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Electrochimica Acta 94 (2013) 219– 228

Contents lists available at SciVerse ScienceDirect

Electrochimica Acta

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ater uptake in thin nylon 6 films as measured by electrochemical impedancepectroscopy and magnetic resonance imaging

.J.W. Reuversa, H.P. Huininka,∗, O.C.G. Adana,b, S.J. Garciac, J.M.C. Molc

Eindhoven University of Technology, Eindhoven, The NetherlandsTNO, Delft, The NetherlandsDelft University of Technology, Delft, The Netherlands

r t i c l e i n f o

rticle history:eceived 18 November 2012eceived in revised form 23 January 2013ccepted 25 January 2013vailable online 8 February 2013

eywords:olyamide 6

a b s t r a c t

Electrochemical impedance spectroscopy (EIS) and magnetic resonance imaging (MRI) are used to mea-sure water uptake in nylon 6 films. Based on the EIS data the uptake process is split into three stages. Atfirst, during the first 3 h, the spectrum is mainly capacitive due to the dry bottom part of the film. Theexistence of a dry bottom part is confirmed by the MRI measurements. In the second stage EIS showsthat small traces of water reach the substrate, whereas MRI still not detects water at the nylon/substrateinterface. This demonstrates the sensitivity of EIS as water at the substrate is detected by EIS before MRIis able to do so. The last stage starts as the waterfront reaches the substrate and the amount of water in

ater uptakeRI

ISielectric spectroscopy

the nylon at the substrate increases.MRI shows that the bulk of the water ingresses into the nylon film as a sharp front. A simple capacitance

model is able to link this ingressing front to the impedance as measured with EIS at high frequency.The detection of water breakthrough and interface processes by EIS illustrates the complementarity

of the techniques. EIS is able to detect small traces of moisture reaching the substrate before the bulkamount of water does. MRI gives a better view on the overall water distribution during uptake.

. Introduction

Polymeric films are often applied on metallic substrates to act as barrier to water and ions in order to prevent corrosion. The waterransport through these coatings is a measure for the protectiveuality of the coating.

This work focusses on water transport in nylon 6 films as mea-ured by two different techniques, i.e. electrochemical impedancepectroscopy (EIS) and magnetic resonance imaging (MRI). Becausef the amide functionality, nylon 6 is able to absorb water up to 9%f its mass. It is generally assumed that the first molecules of waternteract with the amide group and form a hydrogen bond [1]. When

ore water enters the nylon matrix, clustering of water moleculestarts.

Transport of water into polymeric films has been intensivelynvestigated by various techniques: gravimetry [2,3], electro-hemical impedance spectroscopy (EIS) [4,5], magnetic resonancemaging (MRI) [6,7] and other techniques [8].

Mansfield et al. [9] conducted one of the first and most extensiveRI studies into water uptake by nylon. They measured the water

ngress in solid blocks of nylon 6.6 at temperatures between 20 ◦C

∗ Corresponding author.E-mail address: h.p.huinink@tue.nl (H.P. Huinink).

013-4686/$ – see front matter © 2013 Elsevier Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.electacta.2013.01.135

© 2013 Elsevier Ltd. All rights reserved.

and 100 ◦C with MRI. Recently we studied the water uptake processat room temperature in 200 �m thick nylon 6 films [6]. The MRIsignal was quantified and it was shown that the largest part of themoisture moves as a sharp front through the nylon.

With magnetic resonance imaging, spatially resolved water dis-tributions can be measured during the water uptake process witha resolution down to 5 �m [10]. MRI directly measures hydrogendistributions, wherein the quality is dependent on the experimen-tal signal to noise [11]. The smallest detectable amount of moisturedepends on the MRI setup and the experimental settings. If the sig-nal of small amounts of hydrogen is not higher than the noise levelof the setup, these hydrogen cannot be detected. Furthermore, theMRI signal is averaged over a voxel or small volume element. A localdefect, such as a pinhole, can only be detected when this defect isas big as a voxel.

Electrochemical impedance spectroscopy (EIS) can also be usedto measure water uptake in polymer films. EIS has two major advan-tages compared to MRI. First, it is relatively easy to use. Secondly,EIS is able to detect small amounts of moisture at the substrateand is therefore very sensitive to pinholes and imperfections ina coating. Imperfections form conducting channels between the

electrolyte fluid on top of the film and the substrate underneath.

EIS has many applications in the field of coating and corrosionscience. The changing dielectric and conductive properties dur-ing water uptake are used to study the protective properties of an

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20 N.J.W. Reuvers et al. / Electro

rganic layer [12,13]. A saline solution is put on top of the film androm this solution water will start to penetrate the polymer filmnd give rise to a changing impedance.

The measured impedance is the average effect over the wholelm, so the EIS results are not spatially resolved. For a quantitative

nterpretation of the water uptake speed there is a need to assume constant diffusion coefficient. The diffusion constant is calculatedy matching timescales of the changes in film capacitance [14–16].s water diffuses into the film, the dielectric constant of the film

ncreases, which subsequently increases the film capacitance. Theielectric constant of the saturated film is calculated according ton empirical mixing rule, using the initial dielectric constants ofater, polymer and air and their volume fractions [17,18,13,19].

his dielectric constant can then be used to calculate the water vol-me fraction. Impedance data is modeled with networks of resistorsnd capacitances. The capacitor describes the capacitive functionf the polymer and the resistor represents the conducting waterhase in the polymer. To describe data sets, complicated networksf capacitances and resistors are commonly used, often without alear physical justification for each element [16,20,21].

