Effect of mechanical stresses on marine organic coating ageing approached by EIS measurements

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Progress in Organic Coatings 72 (2011) 260– 268

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Progress in Organic Coatings

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ffect of mechanical stresses on marine organic coating ageing approached byIS measurements

. Fredj, S. Cohendoz, X. Feaugas, S. Touzain ∗

aboratoire d’Etudes des Matériaux en Milieux Agressifs EA3167, Bâtiment Marie Curie, Pôle Sciences et Technologies, Université de La Rochelle, Avenue Michel Crépeau,7042 La Rochelle Cedex 01, France

r t i c l e i n f o

rticle history:eceived 14 June 2010eceived in revised form 28 January 2011ccepted 18 April 2011

eywords:echanical deformation

ISarine organic coatings

a b s t r a c t

In this work, the role of a stress–strain state (visco-elastic domain) on the protective properties of twomarine epoxy coatings (with and without VOC) applied onto mild steel was studied. Different stressvalues were applied on coated substrates and bent samples were immersed in 3 wt.% NaCl solution atdifferent temperatures. Non-bent coated samples were also immersed in the same conditions as refer-ences. Electrochemical Impedance Spectroscopy was used to evaluate the organic coating degradationon the compressed and the stretched sides periodically.

The degradation kinetics showed that the tensile mode was very damaging for one coating while aslight effect was observed on the other coating. In the first case, the water uptake was found to be moreimportant in the tensile mode for higher stress values. A particular attention was focussed on the initial

. Introduction

The degradation of organic coatings is usually due to the actionf environmental factors such as water, UV and temperature. Manytudies related the influence of each ageing factor or a combinationf them [1–7] in order to better understand the mechanisms andhe best way to evaluate the coating lifetime. The effect of mechan-cal state was also investigated [8–11] using indentation, uniaxialtress or fatigue and it was shown that stress greatly affects the per-ormances of organic coatings. However, the applied mechanicaltresses generated some unexpected results and no general trendsould be proposed. These remarks may be explained by the fact thathe mechanical state of the polymer under stress was not rigorouslynown in these works.

In a recent paper [12], we proposed a different approach byonsidering the true mechanical state of the polymer. Indeed, theolymer degradation depends on the stress state where the coat-

ng is driven by the strain. Depending on the strain or stress, theolymer can be [13,14]:

∗ Corresponding author. Tel.: +33 5 46 45 87 67; fax: +33 5 46 45 72 72.E-mail address: stouzain@univ-lr.fr (S. Touzain).

- in the elastic domain (EL): this implies that the polymer recov-ers instantaneously its mechanical properties after the strain(reversible process);

- in the visco-elastic domain (VE) where the polymer needs sometime in order to relax and recover its mechanical properties afterthe strain (reversible process);

- in the visco-plastic (VP) domain which is characterized by anirreversible change in mechanical properties after the strain;

- or can be irreversibly damaged.

In our preliminary study, we presented the effect of tensile andcompressed stress in a visco-elastic domain on the degradationkinetics of organic coatings. It was shown that the tensile stressleads to a modification of water ingress in the coating and it wasconcluded that mechanical stress in a VE domain accelerated thedegradation and might be considered as an aggressive parameterlike UV, temperature or water. However, the stress influence onthe physico-chemical properties of the polymer and on the waterdiffusion was not evaluated.

In the present work, two VE stress values were consid-

ganic Coatings 72 (2011) 260– 268 261

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N. Fredj et al. / Progress in Or

rder to determine the origin of mechanisms which werenvolved.

. Experimental

.1. Coatings

Two different, commercially supplied epoxy based coatings onild steel were studied. Sample A is an epoxy-polyamide/amine

aint and sample B is a solvent-free polyamine epoxy paint. Bothoatings present a similar filler fraction (about 22%) but the den-ity of the dry coating A (1.83 g/cm3) is higher than the densityf the dry coating B (1.34 g/cm3). More details about the for-ulations can be found in Ref. [15]. Both coatings were applied

s monolayers on the two sides of degreased low-carbon steel-Panel substrates (SAE1008/1010, R type) with dimensions as00 mm × 100 mm × 0.8 mm. The thicknesses of the dry film werequal to 180 ± 20 �m for coating A and 320 ± 20 �m for coating

(measured using an Elcometer 345 coating thickness gauge),ccording to the product data sheets. In order to provide someepresentative results, three identical samples were tested at theame time in the same conditions. Due to the fact that all samplesehaved in a similar way, the presented results are related to oneepresentative specimen.

