New interpretation of electrochemical data obtained from organic barrier coatings

Electrochimica Acta 46 (2001) 3817–3826

New interpretation of electrochemical data obtained fromorganic barrier coatings

Jorg Vogelsang a,*, Werner Strunz b

a Sika Chemie GmbH, Kornwestheimer Strasse 107, D-70439 Stuttgart, Germanyb ZAHNER-elektrik, Thuringerstrasse 12, D-96317 Kronach, Germany

Received 31 May 2000; received in revised form 29 January 2001

Abstract

After a short introduction into the usage of organic barrier coatings and some related problems of evaluatingcoating performances, the principles of relaxation voltammetry (RV) measurements are given. RV is a newelectrochemical technology in the time domain. The new features of this technology are high sensitivity and arelatively high sampling rate. This allows the measurement of the coating resistance RC and of the coating capacityCC, even if good barrier coatings are used. RV offers a two-step data interpretation: first a very direct and easyaccessible extraction of RC and CC. Second, a much more detailed interpretation of electrochemical processes in thecoating is offered, i.e. dielectric relaxation, diffusion and charge transfer. In addition to the more classicalinterpretation of impedance spectroscopic data, RV permits a more detailed understanding of physical processes andtheir contribution to the relaxation of the previously charged coating surface. Evidence that the interpretation ofbarrier coatings by using only-RC elements is not suitable for the description of time-domain-measurements ofimmersed samples is given. The newly derived model based on RV-data is able to describe a huge number of coatingmaterials under quite different aging conditions. © 2001 Published by Elsevier Science Ltd.

Keywords: Organic barrier coatings; Relaxation voltammetry; Dielectric relaxation; Diffusion; Charge transfer

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1. Introduction

Organic barrier coatings are widely used to protectmetal constructions from corrosion. The severity of thisattack depends on the environment to which the struc-ture is exposed. Those coating systems are described inISO 12944 and some suggestions for the proper selec-tion of coating materials are given, with special empha-sis on material performance during short term testing.

Bridges and energy transmission towers are typicalexamples of such structures, where the degree of corro-sive attack can vary enormously according to ISO12944-5.

It is common practice and well published [1–9] thatbarrier coatings behave like insulators with extremelyhigh resistance in the range of 1010–1012 � cm−2.Those materials are investigated by using electrochemi-cal impedance spectroscopy (EIS) [1] and for a simpleinterpretation of the data an RC couple is used. Rdenotes the coating resistance RC and C denotes thecoating capacity CC, with the dielectric constant �r ofthe coating. Organic coatings are composed mainly bypolymers, pigments and fillers, all having some influ-ence on �r.

From CC it is possible to derive �r with the followingequation: CC=�r�0A/d, where A is the area of thecapacitor (exposed area for measurement) and d is thethickness of the coating. Due to the high thickness ofthe barrier coatings the capacity shows relatively lowvalues, typically in the magnitude of 100–1000 pF.* Corresponding author.

0013-4686/01/$ - see front matter © 2001 Published by Elsevier Science Ltd.

PII: S 0013 -4686 (01 )00668 -5

J. Vogelsang, W. Strunz / Electrochimica Acta 46 (2001) 3817–38263818

Both together, very high resistance and low capacity,lead to extreme measuring conditions, which may causeproblems in obtaining meaningful data by using olderEIS equipment or non-appropriate shielding tech-niques. Most of the suppliers of impedance machinesoffer preamplifiers or other technical features to avoidproblems and to enable a proper measurement in thisdemanding application.

At the initial state of immersion it is quite commonthat the coating resistance RC cannot be measuredbecause it may exceed either the input resistance of thespectrometer or the involved frequency range. But dur-ing subsequent immersion the coatings become satu-rated with water and some conductive paths appear,enabling a detection of RC with increasing immersiontime.

A combination of weathering and EIS-measurementis suitable for the qualification of coatings. Commonlysimple immersion of samples is used. In this case, forallowing an easy procedure of monitoring the samplesit is useful to leave the samples in the measuring cell.Relaxation voltammetry (RV) has been developed ini-tially for easy and reliable testing of barrier coatingswith up to seven potentiostates in parallel. Althoughthe single measurement can take a little more time than

the measurement of a comparable EIS spectrum it ismore efficient, because the numbers of performed mea-surements are significantly higher. The first and also theeasiest step of interpretation of RV-measurements wasthe determination of the total DC-resistance RT and CC

directly from the raw data, without the need of inten-sive curve fitting and modeling of data [2–4].