The goal of this paper is twofold. First, we want explore the com-lementarity of the sensitivity of EIS with the spatial resolution ofRI in a study of water ingress in a polymeric film. Secondly, we aim

o understand how EIS spectra are related to the water distributionn a polymer film during uptake. To this end, the water uptake in

200 �m nylon 6 film is measured and the recorded impedance isxamined and compared with water distributions measured withRI [6].First the EIS data is examined and the water uptake process

s split in three stages. As a next step this data is modeled/fittedsing electrical equivalent circuits. Using the water distributionseasured with MRI, the EIS impedance data is easily explained.

he block-shaped waterfront leads to a simple model for predic-ion of the film capacitance. The predicted film capacitance shows

good agreement with the EIS impedance at a frequency of highrequencies.

. Experimental

.1. Sample preparation

In this study we used 200 �m thick nylon films. The used nylons the commercially available polyamide 6 (Akulon K123, Mw =2, 000, DSM, The Netherlands). Before using any sample it is stored

n an oven at 100 ◦C for 5 h in order to remove residual tracesf moisture from the film. To measure the degree of crystallinityf the samples, differential scanning calorimetry measurementsDSC) using a Mettler 822e are conducted. DSC measurements areonducted with a heating rate of 10 K min−1 in a range between53 K and 533 K. Analysis of the melting peak, using a value of40 J g−1 [22,23] for the melting enthalpy, results in a crystallinityf 23%.

For EIS measurements, the nylon is pressed on a 2 mm thick alu-inum plate. Before application of the nylon layer, the aluminum

late is sandblasted in order to create a rougher surface for betterdhesion. A spacer of 200 �m is put on the aluminum plate and itsnner space (7 cm × 7 cm) is filled with nylon pellets. Subsequentlyhe aluminum plate with the nylon on top is sandwiched betweenwo steel plates and is compression molded at a temperature of80 ◦C for 10 min.

Films for MRI and dielectric measurements are prepared by

ompression molding of pellets between two steel plates, sepa-ated by a spacer of 200 �m. Square films (24 mm × 24 mm) with

thickness of 200 �m are obtained in this way. For the MRI waterptake measurements, the films are cut into circular disks with

ca Acta 94 (2013) 219– 228

a diameter of approximately 11 mm. These disks are attached toa 140 �m thick microscope cover glass using silicone glue (type:Dow Corning 3140). Subsequently, a glass cylinder is glued on topof the cover glass surrounding the nylon film.

For the dielectric measurements films obtained by compres-sion molding are exposed to specific values of relative humidity(RH). Humid conditions are defined by using saturated aqueous saltsolutions. Samples are stored over these salt solutions in a closedcontainer for a period of a week to fully saturate the sample.

2.2. Methods

2.2.1. EISElectrochemical impedance spectroscopy measurements are

conducted over the frequency range from 0.05 Hz up to 1 × 105 Hz.The measurements are done at open circuit potential using a volt-age amplitude of 5 mV. A PMMA tube with an inner radius of1.85 cm is clamped onto the nylon coated aluminum and is sub-sequently filled with 0.05 M NaCl solution. An Ag/AgCl referenceelectrode is used in combination with a platinum mesh as thecounter electrode. The measurement and acquisition system con-sists of a Solartron 1286/1287 electrochemical impedance analyzer.To ensure the reproducibility of the experiment the complete wateruptake process is measured four times.

2.2.2. Dielectric spectroscopyThe dielectric constants of equilibrated films are determined by

using a Novocontrol setup containing a HP precision LCR meter(type: 4284A) and a standard sample cell (type: BDS1100). Thefilms are clamped between two gold plated parallel electrodes witha diameter of 2 cm. A sinusoidal wave with a root mean squarevoltage of 0.1 V is applied in a frequency range between 20 Hz and1 MHz. To increase the accuracy the number of averages is set to 4.

2.2.3. MRIFor a detailed description of the MRI setup we refer to the

literature [6,24,25]. Here the most important issues are brieflydiscussed. A MRI setup in the GARField arrangement is used to mea-sure the water uptake process [10]. Specially shaped magnet polesgive a magnetic gradient of 43 T m−1 at a static field of 1.4 T. TheOstroff–Waugh pulse sequence is used to measure the water uptakeprofiles (˛o

x − � − [˛oy − � − echo − � − ]n) [26]. Using a nominal flip

angle ̨ of 90◦ and a 1 �s pulse, only the first echo (n = 1) is utilizedfor imaging purposes. The inter echo time 2� is set to 100 �s andthe acquisition window is 90 �s. These settings result in a spatialresolution of 6 �m.

2.3. Impedance

2.3.1. Equivalent electronic circuitsImpedance measurements are performed by application of an

oscillating potential over a material and recording the resulting cur-rent. The ratio of the potential with respect to the current is calledthe impedance and can be decomposed in a magnitude and phaseangle. This section will explain the necessary electric elements tofit or model the data resulting from an EIS experiment.

If the current is in phase with the applied potential, the materialacts as a resistor and the resistance is equal to the impedance. Incase the system behaves as a capacitor, the current will exhibit aphase lag of 90◦. The impedance Z/� of a capacitor is a function ofthe capacitance C/F and the angular frequency ω/rad s−1

Z = 1jωC

, (1)

where j is the imaginary number, j2 = −1.

chimica Acta 94 (2013) 219– 228 221

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Z

Tfiωfe

2

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3

bEb

(a)

(b)

Fig. 1. The magnitude (a) and phase angle (b) during water uptake of a nylon 6film as measured with EIS. Based on these measurements the water uptake processcan be divided into three stages. In the first stage I (0 < t < 3 h) capacitive behavioris observed. During the second stage II (3 < t < 5 h), resistive behavior is measured at

