Modelling Film Formation and Degradation of Semi-transparent Exterior Wood Coatings --2007
Transcript of Modelling Film Formation and Degradation of Semi-transparent Exterior Wood Coatings --2007
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
Progress in Organic Coatings 58 (2007) 112
Modelling film formation and degradation of semi-transparentexterior wood coatings
Jan Van den Bulcke a,, Joris Van Acker a, Hans Saveyn b, Marc Stevens a
a Laboratory of Wood Technology, Department of Forest and Water Management, Faculty of Bioscience Engineering, Ghent University,
Coupure Links 653, 9000 Ghent, Belgiumb Particle and Interface Technology, Department of Applied Analytical and Physical Chemistry, Faculty of Bioscience Engineering,
Ghent University, Coupure Links 653, 9000 Ghent, Belgium
Received 20 June 2006; received in revised form 19 October 2006; accepted 19 October 2006
Abstract
Deposition and aggregation of small solidparticles areencountered in many natural and industrialenvironments. These processes areof substantial
significance for the development of a coating film on a wooden substrate. Formulating new coatings with improved performance and lower cost
for exterior wooden joinery, mainly a trial-and-error approach, has a large influence on the initial film forming stage in a coatings life. Therefore
modelling can supply insight in the particleparticlesubstrate interaction. Two approaches are proposed. The first one uses a random point process
to position the cluster centres and particles in a dry film. The second strategy starts with a random scattering of the particles in a wet film followed
by Monte Carlo sampling and subsequently minimization of the total energy of the particle system. Surface roughness and gloss are calculated
from the simulated surface structure. Next to these simulations, surface reconstruction of coated wood with confocal scanning laser microscopy
(CSLM) is used to obtain surface roughness values and deduction of gloss applying the bidirectional reflection distribution function (BRDF)
theory. As semi-transparent systems are the subject of gloss calculation on surfaces measured by CSLM and computer simulation, refractive index
is estimated using an analytical solution of the reflectance and transmittance problem. Withal, coating and subsequent degradation simulation can
become a valuable tool for screening purposes.
2006 Elsevier B.V. All rights reserved.
Keywords: Semi-transparent coating; Film formation; Degradation; Gloss; Roughness; Particle size
1. Introduction
Exterior wooden joinery requires proper finishing with tailor-
made coatings as it is susceptible to environmental degradation
[1]. Once applied, the coatings self are subjected to severe
outdoor weathering due to the impact of UV and thermal radia-
tion, moisture, fungal attack, etc. The interaction between these
parameters causes degradation of the coating, possibly resulting
in increased roughness, gloss loss, fracture, etc.[2].A theoreti-
cal study of these phenomena requires knowledge of the coating
structure, in fact even an additional step back in time, depart-
ing from the liquid film, consisting of particles suspended in the
binder solution.
Dispersions of particles in liquids are present in a wide
range of process industries. They can have sizes ranging from
Corresponding author. Tel.: +32 9 264 61 24; fax: +32 9 264 62 33.
E-mail address: [email protected](J. Van den Bulcke).
fractions of a millimeter down to macromolecular dimensions
Deposition onto a surface due to gravity and aggregation of
small solid particles brought together by collisions are common
phenomena of industrial importance in the chemical, environ-
mental, electronics, mineral and biological sectors[3].Modern
water-borne coatings, which are colloidal systems subjected to
above-mentioned processes, are widely used in different areas of
applications. The pigment volume concentration (PVC) and par-
ticle distribution are two key-parameters influencing the desired
application properties [4]. To get a detailed insight into the
structure of dried finishing films, the development of a coating
can be simulated with the computer. A variety of techniques
is available to extract the equilibrium properties and some-
times the dynamic or kinetic properties of the coating. The
simulation methods can be classified in stochastic and dynamic
categories. The former one uses statistical techniques such as
Monte Carlo sampling, the latter calculates particle positions in
time by means of exact or approximate description of motion
departing from random scattered particles. Several studies have
0300-9440/$ see front matter 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.porgcoat.2006.10.003
mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.porgcoat.2006.10.003http://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.porgcoat.2006.10.003mailto:[email protected] -
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
2 J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112
handled the particle packing problem applying a multitude of
algorithms and calculation techniques: coating on paper [5], fine
particles packing[6], packing of polydisperse spheres [7], of
hard-sphere fluids[8],computer simulation study of spherical
colloids within confined spaces[9], etc. Computer simulation
of particle packings serves various goals, from describing coat-
ing appearance[10]to performance properties of cement-based
materials[11].
The work described here is based on the methods used
by Hunt et al. [12] and Vidal et al. [13]. Both techniques
were implemented to obtain dry coating structures. Viscos-
ity, particle size distribution, solvent evaporation and density
of the particles were required input parameters for the sim-
ulation. All mathematical calculations and visualization were
done in the MATLAB environment. The coating surface was
extracted from this 3D coating structure. Next to simulation,
the surface was also reconstructed using confocal scanning
laser microscopy (CSLM), which is just one of the available
techniques to map the topography of a surface, ranging from
contact systems like atomic force microscopy (AFM) and sty-lus profilometry to non-contact systems like scanning electron
microscopy (SEM) and interferometric microscopy. The out-
come of the experiments in silico as well as the CSLM scans
were subsequently used for surface roughness characterization
and reflection calculations.