The glass transition temperature Tg of free films was measuredy differential scanning calorimetry DSC (DSC Q100 TA Instru-ents). The temperature ramp was 10 ◦C/min in a temperature

ange between −50 and 200 ◦C. Tg is about 55 ± 5 ◦C for both coat-ngs.

The mechanical properties of the organic coatings were deter-ined using loading–unloading–recovery tests as described in [12],

t controlled temperature namely 30 ◦C. The VE/VP limit was foundt 12.5 MPa for coating A and 3.3 MPa for coating B before ageing.uring ageing, these values were found to increase up to 14 and

MPa [16]. Consequently, two stress values were chosen in order tolace both organic coatings in the VE domain where no irreversibletructural strains can develop: 3 and 4 MPa.

.2. Preparation and ageing of the samples

For all the samples, an additional epoxy resin was deposited ontohe coated panel edges in order to avoid water ingress. Then, threedentical coated panels were bent between two supports linkedy two threaded rods (Fig. 1). The bending level was obtained bypplying the 3 or 4 MPa stress at yielding zone to the plates using

MTS tensile test machine and measuring the adequate curvature

Stressed and unstressed panels were fully immersed in a NaCl wt.% solution in a glass vessel at different temperatures using a

Fig. 1. Coated steel panel under tension and compression state.

Fig. 2. Experimental setup for EIS measurements onto bended coated panels.

climatic chamber (VC 0020 Vötsch Industrietechnik) in order toaccelerate water ingress: 25, 35 and 45 ◦C.

2.3. EIS measurements

The protective properties of the stressed and unstressed sam-ples were regularly evaluated using EIS in laboratory at ambienttemperature. For flat (unstressed) samples, a PVC tube (5 cm diam-eter) was temporarily applied onto the coated samples and EISmeasurements were performed in 3 wt.% NaCl solution using a sat-urated calomel electrode as reference, a graphite counter electrode,all of them set into a Faraday cage. For stressed panels, two curvedPVC tubes (5 cm diameter) were designed in order to allow theirtemporary application on the concave side or the convex side ofthe bent coated panels (Fig. 2). So, with these o-ring seal type cells,it was possible to perform EIS measurements on both sides of thestressed panels without interrupting the stress–strain state of thepanels. In all cases, the area of the specimen exposed to investiga-tion was 19.6 cm2.

All EIS measurements were performed with a Gamry Femto-stat FAS 1 at the free corrosion potential. The ac frequency wasswept between 100 kHz and 10 mHz with a 10 mV rms perturba-tion amplitude (10 points/decade). Data analysis was performedby the software ZView (Scribner Associates, USA), using classicalelectrical equivalent circuits (see below). EIS data were fitted in thewhole frequency range to get accuracy on the extracted parametersbut only the HF parameters (film resistance Rf and film capacitanceCf) relative to the intrinsic properties of the coating were consid-ered in this study. It must be noticed that the interfacial parameters(double layer capacitance Cdl and charge transfer resistance Rct)did not show any significant evolution during the studied ageingtime. Then, it can be supposed that no large delamination processoccurred and that the applied VE stress is not relaxed.

3. Results and discussion

3.1. Evidencing the effect of stress onto the degradation kinetic ofthe organic coatings

Typical EIS data are shown in Fig. 3 for the stressed (compres-sion and tension) and unstressed organically coated panels after 4months of immersion. It must be noted that due to the differenceof thickness between the samples for each coating, the impedancemodulus is reduced with respect to the measured thickness ofthe tested sample. As can be seen, the stress influences the EISresponse for coating A, especially in the tensile mode (� > 0), witha low frequency impedance modulus lower than those observedwith compressed or unstressed state. Inversely, the compressedstate gives an impedance response corresponding to better barrierproperties than the unstressed mode. For coating B, the differ-ences between stressed and unstressed states are very low sincethe impedance modulus and the phase angle curves are very similarfor the different stressed states. For long exposure times, the stressvalue does not modify the trends since the reduced impedance