N.J.W. Reuvers et al. / Electro

A non-ideal dielectric material can be considered as a paral-el circuit of an ideal capacitor and a resistor [19]. The resistorescribes the energy dissipation of the material [27], which cane due to the switching of dipoles or to the movement of ions (e.g.H−, H+, Na+, Cl−) under influence of the electric field. Movementf charge carriers results in conduction and conduction is promotedhen the material is plasticized and contains water [16]. Many sys-

ems do not behave as a perfect capacitor. Several explanations forhis phenomena are encountered in literature, such as the pres-nce of a double layer, non-homogeneous coating composition, thexistence of polarizable groups and dipole relaxation [28–31]. Toodel a non-ideal capacitor a so called constant phase element

CPE) or imperfect capacitor can be used [32]. A CPE improves theatch with the measured data as the capacitance is made frequency

ependent. The impedance of a CPE is [31]:

CPE = 1Q

(jω)−n = 1Q

ω−n[

cos(

−n�

2

)+ j · sin

(−n

�

2

)]. (2)

he impedance of a CPE is a function of the amplitude Q /sn �−1 andtting factor n, the imaginary number j and the angular frequency/rad s−1. For n = 1 the CPE is equal to a normal capacitor (Q = C) and

or n = 0 it is equal to a resistor (Q−1 = R). The phase angle of this CPElement over the complete frequency range is equal to −n�/2.

.3.2. Impedance and water uptakeThe analysis of electrical elements to evaluate the impedance

ata was discussed in the previous section. Hereafter, methods toalculate the diffusion coefficient and the water volume fractionre discussed.

The diffusion coefficient characterizes the rate of water uptake,hich can also be estimated from EIS measurements. The first

ssumption for estimating the diffusion coefficient is that the pro-ess is Fickian [5,15,16,20,33]. For a Fickian diffusion process, theiffusion constant is not a function of the concentration. How-ver, for many polymer solvent systems the diffusion coefficients a function of concentration [6,34,35]. Although in many cases noxperimental evidence exists, it is assumed that the uptake processs Fickian.

The second assumption is that a change in capacitance is directlyoupled to a change in moisture content. Assuming that all wateranifests itself in the same way, effects like plasticization andater/polymer interactions are neglected. For a Fickian process the

elation between the amount of uptake and the diffusion coeffi-ient can be found in textbooks [36]. The measured capacitance iset equal to the theoretical mass uptake curve that is known for aickian uptake process. In practice the rate of change of the capaci-ance at the start of the experiment is taken to estimate the diffusionoefficient [20,37].

In electrochemical impedance studies the water volume fractions frequently calculated on the basis of the Brasher–Kingsbury equa-ion [13]. In this equation, the water volume fraction � is calculatedrom the capacitance of the film Cf(t)/F at any time and the capac-tance at the start of the experiment Cf(0)/F. Taking the dielectriconstant of water to be equal to 80, the Brasher–Kingsbury equationeads:

= log(Cf (t)/Cf (0))log(80)

. (3)

. Results and discussion

First the result of the EIS water uptake measurements wille discussed and linked to MRI measurements. Afterwards, theIS measurements are modeled using equivalent circuits and theehavior at high frequency is examined.

low frequencies, being an indication for long distance conduction. The third stage III(t > 5 h)is characterized by an electrochemical process at the metal/nylon interface.

3.1. Stages in water uptake as revealed by EIS

The EIS measurements give information about the water uptakeprocess in the nylon layer. The acquired magnitude and phase angleof the EIS measurements during water uptake are shown in Fig. 1.The time between subsequent curves is 1 h. Based on the behaviorof the phase angle and impedance magnitude, the process data canbe divided into three stages.

During the first stage I (0 < t < 3 h), the phase angle displaysa capacitive behavior with a phase angle � approximately equalto −90◦ over the whole frequency span. The magnitude |Z|/�, asshown in Fig. 1, also displays a capacitive behavior at the start ofthe process (t = 0 h), as indicated by the slope of −1 in the loglog plot.

During the first 3 h the phase angle is independent of frequency, butdrops slowly from −90◦ to about −80◦ over the whole frequencyspan. At the start of the experiment, the nylon film is exposed to

2 chimica Acta 94 (2013) 219– 228

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Fig. 2. Moisture content profiles as obtained from calibration of MRI measurements.The top of the film at the water/nylon interface corresponds to the left side of the

22 N.J.W. Reuvers et al. / Electro

he saline solution and water will start to enter the film. The largestart of the film consists of dry material, which will result in a capac-

tive behavior. Water uptake is visible by a decrease of |Z| since thelm capacitance decreases.

In the second stage II (3 < t < 5 h) the phase angle rapidly dropsn the low frequency range f < 10−1 Hz. The most significant drops exhibited at a frequency of 10 Hz, where the phase angle dropso about −5◦. At 3 h, the magnitude curves starts to deviate fromapacitive behavior as the slope changes toward zero at low fre-uencies. When water penetrates the film, it enhances conduction

n several ways: by mobilization of the polymer matrix and theresence of water itself. Already at 3 h, the phase angle shows signsf a conducting mechanism at a frequency of 10 Hz. This indicateshat at least traces of water have reached the aluminum substrate.

During the third stage III (t > 5 h), the transition from resistiveo capacitive behavior shifts toward higher frequencies. The mag-itude curves in Fig. 1(a), at a time of 5 h, show a horizontal linet low frequencies up to 200 Hz and a slope of minus one at higherrequencies. So, a change from resistive to capacitive behavior is

easured at 200 Hz. After 10 h the phase angle goes toward zerond the magnitude has a plateau at frequencies lower than 200 Hz.his indicates that conduction is taking place throughout the wholelm, implying that the film has to contain a significant amountf water, even at the nylon/metal interface. At high frequencies

> 1000 Hz charge carriers do not have the time to move through-ut the whole film and capacitive behavior is observed at theserequencies. The conductivity at low frequencies when introducing

oisture is in agreement with observations of other authors forylon 4.6 [38].