Research concerning roughness, weathering and their rela-
tion is manifold [14,15]. More specifically, the influence of wood
roughnesson the performance of finishes, is studied by Williams
and Feist[16]and Richter et al.[17].Furthermore, gloss mea-
surements and prediction were made according to the method
of Hunt et al. [12], although this method is more applicable
for opaque coatings. Another method for reflection calcula-tion, the bidirectional reflection distribution function (BRDF)
as expounded by Hebert et al. [18], uses as one of its input
parameters the refractive index which is necessary for the semi-
transparent coatings under test. Therefore, by measuring reflec-
tion and transmission and applying the analytical solution of
Nichelatti [19] the complex refractive index can be found. Semi-
transparency further complicates the gloss calculations in such a
way that part of the light is absorbed and scattered in the coating,
and that roughness of the underlying surface is also of impor-
tance in correct reflectance simulations. The surface of the wood
wastherefore also scanned with CSLM. Similar techniques were
used by McKnight et al. [20]for clear coatings and Sung et al.
[21]for the reflectance of metallic flakes. Recently, Croll andHinderliter[22]and Croll et al.[23]used coating simulation for
the monitoring of the degradation of a coating.
At last, degradation of the digital structure was simulated
while monitoring gloss change and surface roughness as was
also done by Hunt et al.[12]for 2D structures. These changes
were compared with measured gloss and roughness values on
weathered samples.
2. Material and methods
2.1. Characterization of the liquid coating
Five semi-transparent (T), oak-coloured water-borne (W)
wood coatings were manufactured at Akzo Nobel Decorative
Coatings laboratories in Belgium. The basic composition of the
systems is given inTable 1.
Characterization of the liquid coatings included density, vis-
cosity, amount and size of particles.Particles in semi-transparent
coatings are mainly part of the colour paste used in these formu-
lations. The resinous matrix is considered to be a fluid creating
a perfectly smooth surface. However, measurements of particle
size can include any measurable fraction of coating material asagglomerates can be formed.
Densitymeasurements were performed with a Micromeritics
pycnometer by measuring the amount of displaced gas. The dif-
ference between the pressure observed upon filling the sample
chamber and discharging it into a second empty chamber allows
computation of the sample solid phase volume. Gas molecules
rapidly fill the tiniest pores of the sample.
Viscosity profiles were measured with the Paar Physica MCR
Rheometer in controlled shear stress mode (rotational test),
resulting in viscosity values related to shear rate or velocity
gradient (ranging from 105 to 103 s1):
=d
dt(1)
Particle size measurements were carried out at the Depart-
ment of Applied Physical Chemistry, Particle and Interfacial
Technology Groupat GhentUniversity. The AnkersmidCIS-100
computerized inspection system for particle size analysis was
used. Time size mapping called Time of Transition theory is
used here and is applied for direct measurements of particle size.
In fact, the technique is based on the extinction time of a rotating
laser beam by a particle, in which a detection algorithm elimi-
nates signals from intersections that are not crossing the particle
in the middle and thus rejects all chord lengths that do not cor-
respond to the true particle diameter. This results in data on sizedistribution and percentages for each particle size class. More
information can be found in Tsai[24]and Saveyn et al.[25].
Table 1
Coating composition
Coating Resin Resin (%) Solids (%) PVC (%) Water (%)
TW-Ac-Alk Acrylate-alkyd 26 33 1 58
TW-Ac1 Acrylate 39 41 2 48
TW-Ac2 Acrylate 22 31 5 65
TW-PU Polyurethane 35 38 60
TW-PU-Ac Polyurethaneacrylate 30 32 1 63
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112 3
Table 2
Build up of the coating systems
System code Layer 1 Layer 2 Layer 3
TW-3Ac-Alk 1 TW-Ac-Alk TW-Ac-Alk TW-Ac-Alk
TW-3Ac-Alk-Ac TW-Ac-Alk TW-Ac1 TW-Ac1
TW-2Ac TW-Ac2 TW-Ac2
TW-3Ac-Alk-PU TW-Ac-Alk TW-PU TW-PU
TW-3Ac-Alk-PU-Ac TW-Ac-Alk TW-PU-Ac TW-PU-Ac
Zeta potential of theliquid coating wasnot recorded,although
this could be of influence for aggregation and coagulation of
particles. However, it is possible that aggregates are integrated
in particle measurements if they were not broken during dilution
in water.
Fivecoating systems were applied by brush to straight grained
pre-conditioned (12% moisture content) Scots pine sapwood
(Pinus sylvestris L.) boards measuring 32 cm 5 cm 1cm.
Upon coating, the specimens were stored in a conditioning room
for 3 weeks at 20 C and 65% RH. The build up of the systems
is given inTable 2.It is considered that the primer penetrates
the wood completely and is therefore of no importance for the
film forming process. As the topcoats for each finishing system
are equal, the name of the topcoat will be used further instead of
the coating system code. However, one should remember that a
primer was applied on each specimen.
Mass loss during drying of the coating was also recorded to
estimate the drag force the particles experience within the coat-
ing. Therefore mass loss was measured both on a glass substrate
and on wood to separate evaporation from absorption.
2.2. Characterization of the solid coating
Thickness, surface roughness and gloss were mapped.
Thicknessof the dry coating was measured with CSLM as
described in Van den Bulcke et al. [26].Coated wooden cubes
of approximately 1 cm 1 cm 1 cm are impregnated with a
safranin solution. A confocal laser microscope focuses a laser
beam onto the microtomed transverse section of the blocks and
excites the chromophores in the coating and the wood. The
safranin makes it possible to separate the coating from the wood
by proper selection of the wavelength filters. Subsequently the
image is processed to obtain the penetration of the coating in
the earlywood. Measurements were done on coatings applied
on Teflon coated paper and on wood samples. These measure-
ments were done to find out the dry/wet ratio as a parameter for
the structure simulation model.