In a second step the decay curves of the RV-experi-ments were investigated very carefully by analytical andnumerical techniques. On doing this, some fundamentalnew ideas of data interpretation were obtained. In thispaper the underlying considerations and the results aregiven.

2. Experimental

All the EIS-spectra have been recorded with a Zah-ner IM6 impedance spectrometer, using High-Z-Probeas a pre-amplifier, suitable for very high impedancemeasurements. The frequency range was between 100mHz and 100 kHz (sometimes 1 MHz), with five pointsper decade and five samples at each point. The AC-am-plitude was between 5 and 100 mV, depending on theoverall resistance of the measurements. Earlier unpub-lished result have shown that in the case of barrier

Fig. 1. EIS spectra of a coating after 1, 70 and 100 days of immersion. Amplitude=20 mV.

J. Vogelsang, W. Strunz / Electrochimica Acta 46 (2001) 3817–3826 3819

Fig. 2. Different equivalent circuits used to fit barrier coatings,model B is used for a coating with pores. Model D is suitablefor barrier coatings without significant artifacts. Model E fitswell already slightly damaged barrier coatings [16].

3. Results obtained from EIS

Typical results from barrier coatings under continu-ous immersion are shown in Fig. 1. The measurementswere recorded after 1, 70 and 100 days of continuousimmersion. Such curves are commonly interpreted ac-cording to model B in Fig. 2. But for a sufficient fitquality it was necessary to use constant phase elements(CPE) instead of capacitors, otherwise the fits wouldhave been poor. But also other models gave perfect fits,like models D and E in Fig. 2 (using a CPE as CC).Therefore it seems to be difficult to select the ‘right’model for the experiments, but it is quite easy to find a‘suitable’ model. The capability of the EIS method canbe seen in the fast and easy data handling. The ob-tained data of various coating materials can be com-pared to each other, allowing some conclusions andfurther considerations. Even if the curves cannot bedescribed exactly, the results are helpful to achieve aranking of materials. The ranking can be elaboratedindependently from the truth behind the data interpre-tation procedure, because the occurring significant ef-fects that have high dynamic and observed effectsshould be much higher than only 20–30%.

From the usage of the two models (B and D, given inFig. 2) a set of parameters is obtained. Fig. 3 shows theobtained coating parameters which are plotted over thenumber of spectra. The number corresponds to the timeof immersion (see captions). The differences betweenCC are minor and can be expected when using suchequivalent circuits for data interpretation. But there isno existing rule for finding the ‘right’ equivalent circuit.It is no use to focus too much on the problem of datainterpretation with EIS, but is has to be mentioned thatthe results of an apparently ‘simple’ experiment are noteasy to explain. Many opinions are found in the litera-ture about suitable models, but all depend on thedistinctive experimental conditions. In the case of intactbarrier coatings it is quite well known that with theexception of capacitive behavior no other relevantparameters can be found. It has been reported [15] thateven if corrosion was visible under a transparent barriercoating, no traces of corrosion activity were measurableby EIS, moreover the spectra showed a perfect barrier.Although every scientist shows himself to be convincedby his results and his way of interpretation, a completeunderstanding of the results of electrochemical experi-ments with coated metals seems to be still far away.

4. Principle of RV measurements

The principles of the RV technique had been pub-lished earlier [2–4] but a brief introduction will be givenin this section.

coatings 100 mV is still in the range of linear behavior,therefore these measurements are also non-destructive.A classical cell was used with a two-electrode setup,which is sufficient for performing EIS measurements ofbarrier coatings, because precise knowledge of the po-tential of the substrate is not required. Anyway, it ispossible to obtain a rough idea about the state of thesubstrate under a porous coating, even by using aplatinum wire as the counter electrode. The two-elec-trode setup is completely sufficient for most measure-ments; moreover, it mostly prevents problems causedby an extremely high coating resistance, leading tonoisy results and strong fluctuations of open circuitpotentials.

