In situ capacitance measurements for in-plane water vapor transport in paint films

Progress in Organic Coatings 74 (2012) 534–539

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In situ capacitance measurements for in-plane water vapor transport in paint films Weilong Zhang ∗ , Mark R. Jaworowski United Technologies Research Center, 411 Silver Lane, MS 129-90, East Hartford, CT 06108, United States

a r t i c l e

i n f o

Article history: Received 24 March 2011 Received in revised form 14 September 2011 Accepted 30 January 2012 Available online 21 February 2012 Keywords: Water vapor diffusion and transport In-plane transport Capacitance measurement Paint films Electrochemical impedance spectroscopy

a b s t r a c t A capacitance technique has been adapted to study in-plane water vapor transport in paint films. The technique requires an application of electrical contact materials on the paint film surface for capacitance measurements by electrochemical impedance spectroscopy (EIS). The capacitance obtained by EIS using Cu tape and Ag paste as the contact materials are presented. A direct comparison of capacitance and gravimetric measurements demonstrates that the change in the coating capacitance is quantitatively correlated with the total amount of in-plane water vapor transported in paint films. The water vapor diffusion coefficient derived from the capacitance technique agrees with one from the gravimetric method.

1. Introduction The water-transport properties of paint films, both in the through-plane and in-plane directions, are believed to be key factors affecting the corrosion protection performance of paint films. The relevance of water-transport behavior related to a paint film’s protective performance can be seen in the standard testing methods for coatings, such as the ASTM B117 salt spray test and the ASTM G85 series of cyclic corrosion tests. A number of techniques have been developed to investigate water uptake and transport in coatings, including gravimetric [1], capacitance [2–5], and spectroscopic methods [6–9]. The gravimetric technique is the most straightforward method that measures the weight gain or loss of water in coatings. Spectroscopic techniques, although reported as having a number of important advantages, require a sophisticated infrared instrument system. Capacitance techniques have been widely used to assess water transport in coatings [3–5,9–12]. These techniques are based on the assumption that the change in capacitance is due entirely to the water uptake and transport into the film. Because of a large difference between the dielectric constant of water (εw = 80 at 25 ◦ C) and that of the organic coating material (ε typically 3–4), when water penetrates into the coating, its dielectric constant increases resulting in an increase in the coating capacitance, hence, the coating capacitance

∗ Corresponding author. Tel.: +1 860 610 7413; fax: +1 860 660 1480. E-mail address: [email protected] (W. Zhang). 0300-9440/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.porgcoat.2012.01.020

© 2012 Elsevier B.V. All rights reserved.

can be used to understand the water transport in organic coatings. In-plane water transport properties are of special interest for paint and adhesive primer coatings. In the case of paint primers, certain failure modes such as undercutting and filiform attack are expected to be mediated by lateral water transport. In the case of adhesives and adhesive primers, through-plane water transport is generally not significant due to the geometry, and lateral water transport through the bondline is of primary importance. Unfortunately, the large majority of the literature on water transport in coatings has been limited to through-plane water absorption and transport, very little has been given to in-plane (lateral) water transport behavior in organic coatings [13], and there is no information on the isotropy of water transport in primer films. In this paper, we propose a capacitance technique for measurement of in-plane water vapor transport behavior in commercially available aerospace paint primer films. The technique requires an application of electrical contact materials on the paint film surface for capacitance measurements. The effects of using Cu tape and Ag paste as the contact materials on capacitance measurements are discussed. The purpose of this work is to validate the capacitance technique for in-plane water vapor transport from both experimental and theoretical aspects. 2. Theoretical background The capacitance technique is based on the assumption that the change in capacitance is due entirely to the water uptake and diffusion into the film. Two models were proposed to describe the

W. Zhang, M.R. Jaworowski / Progress in Organic Coatings 74 (2012) 534–539

effect of the water permeation in coatings on the capacitance measurements [14,15]. One is discrete model (DM) where the water is assumed uniformly distributed across the film, and the other is continuous model (CM) where a variable water distribution is present in the film. For a cylindrical paint film like the one (inner diameter about 3.5 cm, outer diameter of 6.0 cm) used in this work, the water concentration distribution C(r,t) is not uniform along the radial direction (Fig. 2(a)). According to the concept of CM model, the film can be divided in many parallel infinitesimal thick layers; each can be represented by a simple equivalent circuit consisting of a resistance dR, in parallel with a capacitance dC, as shown in Fig. 2. The capacitance dC is given by: dC =

ε0 ε(r, t) × 2r dr d

(1)

