Determination of exact absorption behaviour in the mid-infrared spectral range of poly(methylmethacrylate) by Fourier transform infrared reflection spectroscopy

Polymer International 44 (1997) 11È18

Determination of Exact AbsorptionBehaviour in the Mid-infrared SpectralRange of Poly(methylmethacrylate) by

Transform Infrared ReflectionFourierSpectroscopy

Maurice Brogly,* Sophie Bistac & Jacques Schultz

CNRS È Institut de Chimie des Surfaces et des Interfaces, 15 rue Jean Starcky, BP 2478, F-68057 Mulhouse Cx, France

(Received 23 December 1996 ; revised version received 24 February 1997 ; accepted 23 March 1997)

Abstract : In the present work we demonstrate that infrared absorption fre-quencies and band shapes of poly(methylmethacrylate) (PMMA) homopolymersvary strongly with the type of spectra recorded. The reason is that, in general,any measured optical quantity, such as absorption, transmittance or reÑectance,is a complicated function of the refractive index, n(l), and the absorption index,k(l), of the material. KramersÈKronig analysis is applied to external reÑectionspectra from a single polymer surface measured near the normal incidence angle.Absorption spectra, k(l), are then deduced and used to calculate grazing anglespecular reÑectance, attenuated total reÑectance, di†use reÑectance and transmis-sion spectra. Then, it is shown that the calculated spectrum for each experimentaccurately predicts the experimental one, proving that di†erences are optical arti-facts and not true sample di†erences. Exact peak absorption for PMMA is1730 cm~1 and should be taken as a reference value for the calculation of fre-quency shifts for further physico-chemical interpretation such as speciÐc inter-actions or molecular orientation.

Polym. Int. 44, 11È18 (1997)No. of Figures : 8. No. of Tables : 3. No. of References : 12

Key words : PMMA homopolymer, infrared spectroscopy, absorption coefficient,spectrum simulation

INTRODUCTION

Fourier transform infrared (FTIR) spectroscopic studiesperformed on polymers are generally done by measure-ments of transmission or absorption spectra as well asattenuated total reÑection (ATR) spectra. For quantitat-ive purposes, such as identiÐcation of compounds, thisapproach is satisfactory. Likewise, quantitative mea-surements can be made on dilute solutions. For concen-trated or strongly absorbing samples, however,

* To whom all correspondence should be addressed.

relationships such as BeerÏs law are frequency invalidand the band shapes may be distorted so that thecentral frequencies are altered. In the present work wedemonstrate that infrared absorption frequencies ofpoly(methylmethacrylate) (PMMA) homopolymers varystrongly with the type of spectra recorded. The reason isthat, in general, any measured optical quantity, such asabsorption, transmittance or reÑectance, is a compli-cated function of the refractive index, n(l), and theabsorption index, of the material. It is then evident thatquantitative optical properties of the sample could becalculated from a knowledge of the values of n(l) and

111997 SCI. Polymer International 0959-8103/97/$17.50 Printed in Great Britain(

12 M. Brogly, S. Bistac, J. Schultz

k(l) as a function of frequency. Real and imaginaryparts of a complex physical quantity describing theinteraction of matter with electromagnetic radiation,such as complex refractive index, are not independent ofeach other, but one part can be calculated by KramersÈKronig analysis if the other part is known. Graf andco-workers1 proposed the calculation of optical con-stants of polymer Ðlms, such as polyvinyl chloride andpolystyrene, by using KramersÈKronig transformation.The transformation they used required speciÐc data,such as the refractive index at inÐnite frequency. From atheoretical point of view, there exist two kinds ofKramersÈKronig analysis : the Ðrst1h2 employs aHilbert transformation from the extinction coefficient,k(l), to the refractive index, n(l), while the second3h6employs that from the power reÑectivity, R(l) to thephase shift, d(l), for reÑection. Bardwell & Dignam3,4have proposed an exhaustive mathematical develop-ment that extends the KramersÈKronig transformationto organic and inorganic materials that exhibit strongabsorption bands, and for analysis at non-normal inci-dence angles (reÑectionÈabsorption infrared). On theother hand, Yamamoto & Masui6 applies this formal-ism to extract the complex refractive index of isotropiccrystals, ceramics and glasses. We decided to apply thisformalism to polymers. While the second approachcannot be applied to transmission spectra, it has somedistinct advantages over the Ðrst kind of KramersÈKronig analysis ; namely, it does not require least-squares reÐnement calculations, which often diverge forstrong dispersion, and, secondly, no prior information(such as the refractive index at inÐnite frequency) aboutthe sample material is required. In this paper, KramersÈKronig is applied to external reÑection spectra from asingle polymer surface measured near the normal inci-dence angle. Absorption spectra, k(l), are then deducedand used to calculate grazing angle specular reÑectance,ATR, di†use reÑectance and transmission spectra. Com-parisons with experiments are discussed.

