Organic coating capacitance measurement by EIS: ideal and actual trends

Transcription

1 Electrochimica Acta 44 (1999) 4243±4249 Organic coating capacitance measurement by EIS: ideal and actual trends F. De orian*, L. Fedrizzi, S. Rossi, P.L. Bonora Laboratory of Industrial Corrosion Control, Materials Engineering Department, University of Trento Via Mesiano 77, Trento, Italy Received 7 August 1998; received in revised form 28 January 1999 Abstract The coating capacitance is one of the most frequently studied parameters obtained by EIS measurements for characterising the protective properties of organic coatings, because by analysing this parameter it is possible to measure the water uptake phenomena (di usion till saturation and further increase) which are very important in barrier coatings. The ideal trend described in many cases is not representative of the actual evolution measured on coatings. Often one phase is missing or a reduction of the coating capacitance is measured. In this work the ideal trend of coating capacitance is compared with some real experimental results, discussing the reasons of disagreement and the limits of the model which seem to be in many cases insu cient and too simple to explain the actual water uptake processes, in particular, when a further increase of the coating capacitance occurs after saturation. The presence of di erent water uptake mechanisms, the heterogeneous distribution of the water in the coating and dimensional variations make the water uptake phenomenon quite complex. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Electrochemical impedance spectroscopy; Organic coatings; Water uptake; Coating capacitance; Delamination 1. Introduction By analysing the capacitance in organic coatings it is possible to evaluate the water uptake phenomena occurring in organic coatings in wet environment [1± 2], because water di usion can modify the dielectric constant of the polymer even if present in very small amounts [4,5]. Moreover, the coating capacitance is a parameter that is easy to measure even in the case of high impedance systems (high thickness coatings) [6]. The barrier properties towards water are very important because the presence of an aqueous solution in the paint can activate the corrosion process [7,8] or can * Corresponding author. cause loss of adhesion and blistering [9]. Hence the coating capacitance (C c ) is a very important source of information concerning the water barrier properties of an organic coating, and in particular by C c measurements it is possible to evaluate the volume fraction of water in the coating [10] and the kinetics of uptake (coe cient of di usion) [11]. In general the theories for evaluating the quantity of water present suppose a homogeneous distribution of water in the coating [12]. In agreement with the most recognised model of water uptake trend in organic coatings [2,5,10,13], it is possible to de ne three phases (Fig. 1). Initially there is an homogeneous water di usion in the coating (phase I). This phase in some cases can be described by Fick's Laws and is the most studied step of the water uptake mechanism. A lot of work has been done /99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S (99)

2 4244 F. De orian et al. / Electrochimica Acta 44 (1999) 4243±4249 Fig. 1. Ideal evolution of coating capacitance with the time of testing in aqueous solutions. in studying this step of the water uptake process, with often complex mathematical calculations [13,14], despite the fact that in general the coating breakdown occurs after saturation and during the homogeneous water uptake the critical property is mainly the ionic di usion in the coating (studied by EIS measuring the coating resistance), more than the water barrier properties. After the rst step there is the saturation of the polymeric matrix with a constant value of the capacitance (plateau), noted in Fig. 1 as phase II. Finally, there is further increase in the water content (phase III) due to more water accumulation in the coating, probably in a heterogeneous way. In some cases a fourth transition phase has been proposed, between saturation and further increase [15]. In many cases the ideal trend shown in Fig. 1 is not representative of the actual evolution measured on coatings. Often one phase is missing, for example, the saturation is di cult to