1266 Volume 57, Number 10, 2003 APPLIED SPECTROSCOPY0003-7028 / 03 / 5710-1266$2.00 / 0q 2003 Society for Applied Spectroscopy

Infrared Re� ection–Absorption Spectra of Metal-EffectCoatings

MARTA KLANJS† EK GUNDE* and MATJAZ† KUNAVERNational Institute of Chemistry, Hajdrihova 19, SI-1001 Ljubljana, Slovenia

The results of studies of infrared re� ection–absorption spectra ofmetal-effect coatings are presented in this paper. Such coatings con-sist of metallic � akes that are dispersed in a polymer binder. Thespectra show two distinct phenomena. One is due to the polymermatrix. The other is due to metallic � akes that are dispersed insidethe layer. The polymer binder causes narrow spectral lines that givea thickness-dependent intensity and position. Metallic � akes changethe average baseline of this spectrum over the entire infrared spec-tral region. This particular effect was evaluated using a simplerough-surface model. Two parameters of the model, the root-mean-square roughness and the correlation length of the rough surface,described the re� ection of the partial beams on the metal � ake sur-faces and scattering on � akes boundaries. The other two parametersare the specular re� ectance and the diffuse re� ectance of the planeuntextured interface between the polymer matrix and the metal� ake surface. Various metal-effect coatings within the same polymerbinder were analyzed. The effect of each metal � ake dispersion wasevaluated by the parameters within the rough-surface model. Theresults were analyzed in terms of the size and the loadings of � akesthat were used in the coatings.

Index Headings: Re� ection–absorption spectroscopy; Metal-effectcoatings; Rough-surface model; Metallic � akes; Optical effects.

INTRODUCTION

Various kinds of platelet pigment are used in moderncoating formulations. This is particularly true for auto-motive coatings. Such pigments are frequently termedluster pigments. When such � akes are dispersed in a near-ly transparent polymeric binder and applied to a sub-strate, they generate additional effects such as angle-de-pendent lightness and hue. The term effect coatings de-notes coatings that provide such angle-dependent ef-fects.1,2

The simplest of luster pigments are the metal-effectpigments. In these, the specular re� ection of light on the� ake surface and scattering on their edges are responsiblefor the angle-dependent optical effects.1–4 Metallic � akesare produced mostly from aluminium in a more-or-lessnarrow particle size distribution. Flakes with a large va-riety of average lateral diameters, ranging from a fewmicrometers up to 100 mm are commercially available,usually produced as lea� ng types and as non-lea� ngtypes. Lea� ng � akes have low surface tension and tendto � oat near the coating surface of the wet coating. Such� akes are distributed near the surface of the cured � lm.Non-lea� ng � akes have a higher surface tension. There-fore, they disperse more evenly through the coating � lm.Here, they act as a large number of minute mirrors lyingat various depths, in various directions. The visual ap-

Received 13 March 2003; accepted 2 June 2003.* Author to whom correspondence should be sent. E-mail: marta.k.

gunde@ki.si.

pearance of such a coating strongly depends on the illu-mination and viewing directions, generating the angle-dependent lightness and hue of the entire coating.5,6 Inthis paper, only those coatings that contain non-lea� ngmetallic � akes are considered.

Matching of the angle-dependent optical effects andthe hue of effect coatings is one of the major problemsof paint research, development, and technology. Mostmethods used for this purpose were developed for coat-ings that contained conventional pigments, for which an-gle-dependent effects are reduced, minimal, or nonexis-tent.7–9 That is the major reason why the microstructureof the metal-effect coatings was analyzed in the � rstplace, using different methods, with special attention be-ing paid to the dispersion and the orientation of metallic� akes in the coatings.10–14 Each of these methods providesunique information concerning metallic � akes and theirin� uence on coating appearance. It is possible to detectthe geometric screening and the optical screening ofneighboring � akes.14 The inclination angle of the selected� ake was measured nondestructively by ion microbeamanalysis.13,14 In most cases, the � akes were oriented ap-proximately parallel to the coating surface.

There are very few reports in the literature that dealwith the analysis of metal-effect coatings using infrared(IR) spectroscopy. Among these are forensic scienceanalyses of automotive � nishes by diffuse re� ectanceFourier transform infrared (FT-IR) spectroscopy.15,16 Ithas been shown that the density of metallic � akes usedin these paints is the primary factor in determining theapplicability of the FT-IR method to analysis.

