Abstract

A potential problem with the attenuated total reflection that is used to measure infrared spectra is described. The problem is the possibility that the anomalous dispersion associated with an infrared absorption band may cause the experimental configuration to move from the attenuated total reflection regime to the specular reflection regime, with consequent distortion of the apparent absorption bands and consequent error in the interpretation of the bands if the problem is not recognized.

© 1995 Optical Society of America

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References

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  1. N. J. Harrick, Internal Reflection Spectroscopy (Harrick, Ossining, New York, 1979), Chap. 3, p. 67.
  2. F. M. Mirabella, “Determination of optical constants,” in Internal Reflection Spectroscopy: Theory and Applications, Vol. 15 of Practical Spectroscopy Series (Dekker, New York, 1994), pp. 325–332.
  3. M. J. Dignam and S. Mamiche Afara, “Determination of the spectra of the optical constants of bulk phases via Fourier transform ATR,” Spectrochim. Acta 44A, 1435 (1988).
  4. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), Chap. 2, p. 71.
  5. C. Chang and S. L. Hsu, “Spectroscopic analysis of poly(p-phenylene benzobisthiazole films,” J. Polym. Sci. Polym. Phys. Ed. 23, 2307 (1985).
    [Crossref]
  6. C. Y. Liang and S. Krimm, “Infrared spectra of high polymers. Part IX: polyethylene terephtalate,” J. Mol. Spectrosc. 3, 554 (1959).
    [Crossref]
  7. F. M. Mirabella and N. J. Harrick, Internal Reflection Spectroscopy: Review and Supplement (Harrick, Ossining, New York, 1985), Chap. 7, p. 50.
  8. F. M. Mirabella, “Strength of interaction and penetration of infrared radiation for polymer films in internal reflection spectroscopy,” J. Polym. Sci. Polym. Phys. Ed. 21, 2403 (1983).
    [Crossref]
  9. R. Belali, “Etude théorique et expérimentale des différents paramètres influençant un spectre d’absorption infrarouge enregistré en réflexion totale attenuée,” Thèse d’Université (Université de Franche-Comté, Besançon, France, 1992).
  10. R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” Am. J. Phys. 50, 982 (1982).
    [Crossref]
  11. R. W. Ditchburn, Light, 3rd ed. (Academic, New York, 1976), Chap. 19, p. 671.
  12. L. Landau and E. Lifchitz, Physique Théorique (Mir, Moscow, 1972), Vol. 4, Chap. 5, p. 187.
  13. L. Tarassov, Bases Physiques de l’Électronique Quantique (Mir, Moscow, 1979), Chap. 2, p. 66.
  14. R. Belali and J. M. Vigoureux, “Absorption of infrared light by isotropic thin films in attenuated total reflection,” J. Opt. Soc. Am. B 11, 1197 (1994).
    [Crossref]

1994 (1)

1988 (1)

M. J. Dignam and S. Mamiche Afara, “Determination of the spectra of the optical constants of bulk phases via Fourier transform ATR,” Spectrochim. Acta 44A, 1435 (1988).

1985 (1)

C. Chang and S. L. Hsu, “Spectroscopic analysis of poly(p-phenylene benzobisthiazole films,” J. Polym. Sci. Polym. Phys. Ed. 23, 2307 (1985).
[Crossref]

1983 (1)

F. M. Mirabella, “Strength of interaction and penetration of infrared radiation for polymer films in internal reflection spectroscopy,” J. Polym. Sci. Polym. Phys. Ed. 21, 2403 (1983).
[Crossref]

1982 (1)

R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” Am. J. Phys. 50, 982 (1982).
[Crossref]

1959 (1)

C. Y. Liang and S. Krimm, “Infrared spectra of high polymers. Part IX: polyethylene terephtalate,” J. Mol. Spectrosc. 3, 554 (1959).
[Crossref]

Belali, R.

R. Belali and J. M. Vigoureux, “Absorption of infrared light by isotropic thin films in attenuated total reflection,” J. Opt. Soc. Am. B 11, 1197 (1994).
[Crossref]

R. Belali, “Etude théorique et expérimentale des différents paramètres influençant un spectre d’absorption infrarouge enregistré en réflexion totale attenuée,” Thèse d’Université (Université de Franche-Comté, Besançon, France, 1992).

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), Chap. 2, p. 71.

Chang, C.

C. Chang and S. L. Hsu, “Spectroscopic analysis of poly(p-phenylene benzobisthiazole films,” J. Polym. Sci. Polym. Phys. Ed. 23, 2307 (1985).
[Crossref]

Dignam, M. J.

M. J. Dignam and S. Mamiche Afara, “Determination of the spectra of the optical constants of bulk phases via Fourier transform ATR,” Spectrochim. Acta 44A, 1435 (1988).

Ditchburn, R. W.