recognise because it is possible to note a change of the slope of the capacitance increase vs the immersion time, instead of a real plateau; or the third phase is completely absent. Another problem is the measurement of a reduction of the coating capacitance. It is di cult to explain this behaviour with the previously discussed model. The aim of this work is to compare the ideal trend of C c with the time of testing with some examples of actual data, trying to discuss the reasons of disagreement and the limits of the model describing the e ect of water uptake on the coating capacitance evaluated by EIS. 2. Experimental The examples of EIS characterisation were performed on di erent materials. The sample substrate was mild steel coated with di erent organic coatings: uoropolymer, epoxy, or acrylic coatings. The electrochemical impedance measurements were performed in the 10 KHz±1 mhz frequency range using Frequency Response Analyser connected to a potentiostat. The amplitude of the sinusoidal voltage signal was 10 mv. The electrochemical tests were carried out in a quiescent aerated aqueous solution with composition speci- ed for each example. The time of testing ranges from 2 to about 500 days depending on the application and on the supposed protection properties of the coatings. The exposed painted sheet area was between 10 and 30 cm 2. The three-electrode electrochemical cell was obtained by sticking a plastic cylinder on the sample sheet and lling it with the test solution. A saturated sulphate electrode (SSE; +640 mv vs SHE) as reference, and a platinum counter electrode, were employed. All the impedance measurements were carried out in a Faraday cage in order to minimise external interference on the system studied. The experimental impedance spectra were interpreted on the basis of equivalent electrical circuits using a tting software (Equivcrt) elaborated by Boukamp [16]. The coating thickness was measured using a Deltascope MP Fisher equipment with a precision, in the thickness range of the studied materials, of 22 mm. The thickness results are the mean value of 20 measurements. 3. Results and discussion Before discussing the experimental result, it is necessary to introduce the basic equations describing how the capacitance of the coating depends on its water content. The coating capacitance C c can be expressed by the following equation: C c ˆ ee o A=d where A is the testing area, d the coating thickness, e the dielectric constant of the medium and e o the free space permittivity. The coating capacitance can be considered proportional with the dielectric constant just considering constant the geometrical parameters, in particular considering constant the coating thickness. This assumption is not always true because the water uptake could cause swelling in the polymeric matrix of the coating. By applying a simple empirical mixing rule it is possible to correlate the apparent dielectric constant at the time t (e t ) the dielectric constant of the polymeric matrix (e m ), the dielectric constant of water (e w ), the volume fraction of water at the time t (f t ) and the 1

3 F. De orian et al. / Electrochimica Acta 44 (1999) 4243± Fig. 2. Evolution of the dielectric constant and exponent n of a CPE element vs the square root of the time of testing for an acrylic coating: saturation present. volume fraction of water at saturation (f s ): e t ˆ em 1 fs e ft W From Eq. (2) can be derived: f t ˆ ln e t ln e 1 fs m = ln e w 3 and through Eq. (1): f t ˆ log C t =C o = log e w where C t is the capacitance after the time t and C o is the initial capacitance. Eq. (4) is the Brasher 2 4 Kingsbury equation [17] and it is widely used for the calculation of the water amount from capacitance measurements in organic coatings. Eq. (2) is based on the assumption that water in organic coatings shows the same behaviour of an aqueous plus non-electrolyte solution (as for example organic solvents as alcohols, or sugar). This means that water is supposed homogeneously distributed in the coating. This hypothesis could be reasonable in the case of homogeneous media, but it is di cult to consider an organic coating homogeneous because of the presence of pigments, defects and holes, areas with di erent chemical compo- Fig. 3. Evolution of coating capacitance vs the time of immersion for a uoropolymeric coating.