The optical properties of materials, based on a dielec-tric matrix with polarizable inclusions, that are smallcompared to the wavelength, may be described by theeffective medium theory.17 The concepts of this theorycan be used in a wide variety of applications, especiallyin condensed materials that possess some kind of granularstructure. This way, the optical response function of thepolycrystalline material can be calculated from data ofits monocrystalline form.18 The theory has also been ap-plied to rough surfaces.18,19 However, the applicability ofthe effective medium theory is restricted to small inclu-sions with, in principle, spherical symmetry. Both de-mands can hardly be accomplished in metal-effect coat-ings.

The average scattering function that describes the op-tical properties of effect coatings is extremely compli-cated. Only a few approaches have been published onthis subject. In one publication, the average backscattercross-section of arbitrarily oriented metallic � akes at op-tical frequencies has been calculated.20 This concise the-oretical work has only a limited value for effect coatings

APPLIED SPECTROSCOPY 1267

FIG. 1. Specular re� ectance of the surface, calculated using Eq. 2.

in which the � akes tend to orient parallel to the samplesurface.10–14

A theoretical model for describing the appearance ofeffect coatings was proposed recently.21 This model con-sists of three sub-models, dealing successively with therough polymer surface, the � ake inside layer, and the dif-fuse basecoat, often applied as an undercoat. This theo-retical model was applied for calculation of the angle-resolved re� ectance and for the orientation distribution of� akes in metal-effect coatings.12

This work continues the study of optical effects en-countered in a study of the IR re� ection–absorption spec-troscopy (IR-RAS) of a fairly thick polymer coating, pub-lished recently.22 A simple model for the optical in� uenceof metallic � akes when they are enclosed in a polymerlayer was developed. For this purpose, simple relationsbetween the surface roughness and the normal-incidencere� ectance of the layer were applied to the metallic � akesthat were distributed within the metal-effect coatings. Theparameters of the simple rough-surface model were re-lated to the microstructure of metallic � akes in the metal-effect coatings.

THEORY

The system studied in this paper consisted of a poly-mer layer containing minute mirrors (metallic � akes), ly-ing at various depths in a way that was approximatelyparallel to the sample surface. A re� ective metal substratewas used. The IR beam impinged the coating surface ata near-normal incidence angle and the intensity of spec-ularly re� ected light was measured. This was the exper-imental setup for the IR-RAS measurements.23 The basicoptical phenomena affecting the measured spectrum werethe re� ection at polymer–metal interfaces, the IR absorp-tion inside the polymer, and the scattering of the IR lightat the edges of the metallic � akes.

Re� ection at polymer–metal interfaces and IR absorp-tion inside the polymer were presented in detail in theprevious article, in which the IR-RAS spectra of a clear-coat (non-pigmented) system were analyzed.22 The IR-RAS spectra are similar to transmittance spectra with aneffective path length of the double thickness of the � lm,in thin layers only. With increasing thickness, the peakintensity and the position changed as a consequence ofcontinuous transformation of a spectral dip (occurring inthe transmission-like spectrum) towards the constant val-ue of bulk re� ectance (i.e., the shape of reststrahlenbands). This transformation caused one or two additionalpeaks to arise that could be resolved at moderate opticalthickness. The bulk re� ectance shape appeared initiallyin a narrow spectral region around the band, with stronginterference fringes on both sides. When the thicknessincreased, this ‘‘bulk spectral region’’ broadened.22

Interferences that were due to successive re� ections atpolymer–metal interfaces and the IR absorption inside thepolymer layer occurred as more-or-less narrow spectralfeatures. However, the spectral dependence of scatteringwas spread over a much broader spectral region. It istherefore very likely that both effects would be possibleto resolve. The scattering of IR light at the edges of me-tallic � akes was generated by the distribution of � akesinside the polymer layer. This distribution, in turn, may

be considered to act as a rough surface structure. Thespectral re� ectance of this structure was described by thesimple rough-surface model that was derived originallyby Davies for the scattering of radar waves from a roughwater surface.24 The theory was developed further byBennett and Porteus25,26 for the plane surfaces of a con-ductor that had surface irregularities that were small com-pared to the wavelength. This model has been applied tovarious rough surfaces. For example, the surfaces usedin solar thermal energy conversion systems were studied.Here, the spectrally selective optical properties wereachieved by the appropriate surface structure.27 Accord-ing to this approach, the surface was described by a sta-tistical model. In the model, the following assumptionsare assumed to have validity:

(1) The standard deviation of the surface, i.e., the root-mean-square (rms) deviation from its main level,or the rms roughness (s), is small compared to thewavelength, l.

