United States Department of Commerce

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NATL INST. OF STAND & TECH R.I.C,

A111D3 fiDM322 PUBLICATIONSJ

NIST Technical Note 1293

A Mathematical Model of Cathodic Delamination

and Blistering Processes in Paint Films on Steel

James Pommersheim, Tinh Nguyen, Zhuohong Zhang,

Changjian Lin, Joe Hubbard

QC

100

.U5753

1293

1992

C.2
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'At Boulder, CO 80303. *Some elements at Boulder, CO 80303.
^c lOO

oisc.

NIST Technical Note 1293

A Mathematical Model of Cathodic Delamination

and Blistering Processes in Paint Films on Steel

James Pommersheim * Tinh Nguyen

Zhuohong Zhang * Changjian Lin **y

Joe Hubbard \ ^

Building and Fire Research laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

* Chemical Engineering Department,

Buckneil University, Lewisburg, PA

** Present Address:

Chemistry Department

Xiamen University, Fujian,

People's Republic of China

May 1992

a

c

^v.^»''°'^o.

d,'.,: \

•^'Xtes o* ^/

U.S. Department of Commerce

Barbara Hackman Franklin, Secretary

Technology Administration

Robert M. White, Under Secretary for Technology

National Institute of Standards and Technology

John W. Lyons, Director
National Institute of Standards U.S. Governnnent Printing Office For sale by the Superintendent

and Technology Washington: 1992 of Documents

Technical Note 1293 U.S. Government Printing Office

Natl. Inst. Stand. Technol. Washington, DC 20402

Tech. Note 1293

72 pages (May 1992)

CODEN: NTNOEF
Abstract

Conceptual and mathematical models are developed for processes which describe

blistering of defect-containing coating on coated steel containing defects exposed to electrolytic solutions. The assumption is made that cations migrating along the coating/metal

interface from an anode at the defect to cathodic sites are responsible for blistering. The

cations are driven by both concentration and electrical potential gradients. The mathematical models are solved to predict ion fluxes and concentrations along the interface and within the blister. Solutions of the models are expressed in terms of dimensionless parameters.

Model variables include blister size, distance between the blister and defect, ion diffusivity

and potential gradients. To substantiate the models, an experiment was designed and con- ducted to measure the transport of cations along the coating/metal interface from the defect to the blister. Sodium ion concentration-time data within a blister were analyzed to

determine model parameters. Under the experimental conditions employed, it was found

that the transport of sodium ions is controlled by potential gradients rather than concentration gradients. Model results indicate that large blisters subject to a potential gradient are more likely to grow than small ones because higher concentrations can build up within

them. Implications of this conclusion for maintaining the integrity of organic coatings are

discussed.

keywords: anode, blistering, cathode, cathodic delamination, conceptual

model, corrosion, defect, diffusion, mathematical model, organic

coatings, paint films, potential gradients, scribe

m
Table of Contents

Abstract iii

Table of Contents iv

Table of Figures v

1. Introduction 1

2. Conceptual Model: Description of the Blistering Process 3

3. Mathematical Model Development 7

3.1 Review of Related Work 7

3.2 Steady State Ion Concentration Profile and Flux 10

3.3 Mathematical Models for the Initial and Propagation Periods 11

3.3.1. Model for the Initial Period (t < 0i) 11

3.3.2. Model for the Propagation Period (t > 6i) 14

4. Experimental 19

4.1 Specimen Preparation 19

4.2 Cation Measurement 21

5. Results and Discussion 25

5.1 Experimental Results 25

5.2 Theoretical Results 27

5.2.1. Steady State Sodium Ion Concentration 27

5.2.2. Steady State Ion Flux 28

5.2.3. Critical Value of Parameter Value p 34

5.3 Comparison of Experimental and Theoretical Results 41

6. Summary and Conclusions 44

7. Nomenclature 45

8. References 47

Appendices 48

I. Experimental Data 49

II. Data Analysis 50

III. Computer Codes 51

IV
Table of Figures

Page

Figure 1. Conceptual Model for Initial Period 5

Figure 2. Conceptual Model for Propagation Period 6

Figure 3. Model System for Cathodic Blistering 7

Figure 4. The Three Types of Predicted Cation

Concentration vs. Time Profiles in a Blister 17

Figure 5. Schematic of Experimental Apparatus

and Specimen Configuration 22

Figure 6. Experimental Apparatus for Cation Measurement 23

Figure 7. Sodium Ion Concentration and

pH within Central Glass Chamber 26

Figure 8. Steady State Sodium Ion Concentration Profile: C vs. r 29

Figure 9. Steady State Sodium Ion Concentration Profile:

C vs. r (with k = 0.1) 30

Figure 10. Steady State Sodium Ion Concentration Profile:

C vs. r (with k = 0.227) 31

Figure 11. Steady State Sodium Ion Concentration Profile:

C vs. r (with k = 0.5) 32

Figure 12. Steady State Sodium Ion Flux, (-F) vs. k 33

Figure 13. Steady State Sodium Ion Flux, (-F) vs. p 35

Figure 14. Steady State Sodium Ion Concentration, Ca/Cq vs. p/p* 37

Figure 15. Steady State Sodium Ion Concentration, Ca/Cq vs. k 38

Figure 16. Critical Value of p* vs. k 40

Figure 17. Sodium Ion Concentration within Blister vs. Time 43

1. Introduction

Corrosion of metals costs the United States about 4.2% of the gross national

product yearly [1]. The use of organic coatings is an effective, economical, and widely

used method to prolong the service life of metals. The coatings are barriers which

help prevent metals from corroding, and protect the substrate from both chemical

and physical attack. Despite recent improvements in coating technologies, problems

continue to exist in providing protection for metals from exposure to potentially corrosive environments.

One of the major problems of coating technology is osmotic blistering. When

foreign ions are present on the surface or leachable ions are present in the coating,

the substrate will not be clean. In the presence of microscopic amounts of water, local

osmotic cells or blisters can be established on unclean substrates [2]. Blistering is considered to initiate at the metal-substrate interface at weak spots randomly distributed

over the substrate surface. Blister growth occurs when there is sufficient water present

in the vicinity of the metal substrate. Osmotically driven diffusion of water through

the coating controls the rate of growth. One of the most severe forms of blistering

is cathodic blistering which can occur when a coated metal with defects in the coating

is exposed to a deleterious environment, for example, when the coating is exposed to

salt spray or is immersed in a salt solution. The high pH within cathodic blisters has

been postulated to cause the delamination of the coating from the metal at the blister

periphery [3-5]. After sufficient time, the blisters may enlarge to a point where adjacent blisters coalesce. This can lead to complete detachment of the coating from the

substrate causing premature failure of the organic coating system by delamination.
Although considerable research on the degradation and adhesion failure of

coatings has been done in the past decade [6,7], little work has been done to quantify

the cathodic delamination and blistering processes. Quantitative study is necessary

to predict the performance of a given coating system in order to obtain estimates of

service life. One reason for the difficulty in quantifying the delamination and bhstering processes is the complexity of the metal/coating system. Many variables affect the

performance and service life of coating systems. In addition to the physical and chemical properties of the coating and the substrate surface, a coating system may contain

inhomogeneities such as air bubbles, microvoids and trapped solvent. Also the coating may be applied to previously poorly bonded or nonbonded areas. These factors

influence the transport of deleterious species through the coating and along the metal/

coating interface and can promote degradation at the interface. Another reason for

the lack of a comprehensive theory for understanding and predicting corrosion protection by a coating is that many different coating formulations are currently employed.

If the effectiveness of coatings is to be increased through development of improved selection and evaluation criteria, it is essential to develop improved methods

for predicting the service life of a coated metal.

In this paper, conceptual and mathematical models are developed for the rate

at which sodium ions are transported from the environment to cathodic blisters in a

coating/metal system. Transport occurs due to the combined effect of diffusion and

an electrical field created by an applied potential gradient. Expressions are obtained

for the sodium ion flux into a blister and the concentration profile between a blister

and its environment. By comparing model predictions with experimental data of sodium ion concentration versus time, the controlling mechanism for ion transport is determined.
2. Conceptual Model: Description of the Blistering Process

The degradation of an "intact" coating on steel immersed in electrolytes can

proceed by the following steps:

1. Coating swelling, polymer conformation change, or pigment percolation

(clustering) result in enlargement or formation of pathways for electrolyte

migration to the metal surface. This can be seen by electrochemical and

spectroscopic measurements [8,9].

2. Corrosion occurs at the base of the pathway which acts as an anode. This

oxidation reaction supplies electrons for the cathodic reactions, which occur

away from the anode and underneath the coating.

3

Cations migrate to the cathodic sites to neutralize the hydroxide ion, forming

highly alkaline and hygroscopic materials. The migration of cations also

induces an electro-osmotic flow of water to the cathodic sites.

4. Alkaline solution causes coating/metal interfacial delamination around the

initial blister, which is cathodic.

5. Hygroscopic materials result in a thermodynamic water activity difference

between the inside and outside of the blister.

6. Osmotic and electro-osmotic pressure differences control the growth rate

of blisters.

7. Alkalinity of blister solution and mechanical stress facilitate can add to the

enlargement process.