262 N. Fredj et al. / Progress in Organic Coatings 72 (2011) 260– 268

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+051.E+041.E+031.E+021.E+011.E+001.E-01

-4 MPa

- ϕ (°)|Z| /e (Ω.cm)

Coating A

σσσ < 0

σσσ > 0

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+051.E+041.E+031.E+021.E+011.E+001.E-01

-4 MPa

- ϕ (°)⏐Ζ⏐/e (Ω.cm)

Coating B

f (Hz)

wabvefittatwou3

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

0 50 100 15 0 20 0 250

- 3 MPa

Durée d'imm ersion (jou rs)

|Z| 0,1 Hz /e (Ω.cm)

Peinture A T= 25 °C

|Z|0.1Hz / e (Ω.cm)

Coati ng A

Imm ersion tim e (day)

|Z| 0,1 Hz /e (Ω.cm)

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

0 50 100 15 0 20 0 250

- 4 MPa

Durée d'immersion (jou rs)

Peinture A T= 25 °C

Imm ersion tim e (day)

Coati ng A

|Z|0.1Hz / e (Ω.cm)

ig. 3. Typical EIS data for the stress and unstressed coated panels (coatings A and) after 4 months of immersion in NaCl 3 wt.% solution at ambient temperature.

oating B. This fact may be understood as an essential differenceetween both organic coatings in terms of interactions with thelectrolytic solution.

EIS data were fitted using classical equivalent electrical circuits2] as previously done with thick marine organic coatings [12,17]Fig. 6a). Constant Phase Elements were used in order to take intoccount for the time constant distribution. The coating capacitancesere then calculated using Brug’s equation [18]:

B = Y1/n0 (R−1

e + Rf−1)

(n−1)/n(1)

here Y0 and n are the CPE parameters, Re is the solution resistancend Rf is the film resistance. The capacitances values were found toe very different depending on the applied stress so normalizedalues (referred to the initial capacitance value) are presented. Thevolution of the normalized capacitance values is shown in Fig. 6bor coating A aged at 25 ◦C. As can be seen, the normalized capac-tance values are greatly affected in the tensile mode, suggestinghat the water uptake is more pronounced under these stress condi-ions. In the compressed mode, the normalized capacitance valuesre lower than the non stressed mode, which leads to the conclusionhat the water uptake is lower. These trends are more important

ver, using a modified Brasher–Kingsbury relation [15], the waterptake was calculated. For coating A, the values were respectively, 8 and 1.5% at 0, 4 and −4 MPa. For coating B, no clear difference

Fig. 4. Evolution of the reduced low impedance modulus of coating A for stressedand unstressed panels during immersion in NaCl 3 wt.% solution at ambient tem-perature.

in normalized capacitance values was observed depending on theapplied stress and the water uptake was found to be about 7% in allmechanical conditions.

These results could be first related to the effect of the stressmode onto the free volume size within the polymer [19]. Indeed, itmay be understood that a tensile mode leads to an opening of thefree volumes and this favors the water uptake while a compressionmode acts at the opposite. It appears that the applied stress leadsto a modification of the degradation kinetic. However, the effect ofstress on the intrinsic properties of the coating and their evolutionsstill remains unclear.

3.2. Effect of stress onto the initial properties of the organiccoatings

In order to better understand the influence of stress on the coat-ings ageing, the relative permittivity εr was calculated from thecapacitance values CB obtained at different temperatures (Fig. 7a)according to:

where ε0 = 8.854 × 10−14 F cm−1, e is the coating thickness and S isthe specimen surface area.