Surface reconstructionwas done with CSLM and compared
with surfaces extracted from simulated structures. Confocal
reconstruction as outlined inFig. 1starts from a series of scans
inz direction which comprises several images from the top to
the inside of the coating until no more signal is detected.
The maximum intensity is considered at the top of the surface
at that particular point. Maximum intensity is determined as the
mean value of the Cauchy distribution fitted to the smoothed
recorded intensities as this distribution gave best fitting results
The Cauchy distribution has following formula:
y=1
b
(xm)2 +b2 (2)
The same procedure is also followed for the surface of
the Scots pine sapwood which was necessary as the semi-
transparency of the coatings results in a partially visible wood
structure meaning that light can reach this surface.Surface roughness of the reconstructed samples was deter-
mined, using an extensive set of parameters. Following param-
eters were used for characterization of the surface roughness,
withNthe total number of points and z the height values:
1. Rta: mean surface roughness:
Rta =z=1
N
Nn=1
|zn| (3)
2. Rt: standard deviation of surface roughness:
Rt =
Nn=1(zn z)
2
N 1 (4)
Gloss measurements are performed on free coatings and
coated wood samples with a Rhopoint Novo-gloss meter at
angles 20, 60 and 85.
2.3. Computer simulation from liquid to solid coating
For the computer simulation of the particle packing, two
methods were elaborated. Both start from a certain volume of
Fig. 1. z-Scan of a coating and reconstructed surface.
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
4 J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112
coating,a m bm cm with known properties (density,
evaporation rate, size distribution, etc.see Section 2.1.)read
in from an EXCEL file. Particles are considered to be spher-
ical, although the authors are aware of the fact that this is an
oversimplification of the diversity of shape of pigments.
Spatial point process or Hunt method[12].This stochastic
technique uses the random placement of particles in a dry film
volume. Particlescan be arranged in predefinedclusters. In short,
the following procedurewas followed. At first thedegree of clus-
tering was chosen by selecting an amount of cluster centres .
Subsequently these centres were randomly spread inx,y and z
directions. The floccules or centres were then filled with par-
ticles, taken at random with a probability proportional to their
percentage andrandomly positioned in such a way that their cen-
tres were within the cluster diameter. A random Poisson process
allocated a different amount of particles to each cluster so that
the sum of all particles equalled the total number of measured
particles or withbeing the mean number of particles per clus-
ters,particles =. When placing a particle in the volume, it
was verified that no overlapping with other particles occurred byreallocating the particle centre if needed. In this way a 3D parti-
cle model of a coating was built using point processes to control
coagulation and local differences in PVC. However, no a priori
informationis available concerning flocculationand coagulation
and in that way the number of clusters has to be chosen arbitrary
although post hoc adjustments are possible after comparison
with measured values. Thus the unknown coagulation could be
changed in such a way that best similarity with measured values
is obtained. However, clustering was not incorporated here as
in the Vidal method[13] abstraction was made from the zeta
potential.
Monte Carlo sampling with energy minimization or Vidalmethod[13].This dynamic method minimizes the energy with
every movement of a particle. The simulation starts with a ran-
dom sampling of particles and positioning them in a 3D matrix
equal to the thickness of the wet coat, considering a well dis-
persed initial state of the fluid. The configuration ofNparticles
can be described by their coordinates and radius:
c = {c1, c2, . . . , cj, . . . , cN}, r = {r1, r2, . . . , rj, . . . rN}
(5)
withcjandrj the centre and radius of thejth particle. LetE(c)
denotethe total energy which shouldbe minimized. Theparticles
experience a gravitation force (Eg), a drag force (Ed) due to thenet result of absorption in the substrate and evaporation of the
liquid and an interaction force (U) preventing particles from
overlapping:
E(c)= Eg(c)+Ed(c)+U(c) (6)
Starting from an initial random distribution of particles in
a wet coating, each particle is shifted in x, y and z directions
using a maximum translation distance. In that way a trial con-
figuration c is generated and is accepted if the movement is
physicallypossible.One iteration is finished till all particles have
been moved once. This procedure can be repeated till packing is
complete or, in terms of wood coating, solvent evaporation and
drainage has stopped and/or viscosity is too high to make any
further movement possible. For detailed information and mathe-
matics see Vidal et al.[13].The particles in the final dry coating
are determined by their centre and diameter. For surface rough-
ness measurements and degradation simulation it is necessary
to extract the surface as a map and the volume as a matrix with
zeros (binder) and ones (particle).
2.4. Gloss prediction
After renderingof thestructuresby thetwo algorithms, thelist
of centres and sizes of the particles was converted to both a 2D
surface and a 3D volume matrix for further processing regarding
roughness, gloss and degradation (cf. this section). The Beck-
mann model of light reflection is valid for opaque coatings[27].
The here used semi-transparent finishes complicategloss pre-
diction as part of the light is transmitted through the coating at
the aircoating interface and scattered on the substrate, partially
in the direction of the coatingair interface. Part of the light is
absorbed in the coating itself, part in the substrate and for thatpurpose, substrate and coating roughness, reflectance and trans-
mittance of the coating have to be determined. Fig. 2illustrates
the interaction of the incident light with a semi-transparent coat-
ing on a substrate.