Cathodic blistering occurs in the neighborhood of coating defects. Continued

exposure to salt spray, constant immersion, or cyclic wet-dry immersion in electrolytes

will lead to enlargement, or a coalescence of the blisters, and eventual total delamina-
tion of coatings. The growing anodic character at the defect area stimulates the cathodic reactions adjacent to it. Cathodic bhstering also occurs when an electric potential is applied across the coated panels. Many coated metals are intentionally or

unintentionally subjected to an electrical potential.

The defect serves as the anode where the iron is oxidized by the half-cell reaction:

Fe > Fe2+ + 2q- . The other half cell corrosion reaction, where the oxygen is reduced (the cathodic reaction), occurs under the coating a short distance away from the defect [3]:

H2O + I/2O2 +2e- > 20H- .

The cathodic and anodic sites are connected by an electrolyte layer. Initially the cathodic and anodic reaction can start at adjacent atomic sites. However, as corrosion

products form and concentration gradients of corrosive species are established, the

reaction sites separate and localize. An increase of this separation can lead to delamination failure. The liquid in cathodic blisters exposed to dilute salt solution is highly

alkaline, while the liquid in neutral blisters under defect-free organic coatings is

weakly acidic to neutral [10].

Although there are many factors that affect the concentration of the solution in

the blister and the rate of the cathodic reaction, two main factors are considered paramount. One is the applied potential and the other is diffusion. Both act to transport

ions in the electrolytic solution from the anode and to the cathode. Mathematical

models are developed here to describe these phenomena and their interaction.

Figure 1 presents a schematic of the model system for cathodic blistering. The

figure shows a physical model of a coating/metal system exposed to a NaCl solution
and gives the route taken by the sodium ions. There is a central bhster in the coating

of radius "a", and a defect (scribe) located at a distance R from the blister. A path

is provided between the blister and scribe beneath the coating film by a channel whose

effective width is 8. As depicted, the sodium ions will enter the channel through the

scribe to reach the blister. The mechanism for ion transport is diffusion in the presence of an imposed electrical field. The movement of sodium ions from the scribe

to the blister can be divided into two sequential stages: an initial period and a propagation period.

scribe KI 1 blister

NaCl

I Solution

Na+

C = Cf

::|-

-^> -:>i-^-T>-^^-.—

<^\

\^ I

NaCl coating

Solution y

-r

\ \ \ \ \ \ \ \ \ \ \ 'IT, \ \ \ \ \ \ \ \ |,, '1,^ 'I- ti^ \^ 1,^' \^\ \ \ ''I,, 1,^ \^ 1,^ 'i,^ n,' i,| 1,^ T,| 3

TtV

^L

channel

^

^

R

metal

(not to scale)

Figure 1. Conceptual Model for Initial Period

Figure 1 presents a profile of the model system during the initial period. In the

conceptual model adsorption on the wall of the channel is assumed to be instantaneous compared to diffusion and charge transfer. It is assumed that the metal surface

within the channel is in the cathodic state and that the electrolyte layer in the channel

is alkaline. These assumptions are consistent with Step 2 of the conceptual model.

Under these conditions, the fixed charges on the metal and the coating surface within

the channel are negative [11]. Consequently, cations are adsorbed on these sites. If
the adsorption is rapid, the concentration of sodium ions will drop to near zero at the

advancing interface (located at a distance rj from the center of the blister solution).

The concentration of sodium ions within the blister will remain near background levels during the initial stage as a moving interface travels in the channel between the

scribe and blister. The time taken for the interface to reach the blister periphery

(rj = a) is the initiation or break through time, Gj. This is the time it takes sodium ions

to first reach the blister site. The quasi-steady state assumption maintains that there

is no additional depletion of sodium ions within the channel as the interface advances

to reach the blister. This is a reasonable assumption considering the large reservoir

of sodium ions in the external solution that are available for transport.

scribe NaCl ^^1

blister

Na+

C = Co

-7K

^

V,|Ca

-I ^:

I ^--^-

NaCl ^o^ti"g

/^

channel

^

^

R

metal

(not to scale)

Figure 2. Conceptual Model for Propagation Period .

Figure 2 presents a profile of the model system during the propagation period.

The propagation period occurs at longer times (t > ©j), after the sodium ions have broken through into the blister. Sodium ions are no longer removed in the channel but

can now pass freely into the blister. In this stage, ions enter the blister as a result of

both diffusion and transport caused by the applied electric field. Ions accumulate

within the blister but no longer within the channel. Their concentration Ca will rise

within the blister during this period.
3. Mathematical Model Development

3.1 Review of Related work

Nguyen et al [12] developed a mathematical model for the cathodic blistering

of protective coatings containing detects on steel immersed in electrolytes. Their

model was based on two basic assumptions: 1) metal cation presence at the cathodic

sites is the main factor controlling the thermodynamic activity of water across the

coating, and 2) lateral diffusion along the coating/metal interface from the defects

to the blisters is the main route of cation transport. The model predicts the concentration profiles and cation flux flowing into a blister as a function of time, blister size,

distance between the blister and defect, ion diffusivity and potential gradient.

blister/ \^;

" scribe

I^Y^i^ ^

organic coating (top

1 W C' = Co

view)

Figure 3. Model System for Cathodic Blistering [12]

The model is based on two-dimensional, radially symmetric diffusion in an

annular domain, a < r' <R. Figure 3 presents a top view of the model system, a is

the radius of the blister, R is the distance between the center of the blister and the
scribe (defect), and r' is the distance between the center of the bhster and any site on

the coated panel between the bhster and the scribe. C is the sodium ion concentration at any site on the coated panel between the blister and the scribe, and Cq is the

sodium ion concentration in the environment.

The cation is assumed to diffuse from the scribe to the blister along the coating/

metal interface. The model developed by Nguyen et al [12] is given by

where t' is the exposure time, D is the effective sodium ion diffusion coefficient under

the coating, ji is the average mobility of sodium ions and E is the strength of the imposed unscreened electrical field.

Equation (1) was rewritten in dimensionless units, in terms of a distance scale

r, a time scale t and a concentration scale C [12]. The resulting dimensionless equation

has the form: —dC =+-— d^C 1 dC +^—p dC ,-,

(2)

with

dt d^r r dr r dr

r -

^'

t -^^'r -^^ n - -^ ^^^^

and k = -

Co L^ R-a ^log(i) ^

AO is the potential difference between a and R, and L is the length scale (L=R-a).
The dimensionless boundary conditions are given by:

C (y^. = (3)

C(y^,0 = l (4)

C (r, 0) = . (5)

Condition (3) corresponds to the fact that the sodium ion concentration at the

bhster periphery is zero at any time. This condition is more Hlcely to obtain for larger

bhsters or at shorter times where the sodium ion concentration remains low. At the

scribe, condition (4) shows that the concentration is constant at Cq. Condition (5) corresponds to the fact that initially there are no sodium ions beneath the coating.

The dimensionless cation flux F flowing into the blister is given by:

l-k \dr)r = k/{l-k)

Nguyen et al [12] solved the above set of equations numerically. They presented

graphical results of the dimensionless concentration and flux as functions of system

parameters.

There are two dimensionless parameters in this problem: the geometric aspect

ratio k and the dimensionless potential gradient^. High p means the applied electric

field in the region between the blister and scribe is large, while low p means the electric

field is small.

It is noted here that since the transfer of sodium ions is caused by both an electric

field and diffusion, the time scale is not determined solely by the dimensionless diffu-
si on time /' = tD/(R-a)^ since the time scale associated with the electric field must

also be considered.

3.2 Steady State Ion Concentration Profile and Flux

In this section the steady state ion concentrations and fluxes are derived for the

model of Nguyen et al [12].

The dimensionless concentration profile for the diffusing cation are governed

by eq (2). At steady state this equation becomes:

d^C 1 d C pd C

d r^ r d r r d r = . (7)

The boundary conditions are still given by eqs (3) and (4). Application of these

conditions to eq (7) results in the following analytical solutions in the absence (p = 0)

and presence (p ^ 0) of an applied electric field:

C(r) =

Ink

In (it) (forp = d) (8)

C{r) =

1-kP

j^ \p

1_. 1-^- (forp ;^0). (9)

When p = 0, there is no applied potential and diffusion is the sole mechanism

for ion transport. Equation (9) can be shown to reduce to eq (8) in the limit as p -* 0.

Application of eq (6) to eqs (8) and (9) results in the following equations for the

dimensionless sodium ion tlux when p = and p ^0:

10
F=^In

(forp = 0) (10)

F = ^

(forp ^ 0) . (11)

The fluxes are negative (k < 1) because ions are diffusing inward in the direction

of decreasing radius. Equation (11) reduces to eq (10) in the limit as p -* 0.

3.3 Mathematical Models for the Initial and Propagation Period

In this section mathematical models are developed and solved for the initial and

propagation periods of the conceptual model presented in section 2.

3.3.1. Model for the Initial Period (t < G/j

In this period, as previously described, the model presumes that a moving interface travels in the channel between the scribe and the blister. The time taken for the

interface to reach the blister periphery is the initiation or break through time Gj.

