modelling film formation and degradation of semi-transparent exterior wood coatings --2007

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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
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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



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.




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]).




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.




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.




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).




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).




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.


http:///reader/full/modelling-film-formation-and-degradation-of-semi-transparent-


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.




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.

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modelling film formation and degradation of semi-transparent exterior wood coatings --2007

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