RV-measurements were performed with a fast elec-trometer. The sampling rate was 600 Hz, sometimes upto 2300 Hz, the accuracy of current measurements wasbetter than 100 fA and the excitation amplitude was 20mV. Details of the measuring procedure are given inthe respective sections below.

For all measurements commercially available barriercoatings were used, complying with the requirementswhich are described in ISO 12944 part 5. One or twopack coatings were used in this work. The chemicalnature of the polymer backbone and other formulationdetails will be mentioned, if necessary, at the respectiveresults.


A coated steel coupon is fixed in a sample holderwhich is commonly used for such experiments. As canbe seen in Fig. 4, a constant potential (+UEXC) isapplied (two or three electrode setup is possible) over aperiod from t0 to t1, resulting in a current which is

charging the surface (CC). After a certain period of timethe current becomes constant (completely charged sur-face) and is then switched off (t1). IEXC is the excitationcurrent measured immediately before the current isswitched off. Now the charged surface is able to relax

Fig. 3. Relative change of coating parameters during immersion, comparison of two models (B and D from Fig. 2) numbers from0 to 8 correspond to 0, 1, 9, 27, 35, 63, 70, 84 and 100 days of continuous immersion. Area was 300 cm2, coating thickness about500 �m.


Fig. 4. A constant anodic potential (solid line) is appliedbetween t0 and t1. After the current turned to be constant(dashed line) the current is switched off (t1) and the potentialis able to relax (between t1 and t2). After a certain period (t2)the same potential is applied cathodically (until t3), with asubsequent relaxation step between t3 and t4. Both relaxationcurves are recorded and averaged.

which are frequently used for the interpretation of EISdata of barrier coatings (Fig. 2, model A–C), it ispossible to derive a function in the time domain by thesolution of coupled differential equations. For shorttimes the series expansion of this function delivers thesimple relation which allows the determination of CC.The decay function (U(t)) and its series expansion forshort times is shown in Eq. (1). From this function theinitial slope (ISL) can be approximated (RT=RC modelA; RT=RC+RCT model B). The extension of the ISL,involving the second term of the series expansion, givesbetter results (ISLex, Eq. (2)). This has already beenexplained in earlier papers [2–4,14]

U(t)=IEXCRT et/RTCC

=IEXCRT−IEXC

CC

t+IEXC

2RTCC2 t2� ···

ISL= limt�0

dU

dt= −

IEXC

CC

(1)

U(t)t�0

=IEXCRT−IEXC

CC

+IEXC

2RTCC2 (2)

In Fig. 6 the non-ideal behavior of a real coating isshown, together with the respective ISL and ISLex-curve. It becomes obvious, that ISLex gives a betterdescription of the initial relaxation phase.

With the mathematical solution of the potential de-cay in the time domain it was possible to confirm thesame values for electronic elements which had beenused to build up an equivalent circuit (model B, Fig. 2)as shown in Fig. 7. The accuracy was in the same rangeas the accuracy of the electronic elements. This demon-stration of the performance of the measuring systemhad already been given earlier in more detail [2–4]. Butfrom Fig. 7 it becomes obvious that a measurement ofa ‘real’ coating has a strong non-exponential behavior.

and this relaxation is measurable via the decay of thepotential (between t1 and t2). The initial drop of thepotential is measured with a sampling rate of 600–2300Hz, then the rate is lowered. The total number ofrecorded points is 1800 for each anodic or cathodichalf-cycle. To complete a full ‘square wave cycle’ theprocedure is repeated using a negative excitation poten-tial (−UEXC). A delay can be introduced between theanodic and cathodic polarization and also after thecompletion of the ‘cycle’.

Typical curves for good and poor coatings are shownin Fig. 5, as well as the lack of noise even with lowsignals.

The DC resistance RT can be obtained directly fromthe current measured before its interruption (steadystate), according to the Ohmic law (RT=UEXC/IEXC).The coating capacity CC is obtained from the initialslope method. For all the basic equivalent circuits,

Fig. 6. ISL and ISLex interpretation of the first data points.Systematic deviations from linear initial stage of potentialdecay become obvious. The total resistance RT was obtainedwith 3.8 G� and CC with 250 pF. ISLex delivered a secondvalue for RT=150 M�.

Fig. 5. Relaxation voltammogram of a good and poor coating.Excitation voltage Uexc=50 mV, texc=120 s, small graph isthe enlarged initial part of the decay (see x-axis).