R. W. Ditchburn, Light, 3rd ed. (Academic, New York, 1976), Chap. 19, p. 671.

Harrick, N. J.

F. M. Mirabella and N. J. Harrick, Internal Reflection Spectroscopy: Review and Supplement (Harrick, Ossining, New York, 1985), Chap. 7, p. 50.

N. J. Harrick, Internal Reflection Spectroscopy (Harrick, Ossining, New York, 1979), Chap. 3, p. 67.

Hilborn, R. C.

R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” Am. J. Phys. 50, 982 (1982).
[Crossref]

Hsu, S. L.

C. Chang and S. L. Hsu, “Spectroscopic analysis of poly(p-phenylene benzobisthiazole films,” J. Polym. Sci. Polym. Phys. Ed. 23, 2307 (1985).
[Crossref]

Krimm, S.

C. Y. Liang and S. Krimm, “Infrared spectra of high polymers. Part IX: polyethylene terephtalate,” J. Mol. Spectrosc. 3, 554 (1959).
[Crossref]

Landau, L.

L. Landau and E. Lifchitz, Physique Théorique (Mir, Moscow, 1972), Vol. 4, Chap. 5, p. 187.

Liang, C. Y.

C. Y. Liang and S. Krimm, “Infrared spectra of high polymers. Part IX: polyethylene terephtalate,” J. Mol. Spectrosc. 3, 554 (1959).
[Crossref]

Lifchitz, E.

L. Landau and E. Lifchitz, Physique Théorique (Mir, Moscow, 1972), Vol. 4, Chap. 5, p. 187.

Mamiche Afara, S.

M. J. Dignam and S. Mamiche Afara, “Determination of the spectra of the optical constants of bulk phases via Fourier transform ATR,” Spectrochim. Acta 44A, 1435 (1988).

Mirabella, F. M.

F. M. Mirabella, “Strength of interaction and penetration of infrared radiation for polymer films in internal reflection spectroscopy,” J. Polym. Sci. Polym. Phys. Ed. 21, 2403 (1983).
[Crossref]

F. M. Mirabella and N. J. Harrick, Internal Reflection Spectroscopy: Review and Supplement (Harrick, Ossining, New York, 1985), Chap. 7, p. 50.

F. M. Mirabella, “Determination of optical constants,” in Internal Reflection Spectroscopy: Theory and Applications, Vol. 15 of Practical Spectroscopy Series (Dekker, New York, 1994), pp. 325–332.

Tarassov, L.

L. Tarassov, Bases Physiques de l’Électronique Quantique (Mir, Moscow, 1979), Chap. 2, p. 66.

Vigoureux, J. M.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), Chap. 2, p. 71.

Am. J. Phys. (1)

R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” Am. J. Phys. 50, 982 (1982).
[Crossref]

J. Mol. Spectrosc. (1)

C. Y. Liang and S. Krimm, “Infrared spectra of high polymers. Part IX: polyethylene terephtalate,” J. Mol. Spectrosc. 3, 554 (1959).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Polym. Sci. Polym. Phys. Ed. (2)

C. Chang and S. L. Hsu, “Spectroscopic analysis of poly(p-phenylene benzobisthiazole films,” J. Polym. Sci. Polym. Phys. Ed. 23, 2307 (1985).
[Crossref]

F. M. Mirabella, “Strength of interaction and penetration of infrared radiation for polymer films in internal reflection spectroscopy,” J. Polym. Sci. Polym. Phys. Ed. 21, 2403 (1983).
[Crossref]

Spectrochim. Acta (1)

M. J. Dignam and S. Mamiche Afara, “Determination of the spectra of the optical constants of bulk phases via Fourier transform ATR,” Spectrochim. Acta 44A, 1435 (1988).

Other (8)

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), Chap. 2, p. 71.

N. J. Harrick, Internal Reflection Spectroscopy (Harrick, Ossining, New York, 1979), Chap. 3, p. 67.

F. M. Mirabella, “Determination of optical constants,” in Internal Reflection Spectroscopy: Theory and Applications, Vol. 15 of Practical Spectroscopy Series (Dekker, New York, 1994), pp. 325–332.

R. Belali, “Etude théorique et expérimentale des différents paramètres influençant un spectre d’absorption infrarouge enregistré en réflexion totale attenuée,” Thèse d’Université (Université de Franche-Comté, Besançon, France, 1992).

F. M. Mirabella and N. J. Harrick, Internal Reflection Spectroscopy: Review and Supplement (Harrick, Ossining, New York, 1985), Chap. 7, p. 50.

