The measurement of the moisture transfer properties of paint films using the cup method
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Progress in Organic Coatings 49 (2004) 270–274
The measurement of the moisture transfer properties
of paint films using the cup method
E.L.J. Goossens, A.J.J. van der Zanden∗ , W.H. van der Spoel
Faculty of Architecture, Building and Planning, Eindhoven University of Technology,
P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Received 18 September 2003; accepted 2 October 2003
Abstract
The cup method has been used to measure the diffusion coefficient (or permeability) of water in free paint films. A dependence on the
layer thickness of the diffusion coefficient could not be measured. The diffusion coefficient depends strongly on the relative humidity. The
measured diffusion coefficient is found to be smaller than the measurement results from the literature on non-free paint films.
© 2003 Elsevier B.V. All rights reserved.
Keywords: Diffusion coefficient; Paint; Cup method; Permeability; Latex
1. Introduction free paint film, when the permeability is given as a func-
tion proposed by Galbraith [3], is given in Section 4. The
Paints are often used to protect an underlying substrate. sorption isotherm of the paint, as reported in [4], is given
Moisture in the substrate or at the surface of the substrate can in Section 5. In Sections 6 and 7, the measurement re-
have deteriorating effects on the substrate. This effect can sults are compared with, respectively, the model prediction
be directly or indirectly, when the moisture favours growth and measurement results on non-free paint films with the
of organisms, which are bad for the substrate. To know the same formulation. Section 8 contains the conclusion and
protecting characteristics of the paint, the moisture trans- discussion.
fer properties of the paint must be known. These proper-
ties are the diffusion coefficient (or permeability) and the
sorption isotherm of water in paint. The present study fo-
2. Paint films
cuses on the measurement of the diffusion coefficient (or
permeability). Classical techniques for this measurement
For the experiments, a waterborne styrene acrylic dis-
are given by Crank and Park [1]. Nowadays, much more
persion wall paint (a latex paint) is used. The composition
advanced, electronic, magnetic or nuclear magnetic reso-
of the wet paint is given in Table 1. The wet paint is ap-
nance techniques are available. See for instance the recent
plied on siliconised paper. The thickness of the wet paint
work of Mamaliga et al. [2], who used a magnetic sus-
layer is controlled by scraping a rod over the wet paint
pension balance to measure the amount of solvent in a
layer at a constant distance from the paper with a con-
polymer. The disadvantage of such techniques is that the
stant velocity. Three wet paint layer thicknesses are used
equipment is expensive. The present study uses the classi-
(120, 250 and 400 m). The paint is then dried at an at-
cal cup method to measure the diffusion coefficient of wa-
mosphere of 60% relative humidity and a temperature of
ter in a paint film. In Section 2, the formulation of the wet
23 ◦ C. Finally, the paint films are detached from the paper.
paint and the production of free paint films is described.
For measuring the thickness of the dry paint films, at least
Section 3 gives the description of one cup covered with a
five free paint films are placed on each other, with on top
free paint film and of the box in which the cup is placed.
of them a glass sheet. With a micrometer, the total thick-
The equations describing the moisture transfer through the
ness of this pile is measured, from which the thickness of
∗ Corresponding author. Tel.: +31-40-247-37-21; one paint film is computed. The resulting three dry paint
fax: +31-40-243-85-95. layer thicknesses are, respectively, 53.0±1.4, 81.0±1.6 and
E-mail address: a.j.j.v.d.zanden@bwk.tue.nl (A.J.J. van der Zanden). 113 ± 4 m.
0300-9440/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.porgcoat.2003.10.008E.L.J. Goossens et al. / Progress in Organic Coatings 49 (2004) 270–274 271
Nomenclature
A permeance surface area of the paint film (m2 )
d thickness of the paint film (m)
D diffusion coefficient (m2 s−1 )
g mass flux (kg m−2 s−1 )
G mass transfer through the paint film (kg s−1 )
h relative humidity (%)
k vapour transfer coefficient (s m−1 )
p water vapour pressure (N m−2 )
Fig. 1. Cup with a saturated salt solution to measure the water vapour
psat saturation water vapour pressure (N m−2 ) transfer through a free paint film.
x position (m)
Greek letters release of a possible pressure difference over the paint film,
α permeability parameter (s) for instance ambient pressure changes, which could cause
β permeability parameter (s) stresses in the paint film, leading to a change in moisture
γ permeability parameter (dimensionless) transfer properties of the film. It has been verified that the
δ permeability (s) mass transfer through the capillary is smaller than the mea-
ρ water content (kg m−3 ) surement error in the mass transfer through the paint film.
