Impedance dispersion on coated metal electrodes

327

Chem, 180 (1984) 327-336 Elsevier Sequoia S-A., Lausanne - Prmted in The Netherlands

J. Elec~roanal

IMPEDANCE

URSULA

RAMMELT

Department

KLAUS

DISPERSION

of

and GEORG

Chemisny,

ON COATED METAL ELECTRODES

*

REINHARD

Technical UniversIry of Dresden. DDR

-

8027 Dresden (G D R)

RAMMELT

Deparzmeni

of Mathematq

Technrcal Unrvers@

of Dresden, DDR

-

8027 Dresden (G D R)

(Received 30th April 1984)

ABSTRACX Usmg the example of a steel/Zn/polyacryIate layer coil-coating system, it IS demonstrated that, to chemical mtensive load impedance, dispersion may occur on electrodes consisting of a metal substrate susceptible to corrosion and a defective polymer layer. For the resulting states of such electrodes, a complex eqmwlent circuit IS developed and verified by expenments The mathematical statements derived on this basis permit m&vidual impedance elements and parameters to be calculated. They explain the cause of the impedance dtspersion qualitatively as a relaxatton time distnbution of the entire electrode process subsequent

INTRODUCTION

In the representation of the results of impedance measurements on electrochemical systems as complex plane plots, depressed semi-circles often appear, whose centres are below the real axis. By analogy to dielectric relaxation, the phenomenon, which is referred to as impedance dispersion, is explained by the distribution of the time constants of the electrode process around a central value. So far, the influence of the roughness of the electrode surface [1,2], selective adsorption phenomena [3] and the non-uniform distribution of the current density on the surface [4,5] have been taken into account. At present, imped‘mce measurements are increasingly gaining interest for the charactkization of corrosion protection by organic coatings on metal substrates [6-121. Many of the publications available in this field also contain complex plane plots showing a depression [11,13-181. The causes for the development of such plots at polymer-coated electrodes have, however, not been explained so far. That is why there is still no equivalent circuit by means of which the course of this cuNe could by unequivocally simulated. It is mere!y known that impedance dispersion only

* Dedicated to the memory of Professor Dr. Dr. h. c. Kurt Schwabe. 0022-0728/84/%03.00

0 1984 Ekevier Sequoia !;.A.

328

occurs on electrodes with defective organic coating where the kind of influencing medium and the immersion time were a great effect [11,13-171. We have devoted comprehensive investigations to the explanation of this phenomenon and its theoretical interpretatron. The first results will be given in the present paper. EXPERIMENTAL

An industrtally produced coil-coating system was selected, the coating of which was highly uniform and, therefore, showed a well reproducible behaviour under mechamcal and chemical load. It consisted of steel sheet (1 mm) wrth a zinc coating (25 & 3 pm) and a thermohardened polyacrylate layer (37 f 2 pm). With an arbor (radms r = 5 mm), thz segments of this material were deformed to a bending angle of 45O. Thus, very fme defects developed in the outer buckling zone which were not visible to the naked eye. Following the working method described above [l], we prepared electrodes with a geometrical surface of 4 cm2, both of the undeformed as well as of the deformed segments. These were subjected to a humid-air cycling with periodrcal additron of sulfur dioxide. An experimental cycle of this intensive load consisted of the followmg phases [ZO]: 8 h exposure at 4O”C, relative humidity CRH) = 100%; 0.066 vol.% SO,; and 16 h drying of the samples at 25 OC and RH < 75%;. Prior to the exposure and subsequent to different test cycles, these electrodes were characterized by impedance measurements. In these measurements, the directly balancing impedance meter BM 507 (TESLA/CSSR) was employed, which covers the frequency range of 500 kHz of>, 10 Hz. 0.5 M KNO, served as the test electrolyte_ The measunng arrangement and other experimental details have already been published [12,13,20]. RESULTS

AND

DISCUSSION

For the representation of impedance diagrams, the pan of variables, the absolute value of the Impedance ]Z] and the phase angle 9, which are pnmarily accessible through impedance measurements for each frequencyf, were converted by means of known transformation equations [7,21] (with o = 2lrf) into the quantities of a series connection consisting of the resistance R, and the capacitive component -(WC,)-‘. Frgure 1 shows representative Impedance diagrams for different states of the coil-coating material tested. It is obviously that the electrode with an. intact polyacrylate layer is characterized in the undeformed state by an ideally capacitive behaviour (Fig. 1, curve 1). For this state, the equivalent circuit EC I in Fig. 2 is valid. Prior to the mtenstve load m SO,-containmg humid an,- the impedance diagram presented in Fig. 1 as curve 2 was determined on electrodes with defects in the organic layer. The centre of the semi-circle in the high-frequency range 2’ is on the real axis wlnle with lower frequencies the effect of diffusion becomes obvious. The corresponding equivalent circuit EC II in Fig. 2 now contains the resistance XX’, of the system representing the defects of the polymer layer, as well as the frequencydependent diffusion impedance Z,( 0). Here, R’, also contains the charge transfer

