-defined snoothly-varying 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,

pseudo-random 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









4-r
-0- 0. r-1




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 non-linearity. Overall, the best precision was

achieved with a phase-varying 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 pseudo-randcm 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

iron-sulfuric acid system using a so-called correlator, a device which

determined the Fourier transform. DeLevie and coworkers (13) have

applied the procedure in the study of ion-conducting 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 "lock-in 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 low-noise potentiostat capable of suppressing

electronic noise to the order of 2.5 x 10-8v/Hz. They (47) have used

this low-noise 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.

Sluyters-Rehbach 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

Sluyters-Rehbach 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 three-element 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 rate-limiting.











OAPEX= P/RPCD






0
C-
cZ


a


Figure 2.12 Complex plane evaluation of the three-element
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

curve-fit 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 Pohlman-Smyrl technique of analyzing the impedance
of the three-element network given in Figure 2.11.




























FREQUENCY (HZ)


FREQUENCY (HZ)




Figure 2.14 Bode plot of frequency response for the three-element
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: State-of-the-Art

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 time-consumption of such processes is eliminated in

principle by fast Fourier transform technology. Using the FFT algorithm

in an on-line 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 three-element
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, pseudo-random 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 low-noise 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 Hewlett-Packard (HP) 5420 digital signal analyzer.

The analyzer continuously monitors and digitizes time-varying 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 three-electrode electrochemical cell. The

response, I(t), is a time-varying 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 analog-to-digital 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 zero-resistance amneter which produces a voltage


















S0


40 -)
S "-I


Si ri













r-4 p
















n1~,















4-J 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 *S4-u
* QH
*r-|4J 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 p-p 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 dot-matrix thermal printer and two integral

tape drives. To permit even faster retrieval from mass storage, the com-

puter was also equipped with two eight-inch 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, four-color 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 signal-carrying 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 set-up 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 set-up state rather

large-typically 15-20. By creating ccmnand sequences in the software

of the HP9845, tedium-induced 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 data-smoothing

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

three-component equivalent circuit model described previously, yielding

two values of resistance and one of capacitance. One may also generate

a theoretical data set for a three-component 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 frequently-repeated operations which may

be stored or reexecuted. Appendix D contains a thorough description of

both the main program and same frequently-used 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 set-up 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 256-element 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

full-scale 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 successively-measured 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 data-tying 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 data-tying 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 Resolution--Amplitude Quantization Error

The HP5420 digitizes the analog voltage signals with twelve-bit

analog-to-digitizer converters. Since one bit is used to indicate

polarity, the converter is able to resolve a full-scale voltage reading

into 211 or 2048 discrete voltage levels. Since the most sensitive

range of the HP5420 is 100 my full-scale, the best that the HP5420 can

resolve is about 50 yv.

Although investigators of anodic films have used AC signals of

50 my p-p (23), the general consensus of electrochemists seems to be

that one should not perturb an electrochemical interface with a signal

greater than 5 mv p-p 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

non-linear behavior. The third possibility is to amplify the signal

before injecting it into the ADC, accepting the deterioration in signal-

to-noise 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 ill-effect.

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 magnitude--requiring

appropriate ranging of the current-to-voltage 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 current-to-voltage 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 double-layer 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 double-layer

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 3-1. 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 signal-to-noise

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 three-element network connections
to the AC-system.

















Table 3-1 Component Values of Simulated Electrodes

Identifier R s() R (0) CD(pF) Rs/R


D 9.97 996 9.94 10.0 x 10-3
E 49.7 996 9.94 49.9 x 10-3
F 100.8 996 9.94 101 x 10-3
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 10-3
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


POHLMAN-S;IYRL TECHNIQUE


20 40
-II G/F (OHMS/HZ)


Figure 3.8 Pohlman-Smyrl 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-
10-1 1 10 1 1d 4 1iD
FFFIENCY (HZ)



BODE ANALYSIS



5





-15


-25

MIN FIN
-35 ---I
10-1 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 experinentally-determined 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)




-4.35E-02








O :.0--G
-a. aoc-e 0.aac-2 -a .ee 02 *I.20E-e2
REPL (OHMS)

(C)
IMPEDaNCE
-6.53E-02









-2. :4-02


.aac--a2 z.B0E *2 -i .oE. -a i. E *-
RESL 'OHMS)

(E)
IMPEDRNCE
-6.E3E-02


-2.35E-02








-2.aE.a 1 I -a, ,
-4 .Ec-a; -.4.90cE-3 -5.2cE-3 -s. -aca3
PEPL c OHMSi


(B)
IMPEDRNCE
+s.53E-*2


+4.35E*ee -









-e.aBeC-a -i .aaE-a -i. ac-a; 1.2BE-a
REFL-.OHMS)

(D)
IMPEDPNCE
-4.5 ------














REPL (OHMS

(F)
IMPEDRNCE
-4.53E:-M


n.c-5Ea2 Z

-i.:ac-az -7


-a.9E-a02



-9.30CE0- -i.3cE-a4 -I.a'c-a" -i. IE-04
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.aec-a, --



-i.3c-el
-.a.aec-ee -.3 Ec 1 4i.aec-al -9. aaE-a
PERL rCHMS1

(B)
:MPEDANCE
-. 33E-' 1 ,


-3 .Ec-3l


5 -in.cEl-al



g a.aaoa


,.J





i
-I

*I


-1..3E..4I ,--------------
-3.00Bsc-l -C.0BECI I .sac.I *L.20Eac-2
RElL (OHMS)
(C)
IMPEDPNCE






-i .c-el -






-!.53C<-81 --------------------
.9. 0BC.+1 l.2926E2 *1.5 -2 I.38E-B2
REFL (OHMS)


:.4r-FrOpIE













-1.S3CE 01 -
-I. nc;-al







**.sEc*a02 .QEc*.2 *S.10Ece2 *5.4ec*a2
RElL (OHMSI


(E)

-.33CE.1 -





-I*3-al -



-1.aaE1a


IMPEDNrCE


-I.S3E* -a
-9.7ec-a2 lie.0eC03 -i.aEc*-3 *-i. E-a3
RESL (OHMS)
(F)
TIPEDRNCE



-3-.6E-01


-i.n3C*el] -
r c.aaE a '.





-irc-al
*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

positive-going 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 so-called "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 low-pass 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 Pohlman-Smyrl 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 near-zero 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 5-72 (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 5-72 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" 10-s 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 G5-72


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 p-p 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 three-element 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 three-element 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 two-lobe behavior a more complicated model than the

three-element 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 three-element 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 three-element 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
five-element 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 double-layer 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.
10-1 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 double-layer capacitance

bf well-behaved 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 off-the-shelf 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 time-invariant 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


_~~




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