THEORY

When electromagnetic radiation interacts with thesurface of an absorbing medium in a reÑection experi-ment, it obeys FresnelÏs laws. The complex FresnelreÑection coefficient at the interface between two mediais expressed as follows :

rü (l) \ JR(l)exp(id(l)) (1)

where d(l) is the phase change of the reÑected wave (atwavenumber l) and R(l) is the power reÑectivity (i.e. theintensity measured by the IR detector). The relationshipbetween the reÑected wave phase change, d(l), and itsmagnitude, R(l), follows a Hilbert transformation, also

called a KramersÈKronig transformation :

d(l@) \ [ l@nP0

= ln R(l)l2[ l@2 dl (2)

Practically, R(l) is measured directly in a reÑectionexperiment. Then, one can deduce d(l). At this point thecomplex Fresnel reÑection coefficient, is completelyrü (l),expressed, and in the case of normal wave reÑection, thecomplex Fresnel reÑection coefficient is simply equal to :

rü (l) \ 1 [ nü (l)1 ] nü (l)

Therefore

nü (l)\ n(l)[ ik(l) \ 1 [ rü (l)1 ] rü (l)

(3)

Thus, by identiÐcation of real and imaginary parts onecan deduce both refractive index and absorption coeffi-cient :

n(l) \ 1 [ R(l)1 ] R(l) [ 2JR(l)cos(d(l))

(4)

k(l) \ [2JR(l)1 ] R(l) [ 2JR(l)cos(d(l))

(5)

In order to obey FresnelÏs description, the infraredreÑectance experiment is performed at a near-normalincidence angle and on an optically thick (3 mm)polymer sample in order to prevent internal multi-reÑections. Once the determination of n(l) and k(l) isdone for a given polymer, we can calculate its transmit-tance or reÑectance in various classic FTIR experi-ments.

Transmission experiments simulation

According to Fresnel formalism the transmittance T (l)of a single Ðlm depends on the complex Fresnel trans-mission and reÑection coefficients as follows :tü (l) rü (l)

T (l)\ tü12(l)tü22(l)1 ] 2rü 1(l)rü 2(l)cos(2d(l))] rü 12(l)rü 22(l)

(6)

where subscripts 1 and 2 refer to the Ðrst air/polymerinterface and second polymer/air interface, respectively.In the case of transmission the phase change d(l) is afunction of the Ðlm thickness, d, and of the wavelength,j. Fresnel coefficients directly depend on thus T (l)nü (l),is known:7

T (l)\ 16nü (l)

(1]nü (l))2[2(1[nü 2(l))cosA4nnü (l)d

jB](1[nü 2(l))2

(7)

where j is the wavelength and d is the Ðlm thickness.Such a calculated transmittance can be compared with

POLYMER INTERNATIONAL VOL. 44, NO. 1, 1997

Exact absorption behaviour of PMMA 13

experimental transmittance obtained in a classic trans-mission experiment.

Reflection–absorption experiment simulation

FTIR reÑection analysis is widely used in polymerscience characterization. ReÑectionÈabsorption experi-ments are generally done to assess properties of thinÐlms adsorbed on reÑecting plane substrates, such asmetal. Information on the polymer/metal interface canbe obtained, such as glass transition temperature of theabsorbed polymer layer or molecular orientation offunctional groups. It is well known that under polariza-tion (i.e. parallel to the incident wave plane), a standingwave is generated at the interface of reÑection that mag-niÐes the IR signal. This e†ect increases with the inci-dence angle and, at grazing angles, nanoÐlms can bestudied. It is then of fundamental importance to con-sider optical artifacts, such as peak shift. Fresnel reÑec-tion coefficients8,9 are used to simulate the opticalbehaviour of a multiphase system. The Fresnel complexreÑection coefficient between two media i and jÈofindices andnü

i(l) \ n

i(l) [ ik

i(l) nü

j(l) \ n

j(l)[ ik

j(l),

respectivelyÈis expressed as follows :

rüijP \

(nj2(l) [ k

j2(l) [ i2n

j(l)k

j(l)nü

i(l)cos(h

i)

[ (ni2(l)[ k

i2(l)[ i2n

i(l)k

i(l))nü

j(l)cos(h

j)