During this period eq (7) describes the facilitated transport of sodium ions. The

boundary conditions are C = at r = Ti and C = Co at r = R. Co, the concentration of sodium ion in the external solution, is presumed constant in the present formulation. The solutions for the quasi-steady state concentration profile and flux are similar to those obtained previously at steady state. If a is replaced by rj, with kj defined

as ri /R, then the mathematics can be transposed directly. Thus, the dimensionless concentration profile and flux in the absence of an electric field (p = 0) are given by

eqs (12) and (13), respectively:

11
In(^ ^ = g = "W ^"^^ = "> '''>

F = ^ (f-;' = 0) (13)

The dimensionless concentration profile and flux in the presence of an electric

field (p ^0) are given by eqs (14) and (15), respectively :

(forp^O) (14)

2np

kf-l

(forp ^ 0) . (15)

As described in the conceptual model, at r = ri an instantaneous adsorption or

reaction process is assumed to immobilize the sodium ion. Because this process is rapid the local concentration of sodium ions will be low. In this case the ion transport

due to the applied electric field will also be low and the total moles flow at r = ri will

approximate the diffusive molar flow. The diffusive molar flow Wd (mol/s) of sodium

ion is given by:

wj = - Qs-j- '^nr-i (16)

at

where e^ is the amount of adsorbed sodium per unit of interfacial area (mol/m^).

12
it will be a constant which only depends on temperature and the nature of the adsorbate-adsorbent system. Another expression for w^ is given by the product of the flux

and the transport area:

Wci = - D

dC

dr' \r'=n

IjiVi 6 (17)

Equating eqs (16) and (17):

dn D d I dC

dt Q

dr' ]r'=ri

(18)

In the presence of an electric field (p ^ 0) the concentration derivative can be

found from eq (14), when:

dr, D 6 Co p 1 dt Qs n [^-i (19)

eq (19) predicts the rate at which the interface moves in from the scribe to the blister.

Separating variables and integrating eq (19) from r = R to r = ri, it follows that:

p + 2 \R

/"jV+2 1 (

n

\2 1 1 2 \RJ p + 2 2 = a'pt (for p ^ 0)

where

a' = D 6 Co

Qs R^

(20)

(21)

The initiation or break through time 9i occurs when rj = a, so that:

e. =

a p p + 2

kP + 2 1 ,,

1 1 2 p + 2 2

(forp ^0) (22)

13
In the absence of an electric field, p = 0, we obtain by a similar procedure:

di-i D d Co 1 -r = — —r- • (23)

R

Integrating similarly, it follows that:

The break through time when p = is given by:

e,=

' la'

*Mln.-lKi iforp = 0) . (25)

Using eqs (22) and (25), respectively, the break through time Q\ taken for cations

to first reach the blister periphery can be calculated with (p ^^ 0) and without (p = 0)

an applied potential gradient.

3.3.2. Model for the Propagation Period (t > 0,j

As shown in figure 2, once the moving interface has reached the periphery of

the blister (ri = a), additional sodium ion will enter due to a combination of diffusion

and transport caused by the electric field. The propagation period begins when the

initial period ends (at t = 0,).

A sodium balance made on the blister in this stage takes the form: — (VCa) = Wd\r' = rt + ^e\r' = a

(^6)

where We is the molar flow caused by the electric field, Vis the volume of solution

in the blister and Ca is its concentration.

14
Equation (17) provides an expression for the diffusion flow, while the electric

field flow is given by:

"'^ = ^''^*^^^'-

(27)

The flux, Fe, caused by the electric field is obtained by dividing by the transport

area of the blister periphery, i.e., 2Tra8:

{R-a)\r\k

These results show that the electrical flow and flux are both proportional to the concentration C.

Combining the diffusion flow (eq (17)) and the ion flow induced by the electric

field (eq (27)):

I

(KG) = Kifl = - D [^\ 2.„ . . 2.. .* 6 MLZ^ C . (29)

This formulation presumes that the volume of solution V in the blister remains constant (fig. 3). Since AO is negative (potential gradient is inward), p will be positive

when the blister is cathodic.

At quasi-steady state, there is no additional depletion of sodium ions under the

coating {dC/dt = 0), and all of the ions which pass under the film arrive in the blister.

The quasi-steady state assumption is reasonable considering the generally small volume of solution under the film relative to the volume of solution in the blister. Also

during the initial period the coating has ample time to adsorb sodium ions. In this

15
case the total molar flow of sodium ions, as expressed by the right hand side of

eq (26), will be constant. Evaluating this constant at /"' = a, and using eq (29), it

follows that:

cICa

dt

271 6 D

V \nil/k)

Co- C/ ^ ^(InlA) ^ (30)

Integrating again provides an expression for the concentration of sodium ions

within the blister as a function of time during the propagation period:

Ca

Co

1a

l_e-«y3 (/-©,) (31)

where

. k In(lA) . 1-k ^ \p* (32)

and

with

^

=

27t d D

V \nO/k)

p* = 1-k

k \n{lIk)

(33)

(34)

/?* is defined as the critical value of the dimensionless electric field. Note that when

p = p*, q; = 0. /?* is solely a function of the aspect ratio k. Therefore, it depends on

the relative size of the blister and the separation of the anodic and cathodic regions.

The model predicts that what occurs within the blister will depend on the relative

values of/? andp*. There are three possible cases: p<p*. p>p* and p=p*. The

16
three types of concentration-time profiles which can result for these cases are depicted

in figure 4.

Ca Cas

Figure 4. The Three Types of Predicted Cation

Concentration-Time Profiles in a Blister

lip <p*, oi is positive, and a steady state concentration Cas within the blister is

reached, Cas is given by:

Co

1

^ ^ln(lA) ^

(35)

1-k

Cas is predicted to be higher than Cq so long as the blister remains cathodic with

respect to the scribe, that is, p > 0. The lower curve in figure 4 depicts this beha\aor.

In the absence of an electric field (p = 0), the steady state value will reach the concentration of sodium ions in the external solution.

If;?>;?*, a is negative, and the concentration is predicted to increase without

limit. In this case eq (31) can be written:

17
r „l<i/!|(<-e,)_i

Co \a\

Here, a steady state concentration of sodium ions within the bhster is not reached.

The concentration is predicted to increase indefinitely so long as sodium ions are

available for transport, so that concentrations within the blister can be many times

the external solution concentration. This behavior is illustrated by the upper curve

in figure 4.

For the special case when /?=/?*, a = 0, and the concentration within the blister

is predicted to increase linearly with time according to:

Ca = P Co(r-0,) . (37)

This is shown by the inclined straight line in figure 4.

The parameters o; and 3 can be evaluated by fitting experimental data to one

of eqs (35), (36), and (37). Further, the parameter p can be calculated from the best

value of q; using eq (32).

The approach to steady state depends on the system time constant r = l/ck;3

given by:

^ V In(lA) 1 ^ V\n{llk) Cas ^jgx ^ In 6 D I -p/p' 271 6 D Co ' ^ ^

Equation (38) presents the system time constant t as a function of the steady

state concentration. It shows that the time constant at each p is directly proportional

to (Cas/Cq). Positive values of r only occur when p < p* . A large diffusion coefficient

18
D gives a low time constant t so that diffusion is more likely to control ion flow (p low).

With a low diffusion coefficient, a high time constant will result and electric field control of flow (p high) is more likely. However, if p equals or exceeds p*, there is no

time constant and the system never reaches a steady state. Since eq (30) is a first order

linear differential equation, the time constant t is equal to the time taken for the concentration to go 63.2% of the way from its initial to its final value Co- The shortest

time constant occurs when p is negative. This occurs when ions flow outward from

the blister solution (counter-current flow). In this case the model solution predicts

that the electric field opposes the diffusion process so that a low steady state concentration can be reached rather quickly. However such a situation is unlikely in practice

because the blister would go from a cathodic to an anodic state, so that the corrosion

reactions which sustain ion transport would occur elsewhere.

4. Experimental

To verify the models an experiment was designed and conducted to measure the

diffusion of cations along the coating/metal interface from the defect to the blister.

Experimental details are provided in this section.

4.1 Specimen Preparation

The specimen configuration for metal cation diffusion along the interface is

schematically shown in figure 5. An SAE 1010 cold rolled steel panel (Q Panel*) with

•Certain commercial equipment is identified in this paper in order to specify

adequately the experimental procedure. In no case does such identification imply

recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that it is necessarily the best available for the purpose.

19
a dimension of 150 x 100 x 0.8 mm was used as the substrate. The specimen was prepared by making a 5 mm diameter perforation in the middle of an as-received, uncoated steel panel. The perforated panel was then glued to a 3.0 mm thick poly (methyl

methacrylate) (PMMA) sheet using a room-temperature-cured epoxy adhesive. A

hole of 2 mm diameter was drilled through the PMMA sheet near the center of the

perforation. A 4 mm diameter disk of the same steel with a copper wire soldered to

it was placed flat on the PMMA sheet at the center of the perforated space. The wire

was then put through the PMMA sheet. Care was taken so that the surfaces of the

disk and of the panel were approximately at the same level. The space between the

5 mm disk and the 4 mm perforation was filled with a room-temperature-cured epoxy.

This epoxy insert served as an electrical insulator between the steel disk at the center

and the rest of the steel panel.

The steel surface of the panel was sanded (sand paper grit no. 320) to produce

a clean and flat surface. Prior to applying the organic coating, the sanded panel was

repeatedly cleaned with methanol then dried with dry air. (A drop of distilled water

spread spontaneously on the panel surface after cleaning, indicating that the surface

was free of organic contaminants.) A commercial, high-build, room-temperaturecured epoxy coating was applied on the panel using the draw-down technique. The

thickness of the dry coating was approximately 450 ]im as measured by an eddy current

gage. After curing for 1 week, a 5 mm diameter disk, of the coating from the same

location where the perforation in the steel was made, was bored to the steel substrate

and removed from the coated panel. A glass tube having an outside diameter of 4.5

mm and a height of 50 mm was placed where the coating disk had been removed.