Fig. 7. Comparison of dummy curve and coating response;dummy equipped with model B and elements with values beingtypical for coatings (see Table 1).

the ordinary ISL method. Now, for measuring andevaluating real coatings, the extended ISL method be-comes necessary, otherwise irregular values for CC

would be obtained. This is the first hint that coatingscannot always be sufficiently described by a simplecapacity. In Fig. 6 the first data points were shown withthe ISL and the extended ISL approximations. It be-comes obvious, that the measured curves deviates muchto far from linearity. Further, using ISLex as a secondway for the determination of the total resistance, thisRT value was obtained with 150 M�, which is verydifferent and much too low compared to the valuewhich was determined from Ohm’s law (3.5 G�). Thesecontradictions are the first hints that an improvementof the theory is required in general, independent fromthe kind of measurement.

A second fact is shown in Fig. 7, giving again someevidence, that the interpretation of results from realcoating systems differs strongly from the basic physicalmodels which are already used for a long time. In Fig.7 an equivalent circuit was used with elements fitted tothe model B similar to a real coating. But as can beshown even for models with very similar parameters,the measurements and the simulation do not reallycorrespond to each other. This has also been brieflydiscussed in the previous section. Furthermore, duringthe discussion of EIS-results it had become necessary tofit model B with two CPE instead of capacitors. Addi-tionally, the discussion of Table 1 is straightforward inthe same sense. In Table 1 the values of the capacitorused for the simulation and of the fitting procedureaccording the ISL and the extended ISL are listed. Thevalue of the coating capacity is remarkably lower afterISLEX compared to ISL, whereas the ordinary ISL issufficient to confirm the value of the dummymeasurement.

It is clearly shown in earlier papers that RV is able tomeasure the coating systems assumed to behave asmodels A, B or C, even with very high resistances andlow capacities. Now it becomes more evident, that themodels A–C are not completely suitable descriptionsfor a larger number of organic barrier coatings. In thecase of paints on car bodies and similar products theclassical models could still have some justification.

6. New approach to physicochemical processes inorganic coatings

In the previous sections it has been demonstratedthat the classical approach is not sufficient for a com-plete description of electrochemical experiments withbarrier coatings. For a deeper understanding of thebasic processes in organic coatings a thorough numeri-cal analysis of the experimental raw data had beenperformed. A brief description of the analytical stepsare given below:

The non-exponential nature can hardly be explained bythe traditional models, a new, more realistic model isrequired.

In the following section the systematic deviationsbetween the classical theory and the results of measure-ment will be enlightened and a new interpretation ofthe data with much higher correlation will be given.

5. Principle of RV data interpretations, failure oftraditional models

It has been demonstrated without any doubt that RVis able to measure correctly in the expected value rangeof resistance and capacitance for barrier coatings. Thishas been done with dummy measurements using hardwired equivalent circuits. As already mentioned above,it was possible to confirm the values of the electronicelements of the dummy circuits. For the determinationof the capacitor simulating the coating capacity CC

from dummy circuits it was absolutely sufficient to use

Table 1An electronic circuit was used as a dummy to simulate thetime behavior with typical values of a real coating; RV is ableto obtain the proper values

Dummy ‘Real’ coatingParameter

Nominal Calculated

1010Uexc (mV)530558Iexc (fA)

330CC (pF) 1098 (357)a32711.2Rpo (G�) 11.0 12.0

Cdl (nF) 6.8 7.0 9.4RCT (G�) 7.5 7.2 6.5

a This value was obtained with the extended ISL, all otherswith mathematics solution.


Fig. 8. With the SQRT(t) transformation three different curveshapes are obtained. For the C-type the long time behavior isin perfect agreement with the term exp[− (�t)0.5], describing acontinuous time random walk diffusion process (y-axis inarbitrary units, x-axis in (s0.5)).

Fig. 10. The potential decays were transformed and normal-ized. The point of inflection was determined for every coatingthickness. It turned out that independent from the coatingthickness the normalized and transformed potential decaysshow an identical potential value for the points of inflection.