(r, t) d 2r × dr

(2)

where (r, t) and ε(r, t) are the resistivity and dielectric constant of the paint film, respectively, ε0 is the dielectric constant of vacuum (8.854 × 10−14 F/cm), d is the film thickness, and dr is the infinitesimal thickness. The total capacitance of the coated film at time t, Ct , can be calculated by integrating Eq. (1) over the entire electrode areas of the film as follows:





R

Ct =

R

dC(r, t) = 2 r0

r0

ε0 ε(r, t) 2ε0 × rdr = d d



R

ε(r, t) × rdr r0

(3)

The total resistance of the coated film, R(t), can be computed by integrating Eq. (2) over the entire coated areas of the film, as follows: 2 1 = R(t) d



R

r dr (r, t)

r0

(4)

In order to relate the dielectric constant of the paint film, ε(r, t), to the water concentration profile C(r, t), the Brasher–Kingsbury equation is used as follows: (r,t)

ε(r, t) = εdry × εw (r, t) =

(5)

ln[ε(r, t)/εdry ] C(r, t) = w ln εw

(6)

ε(r, t) = εdry exp[(ln εw /w ) × C(r, t)]

(7)

where (r, t) is the local water volume fraction of each infinitesimal thick layer, w is the density of water in the film, εdry and εw are the dielectric constant of the dry film and of pure water, respectively. By substituting Eq. (7) into Eq. (3), the total capacitance, C(t), then becomes: Ct =

2ε0 εdry



R

r × exp

d

r0

 ln ε

w

w

 C(r, t) dr

(8)

Note that using expansion of the exponential term in a MacLaurin series, Eq. (8) becomes: Ct =



2ε0 εdry d +

 1 ln ε 6

R

r0 w

w



2

ln εw 1 ln εw r × {1 + C(r, t) + C(r, t) w 2 w

3

C(r.t)

+ · · ·}dr

The total amount of water transported into the film at time t, M(t), is given by:



R

M(t) =

2r × C(r, t)dr

(9)

r0

By substituting Eq. (9) into Eq. (8-1), then Ct = C0 + +

ε0 εdry ln εw 2dw

ε0 εdry

M(t)

 ln ε 2  w

w

d

R

r[C(r, t)]2 dr + · · ·

(8-1)

(8-2)

r0

For the case ln ε/pw  1, the second-order term of the series can be neglected, then: M(t) Ct − C0 = C∞ − C0 M(∞)

The resistance dR is given by: dR =

535

(10)

Eq. (10) suggests that the normalized capacitance change from impedance measurements can be equally translated into the normalized mass change from gravimetric measurements. 2.1. Radial diffusion Given the paint film specimen configuration as shown in Fig. 2(a), it is expected that the mass transport of water vapor in the in-plane direction is controlled by radial diffusion. For the problem of radial diffusion in an infinite medium, assuming that the in-plane water vapor transport follow Fick’s second law:



∂C(r, t) ∂2 C(r, t) 1 ∂C(r, t) =D + r ∂t ∂r ∂r 2



(11)

For non-steady state, the water concentration C(r,t) is given by [16]:



2 exp(−D˛2n t)J0 (r˛n ) C(r, t) = C(r0 ) 1 − r0 ˛n J1 (r0 ˛n ) ∞



(12)

n=1

where J1 (x) is the Bessel function of the first order and ˛ is the root of the Bessel function of the first kind of order zero.

4 M(t) =1− exp(−D˛2n t) M(∞) r 2 ˛2n ∞

(13)

n=1 0

where M(t) is the total amount of water vapor diffused into the film at time t, M(∞) the total amount of water vapor when the film is fully saturated with water vapor (steady state radial diffusion). For a small value of time, we have [16]: 4 (Dt) 1/2 Dt 1 (Dt) 3/2 M(t) = × − 2 − × 3 − ... 1/2 1/2 r0 M(∞)  3 r0 r0

(14)

Combining Eqs. (14) and (10), for a short time approximation, we obtain: 4 Ct − C0 M(t) (Dt) 1/2 Dt 1 = = × − 2 − 1/2 C∞ − C0 r0 M(∞)  31/2 r0 ×

(Dt) 3/2 r03

− ......