Another interesting characteristic of the last stage (t > 5 h) is theevelopment of a minimum in the phase angle at approximately0 Hz. This phenomenon is often attributed to electrochemical pro-esses occurring at the interface, such as the formation of a doubleayer [39,40]. This further indicates that a significant amount of

ater is present at the nylon/metal surface.

.2. Comparison with MRI water profiles

Three stages in the uptake process were identified in the previ-us section. In this section, these stages are compared with wateristributions measured with MRI. Therefore, the three stages inhe water uptake process are re-examined together with the wateristributions measured with MRI.

Fig. 2 shows water distributions as measured with MRI. In previ-us work it was shown how MRI signal intensities can be quantifiednd converted to moisture content � [%] [6]. Moisture content isefined as the percent of weight increase with respect to the dryituation and is shown on the y-axis of Fig. 2. The horizontal axishows the distance in micrometer from the water/nylon interface.he water on top of the film is shown on the left of the figure. Theignal from the liquid water on the left is lower than the signal inhe film because of the relatively long T1 of the water with respecto the repetition time of the MRI experiment (tr/T1 < 1). The glueayer underneath the film is shown on the right side of Fig. 2. Theotted line is the noise level of the MRI measurements and indi-ates that the first 2% of moisture cannot be detected using MRI. Inhe figure, the first MRI profile (17 min) is shown together with therofiles for 3, 5, 10 and 16 h.

The impedance data showed that the system behaves capacitiveuring the first 3 h. This behavior shows the absence of conduct-

ng pathways and thus the absence of pores and holes in the dry

lm. The capacitive behavior is explained by the existence of a dryottom layer, acting as an insulator, which is supported by the MRIeasurements in Fig. 2. This figure shows that only the top 125 �m

ontains a significant amount of water after 3 h of water uptake.

figure. A moisture content below 2% cannot be measured with 1024 averages asindicated by the noise level, the horizontal dotted line. The first measurement at0.3 h is shown together with measurements at times of 3, 5, 10 and 16 h.

The second stage (II) of water uptake takes place from 3 to 5 h.During this time span a resistive component is measured with EIS atthe low frequencies that is attributed to conduction. Charge carrierscan move from electrode to electrode. From the MRI measurementsit is concluded that the waterfront as defined for � above the noiselevel (�> 2 %), has not reached the bottom in this period. The com-bination of MRI and EIS here proves that small traces of water aremigrating ahead of the main waterfront as observed by MRI. Thisillustrates the sensitivity of EIS to small amounts of moisture, aswater is detected at the substrate, before this is measured withMRI. With MRI there is no moisture at the bottom measured beforethe end of this second stage (t = 5 h).

During the final (t > 5 h) stage, a minimum in the phase angleis formed, which is attributed to water accumulating at the inter-face. The frequency range in which resistive behavior is measuredis shifting toward higher frequencies, which is attributed to fur-ther plasticization of the nylon. The MRI profiles show that waterhas reached the substrate but the amount of water is still increas-ing at the substrate. The upper part of the film is almost saturated.This gives rise to increasing plasticization in the whole film. As thepolymer matrix becomes more mobile charge carriers can movemore freely throughout the film. In the EIS measurements, this isobserved by a resistive behavior that shifts slowly to higher fre-quencies. Because of the bottom of the layer is filling up with water,also more water will accumulate at the nylon/metal interface. Theaccumulation of water at the interface is also detected with EIS asthe formation of a minimum in the phase angle.

3.3. Equivalent electrical circuit modeling of EIS data

In Section 3.2 a phenomenological interpretation of theimpedance data is given. Now we know the water distributionsobserved with MRI, equivalent electrical circuits [12,16] are usedto obtain information by fitting the impedance data. Fitting givesquantitative information about the resistance and capacitance ofthe nylon film as fluid enters the film.

Constant phase elements are used to get a better match with the

data, although their physical origin is still a matter of discussion.Several options for the physical origin of the CPE and correspondingfrequency dependent behavior are encountered in literature, suchas rough electrode surfaces, variation of coating composition, the

N.J.W. Reuvers et al. / Electrochimica Acta 94 (2013) 219– 228 223

Re Rf

Qf,1

Qx

I

Fig. 3. Equivalent circuit used to model or fit the water uptake process in the nylonfilm during the first 3 h. The resistance of the electrolyte is Re . The capacitive behavioronc

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Fig. 4. The fit parameters from the equivalent circuits as a function of time. Thevertical dotted lines define the three stages of uptake as discussed earlier. The mainfocus of (a) should be on Qf,1 and Qf,2 and their continuity as a function of time.The corresponding n-values to the constant phase elements are plotted in (b). TheQf,2 describes the resistive (nf,2 < 0.2) behavior of the film and its value shows thatduring the time span from 3 to 5 h water reaches the bottom. The film CPE Qf,1

remains capacitive as nf,1 drops to maximal 0.8 during the water uptake. At the startof an uptake experiment the film resistance Rf and Qx are needed to describe subtleeffects in the data. Starting at 5 h a process occurring at the interface is measuredand fitted by Q . Furthermore, the inset in (b) shows the position of the waterfront

f the nylon film during the first 3 h is modeled with a CPE with amplitude Qf,1 andf,1. The upper branch containing Qx , nx and the film resistance Rf is introduced toompensate for the small minimum in the phase angle at 200 Hz.