The cup is placed in a pressure, temperature and relative hu-
Subscripts midity controlled box. The temperature is 23 ◦ C. The box
1 side 1 can contain 96 cups. The box contains also a pick and place
2 side 2 unit and a balance. The pick and place unit places the cups
i interface consecutively on the balance and back again. Thus, the cups
stay in their climate. The mass of one cup is measured typ-
ically every hour during a few days.
Table 1
Composition of the styrene acrylic dispersion wall paint
4. Moisture transfer through free paint films
Ingredient Function Manufacturer wt.%
Water Solvent God 33.93 The relative humidities at both sides of the paint film
Acronal 290D Binder (styrene BASF 30.03 are denoted h1 and h2 . Besides the resistance against mass
acrylic polymer) transfer in the paint film, there can also be a resistance in the
Tioxide TR92 Pigment (TiO2 ) Tioxide 20.02
air. This resistance is modelled, as depicted in Fig. 2, with
Mikhart 5 Filler (chalk) Provencale 12.71
Acrysol RM-8 Associative Rohm & Haas 2.00 two stagnant air layers. The air layers do not have the same
thickener thickness, due to forced air mixing in the box and none in the
Texanol Coalescent Eastman 0.75 cup. The relative humidities on the air/paint interfaces are
SER-AD FX 504 Pigment Servo Delden BV 0.30 denoted as hi,1 and hi,2 . The solid line in Fig. 2 symbolises
dispersing agent
the relative humidity as a function of position. The thickness
Acticide MX In-can biocide Thor Chemicals 0.15
Tegofoamex 1488 Defoamer Tego Chemie Service 0.10 of the dry paint film is given by d. The mass flux in the paint,
g, depends on the water vapour pressure, p, and the position,
x, and is described in the one-dimensional case with
3. Set-up
dp
g = −δ , (1)
dx
The mass flux through a paint film is caused by creating
different relative humidities on both sides of a free paint
film. The relative humidity below the film is controlled by
using the film to seal a glass cup (with a diameter of 43 mm),
in which a dish is placed with a saturated salt solution (see
Fig. 1). Different relative humidities are created by using
different saturated salt solutions. The paint film is fixed with
vacuum grease between two glass rings. The lower glass ring
is placed against the glass cup, where also vacuum grease
is used to prevent leakage. The inside of the glass cup is
connected to the outside by a capillary with an inner diam-
eter of 1 mm and a length of 2 m. This capillary provides a Fig. 2. Relative humidity as a function of position around a paint film.272 E.L.J. Goossens et al. / Progress in Organic Coatings 49 (2004) 270–274
where δ is the permeability of the paint. The permeability is content of the paint, ρ. In [4], the sorption isotherm of the
chosen to be described as a function of the moisture content paint was shown to be well described by
of the paint, like it was proposed by Galbraith et al. [3], as
98.2h2 + 16,601h
δ = α + βh , γ ρ= . (12)
(2) h2 − 2359.7h + 239,838
where α, β and γ are constants. Using Eqs. (1) and (2), it
will now be derived what the mass transfer through the film 6. Permeability
is, depending on the two relative humidities that are applied
on both sides of the paint film. Because In the experiments, the mass gain or loss of a cup is mea-
h p sured in time. The mass transfer through a paint film is
= , (3)
100 psat caused by a difference in relative humidities inside and out-
side the cup. This difference is approximately 10%, but it is
where psat is the saturation water vapour pressure, Eq. (1)
not the same in all experiments. To make a better compari-
can be written as
son between experiments and theory possible, a normalised
d(h/100) water vapour transfer, defined as
g = −psat δ . (4)
dx
gA G
Integrating this over the paint film, = , (13)
p p
d
psat hi,2 is used, where A is the surface area of the paint film, where
g dx = − δ dh, (5)
0 100 hi,1 the water vapour can go through, and p the difference in
water vapour pressure over the paint film. In Fig. 3, the nor-
gives, for a steady state,
malised water vapour transfer is given as a function of the
psat hi,2 relative humidity. The model (solid lines) has been fitted to