N. Fredj et al. / Progress in Organic Coatings 72 (2011) 260– 268 263

1.E+10

1.E+11

1.E+12

1.E+13

0 50 0 10 00 150 0 2000 250 0 3000 35 00 400 0

-3 MPa

Peinture B

|Z| 0,1 Hz /e (Ω.cm)

Coati ng B

|Z|0.1Hz / e (Ω.cm)

1.E+10

1.E+11

1.E+12

1.E+13

0 500 1000 15 00 2000 250 0

-4 MPa

|Z| 0,1 Hz /e (Ω.cm)

t (s1/2

Coati ng B

|Z|0.1Hz / e (Ω.cm)

t (s1/2

Fig. 5. Evolution of the reduced low impedance modulus of coating B for stressedap

lsAeofr

εtttntltftnt

CB(t)/ CB (t=0)

t (s1/2)

500040003000200010000

-3 MPa

-4 MPa

Peinture A

σσσσ < 0

σσσσ > 0

Coati ng A 1.8

lar reorientations at a molecular scale. From these results, it seems

nd unstressed panels during immersion in NaCl 3 wt.% solution at ambient tem-erature.

Obviously, considering that the coatings do not swell, the evo-ution of εr with time is very similar to the capacitance evolutionince only constant geometrical parameters link both quantities.s can be seen for coating A, the stress and the temperature influ-nce the normalized capacitance evolutions and same trends werebtained for the coating B during ageing. Particular attention wasocussed on the initial capacitance value and then to the initialelative permittivity ε0

r obtained at t = 0 from εr curves (Fig. 7b).The effect of the applied stress was demonstrated by plotting

0r values as a function of the stress (Fig. 8) for the different ageingemperatures (25, 35 and 45 ◦C). From these results, it is clearly seenhat the relative permittivity of non-aged coatings increases withhe temperature. This fact can be explained by the thermo-activatedature of this quantity. More surprisingly, ε0

r values increase whenhe stress level increases, independently from the sign of the stress,eading to quasi-symmetrical curves around the null value. Theserends were observed for both coatings, even if ε0

r values were dif-erent between coatings A and B. The initial permittivity appears

Fig. 6. (a) Equivalent electrical circuit used to fit EIS data. (b) Evolution of thenormalized capacitance of coating A under stressed and unstressed mode duringimmersion in NaCl 3 wt.% solution at ambient temperature.

tribution, according to the theory of thermo-activated processes,the permittivity of the dry coating can then be expressed as:

ε0r = ε̃0. exp

[−�H

]= ε̃0. exp

[−�H0 − |�m| .Va

where �H0 is the activation enthalpy independent of the stress,Va is the activation volume, kB is the Boltzman constant, �m is thehydrostatic pressure and ε̃0 is the athermal term. The applied stress� modifies the shape (deviatoric part of stress) and the volume(hydrostatic part of stress) of the elements, which compose thepolymer network. In the present approach, we consider that devia-toric part of stress does not modify the density of charge. Thus, onlythe hydrostatic pressure �m = 1/3 � is considered in the permittivityrelation (Eq. (3)).

By plotting Ln(ε0r ) vs. 1/T, �H and Ln(ε̃0) can be calculated from

which the dependence of these parameters with the stress can bedetermined (Fig. 9). First, it can be seen that the stress leads toa decrease of the athermal term ε̃0 and of �H, which means anincrease of the exponential energy contribution. As the ε0

r valuesincrease with the stress (Fig. 8), it appears that the energy parthas a preponderant influence on the variation of ε0

r . From the evo-lution of �H vs. the hydrostatic pressure �m, �H0 and Va can becalculated. Assuming a linear relation (Fig. 9), the fitted coefficientsallowed determining �H0 and Va values equal to 4.3 × 10−20 J (i.e.,25.6 kJ mol−1 or 0.3 eV) and 18.1 nm3 for coating A and 7.4 × 10−20 J(i.e., 44.5 kJ mol−1 or 0.5 eV) and 11.5 nm3 for coating B, respec-tively. The energies lower than 1 eV are consistent with the natureof bonds which are involved and suggest that the permittivity canbe associated with an ionic/atomic or a Debye type polarization.However, the values of the activation volume (about 15 nm3) aremore in agreement with the latter case which is related to dipo-

that the energy gap is more important for coating B and that theactivation volume is lower for this coating, which may be relatedwith the chemical properties of this coating. Then, since the effect

0 50 100 150

t (s1/2 )