Two methods are proposed of which the first can be consid-
ered as a simplifiedversion of thesecond. In fact, thefirst method
(further referred to as R1) calculates the surface normals and
starting from these surface normals the reflection percentages
are calculated using classic vector manipulation. This amount
is only partially reflected, due to the transparency of the coat-
ing. Part of the light enters the coating and is absorbed. Another
fraction is scattered on the wood surface and can leave the coat-ing at the same angle as the incident light. The sum of all the
light in the direction equal to the incident beam is considered
to be the reflection percentage. The other method is the bidirec-
tional reflection distribution function (BRDF) theory (further
referred to as R2) and concentrates on reflection taking into
account parameters such as roughness, refractive index calcu-
lation, geometric attenuation due to shadowing and masking,
etc. It is a relative measure of the amount of radiant flux that is
reflected in a certain direction. The different topics of the BRDF
concept are based on the CookTorrance model as expounded
in Hebert et al.[18].It is assumed that the surface is similar to
a distribution of randomly ordered microfacets. The BRDF for
Fig. 2. Interaction of light with a semi-transparent coating on a substrate (after
Hebert et al.[18]).
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112 5
semi-transparent systems is represented by
BRDF(,)=D(,m)G(,)F(,n)
cos cos(7)
with the angle of incidence, the angle of observation, D
the microfacets orientation distribution function, G the atten-
uation owing to surface geometry, Fthe attenuation owing toabsorption of light (Fresnel formulae) andn-the relative index of
refraction.
Complex refractive indexcalculations n() ik() on free
coating films are done in accordance with the analytical method
elaborated by Nichelatti[19].Free coating films were prepared
with a bird film applicator on plastic sheets. After 3 weeks of
drying, thickness was measured with CSLM. Thefree films were
removed from the plastic substrate and mounted in the dual-
beam spectro-photometer for transmittanceTand reflectanceR
measurements in the 400800 nm range from whichnandkcan
be calculated.
2.5. Weathering of the solid coating
2.5.1. Experimental weathering
The coated pine sapwood samples were subjected to weather-
ing as extensively outlined in Van den Bulcke et al. [28]. Briefly,
the samples are aged in an artificial weathering device (Atlas
UVCON). Two cycles W1 and W2 are alternated for several
weeks. The weathering cycle W1 comprises 6 days exposure in
the Atlas UVCON weathering device with limited water spray-
ing, i.e. continuous light and repeating cycles of 102 min without
water spraying followed by 18 min water spraying per day and
finally after 6 days 1 day storage in a deepfreeze. Theweathering
cycle W2 comprises 6 days in the UVCON with a high regimeof water spraying, i.e. 23 h light, 1 h darkness and alternating
exposures of 4 h water spraying, 2 h dry, 10 h water spraying,
2 h dry and 6 h water spraying per day ending after 6 days with
a 1 day storage in a refrigerator. During periods of continuous
light, temperatures reach 50 C, which decrease when spraying
is applied. A series of W1 and W2 cycles causes swelling and
shrinkage of the wood, stressing the coating system severely and
in that waysimulatingoutdoor weathering.Frequently, glossand
roughness are measured on these samples.
2.5.2. Theoretical weathering
Degradation simulation using the virtual particleresin struc-ture is a next step in the evaluation of the virtual coating. Specif-
ically, this amounts to the impact of a ray of light on the surface,
causing the destruction and removal of pieces of the coating.
Only UV degradation is taken into account, influence of mois-
ture (stressstrain resulting in rupture or delamination) is not.
Penetration of theUV beam in the coating depends on theextinc-
tion parameter (k-value), resulting in a decreasing intensity in
accordance with the LambertBeer law:
T =ekc (8)
Particles protect underlying material, which is also imple-
mented. Furthermore, it is assumed that voxels surrounding
particles are extra sensitive to degradation. Therefore the suscep-
tibility to degradation around a particle decreases according to a
3D Gauss-shaped cumulative probability volume while moving
away from the edge of the particle. Summarized, four matrices
are constructed:M1with the coating structure,M2with the sus-
ceptibility of (every voxel of) the coating structure,M3contains
the relative susceptibility of the beam on each voxel, consid-
ering the depth in the coating (LambertBeer extinction) and
M4, a matrix with random numbers. Every in silico weathering
cycle comprises the impact of the UV beam on the coating M1the calculation of the voxel damage taking into account both
M2and M3and generation of the random number matrix M4. A
voxel ofM1is removed if the damage exceeds the corresponding
random number in the M4 matrix. Only material at the surface
can be removed as it is assumed that degradation and remova
of subsurface or in-bulk (polymeric) material is negligible, also
because deterioration processes involve oxygen or water which
does not readily diffuse in the coating. A similar procedure was
followed by Croll and Hinderliter[22].The removal of particles
or agglomerates of particles once the polymeric matrix aroundthem is degraded, is not incorporated as such but was approxi-
mated by slower degradation of the particles.
Whenthese simulatedstructuresare weatheredvirtually, their
properties such as gloss and roughness are followed and com-
pared with the roughness and gloss changes as measured on
real samples. Hereby it is possible to evaluate the practical and
theoretical analysis of the coatings.
3. Results and discussion
3.1. Characterization of the liquid coating
Different measurements were performed and analysed to
obtain model parameters necessary for structure modelling
Fig. 3 displays the different viscosity profiles in function of
shear rate. Density values of the five semi-transparent coating
systems are given between brackets in kg/m3 and are very simi-
lar. Obviously, viscosity decreases as shear rate increases which
is obvious when dealing with thixotropic fluids such as coat-
ings. The coatings TW-Ac-Alk and TW-Ac1 are the extremes
Fig. 3. Viscosity profiles for the five semi-transparent coatings.
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
6 J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112
Fig. 4. Particle size distributions for the five semi-transparent coating systems.
in viscosity differing with a factor of approximately 100 when
measured at a shear rate of 0.01 s1.