(nj2(l) [ k

j2(l) [ i2n

j(l)k

j(l)nü

i(l)cos(h

i)

] (ni2(l)[ k

i2(l)[ i2n

i(l)k

i(l))nü

j(l)cos(h

j)

(8)

where h is the wave angle relative to the normal of thesurface, in the medium studied. Then, for a three-phasesystem the Fresnel complex reÑection coefficient is :

rü 123P (l) \rü 12P (l) ] rü 23P (l)exp

C[i4nnü 2(l)d cos(h2)j

D

1 ] rü 12P (l)expC[i4nnü 2(l)d cos(h2)

jD (9)

where the ambient medium 1 is air the polymer(nü 1(l)),is medium 2 and the substrate is medium 3(nü 2(l)) (nü 3(l)).

is the wave angle relative to the normal of the surfaceh2in the polymer layer, and d is the polymer layer thick-ness. The power reÑectivity, measured by the IR detec-tor is :

R123(l) \ rü 123P (l)rü 123P *(l) (10)

Attenuated total reflection (ATR) experiment simula-tion

ATR experiments are widely used in polymer science inorder to determine surface composition and orientation,as well as concentration proÐles in the vicinity of thesurface. ATR consists of the propagation of the IR wavein an internal total reÑection crystal. An evanescentwave is produced at the interface between the crystal

and a polymer Ðlm and causes an absorption spectrum.ATR experiments were simulated using the same for-malism as a three-medium systemÈeqns (8), (9) and(10)Èbut considering air as medium 1, ATR crystal

in the mid-IR spectral range) as medium 2(n2\ 2É38and polymer as medium 3.

Diffuse reflectance (DRIFT ) experiment simulation

Di†use reÑectance experiments are largely employed toanalyse IR absorption properties of strongly di†usingmedia such as powders. In particular, the properties ofpolymers adsorbed on powders can be studied. In thistechnique the IR beam is di†used in all spatial direc-tions and is therefore focused on the IR detector bymeans of hemispherical mirrors. DRIFT spectra weresimulated using eqns (8), (9) and (10). The followingKubelkaÈMunk10 correction is applied during the cal-culations :

R123@ (l)\ 1 [ R123(l)2R123(l)

(11)

All these mathematical algorithms are used to simulatetransmission, ATR and reÑectance experiments, and arecapable of handling any number of phases and givingexact solutions within the limits of classic electromag-netic theory and linear optics.

EXPERIMENTAL

Infrared transmission, ATR, di†use reÑectance andreÑection spectra were measured with a Bruker IFS 66FTIR spectrometer at a resolution of 2 cm~1 by averag-ing 200 scans. For the mid-IR frequency region, aMCT detector was used. In the case of near-normalincidence reÑection measurements, the angle of inci-dence was Ðxed at 10¡. The reÑection data wereanalysed by the use of the Fresnel equations (see above)for normal incidence. The reÑectance at normal inci-dence was evaluated by scaling the observed reÑectancemeasured at a 10¡ angle of incidence under P polariza-tion :

RP(h¡) \ CPRP(10¡) (12)

where is the reÑectance at an angle of incidence h,RP(h)for the incident radiation polarized parallel to the planeof incidence. The complex reÑectivity of incident radi-ation polarized parallel to the plane of incidence thatreÑects, at an angle of incidence h, at the interfacebetween a transparent medium 1 (air) and an absorbingmedium 2 (polymer) is expressed as :

rü 12P \ (n22 [ k22[ i2n2 k2)cos(h) [ J(n2[ ik2)2sin2(h)

(n22[ k22[ i2n2 k2)cos(h) ] J(n2[ ik2)2 sin2(h)

(13)



The value of the scaling constant is calculated to beCP1É042 for polymer indices andn2\ 1É43 k2\ 0É42.

Various samples of PMMA homopolymer (M1 w \100 000 g mol~1), supplied by Polymer Source Inc., wereused. The reÑection spectrum near normal incidenceangle and ATR spectra were recorded on optically thickÐlms ([1 mm). The resulting spectra are expresed inreÑectance and absorbance units, respectively. Trans-mission experiments were conducted on thin PMMAÐlms obtained by solvent casting on KBr plates. TheÐlms were treated at 160¡C to remove residual solventand the resulting spectra are expressed in absorbanceunits. Di†use reÑectance experiments were performedon PMMA homopolymer powder and thin Ðlms(d \ 10 nm) of PMMA, deposited on gold mirrors byspin-coating (in chloroform), were studied by IRASspectroscopy, at an angle of incidence of 86¡ under Ppolarization.