Epoxy adhesive was used to seal the space between the glass tube and coating. To ensure that the epoxy adhesive did not touch the steel surface and block the lateral diffu20
sion route, a hollow disk of tetrafluorethylene polymer having an outside diameter of

5 mm and inside diameter of 3 mm was situated at the bottom of the glass tube (refer

to fig. 5). The glass tube assumes the function of a constant volume cathodic blister.

A circular scribe through the coating to the steel substrate was made around and

away from the glass tube. The radius between the scribe and the center of the glass

tube was 22.5 mm. The width of the scribe was 2 mm. The scribe provided a defect

through which the cations could enter the system. An open-ended PMMA cylinder

having a height of 50 mm and an inside diameter of 50 mm was placed symmetrically

around the glass tube. For this configuration, the experimental value of the parameter

k was 0.227. A section of the coating from the coated panel portion outside the

PMMA cylinder was removed to the bare substrate. This bare steel section was used

as the working electrode and was connected to one end of a potential-applied source. The other end of the potential-applied source was connected to the copper wire attached to the steel disk. A battery and a potentiostat were tested as sources to apply

the potential difference between the scribe (defect) and the glass tube (blister). However, for an unknown reason, the potentiostat interfered with both the pH and the Na

ion concentration readings. For that reason, the potential source employed in this experiment consisted of two 1.5 V batteries in series connected in series with a variable

resistor. This arrangement provided a current of 45 ± 5 )iA and a corresponding potential of 275 ± 45 mV.

4.2 Cation Measurement

The experimental apparatus for cation measurement in the glass tube is depicted

schematically in figure 5 and shown in the photograph in figure 6. The concentration

of Na ions in the glass tube was measured by a commercial 1 mm tip, Na-selective

21
1_ o o 3 fc: CO 4-J Q.E c cc on o

0)

,9C-) o O o w

(D

T32o

0)

LU IO X

N

.ti o >» ^CQ CO

zOqc

g

Q.

O • of—( M(SJ

V-i coUc

<uBo

a.

00

T3c

cd3afcBwo

-OBo

COin

22
Figure 6. Experimental Apparatus for Cation Measurement

23
minielectrode (World Precision Instruments*). In addition, the pH in the glass tube

was determined as a function of time by a conventional mini pH electrode. A 10x10

mm platinum foil attached to a silver wire was used as the counter-electrode. The

electrodes were connected to a high-impedance (10^^ ohm) pH/ion analyzer (Orion

EA 940*). The analyzer was programmed to record Na ion concentrations and pH

at desired intervals. The ion-selective electrodes respond to activity rather than concentration, where the activity is related to the concentration by the activity coefficient.

However, because the measurement system was calibrated in terms of concentration,

we reported our results in terms of concentration. A switch box was employed to provide simultaneous readings of multiple electrodes. Both pH and Na-selective electrodes were calibrated prior to actual measurements using standard solutions. Before

measurements began, a 0.5 mol/L solution of reagent grade NaCl in doubly distilled,

deionized water was placed in the space between the glass tube and the PMMA cylinder, and doubly distilled, deionized water was added to the inside of the glass tube.

The liquid in the glass tube and in the PMMA cylinder were always kept at the same

level, about 4 mm from the rim. The top end of the glass tube was sealed with molten

paraffin wax and cellophane was used to cover the top of the PMMA cylinder. These

procedures were employed to minimize evaporation of water from both containers.

Two pointed micropipettes were inserted through the wax. One was used to introduce

air into the glass tube at a rate- of approximately 10 bubbles per minute to maintain

the corrosion reactions. This micropipette was also used to add NaCl solution into

the glass tube to maintain the original liquid level. This provides justification for the

model assumption of constant blister volume. The other micropipette was used to release the pressure. To facilitate the handing of the measurement system, both the specimen and the electrodes were attached to separate micromanipulators.

24
5. Results and Discussion

5.1 Experimental Results

Figure 7 shows the pH and Na ion concentrations in the central chamber (control

glass tube) as a function of time. The data on which the figure is based are given in

Appendix I. The concentration of Na ion in the glass tube started to increase after

more than 280 hours of testing, and surpassed the concentration in the PMMA cylinder around 450 h. The pH in the glass tube also started to increase at about 280 h

and reached a value of almost 11 after 430 h; after that it remained essentially unchanged. It should be noted that approximately 2 )il of solution with the same Na ion

concentration as that in the glass tube was added to the glass tube at a time of 650

h in order to restore the original liquid level. This may have disturbed the corrosion

reactions as well as the sodium ion transport process, which may help to explain the

apparently anomalous value of Na ion concentration at 720 h exposure.

The bare steel substrate inside the glass tube did not corrode and remained

"white." The high pH solution and the whiteness of the steel area inside the tube indicate that this area was in the cathodic state during the experiment. On the other hand,

the steel substrate at the scribe became heavily corroded, indicating that these regions

were anodic. These results suggest that the experiment was successful in simulating

the blister formations and delamination processes generally observed around defects

of coated steel panels exposed to electrolytes. The defects serve as the anode where

iron oxidizes (corrodes), and the delamination and blister areas serve as the cathode

where hydroxide ions are formed. Under coatings, pH values as high as 14 have been

measured in cathodic regions [13]. Because of these processes, an induced potential

develops and current flows between the anode and cathode.

25
64000 -

48000 -

SODIUM ION

CONC. ppm

32000 -

16000

• • • • [Na^] sodium ion cone, ppm

o o o o pH

„ L \ . L > 170 340 510

12

11

10

pH

- 9

680 850

TIME (hours)

Figure 7. Sodium Ion Concentration and pH

within Central Glass Chamber .

26
It is interesting to note that the results of the same experiment conducted for

600 h but in the absence of an appHed potential difference between the scribe and the

glass tube showed that: 1) the bare metal in the glass tube and at the scribe corroded

severely, 2) the concentration of sodium ion inside the glass tube varied very little

between the start and the end of the experiment (between 3 and 7 ppm), and 3) the

pH in the glass tube decreased, from 8.2 at the beginning to 7.7 at the end of the exposure. These results indicated that, in the absence of an applied potential, the bare metal inside the glass tube was in the anodic state, and not in the cathodic state as in the

potential-applied case. The cathodes probably remained somewhere under the coating in these experiments.

5.2 Theoretical Results

In this section theoretical results are presented based on the mathematical models developed in section 3. The computer programs used to implement the calculations are given in Appendix III.

5.2.1. Steady State Sodium Ion Concentration

From the previous mathematical analysis, it is clear that, between the scribe and

the blister on a coating/metal interface, two major parameters affect the sodium ion

steady state concentration profile. One parameter is the geometric factor k (aspect

ratio). The other is the parameter p, which is a measure of the relative importance

of the applied electric field as opposed to diffusion as an ionic transport mechanism.

Since these two mechanisms occur in parallel, the faster one will control transport.

Thus, at low values of p, diffusion controls transport while, at high values of p, transport of ions is controlled by the potential gradient created by the electric field. Our

27
experimental results suggest that transport is controlled by the electric field when a

potential is applied across the system.

Figure 8 (plotted from eq (8)) presents the sodium ion steady state concentration

profile with k as a parameter and no potential gradient (p = 0). The value k = 0.227

corresponds to that for the size of blister employed in our experiment. High sodium

ion concentrations are present close to the scribe and decrease along the path from

the scribe to the blister. The concentration gradients, which are proportional to the

slopes of the curves, are lower near the scribe where the ions first enter the channel

under the coating. The x-intercept (k/(l-k)) corresponds to the blister radius (r = a).

The concentration is zero there, as indicated by eq (8).

Figures 9, 10, and 11 (plotted from eq (12)) display the steady state sodium ion

concentration profile with p as a parameter at different values of k. The figures show

that the sodium ion concentration decreases faster at greater values of p near the blister, but slower near the scribe, an effect that is accentuated for smaller blisters, as shown in figure 11. Comparing these three figures shows that, when p is constant, the

gradients of sodium ion concentration profile are smaller at larger values of k. Higher

potential gradients along the path from the scribe to the blister lead to both higher

ion concentrations in the region near the blister and higher gradients. This effect is

expected since higher values of p result in facilitated ion diffusion under the coating.

5.2.2. Steady State Ion Flux

Figure 12 (plotted according to eqs (10) and (11)) displays the steady state dimensionless sodium ion flux plotted against the reciprocal of the aspect ratio 1/k, with

p

given as a parameter. The flux is negative because sodium ions are moving inward

in the direction of decreasing radius.

28
\ 1

=

0.5

1 1

—

>V ^ —

r^

\.

CM ^Nw

CM ^\^^ d ^^v^

II V ^

~ .^_\ \V. - d s. ^s^^^

II \. ^^^^^ ^ ^

V \.