InFig. 4particle distributions of the five finishing systems
are depicted.It is clear that some systems have a small distribution with a
peak value in the lower regions, probably causing the develop-
ment of a solid coating with few rough elements on the surface
and as a result a positive impact on reflection. TW-Ac2 contains
particleswith a size that is considerablyhigher than otherswhich
shall indubitably increase the surface roughness, as roughness
increases if particle size does[29].In general, all systems have
similar distributions, with a shoulder around 0.4m. In accor-
dance with these percentages,particles are fed in the model. This
means that random sampling of the particles is not completely
random as more abundant particles have a higher chance to be
selected according to their probability of occurrence.
An example of mass loss curves are shown inFig. 5,with the
drying speed of two coatings on wood and on glass. It is obvious
that coatings with low viscosity, such as the TW-Ac-Alk, have a
higher drying rate. As mentioned in Section2.2,the difference
between the mass loss on glass and on wood is considered to
be the drag force. This drag force varies in time but to simplify
the problem, a constant value will be maintained through the
simulation process.
Fig. 5. Cumulative mass loss curves of two coatings on glass and wood.
3.2. Characterization of the solid coating
Surface reconstruction of the samples weathered for 0, 1000
and 2000 h was done with CSLM. Surface roughness mea-
sures are listed in Table 3. Clearly, large particles (TW-Ac2)
and high PVC values cause a low gloss [12,30].The decrease
of the average roughness can be attributed to a removal of
peaks, thereby smoothing the surface while an increase is
induced by removal of material creating peaks. However it is
perfectly possible that for profiles clearly different in shape
and spacing, the average roughness value is the same. It is
the rule that gloss decreased during aging, although TW-PU-
Ac is the exception. In general, an increase in the volume of
small spheres increases gloss [5]. This increase is regarded
as a larger shoulder and a shift of the main peak to smaller
sizes.
In short,a comment on thewoodsurface is necessary. Thesur-
face roughness of the wood has, when looking on a macroscale,
a waviness and a roughness pattern, meaning that the waviness
is the result of the earlywoodlatewood alternation, whereas theroughness is the profile superposed on the waviness. The com-
plexity of wood surface characterization is reduced by mapping
only the latewood surface, without taking into account the wavi-
ness. This is justified because wood roughness is measured only
for the sake of gloss prediction.
3.3. Computer simulation from liquid to solid coating
The two structure simulation methods, Hunt and Vidal, were
implemented in MATLAB and as a result 3D particle matri-
ces were built as shown in Fig. 6 for two different coatings,
namely TW-Ac-Alk and TW-PU. While random positioning of
Table 3
Roughness parameters of reconstructed surfaces and measured gloss
t Rta (m) Rt(m) Gloss 60
a (%)
TW-3Ac-Alk 1
0 26.25 2.10 14
1000 29.03 1.81 14
2000 31.28 1.92 10
TW-3Ac-Alk-Ac
0 27.46 1.62 9
1000 23.21 1.55 9
2000 28.03 1.58 7TW-2Ac
0 28.87 1.65 8
1000 22.74 2.22 4
2000 19.24 2.04 3
TW-3Ac-Alk-PU
0 16.43 1.66 53
1000 18.15 1.96 47
2000 17.92 1.38 47
TW-3Ac-Alk-PU-Ac
0 14.96 1.58 21
1000 24.40 1.14 23
2000 15.91 1.36 24
a Measured with Novo-gloss meter.
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112 7
Fig. 6. Particle distribution of two coatings simulated with two methods.
particles (Hunt) gives a scattered distribution, energetic min-
imization (Vidal) results in a system that is physically more
realistic. Within the time limit of drying, particles change posi-
tion under influence of several forces, determined by size of the
particle, viscosity, drying speed and more. The outcome of light
reflection calculations is considered an assessment of aforemen-
tioned simulation technique.
3.4. Gloss prediction
Summarizing, the analytical solution proposed by Nichelatti
[19]results in the calculation of the refractive index and extinc-
tion coefficient. The two parameters are plotted in function
of the wavelength for the five coating systems under study in
Fig. 7. There are only minor differences in refractive index
and extinction coefficient between the different coatings as
expected owing to the same colour used for the semi-transparent
systems. However, an increase in PVC results in a decrease
of transmittance [31], which can be seen in Fig. 7 (higher
extinction coefficient for coatings with higher PVC values,
Table 1).
The average of the refractive index and the extinction coef-
ficient is used in gloss prediction in the Fresnel formulae. Thisaverage refractive index seems to increase with increasing PVC,
as stated in Gate and Preston[30]. The following three situa-
tions are compared: measured gloss,gloss prediction on scanned
surfaces and gloss prediction on simulated coating structures.
The bar graph inFig. 8clarifies the relation between the three
approaches for 60 gloss on the basis of the simplified gloss
prediction method (R1). Generally, low gloss is linked to large
particles.
In general, usingthe differentmodels, glosscalculationsseem
to overestimate gloss on wood, gloss of coatings on glass are bet-
ter approximated, especially by the Vidal approach. The method
based on Vidal gives better results, although still overestimated.
Fig. 7. Wavelength dependency of the refractive index (a) and the extinction
coefficient (b).
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
8 J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112
Fig. 8. Gloss prediction with the simplified model (R1) and using the scanned
surfaces, Hunt and Vidal simulated structures and comparing them with mea-
sured values (1= scanned surface; 2= Hunt; 3 = Vidal; 4= measured on wood;
5 = measured on glass).