(15)

Eq. (15) shows that the diffusivity D can be found by numerical analysis of experimental results from capacitive or gravimetric measurements. It must be pointed out that in deriving Eq. (14), the diffusion is assumed as a non-steady state in an infinite medium, i.e. the outer radium of the paint film is infinite large. As will discussed later, for a finite radial diffusion where the outer radium of the circular

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W. Zhang, M.R. Jaworowski / Progress in Organic Coatings 74 (2012) 534–539

cylinder is limited by the size of the tested paint film, the Eq. (14) is valid only up to a point when the diffusion reaches its steady state. 3. Experimental 3.1. Materials and specimen preparation A commercial non-chromated, two component, epoxy polyamide primer for aerospace applications, 44-GN-098, (hereafter referred to as “aerospace primer” or “primer”), manufactured by Deft Industries, was used for in situ capacitance measurements. To prepare free primer films, wet paint mixture was applied by doctor-knife casting into glass substrates covered with an adhesive Teflon tape. The primer films were cured under air at room temperature for a minimum of two weeks. After curing, the films with thickness ranging from 200 to 300 ␮m were carefully removed from the glass substrates, and stored in a vacuum oven for one week at room temperature to remove any volatiles remaining from the curing processes. The specimen for capacitance measurement consists of a free primer film placed between two Cu foil tapes, or coated with conductive silver paste on both surfaces, defining the film capacitor electrode surface of about 20 cm2 . The paint film has a circular center area (∼10 cm2 ) removed, allowing directly exposure to water vapor from one side. The specimen was clamped and sealed with water vapor resistant gasket to the open mouth of a Payne permeability cup [17] containing water and the assembly was placed in a test chamber with a temperature and humidity controlled at 23 ◦ C (±1 ◦ C) and 25% RH (±1% RH). Fig. 1(a) and (b) shows a schematic of the paint primer film geometry and experimental apparatus for in situ capacitance measurements. 3.2. Electrochemical impedance measurements The capacitance was determined by Electrochemical Impedance Spectroscopy (EIS). The EIS measurements were made using a two electrode arrangement by the Solartron Potentiostat (SI-1287) equipped with a high-frequency response analyzer (SI-1255B). The measurement was conducted in the frequencies ranging from 106 Hz to 1 kHz with an acquisition rate of 10 points per decade, and a 5 mV (vs reference electrode) AC perturbation potential applied. No DC bias voltage was applied. 3.3. Gravimetric measurements For validation purposes, gravimetric measurements (ex situ) were also performed for one sample in conjunction with the capacitance measurements. The weight change of the primer film sandwiched between two Cu tapes was measured over time using a precision balance to an accuracy of 0.01 mg.

Fig. 1. (a) Tested primer film specimen geometry, (b) experimental set-up for in situ measurement of lateral water vapor transport.

about 500 h of exposure as evidenced by no significant changes in the measured impedance and phase angle plots. Another way to interpret above EIS spectra change is to determine the capacitance at a fixed frequency. In this work, the film capacitance was calculated at a fixed frequency of 100 KHz. At such a high frequency, as shown in Fig. 2(b), the film can be represented

(a) Cu Paint film weight change M (t)

4. Results and discussion At the beginning of the water vapor exposure, the impedance measurements reveal a fully capacitive behavior. Fig. 3 shows representative data in the form of Bode impedance and phase angle plots for the primer films under different exposure time, using Ag past or Cu tape as contact electrodes. As shown in Fig. 3, the films exhibit pure capacitive behavior (slope of −1, and phase angle close to −90◦ ) at the beginning (t = 0), but begins to deviate from pure capacitive behavior after 24 h water vapor exposure. The reason for this deviation is the decreasing ionic resistance of the paint film as it becomes hydrated by the water, creating the RC equivalent circuit shown in Fig. 2(b). The film is equilibrated with water vapor after

dr

r

C(r, t) 100%RH 100%RH Water profile

r0

dR

dC

d

R

(b) dR(r,t)

…..

dC(r,t)

…..

R (t)

C (t)

Fig. 2. (a) Schematic representation of a tested primer film. (b) Equivalent circuit model for the film during in-plane water vapor transport.

W. Zhang, M.R. Jaworowski / Progress in Organic Coatings 74 (2012) 534–539

(c)

Primer film w/ Ag paste 1.0E+07

logIZI (Ohm-Cm2)

t=0 1.0E+06

t=24 hr t=360 hr t=750 hr

1.0E+05

1.0E+04 1.0E+03

Slope of -1

1.0E+04

1.0E+05

logIZI (Ohm-Cm2)

(a)

1.0E+07

t = 240 hrs

(d)

Primer film w/ Ag paste

90 85

80

80

75

t=0

70 65

t=24 hr

60

t=360 hr

55

t=750 hr 1.0E+04

1.0E+05

t =500 hrs t =1000 hrs

85

50 1.0E+03

t =24 hr

slope -1 1.0E+04

1.0E+05

1.0E+06

log(f) (Hz)

-thea (degree)