1 1

1 1 1 1 1

1 1

O

csi

• i

^/^""^ 4> CO

1 tS in cc s ^ ' Phc

~1_ o "—

CO l-r 4-> 3 c Q c < 6

CC e

q CO O

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LU 3

_l -a z ^ O (U

-!-> CO

LU

in ^

03

• -«-> o Q C/3

uT o6

3)

CX) dCD

d d d

(°0/^0) "ONOO SS31NOISN3l/Mia '0

29
in

CM

oo

in oIT) LO

o o o

(°0/^0) 'ONOO SS31NOISN3IAIia '0

,3Jo

C3

8

coU

B

OHI6

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>> t-i T3 , <Tt ^

4> > ^ u

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ISo

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roro) 'ONOO ss3nNOiSN3Nia 'o

31
9iO

c

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32
1 1 1 1

\ \

\v\ " \ VyXo.

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- Q.1 \ \

1

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II Q. 1

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oo

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(ss9|uo!su9LU!p) xnid NOi lAiniaos 'd33
As shown in figure 12, the ion flux is much higher when the scribe and bhster are near

one another (when R/a is larger) and decreases rapidly as their distance of separation

increases, approaching a constant flux for smaller blisters.. For constant k values,

when p is larger, the ion flux is greater. For example, the flux when k = 0.1 (R= 10a)

is 2.5 times as high with p = 1 as it is with no electric field (p = 0). This illustrates that

a higher potential gradient causes a higher ion flux. These steady state results for the

ion flux agree with the long time unsteady state predictions of Nguyen et al [12] and

tend to lend validity to the accuracy of both the formulation and numerical solution

they employed.

Figure 13 shows how the predicted dimensionless ion flux F changes with

parameter p with k as a parameter. As is also apparent in figure 12, F increases when

p does. For the same p, F also increases when k increases, but the effect is not as dramatic at larger values of p. For p values larger than about 6, the flux becomes independent of k when k < 0.5. This fact shows that when p exceeds a certain value, different

blister sizes will not affect the steady state ion flux in the path between the blister and

the scribe. Of course, larger blisters will still garner more sodium ions because of their

increased size.

5.2.3. Critical Value of Parameter Value p

In the previous section, the critical value of the dimensionless potential gradient

/7* was defined as p* = (l-k)/k ln(l/k). From the experimental data given in table 1,

k = 0.227, giving ;?* = 2.295. As discussed earHer, when/> >;?* (p value above or

equal to the critical value), there will be no steady state concentration of sodium ion

within the blister, and the final concentration is predicted to increase indefinitely.

34
- 00

CO D. w c/j 0) > c tiT o ^

^ <D E

E s

io 5

DC

E

3

_, o ^ H C^ O 4> < 15 LL C/3 O

^, DC

C\J H C/5 O

LU 3

LU 2i3

Q. .2? - o

C\J

o

'

(ss9|uo!su9UJ!p) xnid Noi lAiniaos 'd35
When p = 0, the steady state concentration within the bhster will reach the value in

the outside solution, while when p < p* a steady state concentration of sodium ion will

be reached within the blister. If p is negative the final concentration of ions is predicted to be less than the external value Cq. In this event the electrical field opposes

the inward diffusive flow of ions.

Figure 14 (plotted using eq (3 1)) shows how the steady state sodium ion concentration in the blister varies with the ratio of/? top*. When/? is less than half of the

critical value/?*, the concentration increases slowly as p increases. However when/?

is greater than this, the concentration rises rapidly becoming unbounded as/? approaches/?* from below. The figure shows that when p = the steady state concentration becomes equal to that in the external solution, while for p values greater than p*

there is no steady state concentration. As shown by the dashed part of the curve, if

negative values of p were possible they would produce somewhat lower steady state

concentrations. These results agree with model predictions.

Figure 15 presents the steady state sodium ion concentration within the blister

versus k (in the range from to 0.9) with p as parameter (for p = -1 to 5). Small values

of k correspond to the situation where the size of the blister is small compared with

the distance between the blister and the scribe, while high k corresponds to a relatively

large blister. The figure shows that when p > 0, the steady state concentration exceeds

the external solution concentration. Concentrations within larger blisters are predicted to be greater than within smaller blisters, the effect being more pronounced

at larger values of p. When p = 0, the final concentration within the blister is predicted

to be equal to that in the external solution regardless of blister size. Negative values

of p

predict that concentrations within the blisters will be less than the external value

with larger blisters being more dilute than smaller. This is unlikely in practice, since

36
Q.

«

>o

u

u

a

o

G

c

oU

col-HB3

4>

•-• CO

41^ CO

t-t CO

2

o in

(ss9|U0!SueLLi!p) qnOO l/MfliaOS '°0 /^O

37
>O

00 u

o

1

CC

CO

^ 8

o O

oU

H c

<

DC E

HO

,2 "^

LJJ

C/5 o Q- ^

CO 5

<

C/3

•>. TJ

J!^

(!> *-> (/3 CM «n O rH

CJ C30 CD CM

i-i

(ss8|U0!SU8UJ!p) ONOO NOI l/^niOOS '°0 /^O

38
as mentioned, the corrosion reactions cannot be sustained at their original site when

the polarity of the scribe and blister are reversed.

Figure 16 displays the way the critical value;?* changes with k, the ratio of a to

R. The experimental values (p* = 2.29 at k = 0.227) are marked on the figure for reference. When k < 0.1, ;?* decreases rapidly with increases in k, while for k values above

0.1, ;?* is not as sensitive to variations in k. Figure 16 shows that for larger blisters

(larger a for the same R) p* is near unity, whereas for small ones, p* can be quite large.

Since/? <p* is the criterion for obtaining a steady state concentration within a blister,

it is less likely that large blisters will develop a steady state concentration of salt within

them. Once the blisters reach a critical size corresponding to p = p* they may continue

to grow. If such a blister enlarges due to the osmosis or cathodic delamination induced

by the increased salt concentration within it, p* vvdll fall even further (provided the

scribe location is fixed). The new larger blister will have more of a tendency to grow

because the higher salt concentration within it will lead to an even higher osmotic pressure. The larger surface area of the larger blister will also draw in more salt than that

in the smaller blister. The high pH within the blister can also lead to delamination

(cathodic) around the periphery of the blister. These factors can cause the eventual

failure of the coating system.

Small or nascent blisters are predicted to be less prone to grow than large ones.

This may supply part of the reason for the induction period often observed with blister

growth. The initial or breakthrough time 0i provides an alternative explanation, as

does the initial unsteady state period.

39
o

in

r^c> • ^^^ jM cc^

^

• o

cu •«o

1- 4> < S

o DC ^ d O

•3

Lli

*•> Q. u

CO

< VO

t-t ^

g

ID 3)

d

CO CM 1-

d dO 3mVA IVOIlldO '*cl

40
5.3 Comparison of Experimental to Theoretical Results

Since the sodium ion concentration does not begin to rise from background levels until almost 280 hours, the initial stage will be of comparable duration. It takes

about this long for the sodium ions to break through into the blister. The initial stage

will end and the propagation stage will begin at this time (t = ©j).

Equation (31) predicts how the sodium ion concentration varies with time. In

this equation, there are two unknown constants, a and 3, which are defined in terms

of the parameters p, k, V, D, and 8. However, there is not enough information to determine all of these parameters individually. The experimental data presented in Appendix I as table 1 were used to find the best values of a and (3. The data analysis algorithm

is presented in Appendix 11 while the computer codes for this calculation are given

in Appendix III. The best values of a and (3 are the ones which minimize the error sum of squares between the predicted and the experimental concentration data.

A Fortran program (refer to FINDAB program in Appendix III) was coded to

employ the curve-fitting method and obtain the best values of a and (3. The experimental data of table 1 show that breakthrough of sodium ion into the blister appears

to occur some time between 264 and 288 h, with a definite breakthrough observed

by 336 h. Thus, the initiation times Q\ = 264 and 288 h were used to perform the data

analysis. This resulted in values for (a, 3) pairs of (-0.4627, 4.48E-03 hr~^) and

(-0.465, 4.84E-03 hr"^), respectively. A nonlinear least square computer program

[14] using the same data set was also employed. It gave equivalent (a, (3) pairs for

the same initiation times. The consistency of the results lends credence to the methods

employed in the data analysis. A somewhat lower error sum of squares was obtained

41
with &i = 264 hours, but the variance ratio (F) test showed that it was not statistically

better than the value for 0j = 288 h.

Figures 17 displays both the theoretical and experimental data of sodium ion

concentration versus time within the blister for the two initiation times. The best value

of p was 3.35 for both breakthrough times. Note that the curves are both curved upward and nearly coincident. The upward curvature shows that the concentration is

increasing without limit. Since p>p* =2.29, the theory predicts that a steady state

concentration will not be reached within the blister. In fact, at the conclusion of the

experiment, the concentration of sodium ions within the blister was over five-fold that

in the external solution. The concentration is predicted to increase without bound as

long as there are sufficient sodium ions in the external solution. If the simulated blister

modeled by the experiment were an actual blister under a coating there is a good

chance that it would keep enlarging for the reasons previously discussed. Further experimental and theoretical work is currently being directed in our laboratories towards an understanding of the mechanisms and modes of blister growth.