The explanation for the differences is multiple:
aggregation and coagulation is not taken into account, partic-
ularly for the Hunt approach this may be crucial;
the reflection (measurement) neglects shadowing and mask-
ing effects of topography;
the simulated surface is too ideal.
However, gloss calculation on the scanned surfaces on the
other hand seems to underestimate the gloss values and this can
be attributed to the fact that the optics of the gloss meter are not
exactly capturing 60 reflected light, but little more. Further, the
topography on microscale is probably not sufficient to predict
gloss on macroscale by assuming that macroscale roughness is asequence of microscale roughness. More information on BRDF
calculation from micro- to macroscale can be found in Westin
et al.[32].
3.5. Weathering of the solid coating
The simulated structure consisting of particle centres and
sizes, is converted to a binary 3D matrix with 1 representing a
particleand0abindervoxel.Thismatrixcanthenbeusedforin
silico aging, with the particles as difficult to degrade while their
near surroundings are treated as vulnerable to UV degradation.
According to the LambertBeer law beam penetration decreases
exponentially with depth in the sample. The results of this kind
of weathering will be evaluated by calculating the change of the
roughness parameters and gloss prediction. It should however
be stressed that the change in gloss is difficult to model using
only the roughness as an affected parameter as colour changes
too and in that way affects the refractive index and extinction
coefficient. Thereforenandkcoefficients of unweathered sam-
ples do not correspond perfectly with weathered ones and gloss
predictions must be evaluated with this in mind.
Mass distribution of particles in the different coatings is illus-
trated by the curves inFig. 9.
It is clear that both approaches have different profiles con-
cerning their mass distribution. The influence of gravity and
viscosity is visible. TW-Ac2, and to a lesser extent TW-Ac1
have an accumulation of particles which may result in roughen-
ingduring aging.TW-Ac2 hasa lowerviscosity andshould resultin increased mass fraction near the bottom, however particles are
generally larger neutralizing the lower viscosity resulting in a
peak near the surface. The opposite is true for the TW-Ac1,
namely smaller particles but also higher viscosity, also result-
ing in a peak. Logically, all coatings have an increased solid
percentage near the bottom owing to gravitation.
Simulation of degradation is schematized in Fig. 10 for
the TW-Ac2 coating. The number associated with cycle is the
amount of iterations in the computer program and is not directly
linked to time as experienced by a specimen in the artificial
aging apparatus. The progressive nature of degradation is clear.
Surfaces scanned by Yang et al. [33]and Croll et al.[23]showsimilar images of weathered coatings. As already stated, mainly
the influence of the particles is noticeable as they are more resis-
tant to UV radiation than the surrounding resin.
The influence on Rta andRtis depicted inFig. 11.All the
parameters have values in the order of magnitude of the mea-
sured data (Table 3).
Mean surface roughness parameterRtaincreases for all coat-
ings during weathering, although the trend flattens after several
Fig. 9. Mass distributions of the different coatings according to the method proposed by Hunt (left) and Vidal (right).
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent
J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112 9
Fig. 10. Simulation of degradation of the TW-Ac2 coating.
cycles for the two polyurethane systems. Results are in accor-
dance with the theoretical data of Hunt et al. [12].Considering
the standard deviation, TW-Ac-Alk and TW-PU-Ac have a sim-
ilar trend, as is the case for TW-Ac1 and TW-Ac2. The standard
deviation for the TW-PU coating is obviously different from the
others with a less steep profile. When comparing these data with
the measured standard deviation results as listed inTable 3,it
is noticed that measured values do not increase as fast as the
simulated ones do. This means that the in silico weathering of
the coatings is probably more severe than the artificial aging in
the UVCON and/or that the susceptibility of the resinpigment
complex differs for the different coating systems. Gloss predic-
tion with the BRDF model (R2) results in the data as represented
inFig. 12.These gloss values have to be considered relative val-
ues, as they are derived from a function which basically has units
in steradians. Nonetheless, the useof the BRDF is here proposed
Fig. 11. Change of two roughness parameters in function of aging simulation.
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent-
10 J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112
Fig. 12. Gloss prediction for the five transparent coating systems using the
BRDF model.
as an indicator for the gloss changes rather than absolute gloss
values.
It is obvious that these values do not correspond to the mea-
sured values. Therefore the susceptibility of the pigment/resin
complex is changed.
Fig. 13 illustrates the effect of simulated aging on gloss
change at 60 calculated with BRDF (R2) and with adapted
resin and pigment degradation rates. The gloss profile is roughly
similar to the measured values.
An effect that is not incorporated here is the change in refrac-
tive index and extinction coefficient during weathering, which
might explain the differences between theory and practice. All
semi-transparent systems give evidence of darkening, resulting
in an increased extinction coefficient and less reflection. This
effect might cause a decrease in reflection instead of increase
as suggested by the simulation model. For the other coatings
however, the effect of roughness has a higher impact on gloss
than colour change does.
Other explanations for the differences can be attributed to
several simplifications/problems:
specific texture of wood, i.e. alternation of latewood and ear-
lywood zones is not considered;
simulated structures do not incorporate aggregation or coagu-
lation of particles, and it is found that this can influence gloss
[4];
degradation susceptibility of resin/pigment particles is not
fine tuned to different coating systems;
gloss measurement device captures light not limited to
1 reflection, i.e. diffuse light is also measured par-
tially+ imperfections in gloss apparatus;
wavelength dependency of refractive index and gloss [34,35];
chalking is not incorporated as such, i.e. by falling out of
particles and could be incorporated when dealing with more
extreme circumstances.