The start was done via the transformation of the timescale into the square root of time. It was found that theresulting curves possess a typical shape when plottingln(U(t)/UEXC) over SQRT(t) (Fig. 8). Three differentshapes (denoted as A, B and C) have been observed inall the experiments, where a large number of differentcoatings had been studied and analyzed after severalperiods of immersion. It was observed that some coat-ings showed A-type behavior first, followed by B- andC-type shapes during prolonged immersion time. Fromthe C-shaped curves at long relaxation times (Fig. 8) itcan be concluded that a common and collective descrip-tion of barrier coatings must involve a diffusion processwhich obeys a square root of time dependency of theform exp(−��Difft), where �Diff denotes a macro-scopic, reciprocal time constant. Such a time law is wellknown for continuous time random walk processes [13].

Further information was accessible by plotting thepotential decay (A and B type coatings) of RV experi-ments in a linear scale over the square root of time(Fig. 9), whereby the raw data were smoothed by apolynomial to eliminate noise contributions. The resid-uals are also presented and demonstrate the quality ofthe polynomial approximation and also the low noiselevel. Solely from the shape of the transients it may berecognized immediately that the curves have a point ofinflection. In Fig. 10 the transformed and normalizedpotential decays of one coating material with differentcoating thickness are shown. The point of inflectionwas determined for every coating thickness. It turnedout that independent from the coating thickness thenormalized and transformed potential decays show anidentical potential value for the points of inflection.

Fig. 9. Linear plot of a potential decay over SQRT(t) andpolynomial fit; residual shows the perfect representation of themeasured curve by the polynomial. This procedure eliminatesnoise.

Fig. 11. The same behavior as in Fig. 10 was found for fourdifferent coatings with quite different coating resistances. Hereagain, the points of inflections have approximately the samevalue on the y-axis.


Fig. 12. Normalized potential plotted over SQRT(t), the besttangents at the point of inflection are plotted together forvarying coating thickness. The intercept with the potentialaxes (UIcpt/UEXC�1.08) again is independent of the coatingthickness.

plot are drawn for varying coating thickness. The samekind of tangents is given in Fig. 13 for different coatingmaterials and again, the same intersect is obtained.

Finally, there was a third mathematical property ofthe dielectric relaxation process itself which was de-duced from the measured transients. The detection ofthis property was the final key in the evaluation of ananalytical solution for the dielectric relaxation process.It was shown, that the zPoI value (z=�t) of the pointof inflection of the transient itself and the values of thepoints of inflection of the first (z �PoI) and the secondderivative (z�PoI) are in the ratio of 1:2:3.

UPoI

UEXC

=0.75UIcpt

UEXC

=1.10 (1.08)

zPoI:z �PoI:z�PoI=1:2:3 (3)

where z=�t.These important mathematical properties, summa-

rized in Eq. (3), gave justification enough for an inter-pretation in terms of a function having such propertiesand also having a physicochemical origin (Eq. (4),transfer function for the dielectric relaxation process).

�(t)=2 exp{− (�DRt)�DR}−exp{−2(�DRt)�DR}

with 0��0.5 and �DR=k2 (4)

The details of this development are not given here,only the results are cited from the original work of oneof the authors [10]. It was found that three processescontribute to the decay of the potential in parallelduring the relaxation experiments. Dielectric relaxationaccording to a ‘two-step’ continuous time randomwalk, charge transfer and diffusion according to a‘one-step’ random walk are the three processes takingplace simultaneously with varying amounts. Theamount of each contribution sums up to one (ACT+ADR+ADIFF=1).

U(t)UEXC

=ACT exp�

−t

�CT

�+ADR{2 exp[− (�DRt)�DR]

−exp[−2(�DRt)�DR]}

+ADiff exp[− (�Difft)�Diff]

0��DR, �Diff�0.5 �ideal=0.5 (5)

The set of functions given in Eq. (5) is suitable todescribe a huge variety of coating materials with differ-ent and varying coating thickness. In Fig. 14 the mea-sured curve and the function are plotted together withthe residuals in order to demonstrate the perfect fit ofthis function with only six adjustable parameters. Usingthis new interpretation it was possible to investigate 17different coating materials with special emphasis on theamount of contribution by the three processes. Thevery low �2 values demonstrate the perfect agreementbetween data and fit. The results are given in Table 2.