RESULTS AND DISCUSSION

Figure 1 shows the normalized mid-IR response of thePMMA carbonyl stretching mode obtained in transmis-sion (TRANS), ATR (ATR), di†use reÑectance (DR),grazing (IRAS 86¡) and near normal (IRAS 10¡) inci-dence angle reÑection experiments. These spectra clearlyshow large changes in both peak position and shape.Two questions may be asked : Ðrst, which experimentgives the correct response in peak position and proÐle?and second, do these di†erences reÑect optical or spec-troscopic artifacts or simply structural di†erences mag-niÐed by the non-equivalent thickness analysed fromone experiment to another? As an example, the grazing

angle specular reÑectance and ATR spectra show anasymmetric carbonyl band, while the transmission andnormal angle specular reÑectance give symmetric gauss-ian proÐles.

Peak position of the CxO stretching mode, inte-grated intensity, half-height width and asymmetryfactor are gathered in Table 1, for each experiment.Peak positions vary widely with a 19 cm~1 wavenumberdi†erence between grazing angle specular reÑectanceand ATR. Band shapes, through the asymmetry factor,are also greatly a†ected. Such e†ects may cause thewrong interpretation of spectra. As an example, it iswell known that carbonyl groups involved in speciÐcinteractions, for example at a metal/polymer interface,or in good solvent, or in polymer blends, exhibit a split-ting of the CxO band in favourable cases and bandasymmetry in less favourable cases.11 Then, consideringgrazing angle specular reÑectance analysis of a thinPMMA layer on gold, it would be wrong to considerthat asymmetry of the absorption band is generated byinterfacial speciÐc interactions. Asymmetry is generatedby optical artifacts as shown later in the paper. Thesame kind of explanation is relevant to the evidence ofpreferential orientation of chain backbone when poly-mers adsorb.12 Alteration of peak proÐle and intensitymay be attributed to non-isotropic polymer adsorption,while in fact they are due only to spectroscopic artifacts.

In order to deduce real CxO band position andproÐle, we use data obtained in normal incidence specu-lar reÑectance, R(l), on optically thick PMMA samples.Figure 2 shows the experimental reÑectance spectrumR(l). Phase change is calculated using eqn. (2). Then n(l)and k(l) are deduced using eqns (4) and (5). Calculated

Fig. 1. Mid-IR response of the PMMA carbonyl stretching mode obtained in transmission (TRANS), ATR (ATR), di†use reÑec-tance (DR), grazing (IRAS 86¡) and normal (IRAS 10¡) incidence angle reÑection experiments.



TABLE 1. CxO stretching mode absorption band quantitative characteristics for

five types of infrared experiments

Experiment CxO peak Integrated Half-height Asymmetry

position intensity width factor

(cmÉ1)

Transmission 1731 24·9 19·3 0·04

ATR 1720 36·5 30 É0·75

Diffuse reflectance 1730 37·6 29·2 É0·56

IRAS 86¡ 1741 27·5 22·3 1·80

IRAS 10¡ 1736 – – –

derivations of refractive index, n(l), and absorption coef-Ðcient, k(l), in the mid-IR spectral range are reported inFigs 3 and 4, respectively. From a theoretical point ofview, the original Hilbert transformation, employedhere from the reÑectivity (R(l)) to the phase shift (d(l))

for reÑection, has some distinct advantages : it does notrequire least-squares reÐnement calculations, whichoften diverge for strong dispersion (case of the CxOfunctional group), and, secondly, no prior information(such as n=) about the sample material is required. The

Fig. 2. Experimental PMMA reÑectance spectrum at 10¡ incidence angle in the CxO absorption region.

Fig. 3. Calculated refractive index n(l) of PMMA in the CxO absorption region.



Fig. 4. Calculated absorption coefficient k(l) of PMMA in the CxO absorption region.

Fig. 5. Comparison of experimental (ÈÈÈÈ) and calculated reÑectance of CxO absorption band by ATR technique.(LLLL)

TABLE 2. Calculated quantitative characteristics of the CxO stretching mode

absorption band for four types of infrared experiments

Experiment CxO peak Integrated Half-height Asymmetry

position intensity width factor

(cmÉ1)

Transmission 1730 22 18·7 0·06

ATR 1721 33·3 29·1 É0·68

Diffuse reflectance 1732 33·9 28·6 É0·53

IRAS 86¡ 1740 25 21·6 1·73



Fig. 6. Comparison of experimental (ÈÈÈÈ) and calculated absorbance of CxO absorption band by transmission(LLLL)technique.

values obtained for n(l) and k(l) for the CxO stretchingmode are fully consistent with values proposed in theliterature.