329

resistance R, of the corrosion process in the defect, which, however, cannot be

separated from lib before the double-layer capacity C, becomes effective. Usually, EC II in Fig. 2 IS taken a:; a basis for the svaluation of impedance

Fag. 1. Expenmental complex plane plots for coated steel electrodes during exposure to 0.5 M KNO, at room temperature. (1) Electrode with Intact organic layer, (2) electrode with defectrve organic layer pnor to the mtensive load, (3) electrode wrth defective organic layer subsequent to 16 cycles of mtenstve load: (4) electrode with defective orgaruc layer subsequent to 24 cycles of intenstve load in SO,-containing humrd an_ Small numbers on the curves indicate the frequency m Hz

I

II

Frg 2. Equivalent circutta for the rmpedance of coated metal electrodes EC I: Electrode with intact organic layer; EC II- electrode with defective organic layer; Cc, capacity cf orgamc film; Rc, msulation resrstance of intact film, Rb, resistance of defects in polymer layer down to the metal substrate, 2, (o), diffuston impedance, R,. electrolyte resistance.

330

measurements on polymer-covered metals in aggressive media [S-13,15-17]_ The results obtained on electrodes with a defective organic layer after prolonged chermcal intensive load, however, cannot be interpreted in this way. Impedance diagrams typical of such electrodes are presented in Fig. 1, curves 3 and 4.. With increasing immersion periods, varying depression of the semi-circle will result in the highfrequency range, the extent of which may be characterized through the depression angle & by which the centre of the respective semi-circle is displaced under the real axis. Figure 3 contains the results from Fig. 1 in the form of Bode plots. In this case, a straight line with a slope of - 1 results for the electrode with intact coating (cf. Fig. 3, ciirve l)_ Its extrapolation to lno = 0 gives the capacity of the polymer layer, C, (cf. ref. 16 and EC I in Fig. 2). Electrodes, the layer of which has defects down to the metal substrate, give a Bode plot showing capacitive behaviour only in the bigbfrequency range. From this part of curve 2 in Fig. 3 which has a slope of - 1, C,, can again be obtained through extrapolation. In the frequency range =G10 kHz, the cour=e of the curve is determined by diffusion_ On the basis of EC II in Fig. 2,

then holds (where the subscript “If

stands for low frequency) and after separating

1.4 -

13-

I

12-

llG r

10.

Q-

0-

7-

6

Fig

3 AC impedance

data from Fig. 1. dsplayed

as Bode plots, In Z VS. Inf_

331

Z,(o);nto

real and imagmary parts:

Z,, = 23; + K+J-~’

cos

7i-

(

~a,

m

)

-~+.a

-a1 sin p

(

1

(2)

The approximation in the square average on lnIIm(Z,,)I=lnK;-a,

lnw

0)

with K;=K,

sin $a, (

)

results in a balancing problem of the first order for the determination of al and K;. RI, immediately results from the real part. If al = 0.5, a true Warburg impedance is of course obtained. In this case, the real ,md the imaginary parts of Z,, are of the same size, and the angle of the complex plane plot running as a straight line in the lower frequency range with the real axis is C/Q= 45 o (cf. Fig. 1). Moreover, K; = a/15, where cris the Warburg coefficient. Finally, (4) generally holds. Curves 3 and 4 shown in Figs. 1 and 3 describe the state of the electrode caused by corrosion of the zinc coating 111the pore bottom of the polymer layer and by plugging these defective spots -with corrosion products of different intensity_ These corrosion products mainly consist of ZnSO, - 7 H,O, ZnO and Zn
[(ai-j,)w”‘]-’

(5)

with A = a/(a2 + b’); B = -b/( a’-+ b2) and 0 c a2 c 1 was chosen for them [23-251. Here, A, B, a and b are constants while az, as a distribution parameter, represents the width of dispersion decreasing with increasing a2. In the general impedance equation Z,(w)

= Re(o)

+jIm(w)

(6)

332

the validity of the Kramers-Kronig

In eqn. (7b) Re(w)= Imfo)

= -AueP~

Au-‘+.

relations [26] will 3e assumed:

Thus one obtains

tan SLY, ( >

B/A = -tan ;a, (

)

and

z2(u)

= K;‘(,io)-“’

For the constants in eqn. (5),

If it is now assumed that the electric behavlour of a corroding metal electrode with a defective polymer layer after an intensive chemical load can be described by EC III in Fig. 4, the general diffusion impedance Z,(o) can be neglected at sufficiently high frequencies. For the remaining high-frequency impedance Z,,, we have z

= R, (1 t K2R&“’ hf ’

(1

t

K,

cos #Do)-J(

R&P

wC,Rb

cos +2)2 + (UC,

+ K2R&.+

sin +s)