4 4246 F. De orian et al. / Electrochimica Acta 44 (1999) 4243±4249 Fig. 4. Evolution of the dielectric constant vs the square root of the time of testing for an acrylic coating: saturation not evident. sition or curing, etc. Moreover, in Eq. (4) it is necessary to introduce the value of the dielectric constant of water. This value is about 80 for free water at room temperature, but the water di used in the organic coating cannot be considered as free water because of the interaction with the polar groups in the polymer. Some authors suggest that the value is probably lower, between 50 and 60 [3,10,18]. Nevertheless, in Eq. (4) the number 80 is always introduced, probably causing an underestimation of the volume fraction of water. Actually, the data analysis of the contribution of capacitive elements to the total impedance is generally obtained by using a constant phase element (CPE) instead of a pure capacitance, in order to consider the non-ideal behaviour of the organic coatings. The value of the exponent n for the angular frequency o, which multiplies the capacitance for giving the admittance, ranges between 1 and 0.97 because of the e ect of dissipative phenomena. It is important to use a CPE instead of a pure capacitance in modelling and tting the experimental results, even when the di erence, like in our case, between the CPE and the pure capacitance is very small because the use of CPE leads to a more precise tting output [5]. All the data presented in this paper are therefore obtained as CPE, but for simplicity and considering that the shift from the ideal behaviour is quite small, all the electrical quantities for the following discussion will be called capacitance and the related parameters dielectric constant, even if this is a clear approximation. The use of the parameter n for describing the behaviour of the coating seems in our case to give the same information than the modulus of CPE, as shown in Fig. 2 where the trend of both the parameters is compared and where it is possible to note that the two trends are, if normalised, identical. For this reason, only the CPE modulus values (capacitances) will be discussed further The homogeneous water uptake: the saturation behaviour Fig. 3 shows a rst case of anomalous behaviour: a decrease of the coating capacitance (C c ) in the saturation range. The material is a uoropolymer coating on mild steel (the thickness is about 200 mm) immersed for a long period in 3.5% NaCl. In this case it is possible to recognise phase I (water uptake in the polymer) and the saturation phase, despite the data dispersion, due to the di culties in measuring by EIS the properties of high impedance coatings as such materials. But after about 200 days of immersion the coating capacitance shows a very strange decrease. Considering Eq. (1) still valid, a reduction of the capacitance can be caused only by an increase of the thickness of the coating, maintaining the water content constant. Actually the thickness of this coating showed an increase due to swelling, but the increase is not so big as to explain completely the reduction of the coating capacitance by a factor of 1.5. However, considering samples with di erent formulations, it was possible to note a capacitance decrease only associated to dimensional variations in the coating, because when the coating thickness was stable, the coating capacitance decrease was not measured. Probably the swelling process also causes a change in the water distribution in the coating, modifying further the capacitance of the coating. In other words, after saturation, the model leading to Eq. (4) is probably not valid and a more complex analysis is necessary.

5 F. De orian et al. / Electrochimica Acta 44 (1999) 4243± Fig. 5. Model and equivalent electrical circuit for a coating with an aqueous layer at the metal-coating interface The heterogeneous water uptake: the after saturation behaviour A very frequent case of anomalous behaviour of capacitance trend, in comparison with Fig. 1, occurs when it is very di cult to see a clear saturation plateau, and a continuous increase of coating capacitance is visible. Fig. 4 shows the dielectric constant e (equivalent to the coating capacitance) trend vs the square root of time of an acrylic coating (thickness about 80 mm) immersed in 3.5% of NaCl. In order to explain the absence of a saturation phase we suppose that the processes of the phase I and III (that are the homogeneous water uptake in the polymeric matrix of the coating and the heterogeneous water uptake at the coating substrate or pigment-matrix interfaces) occur at the same time, overlapping. The polymeric matrix is saturated after the beginning of the water accumulation in speci c weak points of the coating. In this case it is very di cult to obtain quantitative results from the EIS data because Eq. (4) is not applicable at stage III and it is impossible to separate this contribution from the homogeneous water di usion. Also the evaluation of the water uptake rate (e.g., the di usion coe cient) becomes impossible if two di erent mechanisms of water uptake occur at the same time. A con rmation of this hypothesis comes from Fig. 2. This gure shows the trend of the dielectric constant of the same kind of coating, cured in di erent conditions: higher temperature and longer time. The coating seems better cured with the glass transition temperature being higher. The dielectric constant is lower in comparison with Fig. 4 and it is possible to note (actually just for few hours) something similar to saturation. In this case the heterogeneous water uptake kinetics is reduced because of the better curing, allowing to separate the two di erent absorption mechanisms: homogeneous in the polymeric matrix and heterogeneous in the coating defects. The mechanism of further coating capacitance increase after saturation needs more investigation. In the literature it is possible to nd that this growth is generically related to an accumulation of water in heterogeneous way [2,5,10,13]. A very simple model of this presence of water could consider an equivalent electrical circuit as in Fig. 5. In the series with the coating capacitance there is a water capacitance due to a layer of free water somewhere in the coating, for example at the metal coating interface (as in the case of blisters). By assuming the coating thickness and the water in the coating to be constant (therefore constant C c ), it is easy to demonstrate that the total capacitance C t, equivalent to C c and C w, must decrease. In fact: Fig. 6. Evolution of coating capacitance vs the time of immersion for an acrylic coating showing a capacitance reduction.