Although separate values of the diffusion coefficient D and channel height 8 can

not be found, their product D8 can be calculated from the lumped parameter |3. From

the best values of (3 the product D8 is 0.92 E-6 and 0.97 E-6 cm^/s, for initiation times

of 264 and 288 h, respectively. For a channel height of 1 mm the values of D are approximately 1 E-5 cm^/s, which is somewhat lower than the value of the unhindered

or bulk diffusivity of 1.5 E-5 cm^/s for sodium chloride [15],

42
J2O

Lli

i

s

.£3

e

'tfcde

8

e

Q

a

B3

a

2

(ludd) ONOO NOI lAiniOOS '^Q

43
6. Summary and Conclusions

Conceptual and mathematical models have been developed for blistering of organic coatings on metal substrates that results from corrosion when defects are present

in the coating and the coated metal is exposed to electrolytic solutions. Experiments

were conducted in a cylindrical geometry which simulated this situation. Sodium ions

in an outside chamber containing an external scribe or defect which acted as an anode

were transported under the combined influence of diffusion and potential gradients

towards an inner chamber which served the role of a cathodic blister. Solutions to

the model predicted that the steady state sodium ion concentration profile, and the

sodium flux in the region between the blister and the scribe, should be a function of

the dimensionless potential gradient p and aspect ratio k. These predictions are consistent with the long time unsteady state results of the work of Nguyen et al [12].

An unsteady state solution was developed for the concentration of sodium ion

within the blister as a function of time. In the absence of an electric field (p = 0) the

highest ion concentration that can exist within a blister is that in the external solution.

Under the application of a cathodic potential (p > 0), the concentration within the blister is predicted to rise above that in the external solution. A critical value p* of the

dimensionless potential gradient, which is solely a function of the aspect ratio, established the conditions under which the concentration would reach a steady value

(p < p*) or increase indefinitely (p > p*). The model was successfully fitted to experimental data which did showp > p*. For blisters that are changing size, the theory predicts that small blisters will not grow until they reach a critical size corresponding to

(p = p*). Blisters of larger size can grow under the combined effects of cation transport, osmosis, cathodic delamination and mechanical stresses.

The results of this study should be of general applicability to other similar coating and electrolyte systems.

44
7. Nomenclature

a radius of the blister.

a' constant defined by eq (20).

Co sodium ion concentration outside the scribe (or defect).

Ca sodium ion concentration within bhster.

C sodium ion concentration between the scribe and the bhster for the initial

period.

C dimensionless concentration of sodium ion, C = CVCo.

D effective diffusion coefficient of sodium ion under coating.

E strength of electric field.

F dimensionless ion flux between the scribe and the blister.

Fe ion flux into blister caused by electric field.

H height of the blister.

k geometric aspect ratio for the blister, a/R.

kj geometric aspect ratio for the moving interface, ki = ri/R

L length scale

p dimensionless potential gradient.

p* critical value of the dimensionless potential gradient, (k-l)/(k InK)

R radius of the scribe.

r' radial coordinate.

r dimensionless radius.

x\ radius of the moving interface.

t dimensionless exposure time.

t' exposure time.

V volume of solution in blister

Wd molar flow caused by diffusion.

We molar flow caused by the electric field or potential gradient.

QL constant defined by eq (32), 1-p/p*.

45
3 constant defined by eq (33)

Q s amount of adsorbed sodium per unit of interfacial area.

8 channel height.

)x average mobihty of sodium ion.

0j initiation or breakthrough time for the sodium ion.

AO potential difference between scribe and blister.

46
8. References

[1.] Bennett, L. H., Kruger, J., Parker, R. L., Passaglia, E., and Yakowitz, H., Natl.

Bur. Stand., U.S. Spec. Publ. 511-1, 1978.

[2.] Pommersheim, J. M., Campbell, P. and Mcknight, M., "The Mathematical

Modeling of the Corrosion Protective Performance of Organic Coatings,"

Nat. Bur. of Stand. U.S. Technical Note 1150, September 1982.

[3.] Leidheiser, H. Jr., J. Adhesion Sci. Technol., 1 (1987) 79.

[4.] Koehler, E. L., Corrosion, 40 (1984) 5.

[5.] Watts, J. W, J. Adhesion, 31 (1989) 73.

[6.] Funke, W, Leidheiser, H. Jr., Dickie, R.A., et. al., /. Coatings Technology,

58 (1986) 741

[7.] Walter, G. W, Corrosion Sci., 26 (1986) 27.

[8.] Nguyen, T, Byrd, E., and Lin, C, J. Adhesion Sci. Technol, 9 (1991) 697.

[9.] Beaunier, L., Epelboin, I., Lectrade, J. C, and Takenouti, Surface. Technol.,

4 (1976) 237.

[10.] Funke, W, Ind. Eng. Chem. Prod. Res. Dev., 24 (1985) 343.

[11.] Sato, N., Corrosion, 45 (1989) 354.

[12.] Nguyen, T, Hubbard, J.B., and McFadden, G.B., / Coatings Technol,

63 (1991) 43.

[13.] Ritter, J. J. and Kruger, J., in Corrosion Control by Organic Cratings,

Leidheiser, H. Jr. (Ed.), Natl. Assoc. Corros. Eng., Houston, TX, 1981, p. 28.

[14.] Koko, F. W, BUST (Bucknell University Statistics Program).

[15.] Robinson, R. A., and Stokes, R. H., "Electrolyte Solutions," 2nd ed.. Academic

Press, New York (1959).

47
Appendices

I. Experimental Data

II. Data Analysis

III. Computer Codes

48
Appendix I. Experimental Data

Table 1: Experimental Data

1. Data for Blister Size

Radius of blister: a = 0.5 cm

Radius of scribe: R = 2.2 cm

Height of blister: H = 4 cm

Volume of blister: V = ira^H = 3.14 cm^

2. Data for Concentrations (ppm) of Sodium Ion within Blister

Co = 11500 ppm

],ppm) pH

8.05

Time (hours) CA([^

3.3

96 3.7

192 3.4

264 3.7

288 45

336 250

384 2640

432 7300

456 14020

480 15500

576 23300

600 27200

624 29900

648 31900

720 33110

768 47610

816 59420

7.89

8.02

8.06

8.48

10.25

10.93

10.89

10.82

10.87

10.93

10.85

10.87

10.95

49
Appendix II. Data Analysis

The curve fitting method developed here was used to analyze the experimental

data of the sodium ion concentration within the blister versus time.

Equation (31) was used to evaluate the best values of the model constant ce and

3. The experimental data is given in table 1.

Ca

Co a

l_e-a/3(/-e,) For a ^ 0, (31)

where a = 1-p

and fi =

A:In(l/^)

1-k

271 6 D

(32)

(33) V ln(l/k)

In this method the error sum of squares s^ is minimized, where:

and s is the variation ( yi - yc), where yj is the experimental value, and yc is the value

calculated from the model equations and assumed model constants.

The algorithm used to evaluate the best values of a and (3 is as follows:

1. Pick a value of 3;

2. Pick a value of a;

3. Apply the values of a and (3 to eq (31) or eq (37);

4. Plot s^ versus |3 at different a's. Find the lowest value of s^.

5. Pick a new value of 3 and repeat steps 2 to 4.

6. Finally find the global minimum value of s^, and the associated

best values of a and (3.

50
Appendix III. Computer Codes

1. Program SSCONC

2. Program SSFLUXl

3. Program SSFLUX2

4. Program CVSKP

5. Program CCPP

6. Program PK

7. Program FINDAB

8. Program NEWDATA

51
PROGRAM SSCONC

C

c

Q ***************************5 ****************************************

c * * C * TITLE: Steady-State Concentration Profile * C * * C * AUTHOR: Joanne Zhang * C * * C * DATE Coded: February 17, 1990 * C * * C * ORGANIZATION: Chemical Engineering Department * C * LOCATION: Bucknell University * C * Lewisburg, PA 17837 * C * * Q ********************************************************************

c

c

C: PURPOSE:

C

c

C This program calculates the steady-state ion concentration

C profile along the channel beneath coating films with potential

C gradient p and aspect ratio k as parameters

.

C

C

C: VARIABLES:

C

C

REAL C, R

REAL RO, RT, DR

REAL P , K

REAL CON(20), RI(20)

C

c

C: INITIALIZATION:

Q

C

c

c

cc

C: BODY:

c

c

C: Data Input

C

PRINT*, 'PLEASE INPUT THE VALUES OF K

:

READ*, K

C

PRINT*, 'PLEASE INPUT THE VALUES OF P

:

READ*, P

C

C: Calculate RO (r=a) and RT (r=R)

C

RO = K/(l-K)

RT = 1/(1-K)

C

C: Calculate concentration

C

DR = (RT - R0)/20.

R = RO

C

DO 10 1=1, 20

IF (P .EQ. 0.0) THEN

C = 1/LOG(1/K)*LOG(B/R0)

ELSE

C = 1/(K**P-1)*(R0**P/R**P-1)

ENDIF

52
CON(I) = C

RI(I) = R

R = R + DR

10 CONTINUE

c

C: Data output

C

OPEN (UNIT = 9, FILE = 'f2b.5')

C

DO 20 J = 1, 20

WRITE(*, 55) RI(J), CON(J)

WRITE(9, 55) RI(J), CON(J)

20 CONTINUE

C

C

C: TERMINATION:

C

C

55 F0RMAT(1X, F7 . 4 , 3X, F7.5)

C

END

53
PROGRAM SSFLUXl

C

c

Q ***ii***icic**ic*i!ftii****ii*ii:icicl!iciiitl!ic*it**i!*it-k*it*icic1tit*itii:ititit******1c******* c * * C * TITLE: Steady-State Flux vs . K * C * * C * AUTHOR: Joanne Zhang * C * * C * DATE Coded: March 16, 1991 * C * * C * ORGANIZATION: Chemical Engineering Department * C * LOCATION: Bucknell University * C * Lewisburg, PA 17837 * C * * C ******************************************************************

C

C

C: PURPOSE:

C

cC This program calculates the steady-state ion flux along

C the channel beneath the coating films. The flux varies with

C aspect ratio k with potential gradient p as a parameter.