Coating B

300025002000150010005000

0 MPa/25 °C0 MPa/35 °C0 MPa/45 °C-4 MPa/25 °C-4 MPa/35 °C-4 MPa/45 °C

Peinture A

t (s1/2

CB (t)/ CB (t=0)

ocsaaaeeetb

-6 -4 -2 0 2 4 6

25 °C

35 °C

45 °C T ↑

Stress (MPa)

Coating A

-6 -4 -2 0 2 4 6

25 °C

35 °C

45 °CT ↑

Stress(MPa)

Coating B0rε

These results have to be compared with the observations pre-sented above. Indeed, these effects are largely compensated by theenthalpic contribution exp[− (�H/kBT)] since ε0

r values were found

Table 1Thermodynamic coefficients of the relation between ε̃0 and |˛m|.

ig. 7. (a) Evolution of the normalized capacitances with the temperature in com-ression mode (4 MPa) and (b) determination of the initial relative permittivity ε0

case of coating B; 45 ◦C, 4 MPa).

f the stress on the enthalpic contributions appears similar for bothoatings (slopes are very close in the �H plots), it may be under-tood that the coating B is less influenced by the mechanical stressnd that the water uptake process in this coating will be not greatlyffected by the applied stress. However, the values of �H0 and Va

re very close for both coatings and are not different enough toxplain the variations of ε0

r . It can be then considered that the pre-xponential term ε̃0 is also a function of the stress which means anntropy contribution to the thermal activation process. The permit-ivity expression is not as simple as presented in Eq. (3) but shoulde written as:

0r = ε̃0(�m). exp

[−�H0 − |�m| .Va

˜0(�m) = �. exp[

]= �. exp

[�S0 − |�m| .ˇ

�. exp[

]. exp

[−|�m| .ˇ

]= a. exp [−b. |�m|] (6)

In Eq. (5), � is a pre-exponential term that is function of theumber of possible orientations of the molecule and of the fre-uency of the event. �S0 is the entropic part which is independentrom stress. Eq. (5) simplifies into Eq. (6) where the thermody-

Fig. 8. Variation of the initial permittivity ε0r of coatings A and B with the tempera-

ture and the applied stress.

namic coefficients a and b can be calculated when plotting ε̃0 vs. theapplied stress. As can be seen (Fig. 9), straight lines can be obtainedin these plots, demonstrating the dependence of ε̃0 on the stress.The values of a and b coefficients are presented in Table 1. The valueof b is similar for both coatings, indicating that the stress contribu-tion onto the ε̃0 evolution is the same for both systems. However,a is much higher for coating B than for coating A and this allows toexplain the lower ε̃0 values that were found for coating A earlier.This also suggests that the number of possible orientations (� ) ismore important with coating B which seems consistent with thelower density of coating B. It can also be noted that the weight ofthe exponential term dependent from the stress (exp [−b. |�m|]) iswell below the weight of the entropic part independent from stress(a) in Eq. (6).

a b ̌ (J K−1 Pa1)

Coating A 1.2 × 104 2 × 10−6 2.8 × 10−2

Coating B 8 × 107 3 × 10−6 2.8 × 10−2

y = -1.814E-26x + 4.256E-20R2 =0.9592

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06 1.E+06 1.E+06

Tension

Compression

ΔH (J)

⏐σm⏐ (Pa)

Coating A

y = 12366e-2E-06x

R2 = 0.6904

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+061.E+061.E+068.E+056.E+054.E+052.E+050.E+00

Tension

Compression

⏐σm⏐ (Pa)

Coating A

y = 8E+07e-3E-06x

R2 = 0.8605

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+061.E+061.E+068.E+056.E+054.E+052.E+050.E+00

Compression

⏐σm⏐ (Pa)

Coating B

Tension

y = -1.152E-26x + 7.397E-20

R2 = 0.9945

1.E+061.E+061.E+068.E+056.E+054.E+052.E+050.E+00

Tension

ΔH (J)

⏐σm⏐ (Pa)