Then, using the optical constants determined here,the expected band proÐle and CxO peak location fortransmission, ATR, di†use reÑectance and grazing angle

(86¡) specular reÑectance can be calculated using eqn (6)for transmission, and eqns (7), (8) and (9) for ATR andreÑectance experiments.

In Fig. 5 (ATR), Fig. 6 (TRANS), Fig. 7 (IRAS 86¡)and Fig. 8 (DR), calculated and experimental spectraare compared in the vicinity of the CxO stretching

Fig. 7. Comparison of experimental (ÈÈÈÈ) and calculated reÑectance of CxO absorption band by grazing angle(LLLL)reÑection technique.

TABLE 3. Exact absorbing wavenumbers for PMMA CxO stretching mode

Experiment Transmission ATR Diffuse reflectance IRAS 86¡

CxO peak 1730 À2 1721 À2 1731 À2 1740 À2

position (cmÉ1)



Fig. 8. Comparison of experimental (ÈÈÈÈ) and calculated reÑectance of CxO absorption band by di†use reÑec-(LLLL)tance technique.

absorption band. One can note that both the peak posi-tion and the band proÐle agree closely with the experi-mental spectra. Moreover, the calculated intensitiesseem realistic. In the case of ATR simulation, the calcu-lated intensity is multiplied by six, because six reÑec-tions occur during the experiment. Calculatedquantitative values of the peak position, intensity, half-height width and asymmetry factor are gathered inTable 2. Good agreement is observed between thevalues in Table 1 and 2, indicating that proÐle and posi-tion distortion are accurately predicted using opticalconstant calculations. The originality of the mathemati-cal model employed is that no prior information isrequired except the experimental normal incidence spe-cular reÑectance spectrum. We can then deÐne an exactabsorbing wavenumber for the PMMA CxO stretch-ing mode, which depends on the IR technique used.These values, gathered in Table 3, can be used to calcu-late frequency shifts of CxO groups involved in speciÐcinteractions, in the Ðeld of adhesion, for example.Molecular orientation can also be calculated by con-sidering the intensity calculations performed here as ref-erence values in the isotropic orientation case.Furthermore, from Fig. 4, the exact absorbing value ofthe CxO functional groups in the infrared spectralrange is 1730 cm~1, independent of the technique.

CONCLUSIONS

Five types of infrared spectroscopic experiments wereperformed on a PMMA homopolymer sample. The

spectra obtained from these experiments di†ered signiÐ-cantly from each other. The exact absorption behaviourin the mid-IR spectral range of PMMA was deducedfrom the near-normal incidence angle specular reÑec-tance spectrum on the basis of an original mathematicaltransformation that needs no prior information. Then, itwas shown that the calculated spectrum for each experi-ment predicted accurately the experimental one,proving that di†erences were optical artifacts and nottrue sample di†erences. Exact peak absorption forPMMA was 1730 cm~1 and should be taken as a refer-ence value for the calculation of frequency shifts forfurther physico-chemical interpretation, such as speciÐcinteractions or molecular orientation.

REFERENCES

1 Graf, R. T., Koenig, J. L. & Ishida, H., Appl. Spectrosc., 39 (1986)405.

2 Bertie, J. E., Zhang, S. L. & Manji, R., Appl. Spectrosc., 46 (1992)1660.

3 Bardwell, J. A. & Digman, M. J., J. Chem. Phys., 83 (1985) 5468.4 Bardwell, J. A. & Dignam, M. J., Anal. Chim. Acta, 172 (1985) 101.5 Grosse, P. & O†ermann, V., Appl. Phys., A52 (1991) 138.6 Yamamoto, K. & Masui, A., Appl. Spectrosc., 49 (1995) 639.7 Heavens, O. S. in Optical Properties of T hin Solid Ðlms. Dover,

New York, 1965, Ch. 4.8 Hansen, W. N., J. Opt. Soc. Am., 58 (1968) 380.9 McIntyre, J. D. E. & Aspnes, D. E., Surface Sci., 24 (1971) 417.

10 Kubelka, P., J. Opt. Soc. Am., 38 (1948) 448.11 Brogly, M., Nardin, M. & Schultz, J., J. Adhesion, 58 (1996) 263.12 Allara, D. L. & Nuzzo, R. G., L angmuir, 1 (1985) 52.


Documents

Determination of exact absorption behaviour in the mid-infrared spectral range of poly(methylmethacrylate) by Fourier transform infrared reflection spectroscopy