C

C

C: CONSTANTS:

C

C

REAL PI

PARAMETER (PI = 3.14)

C

C

C : VARIABLES

C

C

REAL F(99), K(99)

REAL P

REAL KI

C

C

C: INITIALIZATION:

Q

C

C

C

c

C: BODY:

C

c

C: Input value of P. C

PRINT*, 'Input value of P :

' READ*, P

C

C: Calculate F as a function of K. C

PRINT*, ' K F' KI =0.01

IF (P .EQ. 0.0) THEN

DO 10 1=1, 99

K(I) = I*KI

F(I) = ABS(2*PI/L0G/K(I) )

)

WRITE(*, 55) K(I), r'(I)

10 CONTINUE

54
ELSE

DO 20 I = 1, 99

K(I) = I*KI

F(I) = ABS(2*PI*P/(K(I)**P - 1))

WRITE(*, 55) K(I), F(I)

20 CONTINUE

ENDIF

C

C : Data output

.

C

OPEN (UNIT=9, FILE = 'f3.-l')

C

DO 30 J = 1, 99

WRITE(9, 55) K(J), F(J)

3 CONTINUE

C

C

C: TERMINATION:

C

C

55 FORMAT (F6.3, IX, FlO.6)

C

END

55
PROGRAM SSFLUX2

Cc

Q ******************************************************************

c * * C * TITLE: Steady_State Flux vs . P * C * * C * AUTHOR: Joanne Zhang * C * * C * DATE Coded: March 17, 1991 * C * * C * ORGANIZATION: Chemical Engineering Department * C * LOCATION: Bucknell University * C * Lewisburg, PA 17837 * C * * Q ******************************************************************

C

c

C: PURPOSE:

C

C

C This program calculates the steady-state ion flux along

C the channel beneath the coating films . The flux varies with

C potential gradient p with aspect ratio k as a parameter.

C

C

C: CONSTANTS:

C

C

REAL PI

PARAMETER (PI = 3.14)

C

C

C : VARIABLES

C

C

REAL F(25), P(25)

REAL K

C

C

C: INITIALIZATION:

C

C

C

c

c

C: BODY:

c

C

C: Input value of k.

C

PRINT*, 'Input value of K: ' READ*, K

C

C: Calculate F as a function of P. C

PRINT*,

PRINT*, ' P F' P(l) = -2.0

C

DO 10 I = 1, 25

P(I) = P(l) + (I-1)*0.

5

IF (P(I) .EQ. 0.0) THEN

F(I) = ABS(2*PI/L0G(K)

)

ELSE

F(I) = ABS(2*PI*P(I)/(K**P(I) - 1))

ENDIF

WRITE(*, 55) P(I), F(I)

10 CONTINUE

56
c

C : Data output

.

C

OPEN (UNIT=9, FILE = ' f 4 . . 5

'

)

C

DO 20 J = 1, 25

WRITE(9, 55) P(J), F(J)

20 CONTINUE

C

C

C: TERMINATION:

C

c 55 FORMAT (F6.3, IX, F10.6)

C

END

57
PROGRAM CVSKP

C

c

Q ******************************************************************

c * * C * TITLE: Steady State Concentration * C * * C * AUTHOR: Joanne Zhang * C * * C * DATE Coded: March 20, 1991 * C * * C * ORGANIZATION: Chemical Engineering Department * C * LOCATION: Bucknell University * C * Lewisburg, PA 17837 * C * * Q ******************************************************************

c

C: PURPOSE:

C

C

C This program calculates the steady state ion concentration

C either as a function of the aspect ratio k with potential

C gradient p as a parameter or as a function of potential gradient

C p with the aspect ratio k as a parameter.

C

C

C: VARIABLES:

C

C

REAL K, KI(IO)

REAL P, PI (13)

CHARACTER TYPE*1

REAL CK(IO), CP(13), KK(20)

C

C

C: INITIALIZATION:

Q

c

c

cc

C: BODY:

C

c

C: Input parameters k and p. C

c PRINT*, ' Input the parameter (k or p, and RETURN for quit).'

C READ*, TYPE

C

C IF (TYPE .EQ. 'p') THEN

PRINT*, ' Input value of p:

' READ*, P C

OPEN (UNIT = 9, FILE = ' f 7 . 5

'

)

C

C: Calculate Ca/CO as a function of k.

C

PRINT*,

PRINT*, ' K Ca/CO ' C

DO 10 I = 1, 1000

K = 0. 2 + 1*0. 0001

PP = (1-K)/(K*L0G(1/K)

)

TOL = ABS(PP-P)

IF (TOL .LT. 0.00001) GOTO 100

10 CONTINUE

C

100 CONTINUE

58
DO 20 J = 1, 18

KK(J) = J*K/20

C KK(J) = KK(J)*3.5

C

IF (J .EQ. 1) KK(J) = 0.01

C

CK(J) = 1/(1 - P*KK(J)*L0G(1/KK(J) )/(l-KK(J)))

c

C: Data output

C

WRITE(9, 55) KK(J), CK(J)

WRITE(*, 55) KK(J), CK(J)

C

20 CONTINUE

C

C

c ELSEIF (TYPE . EQ . 'k') THEN

c PRINT*, ' Input value of k: ' c READ*, K

C

C: Calculate Ca/CO as a function of p.

C

c DO 30 I = 1, 13

c IF (I .EQ. 13) THEN

c PI(I) =0.5

c ELSE

c PI(I) = (I-2)*1.0

c ENDIF

c CP(I) = 1/(1 - PI(I)*K*L0G(1/K)/(1-K)

)

c 30 CONTINUE

C

C: Data output.

C

c OPEN (UNIT = 19, FILE = 'cacO.kO.5')

C

c PRINT*,

c PRINT*, • P Ca/CO ' C

c DO 40 J = 1, 13 c WRITE(19, 55) PI(J), CP(J)

c WRITE(*, 55) PI(J), CP(J)

c 40 CONTINUE

C

c ELSE

c GOTO 100

c ENDIF

C

C

C:

C

TERMINATION:

C

55 FORMAT (IX, F6.3, IX, F10.6)

C

c 2 00 CONTINUE

C

END

59
PROGRAM CCPP

C

C

Q ******************************************************************

C * * C * TITLE: CA/CO VS. P/P* * C * * C * AUTHOR: Joanne Zhang * C * * C * DATE Coded: March 26, 1991 * C * * C * ORGANIZATION: Chemical Engineering Department * C * LOCATION: Bucknell University * C * Lewisburg, PA 17837 * C * * C ******************************************************************

C

C

C: PURPOSE:

C

C

C This program calculates the dimensionless ion concentration

C CA/CO as a function of the ratio of the potential gradient p

C and its critical value p*.

C

C

C : VARIABLES

:

C

C

INTEGER N

PARAMETER (N = 51)

REAL CC(N), PP(N)

REAL P

C

C

C: INITIALIZATION:

C

C

C

C

C +H C

C: BODY:

C

C

OPEN (UNIT = 9, FILE = 'f5.-0')

C

C: Data calculation

C

PRINT*,

PRINT*, ' PP, CC

DO 10 I = 1, 51

P = 1.9/50.

PP(I) = -1 + (I-1)*P

C

CC(I) = 1/(1-PP(I))

c

C : Data output

C

WRITE(9, 55) PP(I), CC(I)

WRITE(*, 55) PP(I), CC(I)

10 CONTINUE

C

c

C: TERMINATION:

c

C

55 FORMAT (IX, F7 . 3 , IX, FlO 3)

C

END

60
PROGRAM PK

C

C

Q ******************************************************************

C * * C * TITLE: P* VS. K * C * * C * AUTHOR: Joanne Zhang * C * * C * DATE Coded: March 26, 1991 * C * * C * ORGANIZATION: Chemical Engineering Department * C * LOCATION: Bucknell University * C * Lewisburg, PA 17837 * C * * Q ******************************************************************

C

C

C: PURPOSE:

C

C

C This program calculates the critical value of potential

C gradient p, p*, as a function of aspect ratio k.

C

C

C : VARIABLES

:

C

C

INTEGER N

PARAMETER (N = 101)

REAL K(N), PSTAR(N)

REAL KKl

C

C

C: INITIALIZATION:

C

C

C

C

C

C : BODY

:

C

C

OPEN (UNIT = 11, FILE = ' f a6 '

)

PRINT*,

PRINT*, • K, P*'

C

C: Calcualte p* as a function of k.

C

DO 10 I = 1, 101

KKl = 0.9/100

C

IF (I .EQ. 100) THEN

K(I) = 0.999

ELSE

K(I) = 0.1 + KK1*I

ENDIF

C

PSTAR(I) = (1-K(I))/(K I)*L0G(1/K(I)))

C

C: Data output.