xistence of a double layer and dissipative processes [39,28–30]. Aumber of dielectric spectroscopy measurements have been per-

ormed to investigate the origin of the CPE in this study. Dielectriceasurements have been performed on nylon films equilibratedith water vapor at a certain RH. In these dielectric measurements

he phase angle also shows a similar slow variation as a functionf frequency when the nylon film is almost saturated with mois-ure. In EIS measurement the same frequency dependent effect inhe phase angle is observed and this effect is described by the n-arameter in the CPE. Assuming the film to be a parallel R-C circuit,he phase angle drop as a function of frequency is caused by dis-ipation in the resistance. Dissipative processes are characterizedy the imaginary part of the dielectric constant or the loss factor27]. Dielectric spectroscopy measurements showed that the lossactor appears to be dependent on the amount of moisture in thelm. The loss factor increases with increasing moisture content.ore moisture gives rise to plasticization and more mobility. This

nables molecules, dipoles and ions to follow the electric field andhereby absorb energy. A high loss factor and dissipative processesn polyamides are attributed to motions of methylene and amideroup or even the polymer backbone [41]. This was also found byn other author [42]. Energy dissipation as a result of moisture andlasticization in the nylon is the physical origin of the CPE in thistudy.

The three stages during water uptake and their modeling willow be discussed. The water uptake during the first 3 h (I) isodeled with the circuit in Fig. 3. The lower branch in Fig. 3 is the

lm capacitance Qf,1/sn �−1, which is modeled by a CPE. This CPEhould be continuous throughout the process and is described byts amplitude Qf,1 and parameter nf,1. As in many corrosion/coatingtudies the amplitude (Q in Eq. (2)) of the CPE is considered to char-cterize the system [17,32]. The electrolyte is modeled by Re/� with

value of 0.177 �. The film resistance Rf is equal to 3.5 × 106 � andonstant during the first 3 h. Together with CPE Qx/sn �−1 with nx,he resistance Rf/� is used to model the minor drop of the phasengle at approximately 200 Hz as seen in Fig. 1(b).

At the start of the first stage the film is dry. This dry state isnalyzed first. For the dry film n = 1 indicating that the CPE behavess a perfect capacitor. Using properties of the dry film as input,he capacitive impedance at the start of the experiment can benderstood by estimation of the capacitance and resistance of thery film. The capacitance of a dry film can be approximated byq. (1), using a dielectric constant � of 3 [43]. This gives a capac-tance of 1.4 × 10−10 F, which is close to the value of our firstt/measurement for the film CPE (Qf,1 in Fig. 4(a)). A dry nylon filmas a resistance of 1 × 1015 � [44]. Considering the film to be a par-llel R-C circuit, the frequency at which the system switches fromesistive to capacitive behavior is given by 1/(RC). For the dry nylonlm a frequency of 1 × 10−5 Hz is calculated. Since the measure-ents start at 0.1 Hz, only capacitive behavior is observed in a dry

ayer.

During the first 3 h (stage I) the EIS measurements show a capac-

tive behavior since the phase angle is constant and close to −90◦

nf,1 = 1) over the whole frequency range, Fig. 1(b). The film con-tant phase element (CPE) Qf,1 increases slightly but the spectrum

int

normalized by the film thickness. This gives an overview of the water uptake duringthe first 5 h as determined from the MRI profiles (◦).

is capacitive since the n-values nf,1 are close to one, as can be seenin Fig. 4(b). The overall behavior of the circuit is capacitive. Therelative importance of the upper branch containing Qx and Rf isnow shown by a simple estimation. The presence of Rf in the upperbranch gives an impedance difference with respect to the lowerbranch of 1 × 107 �. Meaning that the relative importance of Qx

and Rf is small. Its existence might be attributed to a process at the

water/nylon interface during this first stage. The low impedance ofQf,1 makes this film CPE the dominating process during the first 3 h.

During the first 3 h the impedance is dominated by the capaci-tive behavior of the film as fitted by Qf,1/sn �−1. Although the upper

224 N.J.W. Reuvers et al. / Electrochimica Acta 94 (2013) 219– 228

II

Qf,2 ( nf,2<0.2)

Qf,1

Re

Fig. 5. The equivalent circuit for the second stage (II) from 3 to 5 h. Just like in Fig. 3,CPE Qf,1 describes the capacitive behavior of the film. Conductive effects are modeledbb

peol[

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fitp

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a

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Fig. 7. A comparison between measured data and results of the equivalent circuit

y Qf,2 with nf,2 ≤ 0.2. Conductance becomes more pronounced after 3 h as is showny the increase of Qf,2 in Fig. 4(a).

art of the nylon film is water saturated at 3 h its conducting prop-rties are not visible in the EIS data. This is due to the dry lower partf the film which does not contain water as observed by MRI. Thisower part is not plasticized: i.e. it acts as a barrier for conduction45,46].

In the second stage (II) the phase angle drops significantly,s shown in Fig. 1(b), and this is now dominating the spectrum.n this period the elements Qx and Rf are removed and a sec-nd CPE is introduced Qf,2/sn �−1 with factor nf,2, see Fig. 5. Asts n-value is close to zero (nf,2 < 0.2), Qf,2 mainly behaves as aesistor. The film CPE Qf,1 is continued from the first stage andncreases significantly, see Fig. 4(a). This CPE increases due to thencrease of the dielectric constant, meaning that a large amountf water is entering the film. Moisture increases the conduc-ance in the film, leading to the introduction of Qf,2 to describehe resistive properties of the film. This conduction mechanisms now dominating the spectrum and Qx cannot be distinguishednymore.

The sharp increase of Qf,1 indicates that water is entering thelm, but also that the water uptake is not finished at t = 5 h. Fur-hermore, water reaches the metal substrate through conductingathways, considering the resistive behavior of Qf,2.