Coating B

Compression

) with

tisaobdppmtasiarntse

Fig. 9. Linear dependency of ε̃0 and �H parameters from Eq. (3

o be higher for coating A. From this thermodynamic treatment,t can be concluded that two antagonist effects are involved. Thetress leads to a permittivity decrease with the entropic term ε̃0nd in the same time to an increase with the enthalpic part. Inther words, the stress provides energy to orientate the dipolesut also favors the organization within the system, which makesifficult statistically the dipole reorientation and then, leads to aermittivity decrease. However, globally, the trend is towards aermittivity increase, contrary to others works with charged poly-er systems [22]. It must be noted that in this latter study, the

ensile stress was up to 45% which is well higher than our casend that conductive fillers (carbon black) were considered in aimple polymer system. The organic coatings under investigationn the present paper have a complex formulation so the inter-ctions between each component are difficult to link with ouresults. Consequently, the conclusions of these authors might beon applicable to our systems. With this point in mind, it seemshen necessary to explore in more details our approach with modelystems where the chemical composition will be known morexactly.

. Effect of stress onto the water uptake process

Since the value of the capacitance value at t = 0, C0, was knownrom previous results, the diffusion coefficient D of water was cal-

the absolute value of the hydrostatic stress for both coatings.

culated using [23]:

log(Ct/C0)log(CS/C0)

√t (7)

where Ct is the capacitance value at time t and CS is the capacitancevalue at saturation. As it is clearly seen in Fig. 10, the values ofthe diffusion coefficient increase when the temperature increases,showing the thermo-activated nature of this process for both coat-ings. This result is observed whatever are the nature and the signof the stress (tension or compression) and the values are coherentwith previous studies on polyepoxyde resins [24,25]. However, theinfluence of stress is different: the diffusion in coating A is greatlyfavored in the tension mode while the compression mode enhancedthe diffusion in the coating B. The fact that the tension facilitatesthe diffusion was already reported by many authors [26–29]. It isbelieved that the stress leads to a modification of the arrangementof the polymer chains and to a multiplication of the free volumesthat are able to be filled by water. These two effects are then essen-tial to explain the rapid degradation of coating A under tensile

The thermodynamic approach presented above with the per-mittivity can be applied in order to separate energy and structural

-5 -4 -3 -2 -1 0 1 2 3 4 5

25 °C

35 °C

45 °C

σ (MPa)

D (10-9

cm2/s)

T ↑Coating A

-5 -4 -3 -2 -1 0 1 2 3 4 5

25 °C

35 °C

45 °C

σ (MPa)

D (10-9

cm2/s)

Coating BT ↑

Fig. 10. Influence of the temperature and the applied stress onto the diffusion coef-fi

wt�fi

Table 2Thermodynamic parameters of the relation between D and |˛m|.

Coating A B

Mechanical state Tension Compression Tension Compression

Ks (J/K) 4 ×1017 3.5 × 1017 15 × 1017 12 × 1017

[Ln(D0) + �S0/kB] 3.8 3.9 49 49

cient values for both coatings.

ontributions. The diffusion coefficient, independent from stress,an then be expressed as [30,31]:

= D0 exp[−�G0

]= D0 exp

(�S0

(−�H0

here D0 is the pre-exponential term, �S0 and �H0 are, respec-ively, the entropy and enthalpy associated to the energy barrier

G0. If the coating is submitted to a stress, then the diffusion coef-cient can be written as:

= D0 exp[− �G

]= D0 exp

(−�H

= D0 exp(

�S0 − Ks |�m|kB

(−�H0 − V |�m|

here Ks is a coefficient representing the entropy modification dueo the hydrostatic pressure �m and V is a volume related to an acti-ation volume of the diffusion process. First, the Eq. (10) can beeduced to Eq. (11) where D̃0 represents the entropic contribution.[

= D̃0 exp −kBT

The presentation of each part D̃0 and �H separately as a func-ion of |�m| in Fig. 11 validates the formalism since straight lines

�H0 (kJ/mol) 85 84 201 200V (nm3) 28 19 86 76

are obtained. This shows that both quantities are function of themechanical stress: the entropic part decreases and the enthalpiccontribution increases (due to a �H decrease) when the hydro-static stress increases. The entropic part decrease means that thecoating systems are more and more orderly and the number of pos-sible pathways for diffusion is limited. In other words, the diffusionprocess would be oriented by the stress. However, the increaseof the enthalpic contribution exp[− (�H/kBT)] indicates that theenergy gap to go through is decreased so the water diffusion isfavored by the stress. Finally, it can be stated that the diffusion pro-cess in the two organic coatings is governed by two energeticallyantagonist effects: the enthalpic contribution which favors the dif-fusion and the entropic contribution which tends to slow down thediffusion.