g=− δ dh. (6)
100d hi,1 the experimental values (symbols), where k1 , k2 , α, β and
γ have been used as fit parameters. For every experimental
Using Eq. (2), Eq. (6) is integrated to value, the inaccuracy is the standard deviation of five exper-
psat β γ+1 γ+1 iments, which are performed at the same time. Thus, sys-
g=− α(hi,2 − hi,1 ) + (hi,2 − hi,1 ) . (7) tematic errors, such as for instance a possible non-purity of
100d γ +1
a saturated salt solution, leading to a different relative hu-
The mass transfer through the air layers is described with a midity inside the cup, are not included in the error bars. The
vapour transfer coefficient k. For a steady state, it holds that obtained values of k1 and k2 , respectively, 2.5 × 10−11 and
g = psat k1 (h1 − hi,1 ) = psat k2 (hi,2 − h2 ), (8) 5.0 × 10−11 s m−1 , correspond to a stagnant air layer thick-
ness of, respectively, 7.8 and 3.9 cm. The distance between
which leads to the surface of the saturated salt solution and the paint film
g is only 4 cm, thus the obtained value for k1 is physically
hi,1 = h1 − (9)
psat k1
and
g
hi,2 = h2 + . (10)
psat k2
Substituting Eqs. (9) and (10) into Eq. (7) gives
psat α g g
g=− h2 + − h1 +
100d psat k2 psat k1
γ+1
psat β g
− h2 +
100d(γ + 1) psat k2
γ+1
g
− h1 − . (11)
psat k1
5. Sorption isotherm
Fig. 3. Comparison of theoretical and experimental values (respectively,
lines and symbols) for the normalised water vapour transfer as a function
The sorption isotherm is the equilibrium relation between of the relative humidity (RH) for the wet layer thicknesses 120, 250 and
the relative humidity surrounding the paint and the water 400 m.E.L.J. Goossens et al. / Progress in Organic Coatings 49 (2004) 270–274 273
Table 2
Permeability parameter values
Wet layer α (kg m−1 s−1 Pa−1 ) β (kg m−1 s−1 Pa−1 ) γ (–)
thickness (m)
120, 250, 400 1.5 × 10−14 2.3 × 10−23 5
120 1.5 × 10−14 1.8 × 10−23 5
250 1.7 × 10−14 2.0 × 10−25 6
400 3.8 × 10−14 7.0 × 10−35 11
Fig. 4. Normalised water vapour transfer with physically realistic stagnant
air layers on both sides of the paint film.
unrealistic. The fit procedure is repeated with fixed stag-
nant air layer thicknesses of 4 cm in the cup and 1 cm in the
moderately mixed box, or, equivalently, with values of k1
and k2 , respectively, 4.88 × 10−11 and 19.5 × 10−11 s m−1 .
The result is given in Fig. 4. The difference between Figs. 3
and 4 is only minimal, which implies only a weak depen-
dence of the water vapour transfer on the vapour transfer Fig. 6. Permeability of the paint as a function of the relative humidity.
coefficients. Thus, the resistance against water vapour trans-
fer lies mainly in the paint film and not in the stagnant air
layers. In Fig. 4, almost all experimental values for the wet the same fixed k1 and k2 values as before. Thus, the model
layer thickness of 120 m lie below the theoretical values, is fitted to the experiments for each wet layer thickness sep-
and all experimental values for the wet layer thickness of arately. This brings not an improvement of the results, be-
400 m lie above the theoretical values. This could suggest cause Fig. 5 gives, for relative humidities smaller than 40%,
that the permeability is different for the three wet layer thick- values of the normalised flux for the 400 m film which are
nesses. In Fig. 5, the theoretical values are compared with larger than those for the 120 m film. This physically unre-
the experimental values, where the permeability parameters alistic result shows that, from these experiments, a possible
are assumed to be wet layer thickness dependent, but with layer thickness dependency of the permeability cannot be
concluded. This strange fit result is caused by the experi-
mental results below 60% relative humidity, where the mea-
sured normalised flux for the 250 m wet layer thickness is
smaller than that for the 400 m wet layer thickness. This
might be caused by irregularities in the paint film, such as
entrapped air bubbles or pinholes. Thick paint films have
a larger risk for such irregularities than thin films. The ob-
tained permeability parameter values are given in Table 2.