4. Conclusions
An attempt was made to model the film formation process
using two different methods, based on Hunt et al.[12]and Vidal
et al.[13].Therefore particle sizes, viscosity, evaporation anddensity of theliquidcoatings were measured.Glossof these sim-
ulated surfaces was determined applying a simplified version of
the BRDFfunction, thereby usingthe surface normals, refractive
index and extinction coefficient, the last two calculated follow-
ing the analytical solution of Nichelatti [19] based on reflectance
andtransmittance data of a coating slab.The same procedurewas
followed for surfaces of real specimen, scanned with confocal
scanning laser microscopy. Comparison of scanned, simulated
and measured gloss yielded the general conclusion that abso-
lute gloss prediction is difficult, although relative similarities
are possible. Further research should include visual evaluation
of the model using TEM or other imaging tools [4].Apart fromstatic measurements, a dynamic weathering was applied on the
simulated structures by implementation of a destruction system
similar to the one used in Croll and Hinderliter[22]and Croll et
al.[23].Their application however aims at pigmented systems
on a uniform substrate, whereas the added difficulty here con-
cerns the anisotropic nature of the substrate and the transparency
of the coating. Nonetheless, the results of virtual degradation
demonstrate the usefulness of the theoretical approach using
Fig. 13. Change of gloss in function of aging simulation with adapted susceptibility values and comparison with measured gloss changes during weathering.
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent-
J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112 11
a very comprehensible degradation model, although the model
would probably improve as coagulation is included in the film
formation, the scale of film formation is raised to implement the
waviness of the wood, the reflectance of the wood is mapped,
and colour changes during weathering are included. Further-
more, realistic degradation should also include the influence
of moisture changes on the coating resulting in stressstrain
behaviour [36,37], an effect amplified by theshrinkage andswell
of the substrate. In that way outdoor weathering can be simu-
lated fairly accurately, also taking into account the photon flux,
angle of incidence and chemical susceptibility of different coat-
ing constituents. The impact of rain on loose particles and small
towers of polymeric material might also increase the accuracy
of the model, especially when a more aggressive environment
is simulated. Next to gloss, many other parameters could be
predicted then. Also incorporation of weather data can increase
the accuracy[38].From the point of view of the coatings, the
polyurethane coatings seems to behave very well both in theory
as practice,whereas acrylic systems are inferior. Highglosscoat-
ings are more resistant when considering the roughness changeswithin the time frame monitored. The influence of only slightly
different particle distributions is remarkable.
Withal, simulation is worth the effort and results in a better
understanding of aging and the (inter)relation of coatingwood
properties.
Acknowledgements
The authors owe their gratitude to E. Mol of the Laborato-
ries of Akzo Nobel Decorative Coatings Vilvoorde, Belgium for
the formulation of the coatings and the use of the Micromeritics
pycnometer and Paar Physica rheometer. The assistance of Dr.J. Verschuren (Department of Textile Engineering, Ghent Uni-
versity) with the reflectance and transmittance measurements
is highly appreciated. Furthermore, the authors also would like
to thank Professor P. Van Oostveldt (Department of Molecular
Biotechnology, Ghent University) for the use of the confocal
scanning laser microscope.
References
[1] S.T. Chang, D.N.S. Hon,W.C. Feist, Photodegradationand photoprotection
of wood surfaces, Wood Fiber 14 (1982) 104117.
[2] M. de Meijer, Review on the durability of exterior wood coatings withreduced VOC-content, Prog. Org. Coat. 43 (2001) 217225.
[3] M. Elimelech, J. Gregory, X. Jia, R.A. Williams, Particle Deposition
& AggregationMeasurement, Modelling and Simulation, Butterworth-
Heinemann, Woburn, 1995.
[4] F. Tiarks,T. Frechen, S. Kirsch, J. Leuninger, M. Melan, A. Pfau, F. Richter,
B. Schuler, C.L. Zhao, Formulation effects on the distribution of pigment
particles in paints, Prog. Org. Coat. 48 (2003) 140152.
[5] G. Eksi, D.W. Bousfield,Modeling of coating structuredevelopment, Tappi
J. 80 (1997) 125135.
[6] R.Y. Yang, R.P. Zou, A.B. Yu, Computer simulation of the packing of hue
particles, Phys. Rev. E 62 (2000) 39003908.
[7] A.R. Kansal, S. Torquato, F.H. Stillinger, Computer generation of dense
polydisperse sphere packings, J. Chem. Phys. 117 (2002) 82128218.
[8] J.F. Zhang, R. Blaak, E. Trizac, J.A. Cuesta, D. Frenkel, Optimal packing
of polydisperse hard-sphere fluids, J. Chem. Phys. 110 (1999) 53185324.
[9] M.S. Chun, Computer simulation study on the concentrationdistribution of
sphericalcolloids within confined spaces of well-defined pores, Macromol
Theory Simul. 8 (1999) 418427.
[10] M.E.McKnight,J.W.Martin, Advanced methodsand models fordescribing
coating appearance, Prog. Org. Coat. 34 (1998) 152159.
[11] D.P. Bentz, E.J. Garboczi, C.J. Haecker, O.M. Jensen, Effects of cemen
particle size distribution on performance properties of Portland cement-
based materials, Cem. Concr. Res. 29 (1999) 16631671.
[12] F.Y. Hunt, M.A. Galler, J.W. Martin, Microstructure of weathered painand its relation to gloss loss: computer simulation and modelling, J. Coat.
Technol. 70 (1998) 4554.