R. W. Ditchburn, Light, 3rd ed. (Academic, New York, 1976), Chap. 19, p. 671.

L. Landau and E. Lifchitz, Physique Théorique (Mir, Moscow, 1972), Vol. 4, Chap. 5, p. 187.

L. Tarassov, Bases Physiques de l’Électronique Quantique (Mir, Moscow, 1979), Chap. 2, p. 66.

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Figures (6)

Fig. 1
Fig. 1

Shape of a dispersion curve with respect to decreasing wave numbers: (a) variation of the absorption index κ of the refractive index n2 + , (b) effect of the dispersion on the real part n2 of the refractive index of the medium, (c) variation of the critical angle of total reflection θc. Curve (b) shows that the index of refraction has a sharp maximum at a value k, which is slightly smaller than k0. This increase of n2 causes the condition of total reflection n1 sin θ > n2 to be unfulfilled in the high refractive-index zone (which appears as the hatched sections in the figure). In this region of the spectrum, the band is not observed in attenuated total reflection but in specular reflection.

Fig. 2
Fig. 2

Dispersion curve of PET. This figure shows the variation of the real part n2 of the refractive index of PET with respect to the wave number. When an incident angle of 45° and when a KRS − 5 prism with n1 = 2.38 are used, only the regions of the spectrum that verify the relation 2.38 sin 45° > n2 are analyzed by ATR (this part corresponds to all parts of the spectrum appearing under the dashed–dotted horizontal line). In other regions, the condition of total reflection is not fulfilled so that the bands located at 790, 1040, 1343, and 1725 cm−1 are analyzed by specular reflection.

Fig. 3
Fig. 3

Effect of the dispersion on the PET band at 1725 cm−1. The incident angle used is 40°. Light is unpolarized. As expected from Figs. 1 and 2, the right-hand side of this band is not obtained in the ATR configuration but in specular reflection. This causes the band to be more intense in the right-hand side and consequently to have a distorted shape.

Fig. 4
Fig. 4

Effect of the dispersion on the shape of the PET band at 1725 cm−1 for different values of the incident angle θ: (a) When θ = 60°, the whole spectrum fulfills the ATR condition (this can be seen in Fig. 2 by drawing the horizontal line at 2.38 sin 60° = 2.06. In fact, in that case the whole dispersion curve of Fig. 2 appears under this value of 2.06); (b), (c) When θ in near the critical angle, the whole band is not obtained in total internal reflection. Its right-hand part corresponds to specular reflection; a part of the incident energy is consequently lost in the second medium and that part of the band appears to be more intense, making one shoulder appear at 1680 cm−1.

Fig. 5
Fig. 5

Variations of the absorption probabilities ΠTE and ΠTM according to θ. The refractive index of the sample is taken to be n ^ 2 = 1.5 + j0.03; the thickness of the sample that is sandwiched between KRS − 5 (n1 = 2.38) and air (n3 = 1) is 100 μm. The critical angle is then 39.06.°

Fig. 6
Fig. 6

Variations of the PET baseline (that is, of the absorbance of the sample when no absorption occurs) with respect to the wave number for different values of the angle of incidence θ. The curves are deliberately and regularly offset in order to compare their variations more easily. When the angle of incidence is far from the critical angle of total reflection, the baseline is 0, which shows that all the incident energy is reflected toward the detector (and consequently that total reflection occurs). When the angle of incidence decreases, the baseline is not 0 anywhere, although no absorption occurs. This shows that some light is lost in the second medium and consequently that we are not working in ATR.

Equations (6)

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n 1 sin θ c = n 2 .
n ^ 2 = n 2 + j κ ,
n ^ 2 cos θ 2 = ( n ^ 2 2 - n 1 2 cos 2 θ ) 1 / 2 = α = p + j q .
Π TE = n 1 ω 0 3 ρ S D 2 24 π 2 0 c 3 cos θ | t 12 1 + r 12 r 23 exp ( j 2 ω 0 c α d ) | 2 × { 1 - exp ( - 2 ω 0 c q d ) 2 ω 0 c q [ 1 + r 23 2 exp ( - 2 ω 0 c q d ) ] + exp ( - 2 ω 0 c q d ) { [ r 23 exp ( j 2 ω 0 c p d ) - 1 j 2 ω 0 c + c . c . ] }
Π TM = n 1 ω 0 3 ρ S D 2 24 π 2 0 c 3 n ^ 2 2 cos θ | t 12 1 + r 12 r 23 exp ( j 2 ω 0 c α d ) | 2 × { ( p 2 + q 2 + n 1 2 sin 2 θ ) [ 1 - exp ( - 2 ω 0 c q d ) 2 ω 0 c q ] × [ 1 + r 23 2 exp ( - 2 ω 0 c q d ) ] + ( - p 2 - q 2 + n 1 2 sin 2 θ ) exp ( - 2 ω 0 c q d ) × { [ r 23 exp ( j 2 ω 0 c p d ) - 1 j 2 ω 0 c + c . c . ] }
A ( θ , ν ) corrected = A ( θ , ν ) - A ( 60 ° , ν ) .

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