In order to have more information on the weight of each con-tribution, the parameters from Eq. (10) were calculated. For theentropic contribution variation, it can be written Ln(D̃0) = Ln(D0) +(�S0/kB) − (Ks/kB) |�m|. This late equation allow us to calculateKs, and [Ln(D0) + �S0/kB]. For the enthalpic contribution �H, thelinear variation can be translated as �H = �H0 − V |�m| and theactivation volume can be estimated. The values of the differentparameters are presented in Table 2. All Ks values are positive:this means that the hydrostatic pressure leads to a decrease of thesystem entropy, whatever is the nature of the stress. This effectseems more pronounced in the case of coating B. The entropic term[Ln(D0) + �S0/kB], independent from the stress, is ten times higherfor coating B than for coating A. This suggests that the diffusionprocess is favored in coating B while it is less favored in the caseof coating A. However, it can be seen that the enthalpic term inde-pendent from the stress, �H0, is higher in coating B than coating Awhich indicates that the diffusion process is favored in the coatingA. Hence, this late result is in opposition with the previous findingbased on the entropic contribution.

Then, it appears that the evolution of the entropic and enthalpiccontributions with stress have opposite effects onto the diffusionprocess. This result allows to explain higher diffusion coefficientfor coating B when the temperature increases while higher diffu-sion coefficients were found for coating A at lower temperatures.Finally, from the positive free volume values, it can be stated thatthe stress provides to the coating system a part of the energy neces-sary to cross the energy barrier which is demanded for the diffusionof water molecules. It can be also remarked that the free volume val-ues are higher in the tensile mode for both coatings which showsthat the diffusion is favored under this stress state. So, the rea-son why the diffusion coefficients of coating B are higher undercompression mode can be conclusively explained by the competi-tion between the enthalpic and entropic contributions, respectivelyPH = exp(V |�m| /kBT) and PS = exp(−(Ks |�m| /kB)). Both quantitiesare plotted vs. the stress (Fig. 12) assuming that the evolutions ofKs and V with stress are negligible. It can be seen that the evolutionof the diffusion coefficient with stress is mainly governed by theenthalpic contribution for coating A while the evolution of the dif-

1.E+061.E+061.E+068.E+056.E+054.E+052.E+050.E+00

Tension

Ln (D0)

⏐σm⏐ (Pa)

Coating A

Compression

1.1E-19

1.2E-19

1.3E-19

1.4E-19

1.5E-19

1.E+061.E+061.E+068.E+056.E+054.E+052.E+050.E+00

Tension

Compression

ΔH (J)

⏐σm⏐ (Pa)

Coating A

1.5E-19

1.7E-19

1.9E-19

2.1E-19

2.3E-19

2.5E-19

2.7E-19

2.9E-19

3.1E-19

3.3E-19

3.5E-19

1.E+061.E+061.E+068.E+056.E+054.E+052.E+050.E+00

Tension

Compression

ΔH (J)

⏐σm⏐ (Pa)

Coating B

1.E+061.E+061.E+068.E+056.E+054.E+052.E+050.E+00

Tension

Ln (D0)

⏐σm⏐ (Pa)

Coating B

Compression

Fig. 11. Linear dependency of the entropic contribution D̃0 and of the activation enthalpy �H from Eq. (11) with the absolute value of the hydrostatic stress for both coatings.

Peinture A

Peinture B

Peinture BCoati ng A

Coati ng B

Stress

Fig. 12. Influence of the enthalpic (PH) and entropic (PS) contributio

. Conclusions

The degradation kinetics of two marine organic coatings weretudied using EIS under mechanical stresses in a visco-elasticomain. From these results, it can be concluded that:

the sign of the stress (tensile or compressed mode) has a different

Stress

the diffusion coefficient (D) evolution with stress for both coatings.