In Fig. 11 curves for different coating materials arepresented in the same manner as in Fig. 10. Althoughthe used materials had quite different coating resis-tances, it is clearly found that independent from thecoating thickness or its nature the relation of the poten-tial value at the points of inflection (UPoI) and theexcitation potential (UEXC) of the normalized transientsare around the same value. This astonishing behaviorgives evidence for a very systematic and mathematicallywell defined, but yet unknown, decay function U(t).

A second astonishing fact was obtained when regard-ing the ordinate where the best tangents at the point ofinflection intersect the potential axes (UIcpt). Again,independent from coating thickness or type of coatingmaterial all the curves intersect at the same point on thepotential axis. In Fig. 12 the best tangents through thepoint of inflection of the linear potential—SQRT(t)—

Fig. 13. Normalized potential plotted over SQRT(t), like inFig. 12 the best tangents show the same intercept for differentcoatings.


Fig. 14. Data fitted with the three processes as formulated inEq. (4). The residuals are in the range of the noise of theequipment.

parameters and is suitable for a large number of materi-als, whereby it seems to be independent from the agingperiod, which means as far as the coating remains acoating and complete deterioration of the coating hasnot taken place.

The traditional interpretation using equivalent cir-cuits sometimes requires more parameters and themodel may change during immersion (or other weather-ing conditions).

This new interpretation allows the monitoring ofcoatings with respect to the three processes involved,the evolution of the parameter with time can be fol-lowed. While using EIS it may happen that the modelfor data interpretation has to be modified duringmonitoring.

A similar concept of parallel processes with diffusion,capacitor and resistance has been used earlier, with alsogood fitting results over a relatively long immersionperiod. A model consisting of a CPE, a Warburgdiffusion impedance and a resistor in parallel, withelectrolyte resistance in serial (see model D in Fig. 2)was used [11,12]. But in these papers the meaning of theparameters were not fully understood, they were onlyused due to the perfect fits.

The physico-chemical behavior of organic barriercoatings seems to be better understandable in terms ofdielectric relaxation, charge transfer and diffusion in-stead of equivalent circuits. But even with RV, thecorrelation of electrochemical results and outdoor per-formance of organic coatings has still to be established.With this new interpretation a direct link to materialproperties is available.

7. Discussion and conclusion

It was shown that the traditional interpretation ofelectrochemical results is doubtful and a new interpreta-tion was introduced, using the three fundamental pro-cesses taking place in the coating during the relaxationof the charged ‘coating capacitor’. This new interpreta-tion is able to cover a remarkable number of coatingmaterials and material properties like number of com-ponents, number of layers, drying process and coatingthickness. The great advantage is that the physicalnature of the processes involved can be easily under-stood. The interpretation requires six adjustable

Table 2Fitting results of 17 different coatings using Eq. (5); unless otherwise noted �DR=�Diff=0.5

ACT (%)IEXC (10−12A)RT (109�)No. �Diff (s−1)ADR (%) ADiff (%) �CT (s−1) �DR (s−1) �2 E (10−5)

167 0.30 0.022 –1a –– ––�992.3 80.9 16.8 13.9 0.0302 0.00675 240.27

1.119 1.1 95.5 3.5 0.31 0.089 0.001 531.811 9.3 82.8 7.9 2.70 0.339 0.015 44

70.0020.2335.992.25 84.713.12.0106.63.0 8.0 62.2 29.8 1.46 0.683 0.021 76

2.8 7.1 10.8 74.27 15.0 11.4 0.154 0.030 0.820.0760.6392.5818.08 75.16.97.72.6

2.3 17.4 11.7 81.69 6.7 1.60 0.670 0.166 41.6 66.6 31.210 0.832.0 0.283 0.032 714.7

1.1 12.1 1.9 75.011 23.1 0.10 1.028 0.100 40.82 24.2 14.4 73.512 12.1 43.5 0.966 2.365 30.66 30.6 7.2 74.713 18.1 3.09 0.582 0.080 3

62.112.3156 11.0891.1412.100.26 25.6140.2315b 8.1 52.189.5 39.8 1.53 12.5 0.025 6

0.4524.964.211.389 41.2070.22 0.02816c

13.21260.1617 42.4 0.83 11.2 0.48144.4 2

a ‘Pure capacitive behavior’.b �Diff=0.374.c �DR=0.384.


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New interpretation of electrochemical data obtained from organic barrier coatings

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