(2) The distribution of surface irregularities is Gauss-ian about the mean surface level.

(3) The autocovariance function of the surface irreg-ularities is Gaussian, with the standard deviation, a.

The net re� ectance (R(l)) of such a rough surface that isilluminated by a parallel beam of wavelength l that is ata near-normal incidence angle is a sum of two contribu-tions. One of these contributions could be due to specularre� ection and the other would be due to diffuse re� ectionor scattering.24–27 Thus:

R(l) 5 R s(l) 1 Rd(l) (1)

Here, Rs(l) denotes the specular contribution and Rd(l)denotes the diffuse contribution to the net re� ectance.The specular re� ectance of such a system can be de-scribed by the following equation:24–27

Rs(l) 5 R0,sexp[2(4ps/l)2] (2)

Here, R0,s denotes the specular re� ectance of the planeuntextured surface made from the same material. s is therms roughness of the surface and l is the wavelength ofthe incident light. According to the Eq. 2, at small lvalues, the specular re� ectance Rs approaches to zero.When l increases, the re� ectance slowly increases andtends to reach the R0,s value. The rate of change dependson the rms roughness s: the smaller the value of the s,the narrower the spectral region, where specular re� ec-tance rises to the R0,s value (see Fig. 1).

1268 Volume 57, Number 10, 2003

FIG. 2. Diffuse re� ectance of the rough surface calculated using Eq.3: (a) variation of a and R0,d for s 5 1 mm, and (b) variation of s forR0,d 5 1, a 5 10 mm.

TABLE I. Data for the applied aluminum � akes: the size distri-bution and the average particle sizes in the pigment concentrate.All � akes are of the non-lea� ng types and of the ‘‘silver dollar’’shape. The form factor (the quotient of the � ake thickness dividedby the � ake diameter) is from 1:50 to 1:500. Data is from the pro-ducer, Eckart Werke Germany.

Sample Size distribution, mm Average size, mm

V1V2V3

5–196–37

34–75

121849

The diffuse contribution (Rd(l)) to the near-normal re-� ectance of the rough surface is de� ned as: 24–27

2 2R (l) 5 R [1 2 exp(4ps /l) ]{1 2 exp[2(pah /l) ]}d 0,d

(3)

Here, R0,d is the diffuse re� ectance of the plane, untex-tured surface made from the same material, h is the coneacceptance angle of the measuring equipment, and a isthe correlation length of the rough surface. The measuredpart of the diffuse re� ectance depends strongly on theacceptance angle during measurements (h). For non-hemispherical measurement geometry, this angle is � xedat a small value. The diffuse re� ectance at � xed h de-pends on a, R0,d, and s according to Eq. 3. This is illus-trated in Fig. 2, for which the diffuse re� ectance wascalculated with a � xed value of h 5 0.21 (acceptanceangle of approximately 128). At small wavelengths l, thediffuse re� ectance of the rough surface approaches R0,d.At larger wavelengths the diffuse re� ectance slowly ap-proaches to zero value. The rate of the change dependson two parameters, the correlation length (a) and the rmsroughness (s) of the surface. Larger a values lead to abroader spectral region where the diffuse re� ectance isequal to R0,d. However, the variation in h has practicallyno in� uence.

EXPERIMENTAL

Materials. Metal-effect pigment concentrates that con-tained three different sizes of non-lea� ng aluminium� akes were used in our study. The corresponding data aregiven in Table I. All of the pigments were of the non-

lea� ng types and of the ‘‘silver dollar’’ shape, i.e., theyhad smooth edges. All of the coatings were prepared us-ing an acrylic binder, with the addition of 1 vol %, 3 vol%, and 5 vol % of aluminium � ake concentrates to theacrylic base during constant mixing. Two additives wereincluded in the formulation (silicon based and a wax dis-persion) to improve leveling and orientation of the alu-minium � akes. Wet samples were air-sprayed under thesame conditions and in the same manner over aluminiumsheets to a thickness of approximately 20 mm. This is atypical thickness for automotive applications of effectcoatings. Clear-coat samples with different thicknesses(10–30 mm) were prepared using similar formulation,without aluminium � akes. The thickness of all coatingswas measured using a micrometer assembly.