In this table, the values for the thickness independent fit is
given also, and the resulting theoretical permeability as a
function of relative humidity is plotted in Fig. 6.
7. Comparison with other techniques
The mass transfer through a paint film can also be de-
scribed with a diffusion coefficient, D, as
Fig. 5. Normalised water vapour transfer, where the model has been fitted dρ
to the results for each layer thickness separately. g = −D . (14)
dx274 E.L.J. Goossens et al. / Progress in Organic Coatings 49 (2004) 270–274
The present study, however, uses free paint films, while the
mentioned literature obtained values for paint films attached
to a substrate. It could be that detaching a paint film from a
substrate releases tensions in the film, from which the paint
film changes shape and also its moisture transfer properties.
Irregularities in the paint film such as entrapped air bub-
bles or small cracks could only increase the flux through
the paint film. Thus, paint films without such irregularities
would have even smaller values for the diffusion coefficient
than as presented in Fig. 7. The other values in Fig. 7 were
obtained with techniques that are not sensitive for such ir-
regularities. For the results of other paint formulations, see
[7].
Fig. 7. Comparison of the here obtained results of the diffusion coefficient Acknowledgements
(curved line) with the values found in the literature (dotted and solid
line pieces from, respectively, a sorption technique and an interferometric The authors are grateful to Roalt Bruininks, Guus Theuws,
technique). Wout van Bommel and Harrie Smulders for the fast technical
support. One of the authors (EG) is, thanks to Prof. Stache
Combining Eqs. (1) and (14) and using Eq. (3) leads to Bancken, partly supported by ‘NWO-Technologiestichting
psat dh STW’ Project no. DCT.4010, Subproject IV-b ‘Water bal-
D=δ . (15) ance of water-borne paint systems on plaster substrates
100 dρ
in relation to fungal growth’. The authors are grateful for
From the here obtained results of the permeability measure- the paint that has been made available by the companies
ments and the sorption isotherm, the diffusion coefficient is Akzo Nobel Coatings, DSM Resins, and Sigma Coatings
calculated with Eq. (15) and is presented in Fig. 7 as the solid Research.
line. This result is compared with the results of the sorption
technique [5] and the results of the interferometric technique
[6], which are both results obtained from exactly the same References
wet paint formulation, but attached to a stainless-steel sub-
strate instead of a free paint film. [1] J. Crank, G.S. Park (Eds.), Diffusion in Polymers, Academic Press,
London, 1968, Chapter 1, pp. 1–39.
[2] I. Mamaliga, W. Schabel, M. Kind, Chem. Eng. Process., in press.
[3] G.H. Galbraith, R.C. McLean, J.S. Guo, Moisture permeability data
8. Conclusion and discussion presented as a mathematical relationship, Build. Res. Inform. 26 (1998)
157–168.
The traditional cup method has been used in a slightly [4] A.J.J. van der Zanden, E.L.J. Goossens, The measurement of the
sorption isotherm of water in paint films, Chem. Eng. Process., in
improved form to measure the moisture transfer properties
press.
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measured by recording the mass of the cup in time. From diffusion coefficient and the sorption isotherm of water in paint films,
these data, the permeability of the paint is computed. The Chem. Eng. Sci. 58 (2003) 1521–1530.
permeability depends heavily on the moisture content of the [6] E.L.J. Goossens, A.J.J. van der Zanden, H.L.M. Wijen, W.H. van
der Spoel, The measurement of the diffusion coefficient of water in
paint. A layer thickness dependency of the permeability can-
paints and polymers from their swelling by using an interferometric
not be concluded from the present experiments. The values technique, Prog. Org. Coat. 48 (2003) 112–117.
of the diffusion coefficient, as found in the literature, are [7] E.L.J. Goossens, The moisture transfer properties of coated gypsum,
much larger than the values obtained in the present study. Ph.D. Thesis, Eindhoven University of Technology, 2003.You can also read