Water moves through the conducting pathways to the metalubstrate and causes interface processes in the last stage (III) of theater uptake process (t > 5 h). For this reason the electronic circuitodel had to be extended with a CPE in series with Qf,2 to describe

nterface effects: Qint with nint, see Fig. 6 [16,37,39]. Constant phaselements Qf,1 and Qf,2 are continued from the previous stage. Thelm capacitance Qf,1 is about stationary, which indicates that theylon film is almost saturated. The film starts to fill up completelynd this increases the conductance even further. This increase inonductance is fitted by the increase of Qf,2 (nf,2 = 0). As nf,2 = 0 forf,2, this CPE acts as a perfect resistor. The decreasing impedancean be seen as an increase of the CPE magnitude or decrease of theesistance. Water accumulating at the aluminum/nylon interfaceives rise to the formation of interface processes, leading to a min-mum in the phase angle and a trend to display more phase lag at

frequency of 0.1 Hz. Interface processes are introduced in the cir-uits by Qint/sn �−1 and nint. The nature of this interface process is

ound by fitting the CPE to the data and includes both a resistivend capacitive component as nint = 0.85.

To verify the quality of the fit a comparison between the equiv-lent circuits and the measured data is shown in Fig. 7. The figure

III

QintQf,2(nf,2 =0)

Qf,1

Re

ig. 6. The equivalent circuit for the last part (t < 5 h) of the uptake process, stage (III).ust like in the previous two stages CPE Qf,1 describes the capacitive behavior of thelm and Qf,2 the conductive behavior. Conductive effects are modeled by Qf,2 withf,2 = 0. The minimum in the phase angle at 10 Hz is a result of interface processesnd is described by Qint .

modeling. (a) The magnitude of the impedance and (b) the phase angle. Measuredcurves are shown for each stage of the uptake process, at, respectively, 2, 4 and 10 h.The equivalent circuit data is shown with symbols at 2 h (�), 4 h (◦) and 10 h (�).

shows the phase angle and magnitude of the impedance as a func-tion of the frequency. The phase angle is used to compare the resultof the fitted models and the data, because it contains more detailsthan the magnitude. Curves are shown for a time of 2, 4 and 10 hduring uptake.

During the second stage (3 < t < 5 h) the largest discrepancybetween the chosen circuits and the data is found with a chi-squared of 0.008. At a time of 4 h it can be seen in Fig. 7 that the maindifference is located at frequencies higher than 1 × 104 Hz which isnot troublesome because all significant changes take place at lowerfrequencies. The chosen circuits give a good representation of thedata.

Now we know the exact relation between the EIS spectra and thepresence of water in nylon-6, the film capacitance is used to esti-

mate a diffusion coefficient that describes the water uptake process.Assuming a Fickian diffusion process, the time needed to reach astationary value for the film CPE Qf,1 is used to estimate the diffusioncoefficient. For a Fickian diffusion process, the relation between

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he film thickness l/m, time t/s and the diffusion coefficient D is: =

√4Dt. The CPE Qf,1 takes 5 h to become stationary. Using a film

hickness of 200 �m and assuming a Fickian diffusion process thestimated diffusion coefficient is 1.8 × 10−12 m2 s−1. This value is inine with diffusion coefficients on the basis of MRI measurements6], ranging from 10−14 to 10−12 m2 s−1 showing a distinct non-inearity. However, as EIS is a bulk method, no information abouthe concentration dependency of the diffusion coefficient can bebtained.

The modeling of the impedance data revealed severalhenomena. During the first 3 h the spectrum remained capaci-ive, revealing the domination of the dry part in this time span.t 3 h a change toward resistive behavior is detected revealing

hat at least small amounts of water have reached the alu-inum substrate of the film. Even though small amounts of water

ave reached the substrate more water is still entering the films is observed by the gradual but significant increase in Qf,1.nother phenomena, detected from 5 h onwards, is the accumu-

ation of water at the interface and the formation of a doubleayer. Furthermore an approximated diffusion coefficient is cal-ulated, which is in agreement with values found in an earliertudy.

.4. High frequency data and the waterfront

The MRI measurements show that the main part of the waterigrates through the film with a reasonable sharp front (see

ig. 2). Assuming a totally sharp front, the capacity of the filman be modeled by two capacitances in series. The model is com-ared with the EIS measurements at high frequencies to seehether this ingressing waterfront also can be extracted from EISeasurements.At high frequencies the EIS measurement also shows capacitive

ehavior and this is used for a evaluating the results of the model.he spectrum is considered to be capacitive at high frequenciesven though the phase angle drops from −90◦ to −75◦ during theater uptake. Loss phenomena, like long distance conduction, doot occur at higher frequencies and the material exhibits capacitiveehavior with a phase angle of −90◦. At high frequencies the motionf charge carriers is suppressed and the impedance of the film isainly determined by the dielectric constants of the wet and dry

art of the film. Therefore, the waterfront can be modeled by aeries circuit of two capacitances. The predicted capacitance fromhis model will be compared with the EIS data at a frequency of

× 105 Hz.

ig. 8. The film capacitance during the first 5 h as calculated from the EIS data (�) and eqy the capacitance model (b). (a) The capacitive part of the film from equivalent circuit mata at 1 × 105 Hz. (b) The capacitance as calculated from our model. To calculate Ct MRI mptake. The dotted lines for Ct show a the result of a 10 �m thickness variation.

ca Acta 94 (2013) 219– 228 225

First the total capacitance of the coating is calculated from theEIS data, assuming the film to be a parallel RC-circuit, where Cand R are functions of the frequency ω. The relation between theimpedance and the total capacitance C is given by:

C(ω) = − Zi

|Z|2ω. (4)

In this equation is Zi/� the imaginary part of the impedanceand |Z|/� is the magnitude of the impedance. The total coatingcapacitance at high frequency CHF/F is calculated from the EIS mea-surements at a frequency of 1 × 105 Hz using Eq. (4). The resultingcapacitance is plotted as a function of time in Fig. 8(a) up until atime of 5 h when the water has reached the bottom of the nylonfilm.