-thea (degree)

90

t= 0

1.0E+05

log(f) (Hz)

(b)

Primer film w/ Cu tape

1.0E+06

1.0E+04 1.0E+03

1.0E+06

537

75

t= 0

70

t =24 hr

65

log(f) Hz

t = 240 hrs

60

t =500 hrs

55 50 1.0E+03

1.0E+06

Primer film w/ Cu tape

t =1000 hrs 1.0E+04

1.0E+05

1.0E+06

log(f) Hz

Fig. 3. Bode plots showing (a and c) impedance of aerospace primer films at different exposure time; (b and d) phase angle plots of measured impedance at different exposure time, using Ag paste and Cu tape, respectively.

by a simple equivalent circuit consisting of a resistance R, in parallel with a capacitance C determined by the following equation: C=

−Z  2f (Z  2 + Z  2 )

(16)

where Z and Z are the real and imaginary part of impedance measured at a fixed frequency of 100 kHz. Table 1 shows the initial film capacitance calculated from the EIS data measured using Cu and Ag paste as contact electrodes, respectively. Using these initial film capacitance and corresponding film geometries, the dielectric constant for each film was calculated by the following equation: ε=

d d C0 = C0 ε0 A ε0 (R2 − r02 )

(17)

where A is the area of the test film covered with Cu or Ag paste whose inner and outer radii are r0 and R respectively, and ε0 is the dielectric constant of vacuum (8.854 × 10−14 F/cm), d is the film thickness, and C0 is the initial film capacitance measured by EIS. To verify the capacitance measurements, 10 mil thick Teflon films from Dupont was also tested using both Cu and Ag paste as contact electrodes. As shown in Table 1, the value of dielectric constant of Teflon film measured using Cu tape as contact electrodes is very close to what reported by Dupont [18]. The value of dielectric constant for the aerospace primer films is about 3–4. Comparing to the measurements using Cu tape, both Teflon and aerospace primer films showed a slightly higher dielectric constants from the measurements using Ag paste as contact electrodes, indicating that some residual water or solvent from Ag paste was absorbed by the films during the experiment or retained from the curing process. Therefore, Cu tape is preferred to Ag paste as contact materials for paint film capacitance measurements. Fig. 4 shows typical capacitance evolution as a function of the square root of the exposure time for the primer films, measured using Ag paste and Cu tape as the contact materials, respectively.

The capacitance was observed to increase linearly with the squareroot of the exposure time from the initial primer film capacitance C0 to an equilibrium value of the film capacitance C∞ , as shown with arrows on the left and right scales, respectively in Fig. 4. Two different water vapor transport phases are clearly distinguished: a linear increase of the film capacitance to the square root of the time in the initial stage, which is believed due to the in-plane water vapor transport by non-steady radial diffusion, followed by the appearance of a plateau where the film is fully saturated with moisture, indicating that water vapor transport is occurring at the rate dictated by steady state radial diffusion. Interestingly, the capacitance time decay plots shown in Fig. 4 are consistent with the models of water (liquid) uptake and transport (through-plane) reported in organic coatings [19]. The presence of the plateau in the capacitance time decay plots (Fig. 4) makes it possible to extract the water vapor transport properties from capacitance measurements as discussed as follows.

Fig. 4. Capacitance changes as a function of the square root of the exposure time for primer films measured by Ag paste and Cu tape, respectively.

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W. Zhang, M.R. Jaworowski / Progress in Organic Coatings 74 (2012) 534–539

Table 1 Dielectric constants of films calculated from capacitance measurements using Ag paste or Cu tape as contact electrodes. Film

Thickness (mm)

Contact electrode

C0 (F)

ε (calculated)

Aerospace primer

0.268 0.330 0.300

Ag (paste) Cu tape Cu tape

2.95E−10 1.65E−10 2.17E−10

4.56 3.13 3.75

ε (literature) 3–4

Teflon

0.260 0.260

Ag (paste) Cu tape

1.62E−10 1.34E−10

2.48 2.13

2.0618

The capacitance data plotted in Fig. 4 can also be arranged as the normalized capacitance change (Ct − C0 )/C∞ − C0 ) as a function of the square root of the exposure time. As discussed above, if the radial diffusion of water vapor in a film follows Fick’s Laws, all capacitance data plotted as the normalized capacitance change (Ct − C0 )/C∞ − C0 ) must lie on a unique curve as described by Eq. (14) for a small time: M(t) 4 (Dt) 1/2 Dt 1 (Dt) 3/2 = × − 2 − × 3 − ...... 1/2 1/2 r M(∞)  3 r0 r0 0