6 4248 F. De orian et al. / Electrochimica Acta 44 (1999) 4243±4249 Fig. 7. Evolution of coating capacitance vs the time of immersion for an epoxy waterborne coating. C t ˆ 1= 1=C w 1=C c ˆC c C w = C c C w ˆ C c = 1 C c =C w and therefore, being C c /C w >0, it is proved that C t < C c. The model in Fig. 5 is therefore too simple and in general not correct. There are some few cases in which the model in Fig. 5 can be applied, when a large delamination occurs at the metal-coating interface. Fig. 6 shows the coating capacitance trend of an acrylic coating (thickness 30 mm) on mild steel immersed in 0.3% Na 2 SO 4 solution. After an initial increase during the initial 10 min, the coating shows a relevant decrease of the coating capacitance, without swelling; the coating thickness measured after immersion, is not di erent from the initial thickness. At the end of testing the coating was completely detached from the substrate and a layer of electrolyte was present on the surface. By using Eqs. (5) and (1), assuming C t as the total coating capacitance, C c as the maximum value of the capacitance (the real value of C c could be higher) and e w equal to 80, the water layer thickness can be estimated in the order of 10±20 mm, which is reasonable with the water amount observed in the blisters at the end of testing. Therefore the model for explaining Fig. 4 (coating capacitance increase) should be quite complex. The actual distribution of water in the coating after saturation is probably quite complex. Beside of the water saturating the coating, there are clusters of water at the metal-polymer interface, in pores in contact with the external surface, in holes inside the coatings, at pigment-matrix interface, etc. This very complex water distribution causes a very di cult or impossible precise calculation of the water content by capacitance 5 measurements and the conditions are far from possible to apply to Eq. (4). A last example of anomalous behaviour in comparison with Fig. 1 occurs when the third phase is not observable. Fig. 7 shows the trend of the capacitance of a epoxy waterborne coating with 50 mm of thickness immersed in 0.1 M KNO 3. Also after a long immersion in the testing solution, it is impossible to note any relevant shift from the saturation value, neither showing a further increase nor a decrease of the capacitance, as in the example in Fig. 3. The coating under study is an experimental one, without any kind of pigments, cured in optimised conditions, and deposited without any speci c pretreatment of the substrate surface, and therefore with a poor adhesion. Considering the di erent water locations previously described, the main mechanism of water accumulation is at the metal interface. The situation is therefore similar to the example in Fig. 6, with a coating capacitance reduction following the model in Fig. 5. In fact at the end of the testing, the coating adhesion was near to zero with a complete detachment of the coating layer and the presence of humidity on the metal surface. A possible explanation of this behaviour can be found considering the values of total capacitance and the dispersion of these data. In the testing conditions, measuring di erent samples, a theoretical data dispersion was found in the order of 5±7% maximum, caused by the limits in the equipment. The actual dispersion is less, about 2± 3%. In order to be able to measure an e ective coating capacitance reduction, this decrease must be higher than 3% of the saturation value and therefore higher than about F/cm 2. By applying Eq. (5) and assuming C c as the saturation value and C t the saturation value reduced by 3%, it is possible to obtain the value of C w, capacitance of the aqueous layers with a