[13] D. Vidal, X.J. Zou, T. Uesaka, Modeling coating structure developmen
using a Monte Carlo deposition method. Part 1. Modeling methodology,
Tappi J. 2 (2003) 38.
[14] A. Temiz, U.C. Yildiz, I. Aydin, M. Eikenes, G. Alfredsen, G. Colakoglu
Surface roughness and color characteristics of wood treated with preser-
vatives after accelerated weathering test, Appl. Surf. Sci. 250 (2005
3542.
[15] X.F. Yang, S.G. Croll, Accelerated exposure of pigmented anticorro
sion coating systems, Surf. Coat. Int. Part B: Coat. Trans. 87 (2004) 7
13.
[16] R.S. Williams, W.C. Feist, Effect of preweathering, surface-roughness, and
wood species on the performance of paint and stains, J. Coat. Technol. 66
(1994) 109121.
[17] K. Richter, W.C. Feist, M.T. Knaebe, The effect of surface-roughness on
the performance of finishes. 1. Roughness characterization and stain per-
formance, For. Prod. J. 45 (1995) 9197.
[18] M. Hebert, P. Emmel, R.D. Hersch, A prediction model for reflection on
varnished metallic plates, in: Proceedings of the FirstEuropeanConference
on Color in Graphics, Imaging and Vision, Poitiers, 2002.
[19] E. Nichelatti, Complexrefractive index of a slabfrom reflectanceand trans-
mittance: analytical solution, J. Opt. A: Pure Appl. Opt. 4 (2002) 400
403.
[20] M.E. McKnight, T.V. Vorburger, E. Marx, M.E. Nadal, P.Y. Barnes, M.A
Galler, Measurements and predictions of light scattering by clear coatings
Appl. Opt. 40 (2001) 21592168.
[21] L.P. Sung, M.E. Nadal, M.E. McKnight, E. Marx, B. Laurenti, Optica
reflectance of metallic coatings: effect of aluminum flake orientation, J.
Coat. Technol. 74 (2002) 5563.
[22] S.G. Croll, B.R. Hinderliter, Monte Carlo approach to estimating coating
service lifetime during weathering, Surf. Coat. Int. Part B: Coat. Trans. 88
(2005) 177183.
[23] S.G. Croll, B.R. Hinderliter, S.S. Liu, Statistical approaches for predicting
weathering degradation and service life, Prog. Org. Coat. 55 (2006) 75
87.
[24] C.H. Tsai, An assessment of a time-of-transition laser sizer in measuring
suspended particles in the ocean, Mar. Geol. 134 (1996) 95112.
[25] H. Saveyn,T.L. Thu,R. Govoreanu, P. Van der Meeren, P.A. Vanrolleghem
In-line comparison of particle sizing by static light scattering, time-of-
transition, and dynamic image analysis, Part. Part. Syst. Char. 23 (2006)
145153.
[26] J. Van den Bulcke, V. Rijckaert, J. Van Acker, M. Stevens, Quantitative
measurement of the penetration of water-borne coatings in wood with con-focal laser microscopy and image analysis, Holz Roh Werkst. 61 (2003)
304310.
[27] P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves
from Rough Surfaces, MacMillan, New York, 1963.
[28] J. Van den Bulcke, V. Rijckaert, J. Van Acker, M. Stevens, Adhesion
and weathering performance of water-borne coatings applied to differ-
ent temperate and tropical wood species, J. Coat. Technol. 3 (2006
185191.
[29] D. Vidal, X.J. Zou, T. Uesaka, Modeling coating structure developmen
using a Monte Carlo deposition method. Part 2. Validation of the model
and case study, Tappi J. 2 (2003) 1620.
[30] L.F. Gate, J.S. Preston, The specular reflection and surface-structure of
emulsion paint films, Jocca-Surf. Coat. Int. 78 (1995) 321330.
[31] G.T. Nolan, P.E. Kavanagh, Computer-simulation of particle packing in
acrylic latex paints, J. Coat. Technol. 67 (1995) 3743.
-
5/25/2018 Modelling Film Formation and Degradation of Semi-transparent Exterior W...
http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent-
12 J. Van den Bulcke et al. / Progress in Organic Coatings 58 (2007) 112
[32] S.H. Westin, J.R. Arvo, K.E. Torrance, Predicting reflectance functions
from complex surfaces, in: Proceedings of the SIGGRAPH92, Comput.
Graphics 25 (1992) 255264.
[33] X.F. Yang, D.E. Tallman, G.P. Bierwagen, S.G. Croll, S. Rohlik, Blister-
ing and degradation of polyurethane coatings under different accelerated
weathering tests, Polym. Degrad. Stab. 77 (2002) 103109.
[34] W.E. Vargas, Optical properties of pigmented coatings taking into account
particle interactions, J. Quant. Spectrosc. Radiat. Transfer 78 (2003)
187195.[35] W.E. Vargas, D.E. Azofeifa, N. Clark, Retrieved optical properties of thin
films on absorbing substrates from transmittance measurements by appli-
cation of a spectral projectedgradientmethod, ThinSolid Films 425(2003)
18.
[36] M. Oosterbroek, R.J. Lammers, L.G.J. Vanderven, D.Y. Perera, Crack for-
mation and stress development in an organic coating, J. Coat. Technol. 63
(1991) 5560.
[37] D.Y. Perera, On adhesion and stress in organic coatings, Prog. Org. Coat.
28 (1996) 2123.
[38] D. Burch, J.W. Martin, M.R. Van Landingham, Computer analysis of a
polymer coating exposed to field weather conditions, J. Coat. Technol. 74(2002) 7586.