(14)

These results are shown in Fig. 5(a) and (b) for the primer films measured by Ag paste and Cu tape, respectively. Fitting Eq. (14) by adjusting the value of diffusivity D to the capacitance data gives diffusion coefficient of about 7.5 × 10−7 and 8.5 × 10−7 cm2 /s for primer films w/Ag paste and Cu tape, respectively. Note that both diffusivity curves of Eq. (14) match well with the capacitance data from the initial stage of the water vapor transport when the film capacitance changes linearly to the square root of the exposure time. There exists significant discrepancies between the experimental data and the diffusivity curve described by Eq. (14),

Fig. 5. (a and b) Normalized capacitance measured using Ag paste (a) or Cu tape (b) as contact materials as a function of the square root of the exposure time. The dotted lines were determined using Eq. (14) giving the best fit (diffusivity D) to the experimental data.

Fig. 6. Capacitance and mass change as a function of the square root of the exposure time for the primer film measured using Cu tape as contact materials.

indicating that water vapor transport is no longer under non-steady state diffusion after the initial stage. For the purpose of validation, the weight gain of one paint film sample was measured along with the capacitance measurement. Fig. 6 shows both capacitance and gravimetric data as a function of the square root of the exposure time. Both the capacitance and gravimetric measurements show two distinct stages: an initial linear increasing to the square root of the exposure time, followed by the appearance of a plateau where both capacitance and weight gain reaches their equilibrium values. Note that the transition timing point for both capacitance and gravimetric data from the linear to the plateau match well each other, indicating that the coating capacitance change is well correlated with the amount of in-plane water vapor transported in paint films. Now a direct comparison between capacitance and gravimetric measurements can be made. Both capacitance and gravimetric data plotted in Fig. 6 can be re-arranged as the normalized capacitance/mass change (Ct − C0 )/C∞ − C0 ), and M(t)/M(∞), and the

Fig. 7. Normalized capacitance and mass change as a function of the square root of the exposure time for the primer film measured using Cu tape as contact materials.

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539

Table 2 In-plane diffusion coefficients estimated from capacitance and gravimetric methods. Paint films

Aerospace primer

In-plane diffusion coefficient (×10−7 cm2 /s) Thickness (mm)

Electrode

Capacitance technique

Gravimetric

0.268 0.330 0.300

Ag-paste Cu tape Cu tape

8.5 7.5 5.0

– – 4.0

results are plotted in Fig. 7 as a function of the square root of the exposure time. The results show that there is reasonable agreement between the capacitance and gravimetric measurements. Fig. 7 also validates Eq. (10) in experimental, showing that the normalized capacitance change can be equally translated into the normalized mass change from gravimetric measurements. A series of diffusivity curves described by Eq. (14) can be computed using water vapor diffusivity D as an adjustable parameter. The solid lines in Fig. 8(a) and (b) represent the best agreements between the experimental and computed data, giving the diffusion coefficients of about 4.0 × 10−7 and 5.0 × 10−7 cm2 /s, respectively. These results also indicate that there is agreement between the capacitance and gravimetric measurements, which supports the suitability of the capacitance technique for in-plane water vapor

transport measurement in the paint film. As discussed above, a significant deviation from the theoretical curves computed for an infinite geometry is observed for long exposure times when water vapor diffusion reaches a steady state. Table 2 summarizes the diffusion coefficients obtained for water vapor in aerospace primer films. The value of diffusion coefficient derived from capacitance measurement is in good agreement with one obtained from gravimetric method. The relatively close agreement between the particle-filled Ag paste and solid adhesive Cu tape measurements indicates that water vapor transport at the interfaces is not a controlling factor in this work. 5. Conclusions A capacitance technique was adapted and validated for studying in-plane water vapor transport in paint films. The technique requires an application of electrical contact materials on the paint film surface for capacitance measurements. A direction comparison of the capacitance data with gravimetric results showed reasonable agreement between the capacitance technique and the gravimetric method. The developed technique provides a new approach to investigating in-plane water vapor diffusion and transport quantitatively. The technique is also expected applicable for the measurements of water (liquid) and inhibitor species transport in paint films. Further comparative studies of through-plane and in-plane water vapor transport and the transport rates of corrosion inhibitors and other ionic species are under investigation. Acknowledgment This work was performed under SERDP Project WP-1620. References

Fig. 8. (a and b) Normalized mass (a) and capacitance (b) measured using Cu tape as contact materials as a function of the square root of the exposure time. The solid lines were determined using Eq. (14) giving the best fit (diffusivity D) to the experimental data.

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