Measurements. The IR-RAS spectra of all sampleswere measured using a Fourier transform infrared spec-trophotometer, Perkin-Elmer System 2000, equipped witha near-normal specular re� ectance accessory in the 5000to 400 cm21 wavenumber region (2 mm , l , 25 mm).The measurement acceptance angle was estimated to bearound 12–158. An uncoated aluminium sheet was usedas the reference. The substrate roughness was treated inthis way. No polarization of IR light was applied. TheIR spectrum of the binder itself was measured in thetransmission mode. For this purpose, the very thin binderlayer was prepared on the NaCl plate and measured withtransmission measurement geometry.

RESULTS AND DISCUSSION

Infrared spectral features in IR-RAS spectra are gen-erated from the contributions of the polymer binder andof the aluminum � akes. The binder generates the IR ab-sorption bands in the so-called � ngerprint region. Thealuminium � akes affect the baseline within the wholespectral region.

Infrared Bands Due to the Polymer Binder. The IR-RAS spectra of different layer thicknesses of binder lay-ers are represented in Fig. 3. All of the IR-RAS spectraare strongly thickness dependent. To analyze various op-tical effects for the particular layer thickness and mea-suring geometry, the IR transmission spectrum of the thinbinder layer was measured. This spectrum is also shownin Fig. 3.

Two types of optical phenomena were evaluated in theIR-RAS spectra of binder layers. These are the interfer-ence fringes and the distortion of absorption bands. Botheffects are thickness dependent. The interference fringesare generated by multiple re� ections of the IR beamthroughout the layer. They can be seen most clearly inthe transparent part of the spectrum (2700–1880 cm21).

APPLIED SPECTROSCOPY 1269

FIG. 3. IR transmission spectrum of the binder and IR-RAS spectra ofthe clear-coat layers on the aluminium substrate. The correspondinglayer thicknesses (in mm) are denoted in the � gure.

FIG. 5. IR-RAS spectra of some effect coatings: (a) concentration ef-fect and (b) size effect. The IR-RAS spectrum of the clear coat is shownfor comparison. Thickness of all coatings is approximately 20 mm.

FIG. 4. Optical distortions in IR-RAS spectra of the binder layers: (a)the thickness-dependent intensity of the weak IR band, and (b) theformation of the reststrahlen band for the strong IR band. The corre-sponding layer thicknesses (in mm) are indicated on the � gure. The IRtransmission spectrum of the binder is shown for comparison.

The two successive maxima (or minima) may be used tocalculate the thickness, d, of the layer if its refractiveindex, n, in the particular transparent part of the spectrumis known. The equation used for this purpose is:

2n( 2 2 1)d 5 1n n (4)

Here, 1 and 2 denote the wavenumbers of two succes-n nsive interference maxima or minima. The refractive indexof the binder used, in the transparent region, was calcu-lated using this equation, considering the measured layerthickness. The value n 5 1.5 6 0.03 was obtained in thisway.

Some theoretically predicted distortions of absorption

bands22 were also obtained in the present work. Thethickness-dependent peak intensity can be observedclearly from the weak phonon band of mono-substitutedbenzene in the para position, located at 845 cm21 (Fig.4a). The carbonyl band at 1733 cm21 appears in all IR-RAS spectra in the bulk re� ectance shape (i.e., reststrah-len band). Here, the original spectral dip is already trans-formed into the re� ectance peak that is oriented upwards.Its intensity is independent of the layer thickness (Fig.4b).

Spectral Properties of Coatings Containing Alumin-ium Flakes. When aluminium � akes are distributed with-in the coating, the IR-RAS spectrum changes signi� -cantly. This is shown in Fig. 5 where the spectrum of theclear coat is compared to the spectra of some metal-effectcoatings. The in� uence of different loadings of the � akesis shown in Fig. 5a where the spectrum of clear coat iscompared to the spectra of effect coatings containing 1vol %, 3 vol %, and 5 vol % of the V1 � akes. The sizeeffect is shown in Fig. 5b. Here, the IR-RAS spectra ofeffect coatings with 3 vol % of V1, V2, and V3 � akesare shown (see also Table I). Similar spectra were ob-served on samples that contained other types of � akes.The � gures show that the spectral shape of the baselinedepends on the size and the loadings of � akes inside thecoating. The IR absorption bands, due to the polymerbinder, are detected only if the baseline is higher than;8%. Below this re� ectance, only upward-oriented peakswith the reststrahlen shape are detected. The spectral re-gion with the interference fringes starts at much higherwavelengths (i.e., lower wavenumbers) than for the dryclear-coat formulation. Fringes appear only for coatings