C

WRITE(11, 55) K(I), PSTAR(I)

WRITE(*, 55) K(I), PSTAR(I)

10 CONTINUE

61
c

c

C: TERMINATION:

C

C

55 FORMAT (IX, F7.3, IX, FlO.4)

C

END

62
PROGRAM FINDAB

C

C

Q ******************************************************************

C * * C * TITLE: FIND ALPHA AND BETA * C * * C * AUTHOR: Joanne Zhang * C * * C * DATE Coded: April 10, 1991 * C * * C * ORGANIZATION: Chemical Engineering Department * C * LOCATION: Bucknell University * C * Lewisburg, PA 17 837 * C * * Q ******************************************************************

c

c

C : PURPOSE

:

C

C

C This program evaluates the model constant ALPHA and BETA

C by guessing ALPHA and BETA, calculating the variation (s**2)

C of the theoretical value and the experimental data. The best

C values of ALPHA and BETA can be obtained by minimizing s**2.

C

C

C: LOCAL CONSTANTS:

C

C

REAL CO

PARAMETER (C0=11500)

REAL THATA

PARAMETER ( THATA= 3 3 6)

INTEGER N, M

PARAMETER (N = 26, M = 11)

C

C

C: LOCAL VARIABLES:

C

C

REAL ALPHA(N)

REAL CA(M), T(M)

REAL TPRIM(M) , CACO(M)

REAL S(N)

REAL LN(M)

C

C

C: INITIALIZATION:

C

C

C

C

C: BODY:

C

C

C: Read experimental data from data file.

C

OPEN (UNIT=9, FILE = 'tca.dat')

C

PRINT*,

PRINT*, ' CACO TPRIM ' C

DO 10 J = 1, M

READ(9, *) T(J), CA(J)

TPRIM(J) = T(J) - THATA

CACO (J) = CA(J)/CO

PRINT*, CACO(J), TPRIM(J)

10 CONTINUE

63
c

C: Input value of BETA.

C

PRINT*,

PRINT*, ' INPUT VALUE OF BETA: ' READ*, BETA

C

C: Find the best ALPHA.

C

OPEN (UNIT = 11, FILE = 'alpha.dat')

DO 20 I = 1, N

C

C: Input value of ALPHA.

C

READ (11, *) ALPHA(I)

c PRINT*,

c PRINT*, ' Input value of ALPHA: ' c READ*, ALPHA(I)

C

C: Calculate CA vs. TPRIM and S

C

CALL EQ(ALPHA(I), BETA, CACO, T, TPRIM, S(I))

C

C: Ask for next value of ALPHA.

C

20 CONTINUE

C

C: Write and store ALPHA, S in a data file.

C

OPEN (UNIT = 29, FILE = ' ab . 2 . '

)

C

PRINT*,

PRINT*, ' ALPHA, S' DO 40 J =1, N

WRITE(29, 44) ALPHA(J) , S(J)

WRITE(*, 44) ALPHA(J), S(J)

40 CONTINUE

C

C: TERMINATION:

C

C

44 FORMAT (IX, F6.2, IX, FlO 5)

C

c

c

c

STOP

END

SUBROUTINE EQ(AL, BETA, CACO, T, TPRIM, SS) c REAL AL, BETA, SS

REAL TPRIM(13), CACO (13)

C

REAL Y(13)

C

C: Calculate Y by using ALPHA, BETA.

C

SS = 0.0

IF (AL .EQ. 0) THEN

DO 100 1=1, 13

Y(I) = BETA*TPRIM(I)

SS = SS + (Y(I)-CAC')(I) )**2

100 CONTINUE

ELSE

DO 110 1=1, 13

Y(I) = (1/AL) *(1-EXP(-AL*BETA*TPRIM(I) )

)

SS = SS + (Y(I)-CACO(I) )**2

110 CONTINUE

ENDIF

RETURN

END

64
PROGRAM NEWDATA

C

C

c ******************************************************************

c * * C * TITLE: Theoretical Data Calculation * C * * C * AUTHOR: Joanne Zhang * C * * C * DATE Coded: April 30, 1991 * C * * C * ORGANIZATION: Chemical Engineering Department * C * LOCATION: Bucknell University * C * Lewisburg, PA 17 83 7 * C * * Q ******************************************************************

C

C

C: PURPOSE:

C

C

C This program calculates the theoretical data points by using

C the best values of the nodel parameter Alpha and Beta. The set

C of theoretical data will be used to make a backplot of the

C experimental data.

C

C

C : CONSTANTS

:

C

C

REAL ALPHA, BETA

PARAMETER (ALPHA =-0.4 62. BETA = 4.84E-3)

C

REAL CO

PARAMETER (CO = 11500)

REAL THETA

PARAMETER (THETA = 288.)

C

INTEGER N

PARAMETER (N = 17)

C

C

C : VARIABLES

:

C

C

REAL CA ( N )

, T ( N

)

REAL TLl, TL2, CI, C2

C

C

C: INITIALIZATION:

C

C

C

Cc ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

C

C: BODY:

C

C

OPEN (UNIT = 15, FILE = ' old . dat '

)

OPEN (UNIT = 16, FILE = 'new3.dat')

C

PRINT*,

PRINT*, ' T CA'

C

DO 10 I = 1, N

READ (15, *) T(I)

IF (T(I) .LT. 3 00) THEN

CA(I) = 0. ELSE

65
IF (ALPHA .EQ. 0) THEN

CA(I) = CO*BETA*(T(I)-THETA)

ELSE

CA(I) = CO/ALPHA *(1-EXP(-ALPHA*BETA*(T(I)-THETA) )

)

ENDIF

ENDIF

10

WRITE(*, 55) T(I), CA(I)

WRITE(16, 55) T(I), CA(I)

CONTINUE

TLl = 850

TL2 = 890

IF (ALPHA . EQ . ) THEN

CI

C2

ELSE

CI

C2

ENDIF

C0*BETA*(TL1-THETA)

C0*BETA*(TL2-THETA)

CO/ALPHA *(1-EXP(-ALPHA*BETA*(TL1-THETA) )

)

CO/ALPHA * ( 1-EXP ( -ALPHA*BETA* ( TL2-THETA ) )

)

C

C:C

c

PRINT*,

PRINT*, TLl, CI

PRINT*, TL2, C2

TERMINATION:

55 FORMAT (IX, F6.0, IX, F13.2)

1 END

66
NIST-114A

(REV. 3-90) U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

1. PUBUCATION OR REPORT NUMBER

NIST/TN-1293

2. PERFORMING ORGANIZATION REPORT NUMBER

3. PUBUCATION DATE May 1992

4. TITLE AND SUBTITLE

A Mathematical Model of Cathodic De 1 am i na t i on and Blistering Processes

in Paint Films on Steel

5. AUTHOR(S)

James Pommersheim, Tinh Nguyen, Zhuohong Zhang, Changjian Lin, and

IlL£ Hiihh;^ r d

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

GAITHERSBURQ, MD 20899

7. CONTRACT/GRANT NUMBER

e. TYPE OF REPORT AND PERIOD COVERED

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE. ZIP)

Same as item #6

10. SUPPLEMENTARY NOTES

11. ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBUOGRAPHY OR

UTERATURE SURVEY, MENTION IT HERE.)

Conceptual and mathematical models are developed for processes which describe blistering

of defect-containing coating on coated steel containing defects exposed to electrolytic

solutions. The assumption is made that cations migrating along the coating/metal interface

from an anode at the defect to cathodic sites are responsible for blistering. The cations

are driven by both concentration and electrical potential gradients. The mathematical

models are solved to predict ion fluxes and concentrations along the interface and within

the blister. Solutions of the models are expressed in terms of dimensionless parameters.

Model variables include blister size, distance between the blister and defect, ion

diffusivity and potential gradients. To substantiate the models , an experiment was designed

and conducted to measure the transport of cations along the coating/metal interface from the

defect to the blister. Sodium ion concentration-time data within a blister weT?e analyzed to

determine model parameters. Under the experimental conditions employed, it was found that

the transport of sodium ions is controlled by potential gradients rather than concentration

gradients. Model results indicate that large blisters subject to a potential gradient are more likely to grow than small ones because higher concentrations can build up within them.

Implications of this conclusion for maintaining the integrity of organic coatings are

di scussed

.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITAUZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

anode; blistering; cathode; cathodic delamination; conceptual model; corrosion; defect;

diffusion; mathematical model; organic coatings; paint films; potential gradients; scribe

13. AVAILABIUTY UNUMITED

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS). X

X ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE, WASHINGTON, DC 20402. ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD, VA 22161.

14. NUMBER OF PRINTED PAGES

72

15. PRICE

ELECTRONIC FORM U.S. G.P.0.:1992-311-891:60029



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basis for common understanding of the characteristics of the products. NIST administers this program as a supplement to the activities of the private sector standardizing organizations.

Consumer Information Series -Practical information, based on NIST research and experience,

covering areas of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's technological marketplace.

Order the above NIST publications from: Superinterident of Documents, Government Printing

Office, Washington, DC 20402.

Order the following NIST publications -FIPS and NISTIRs-from the National Technical

Information Sen/ice, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS PUB) -Publications in this series collectively constitute the Federal Information Processing Standards Register. The

Register serves as the official source of information in the Federal Government regarding

standards issued by NIST pursuant to the Federal Property and Administrative Services Act of 1949 as amended. Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order

11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal

Regulations).

NIST Interagency Reports (NISTIR)-A special series of interim or final reports on work

performed by NIST for outside sponsors (both government and non-government). In general,

initial distribution is handled by the sponsor; public distribution is by the National Technical

Information Sen/ice, Springfield, VA 22161, in paper copy or microfiche form.
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