The capacitance is increasing when time progresses. This is dueto the increasing wet part of the film with a high dielectric con-stant as the waterfront progresses. More water into the nylon filmincreases the capacitance, since a higher dielectric constant of thewater fraction is involved [17].

For comparison, the capacitive part of the film CPE (Qf,1) usedin the equivalent circuit modeling is calculated by combining theEqs. (2) and (4). This calculation is done at 1 × 105 Hz. The result ofthis calculation is shown as CHF

f,1 /F (◦) in Fig. 8(a). The datapoints inFig. 8(a) show a discontinuity at 3 h. At 3 h the uptake process entersthe second stage (II) and a switch is made from one equivalent cir-cuit to another. This results in a discontinuity in CHF

f,1 . Nevertheless,from Fig. 8 is concluded that the capacitance calculated from theequivalent circuit modeling CHF

f,1 is in good agreement with the val-

ues of CHF. It is concluded that the same information about wateruptake is obtained either by fitting or by direct calculation of thecapacitive properties at a frequency of 1 × 105 Hz. The capacitivebehavior of the nylon film dominates the impedance at high fre-quencies.

To model the data at 1 × 105 Hz, a capacitance model isintroduced. This model considers water ingress as a change inthickness of a dry and a wet layer. The thickness of the wet layerincreases, while the thickness of the dry layer decreases as wateringresses. The relation between the capacitance of a parallel platecapacitor and the spacing of the plates is given by: C = (��0A) d−1,wherein A/m2 is the surface area, d/m is the spacing of the plates,

�0/F m−1 is the permittivity of free space and � is the dielectricconstant of the layer material. The capacitance model is shown inthe inset of Fig. 8(b), where the capacitors represent the wet anddry parts of the film. The capacitance of the total film Ct/F can be

uivalent circuit modeling (◦) at high frequency (a) and the capacitance calculatedodeling is equal to the capacitive part as directly calculated from the impedance

easurements are used as input for the position of the waterfront in the film during

2 chimi

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stant is not equal to 80. For nylon, it is known that part of absorbedwater strongly interacts with the polymer in the form of hydrogenbonds. Furthermore, the increase in dielectric constant is not solelydue to water. The nylon film will be plasticized by the water, which

26 N.J.W. Reuvers et al. / Electro

elated to the capacitance of the wet Cw/F part and the dry part Cd/Fs follows:

1Ct

= 1Cw

+ 1Cd

. (5)

he capacitances Cd and Cw can be substituted by the expressionor a parallel plate capacitor. This leads to:

1Ct

= f

�w�0A+ d − f

�d�0A. (6)

he total thickness of the film is d and the area exposed to salineolution is A. The total film thickness d is equal to 200 �m. Therea A is 10.8 × 10−4 m2 and the permittivity of vacuum �0 is.85 × 10−12 F m−1. The dielectric constant of the wet and dry part

s �w and the dielectric constant of the wet part is �d. The size of theapacitor representing the wet layer is given by the position of theaterfront with respect to the top of the film as given by f/�m. The

ize of the dry capacitor decreases proportionally with the frontosition and is given by d − f/�m.

To validate the model Ct is calculated by using the front positions obtained with MRI and compared with CHF obtained with EIS.he front position f is defined as the position of the front at 2%oisture content, i.e. the smallest amount of water detectable by

ur MRI setup. The position of the front, scaled by the film thickness,s shown in the inset of Fig. 4(b). The capacitance Ct increases fasturing the first hours whereafter the rate of increase slows down.his is explained by the water distribution, see Fig. 2. The largeoncentration gradient when the nylon is still dry, causes the fronto cover 50 �m within the first 17 min. After 1 h the front speedlows down and the front reaches the bottom of the film just before

h.Additionally the dielectric constants of the wet and dry zones

re needed in order to predict Ct. These dielectric constants areased on the high frequency capacitance CHF. The value for the drylm is calculated on 0 h and at 5 h the value for the wet film is cal-ulated. The dielectric constants of the dry �d and wet �w zonesre 5 and 14, respectively. In order to verify these values dielec-ric spectroscopy measurement have been performed. From theielectric spectroscopy measurements the real part of the dielectriconstant at 1 × 105 Hz is taken for this comparison. The resultingalues are 3 and 9 for the dry and wet system, respectively. Theielectric constants based on CHF and the values from the dielectricpectroscopy measurements are listed in Table 1.

There is reasonable agreement between the dielectric spec-roscopy values and the ones calculated from CHF. The discrepancyan be attributed to poor contact between the measuring electrodend the nylon film. The existence of thin air layer lowers the effec-ive value of the dielectric constant.

Fig. 8 shows CHF as taken from the EIS measurements and theapacitance Ct as calculated by the model. A source of error in thisodel to calculate Ct are small variations in the film thickness.

mall variations are likely present as the EIS measurements require rather large area of 10.8 × 10−4 m2. A local thickness variation of

0 �m results in different capacitive values as the dotted lines inig. 8(b) show. The model is able to predict the trend of the highrequency capacitance CHF, given its sensitivity for small and localariations of the film thickness.

able 1ielectric constants calculated from CHF and values measured with dielectric spec-

roscopy. The higher dielectric constant of water increases the dielectric constant ofhe nylon film when containing water.