7 F. De orian et al. / Electrochimica Acta 44 (1999) 4243± thickness obtained through Eq. (1), higher than 20 mm, which is a value too high for these samples (actually no blisters were visible). For thickness of the water layer lower than 20 mm, the total capacitance reduction is inside the experimental error (3%) and is not measurable. One further aspect that probably should be taken in account for an accurate value of the coating capacitance is the correct value of e w. As previously mentioned, this value is assumed normally as 80, but it is known that it is probably more close to 60 [18]. However, the value is always considered constant. Actually, after saturation, the formation of a cluster in the coating could cause a change in the value of the dielectric constant of water. In fact the water present in the cluster is free water, with a dielectric constant close to 80. It means that the mean value of e w should increase after saturation, giving a contribution in increasing the coating capacitance that is not actually due to more water in the coating but it is caused by an increase of the mean value of the dielectric constant of water (Eqs. 1 and 2) and therefore causing an apparent increase of water uptake even in the case of constant water amount. A further investigation in the direction of the measure of a precise value of e w in organic coating could be useful in order to have more precise values of water uptake and more information on the actual status of the water inside organic coatings. 4. Conclusions The actual trend of the capacitance of an organic coating immersed in an electrolyte is often di erent from the ideal trend in Fig. 1, as shown by the few examples discussed. The model describing the water uptake mechanisms seems to be insu cient in many cases and too simple to explain the actual water uptake processes, in particular, when a further increase of the coating capacitance occurs after saturation. The presence of di erent water uptake mechanisms, in some cases at the same time, and the heterogeneous distribution of the water in the coating and dimensional variations make the water uptake phenomenon quite complex. Probably it is impossible, apart from the very initial stage of water uptake, to nd a general model describing quantitatively the water absorption processes from capacitance values, and only models with restricted validity or qualitative comparisons of similar materials are possible. An e ort to study these mechanisms in depth, by developing new models for the EIS data interpretation seems necessary in the future in order to better understand the water barrier properties of protective organic coatings. These new models, as suggested also by Leidheiser 20 years ago [19], must take into account the heterogeneous nature of an organic coating, and moreover, have to include the dimensional changes and the e ective dielectric constant of water in polymers. Acknowledgements The authors acknowledge L. Benedetti, R. Scottini, M. Del Grosso Destrieri, J. Vogelsang and F. Buratti for their assistance in the electrochemical measurements. References [1] A. Amirudin, D. Thierry, Prog. Org. Coat 26 (1995) 1. [2] F. Bellucci, L. Nicodemo, Corrosion 49 (1993) 235. [3] M.M. Wind, H.J.W. Lenderink, Prog. Org. Coat 28 (1996) 239. [4] R.C. Weast, Handbook of Chemistry and Physics, CRC Press, Cleveland, [5] E.P.M. van Westing, G.M. Ferrari, J.H.W. de Wit, Corrosion Sci. 36 (1991) 957. [6] F. De orian, L. Fedrizzi, S. Rossi, Corrosion 54 (1998) 598. [7] J.H.W. DeWit, in: P. Marcus, G. Oudar (Eds.), Corrosion Mechanisms in Theory and Practice, Marcel Dekker, Inc, 1995, p [8] W. Funke, in: A. Wilson, J. Nicholson, H. Prosser (Eds.), Surface Coatings 1, Elsevier, [9] W. Funke, JOCCA 9 (1985) 119. [10] S.A. Lindqvist, Corrosion 41 (1985) 69. [11] F. De orian, L. Fedrizzi, P.L. Bonora, Corrosion Sci. 38 (1996) [12] D.H. van der Weijde, PhD Thesis, Delft University, [13] F. De orian, L. Fedrizzi, J. Adhesion Sci. Technol. 13 (1999) 629. [14] Z. Kolek, Prog. Org. Coat. 30 (1997) 287. [15] J.H.W. de Wit, in: J.M. Costa, A.D. Mercer (Eds.), Progress in Understanding and Prevention of Corrosion, The Institute of Materials, London, 1993, p [16] B. Boukamp, Solid State Ionics 20 (1986) 31. [17] D.M. Brasher, A.H. Kingsbury, J. Appl. Chem. 4 (1954) 62. [18] J.B. Hasted, Aqueous Dielectrics, Chapman and Hall, London, [19] H. Leidheiser, Prog. Org. Coat. 7 (1979) 79.