- the initial relative permittivity of both coatings appears as athermo-activated function of the absolute value of the appliedstress; this is mainly due to the energy (enthalpic part) affordedby the stress;

- the diffusion coefficient of water appears as a thermo-activatedfunction of the value of the applied stress; however, two ener-getically antagonist effects act in parallel and have an influence

With commercial coating formulation, it is difficult to go fur-ther in our analysis but a natural continuation of this work is

2 ganic

68 N. Fredj et al. / Progress in Or

o study a model system. This is currently in progress in ouraboratory.

cknowledgements

This work was carried out in the framework of ACI ECD 2004rom Ministère de la Recherche, grant 2004/0090/DR16. We arelso grateful to Conseil Général de la Charente Maritime (France)or the PhD financing.

eferences

[1] M.W. Kendig, H. Leidheiser, J. Electrochem. Soc. 123 (1976) 982.[2] L. Beaunier, I. Epelboin, J.C. Lestrade, H. Takenouti, Surf. Technol. 4 (1976) 237.[3] M. Kendig, F. Mansfeld, S. Tsai, Corros. Sci. 23 (1983) 317.[4] A. Miszczyk, K. Darowicki, Corros. Sci. 43 (2001) 1337.[5] X.F. Yang, J. Li, S.G. Croll, D.E. Tallman, G.P. Bierwagen, Polym. Degrad. Stab. 80

(2003) 51.[6] S. Touzain, Q. Le Thu, G. Bonnet, Prog. Org. Coat. 52 (2005) 311.[7] F. Deflorian, S. Rossi, L. Fedrizzi, C. Zanella, Prog. Org. Coat. 59 (2007) 244.

Coatings 72 (2011) 260– 268

13] E.L. Thomas, Structures and properties of polymers, in: R.W. Cahan, et al. (Eds.),in: Mater. Sci. Technol., vol. 12, VCH, 1993.

14] N. Brusselle-Dupend, D. Lai, X. Feaugas, M. Guigon, M. Clavel, Polym. Eng. Sci.41 (2001) 66.

15] N. Fredj, S. Cohendoz, X. Feaugas, S. Touzain, Prog. Org. Coat. 67 (2010)287.

16] N. Fredj, S. Cohendoz, X. Feaugas, S. Touzain, Prog. Org. Coat. 69 (2010) 82.17] Q. Le Thu, H. Takenouti, S. Touzain, Electrochim. Acta 51 (2006) 2491.18] G.J. Brug, A.L.G. Van Den Eeden, M. Sluyters-Rehbach, J.H. Sluyters, J. Electroanal.

Chem. 176 (1984) 275.19] X. Zhang, B. Boelen, P. Beentjes, J.M.C. Mol, H. Terryn, J.H.W. de Wit, Prog. Org.

Coat. 60 (2007) 335.20] H. Eyring, J. Chem. Phys. 4 (1936) 283.21] A. Dyson, J. Soc. Chem. Ind. 69 (1950) 205.22] A. Mdarhri, C. Brosseau, F. Carmona, J. Appl. Phys. 101 (2007), art. no. 084111.23] F. Bellucci, L. Nicodemo, Corrosion 49 (1993) 235.24] S. Roy, K. Vengadassalam, Y. Wang, S. Park, M. Kenneth, Liechti, Int. J. Solids

Struct. 43 (2006) 27.25] S. Popineau, C. Rondeau-Mouro, C. Sulpice-Gaillet, M.E.R. Shanahan, Polymer

46 (2005) 10733.26] G. Yaniv, O. Ishai, Polym. Eng. Sci. 27 (1987) 731.27] A. Agarwal, M. Tomozawa, W.A. Landford, J. Non-Cryst. Solids 167 (1994) 139.28] M. Tomozawa, Phys. Chem. Glasses 39 (1998) 65.

247 (2007) 11.30] H. Eyring, T. Ree, in: F.R. Eirich (Ed.), Rheology II, Academic Press, New York,

1958.31] M.E. Glickman, Diffusion in Solids, John Wiley and Sons, New York, 2000.

Effect of mechanical stresses on marine organic coating ageing approached by EIS measurements

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