Dielectric spectroscopy CHF

Dry 3 5Wet 9 14

ca Acta 94 (2013) 219– 228

As the waterfront runs into the film, the thickness of the wetlayer of film increases. The question arises, when the capacitanceof the wet part of the film Cw gives a significant contribution to thetotal film capacitance Ct. It is concluded from the equivalent circuitmodeling that the behavior is only completely capacitive duringthe first 3 h, see Fig. 4(b). The influence of the wet part can directlybe shown through application of the front model. To determine therelative importance of the wet part of the film in the high frequencyapproach, Eq. (6) is rewritten into:

1Ct

= 1Cw

(Cw

Cd+ 1

). (7)

In this equation Cw refers to the capacitance of the wet part of thefilm and Cd to the dry part of the film. The importance of the dry partis given by the ratio Cw/Cd. If this ratio is larger than one, the capac-itance of the dry part has a larger influence on the total capacitanceCt than the capacitance of the wet part.

The ratio Cw/Cd is plotted as a function of time in Fig. 9. After3.5 h the ratio Cw/Cd is equal to one, which marks the transitionfrom dominance of the dry part to dominance of the wet part. Thisfinding is consistent with earlier conclusions from the equivalentcircuit analysis. During the first stage I (0 < t < 3 h) the behavior wascompletely capacitive as now is understood by the domination ofthe dry part. After 3 h the behavior starts to deviate from capacitivebehavior as shown by the film CPE Qf,1, nf,1 in Fig. 4(b). It is con-cluded that the wet part of the film also starts influencing the highfrequency part of the EIS measurements after 3 h of uptake.

Using the capacitance CHF as the film capacitance the watervolume fraction can be calculated using the Brasher–Kingsburyequation (3) [13,19,47]. During the first 5 h of water uptake the filmcapacitance approximately doubles as shown in Fig. 8(a). A value of80 for the dielectric constant of water gives a water volume fractionof 0.18. This means that 18% of its volume or 16% of its mass wouldbe occupied by water. As the maximal absorbed amount of mois-ture for this material is equal to 7.5% [6], the number calculatedby the Brasher–Kingsbury equation is too high. The mismatch canbe explained through the existence of swelling and interactionsbetween water and polymer by hydrogen bonding [48]. Water isnot residing in the film as free/liquid water, so its dielectric con-

Fig. 9. The ratio of the capacitance of the wet part Cw and the capacitance of the drypart Cd as a function of time. This figure shows that the capacitance of the wet partbecomes dominant after 3.5 h.

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ill also lead to an increase of the dielectric constant � as illus-rated by the dielectric temperature/moisture study of Steeman and

aurer [38]. Consequently, the moisture fraction in nylon 6 can-ot be calculated on the basis of the Brasher–Kingsbury equation,ecause of the occurrence of swelling, polymer water interactionnd plasticization.

Finally it is concluded that the main part of the water runshrough the film as a sharp front. The series capacitance modelsing the position of the waterfront and the dielectric constants as

nput is able to predict the capacitive part of the EIS impedance at frequency of 1 × 105 Hz. The capacitive part as calculated directlyrom the EIS data is remarkably similar to the capacitive part ofhe film CPE Qf,1 as fitted in the equivalent circuit modeling. Bothive the same information about the waterfront. The series capac-tance model also revealed that the dry part of the film dominateshe impedance behavior up until 3 h, which is in agreement withndings from equivalent circuit modeling.

. Conclusions

The water uptake of 200 �m thick nylon 6 films is studied withlectrochemical impedance spectroscopy (EIS) and MRI measure-ents.Based on the EIS measurements the uptake process is divided

nto three stages. During the first stage of water uptake the spec-rum as measured by EIS is capacitive. When this first stage ends the

RI measurements show that at the bottom of the film a dry parttill exist. The water has only penetrated the top of the nylon filmnd a dry layer still exist, which dominates the impedance behaviornd results in the capacitive spectrum.

During the second stage the EIS spectrum becomes resistive.mall amounts of water reach the substrate and lower the resisti-ity of the film. Charge carriers are now able to move from electrodeo electrode. The MRI is only able to measure moisture quantitiesarger than 2%. The MRI profiles show that the bulk part of the waters close to the substrate at the end of this stage. EIS has a higher sen-itivity showing that small amounts of moisture precede the fronts measured by MRI. The film resistance, as fitted by equivalent cir-uits, shows a sharp decrease in the period from 3 to 5 h, indicatinghe existence of conduction from electrode to electrode.

Although only the leading edge of the waterfront has reachedhe substrate at the start of the third stage the film is not fullyaturated. The film becomes gradually more and more saturated aseen by both MRI and EIS. In the equivalent circuits modeling this isetected by a stationary film resistance. The EIS spectra show a min-

mum in the phase angle, which indicate the presence of electroderocesses.

The majority of the water moves into the nylon with a block-ike front as observed in MRI measurements. By means of a simpleapacitance model the position of the waterfront is coupled to theotal film capacitance. This model establishes the relation betweene MRI data and the EIS measurements, as the calculated filmapacitance from the model and the capacitance from the EIS mea-urements show the same trend and matching values. The positionf the waterfront in the nylon film is successfully coupled to thempedance measured with EIS at a frequency of 1 × 105 Hz. This

eans that the movement of the main amount of water into the filman be measured both by EIS and MRI imaging. Furthermore thisnderlines the validity of simplifying a nylon film with an ingress-

ng waterfront in two layers with distinct dielectric properties, with high and a low dielectric constant, respectively.

EIS is able to detect small traces of water which cannot beetected by MRI. The impedance data combined with the wateristributions from a MRI study are successfully used to furthernderstand the water transport in nylon 6.

[

ca Acta 94 (2013) 219– 228 227

Acknowledgements

This research is supported by the Dutch Technology FoundationSTW, which is part of the Netherlands Organization for ScientificResearch (NWO) and partly funded by the Ministry of EconomicAffairs, Agriculture and Innovation. The authors would like to thankHans Dalderop and Jef Noijen (TU/e) for their daily support. Forhelp with dielectric measurements we would like to thank HartmutFischer and Daan van den Ende (TNO).

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