1270 Volume 57, Number 10, 2003

FIG. 6. Fitting results for specular (dashed line) and diffuse component(points) of the rough surface model applied for effect coatings with (a)1 vol %, (b) 3 vol %, and (c) 5 vol % of V1 � akes.

with a small loading of � akes and/or if larger � akes areused. Otherwise, they are completely masked, most likelydue to the scattering on the edges of � akes. No interfer-ence fringes that were generated by the multiple re� ec-tions between neighboring � akes were detected. Theseresults con� rm issues raised in the IR analysis of auto-motive � nishes in forensic science applications15,16 andshow the conditions for applicability of the analyticalmethod.

Figure 5 shows that the average baseline dependsmostly on the properties of the � akes, and therefore, thecontribution of transparent medium can be neglected. Thealuminium � akes that were distributed in a metal-effectcoating can be described as a rough surface. The param-eter, s, of the simple rough-surface model is related tothe height of the surface irregularities. For our system, smay be estimated from the average thickness of metallic� akes. Flake-shaped pigments have an extremely largeform factor of 1:50 to 1:500, i.e., the ratio between � akethickness and � ake diameter. Then, the thickness of allapplied � akes is well below 0.5 mm (see also Table I). Itmay be concluded that s is considerably smaller than thewavelength of the IR light. We infer that the distributionof the heights and of the lateral extensions of the roughsurface structure are Gaussian. Therefore, the simplerough surface model (Eqs. 1–3) was applied to the anal-ysis of the distribution of � akes inside the coatings. Here,the � akes are oriented parallel to the coating surface, asproven by various experiments.13,14

In order to apply the rough surface model, the scale ofthe measured spectra was transformed from the wave-number (in cm21) basis to the wavelength l (in mm)mode. Calculation was achieved by the � tting of the mea-sured re� ectance with the analytical function, obtainedby combining Eqs. 1–3. The rms roughness (s), the cor-relation length (a), and the specular and the diffuse re-� ectance of the untextured surface (R0,s and R0,d, respec-tively) were considered as free parameters in the proce-dure. These de� ne the average envelope of the IR-RASspectrum well within a reasonable error. All of the cal-culations were performed using the Origin t software(Microcal Software), applying the built-in nonlinear least-squares � tting procedure. The complete IR-RAS spec-trum of a metal-effect coating was used for the � t curve.The � tting function was de� ned according to Eqs. 1–3.Here, s, a, R0,s, and R0,d were considered as the � ttingparameters. The procedure was controlled by suitableconstraints applied to � tting parameters. This way, theirphysical meaning was preserved (e.g., negative valueswere protected). Those spectra that had almost no fringescould be � tted to tight tolerances. However, for the spec-tra with strong fringes, lower tolerances were applied.Therefore, different errors were obtained for the same� tting parameter in various samples.

The results for the samples containing 1 vol %, 3 vol%, and 5 vol % of V1 � akes (their IR-RAS spectra aregiven in Fig. 5a) are shown in Fig. 6. The � tting param-eters for all of the samples are shown in Fig. 7. Thefringes were very clearly observed if a small concentra-tion of � akes is used and/or if large � akes are used.Therefore, different errors for different � ake loadings anddimensions were obtained. They are shown as error barsin Fig. 7.

At higher volume loadings of the � akes, larger s val-ues are to be expected. Nevertheless, such an effect wasobtained only at loadings of � akes that were lower than3 vol % (Fig. 7a). When the loading of the � akes isincreased above this value, s diminishes. This effect maybe explained by invoking an optical screening effect. Be-cause of this, the light cannot scatter from entire metallicboundaries of all � akes. Thus, the height of surface ir-regularities gets smaller.

At 1 vol % of � akes, s slowly increases with the sizeof the � akes (Fig. 7a). This � nding is in good agreementwith the predictions from the model. If larger � akes areused at a � xed volume loading, the number of � akes issmaller. This effect is described by the higher surfaceirregularities in the rough surface model, i.e., larger s.At higher loadings of � akes this effect is most likelycombined with the optical screening effect. The net result

APPLIED SPECTROSCOPY 1271

FIG. 7. Fitting parameters as a function of the average particle size of aluminium � akes: (a) rms roughness, s, (b) correlation length, a, (c) specularre� ectance of the plane untextured surface, R0,s, and (d ) diffuse re� ectance of the plane untextured surface, R0,d. The calculation errors are representedby error bars.

is a diminishing of the s value when coatings with larger� akes are analyzed. The optical screening effect was alsodetected for similar effect coatings using optical spec-troscopy in the visible and IR spectral regions.14 The det-rimental effect of a higher loading of aluminium � akeswas found in coatings that contained between 3 vol %and 5 vol % of � akes.