Rb + K, R&F'2sin &)’

(12)

where cj~~ = E+ 2

m ,,co II

Z,(w I

I Z,(w) FIN. 4 Eqmvalent circuit model for the Impedance of a metal electrode v&h a defctwe subsequent to an intensive chenucal load (EC III).

organic layer

333

From the general equation of a circle with coordinates x0, y. of its centre p. and the radius r, it follows with respect to eqn. (6) that [Re(w)

-x0]’

+]Im(w)

-u,,]‘=

r2

(13)

By comparing the coefficients of eqns. (12) and (13) with respect to the equation 2x, + 2y,,oC,,R’, + (2x,K,Rb

cos &, - 2yOK2Rb sin +2)wa’ = Rb

(14)

we obtain for the position of the centre --

XCJ-

R’,

K,R&f==

25

yo’

2

2

(K,R&==

sin

emsGz @2)

-

wC,Ri,

(15)

The circle representation requires y,, = constant, i.e. y, independent of w. Thus, a circular course of the impedance is obtained only when (a) cy2= 1 (no depression); (b) oC,R’,, = 0. that is Co = 0, because R’, and o P 0. Consequently, the impedance diagram of an electrode with a defective polymer layer has the form of a semi-circle only if the capacity of the polymer layer Co (CL Fig. 4) is negligibly small. In this case, the coordinates of the centre are x0-

,

-- Rb 2

yo=

-+

cot+2

(154

and the depression angle (p, by which the centre of the semi-circle is displaced under the real axis results from s2 = ;

- qJ2

06)

For the establishment of the elements in EC III, at frrst the drffusion-dependent constants K, and (Y, as well as the resistance Rb are determined accordmg to eqns. (l)-(4)). The dispersion parameters Kz and LYEas well as C,, are then obtained from the admittance of the reduced equivalent circuit (index r) reman&g only as a parallel arrangement of CO and Z,(w): Y, = z,-’

= K,o” 2 cos mz+j( WC, + K2WP’ sin +2)

(17)

by linear balancing calculation of the first order, (a) Kz and ‘Ye from the relatronships ln~Re(Y,)~=lna+a,Inw where a=K,cos

% ( 2

21

(b) CO from the equation

w-‘Im( Y,)- K20a2-' sin ;a, (

1

= c,

331

TABLE

I

Results from impedance measurements on zinc-coated steel electrodes with a defective polymer layer pnor (state 2) and subsequent (states 3 and 4) to the intensive load m SO,-contatnmg humid air

Parameter

State 2

CJF

1.4x10-‘0 1.4~107 066

cm-2 cm-’

K;/CZ s-‘~ a1

Rb/kL?cm’ K2 (12 &/”

82 -

-

State 3

State 4

1.4x 10-10 45 x 10’ 047

1.4% 10-10 1.8x lo6 0.48

11.6

46.3

3.9x10-9 0.705

43x10-” 0 80

26 5

18

The parameters determined for curves 2, 3 and 4 in Figs. 1 and 3 are listed in Table 1. The test of the validity of EC III shown in Fig. 4 for the states of the electrodes with a defective organic coating after an intensive load in an aggressive medium was accomplished with the help of the parameters given in Table 1. As is obvious from Fig. 5, the simulated and experimentally obtained impedance diagrams are in good agreement.

b / 2k

i:

20% / /

o5oOk

i?g 5. Simulated (Q) and experimentally obtained (0) complex plane plots of the electrode with a defectwe orgamc layer subsequent to 16 cycles of mtenswe chermcal load

335

CONCLUSIONS

The results presented first of all show that in its intact state the organic layer of the investigated technological coil-coating system reveals an ideal capacitive behaviour. The complex impedance of the electrodes, the polymer film of which has defects down to the metal substrate, however, is determined by the electrochemically effective total area in these defects. The complex plane plot of such electrodes m the high-frequency range has the shape of a semi-circle which may be represented by a single R-C component in parallel connection_ This means it contains only one time constant r = RC, which has the significance of a relaxation period in electrochemistry_ If solid corrosion products of the metal substrate develop in the defects of an organic coating, impedance diagrams will result whose semi-circle have then centres below the real axis in the high-frequency range. As could be shown. this impedance dispersion may be represented in the form of a complex impedance, Z,( 0) = K,’ ( jw)-+, by introducing frequency-dependent resistances and capacities into the equivalent circuit. It may be concluded at least qualitatively that, in analogy to other solid electrodes [1,2,4,5], the causes may be attributed to a distribution of the relaxatton ttme of the multifarious processes on the corroding electrodes with a defective polymer layer. The investigations are being continued usmg different model electrodes with the arm of enabling us to assign the parameters introduced to different subprocesses and to derive correlations for the rate of the corrosion of the respective electrode material 1271. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 13 16 17

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