Parameter a depends on the size of � akes and on theirloading in the coating (Fig. 7b). For coatings with larger� akes, larger a values were obtained. For smaller volumeloadings of � akes with equal size, the value of parametera is higher. Therefore, both dependencies of correlationlength a (i.e., as a function of the size of � akes and oftheir loading) can be explained by the lateral dimensionsof � akes inside a particular coating. If large � akes areused, the lateral dimensions of the aluminium structurethat scatters the IR light inside the effect coating are larg-er too. The effect is not linear; the rate of change dimin-ishes when larger � akes are applied.

R0,s and R0,d are the two further � tting parameters ofthe simple rough-surface model. They represent the spec-ular re� ectance and the diffuse re� ectance, respectively,of the plane untextured surface made from the same ma-terial. These parameters in� uence the IR-RAS spectrumin the separate spectral regions, R0,d at lower wavelengthsand R0,s at higher wavelengths. These values may there-fore have different magnitudes. Such results were ob-tained for our samples (Figs. 7c and 7d). Both � ttingparameters depend on the volume loading of the � akesand on the size of the applied � akes. The reasons for thisconcern the optical properties of the plane untextured sur-

face made from the same material. This is a � ctitioussample, representing the effective interface between thepolymer and the aluminium � ake. Its properties maychange with the size of � akes and with their volume load-ings. The properties of parameter R0,d are the most inter-esting from the analytical point of view. The R0,d valuedepends linearly on the size of � akes, at a � xed volumeloading of � akes (Fig. 7d). The value of the R0,d is higherfor coatings that have a smaller loading of � akes. Theoptical screening effect becomes important for larger vol-ume loadings. However, the values of the R0,d parameterdo not change with further increase in the loading of� akes.

CONCLUSION

The IR-RAS spectra of metal-effect coatings involvetwo speci� c optical phenomena, one caused by the ab-sorption of IR light inside the polymer binder, the otherby the re� ection and scattering of light by the system thatcontains metallic � akes dispersed inside the coating. Bothhave a completely different spectral dependence and canbe separated accordingly.

The polymer binder generates narrow spectral bandswith a thickness-dependent intensity and position. Mul-tiple re� ections of the IR beam throughout the layer maygenerate interference fringes that are superimposed on thespectrum of the polymer binder. The metallic � akes dis-turb the constructive interference and, because of this, inthe IR-RAS spectra of effect coatings with higher volumeloading of � akes no interference fringes appear.

1272 Volume 57, Number 10, 2003

The most important in� uence of metallic � akes is thechange in the average baseline that occurs over the entirespectral region in the IR-RAS spectra of metal-effectcoatings. The simple rough-surface model with four pa-rameters might describe this effect. Two parameters ofthe model denote the properties of the rough surface: therms roughness, s, and the correlation length, a. The othertwo parameters are the specular re� ectance and the dif-fuse re� ectance of the plane untextured interface betweenthe polymer and aluminium � ake surface. All of the fourparameters of the model depend on the size and on thevolume loadings of � akes that are distributed inside thecoatings. The optical screening effect was detected whenthe loading of the � ake was increased above 3 vol %.This particular effect was obtained for all sizes of alu-minium � akes. The size effect is manifested most clearlyin changes of parameters a and R0,d at � xed volume load-ings. Both increase with the size of � akes used. The pa-rameter R0,d increases linearly.

The simple theoretical model was used to evaluate thein� uence of metallic � akes on the IR-RAS spectra of apolymer binder. This model was derived originally forapplication with randomly rough surfaces, with rmsroughness values that are small compared to the wave-length, and considers only the essential features of thecomplex effect. Nevertheless, the theoretical model de-tects the variations in the size of � akes and their loadinginside the coatings. This may represent a basis for prac-tical application to the analysis of metal-effect coatings.Moreover, it offers the possibility of predicting the opticalproperties of such samples over a wide IR spectral region.

ACKNOWLEDGMENTThe authors acknowledge Mrs. Natas†a Barle (Color Medvode, Slo-

venia) for her carefu l preparation of the samples and for her helpfulsuggestions.

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