- Email: [email protected]
The far-infrared optical constants of polypropylene, PTFE and polystyrene
~20~0891/92 $5.00 i- 0.00 Pergamon Press plc
Infrared Phys. Vol. 33, No. 1, pp. 33.--38, 1992 Printed in Great Britain
THE FAR-INFRARED OPTICAL CONSTANTS OF POLYPROPYLENE, PTFE AND POLYSTYRENE J. R. BIRCH Division of Electrical Science, National Physical Laboratory, Teddington, Middlesex lWl1
OLW, U.K.
(Receitfed 29 July 199i) Abstract-The
far-infrared optical constants of polypropylene, PTFE and polystyrene have been determined in the spectral region between 50 and 500 cm-’ at a temperature of 290 K by the method of dispersive Fourier transform spectroscopy.
INTRODUCTION Low loss polymers are widely used for the construction of lenses and windows throughout the far-infrared spectral region. There consequently exists a considerable body of info~ation on their transmission spectral properties. There is, however, substantially less information available about the detailed spectral variation of both optical constants, the refractive index and the absorption coefficient, of such materials. In addition, such info~ation as is available on the refractive index is often limited by random uncertainties at the percent or so level. This can result in constant values being assigned to the far infrared refractive indices of such materials. While information at this level of uncertainty is generally adequate for most optical element design purposes, it does obscure both any local dispersion across an absorption band and any underlying larger scale dispersion due to distant strong loss processes, thereby inhibiting detailed studies of the microscopic dynamics of the polymers. A notable exception to this is provided by the measurement method of dispersive Fourier transform spectroscopy (DFTS). (I+ This allows the spectral variation of both the absorption coefficient and the refractive index of a material to be determined from a measurement of the attenuation and phase shift imposed on an electromagnetic wave by its interaction with a specimen, either in transmission or reflection. Present instrumentation allows the refractive index spectrum of a reasonably transparent polymer specimen to be determined with an accuracy of between parts in 10’ and 106, and a precision that can be as large as parts in 104. This difference between accuracy and precision arises from the difficulty of producing polymer specimens with a sufficiently well-defined optical thickness to allow the very high accuracy of the phase measurement to be carried over into the refractive index calculation. The method has been used to study the optical constants of a number of polymers and polymer-based composite materials in the technologically important near millimetre wavelength spectral region from N 3 to 40 cm--’ ( -90 to 1200 GHz), (*-“) but has only been used to study relatively few such materials in the far-infrared.““‘@ In the present work this sparce data base is extended with the report of the results of DFTS studies in the 50-500 cm-’ spectral region on polypropylene, polytetrafluoroethylene and polystyrene at 290 K.
EXPERIMENTAL The refraction and absorption spectra of each specimen were calculated from its phase shift and attenuation spectra as determined by the technique of dispersive Fourier transform spectroscopy in the spectral region between 50 and 500 cm-‘. This was done using two interferometers.(17) One of these interferometers was based on the Martin-Fuplett polarising wire grid configuration,@) and was used with a quartz-window Golay cell for measurements in the spectral region below 110 cm-‘. The second instrument was a conventional two beam interferometer with a thin film melinex beamdivider, and was used with a diamond-window Golay cell to cover the spectral region above Q Controller, Her Majesty’s Stationery Of&e, 1991. 33
J. R. BIRCH
34
110 cm-‘. In both instruments the specimen holder had a load lock construction so that a specimen could be inserted into, and removed from, the interferometer without affecting its vacuum environment.(‘g’ Thus, the mechanical stability of the instrument was unaffected by specimen changing, thereby avoiding the requirement for a stabilisation period after each change of specimen. All of the measurements were made at a temperature of 290 K and with a spectral resolution of -4 cm-‘. The specimens were all 50 mm diameter discs, with thicknesses of 3.1 mm (polypropylene), 2.1 mm (PTFE) and 2.0 mm (polystyrene). RESULTS The refraction and absorption spectra of all the specimens used in this study are presented in Figs l-3. Each spectrum is the average of four independent determinations. The reproducibility of these was such as to suggest a level of random uncertainty in the refraction spectra of about 10m5 above 110 cm-’ and a few times lo-’ at lower wavenumbers. In the absorption spectra the random uncertainties were typically of the order of 0.05 cm-‘. Polypropylene Polypropylene is not widely used as a lens material as it has a somewhat higher level of absorption than is found in polyethylene or TPX. Chantry et al., (*O)however, suggest its use as an
‘.4g85 I 1.4960 z -0 .c .-t z
1.4975 -
s n” 1.4970 -
I,..,I..,.I..,,I.,.,l...,l.,.,l..,.I,...I, 100 150 200
50
50
100
150
200
250
300
350
400
45c
250
300
350
400
450
Wavenumber Fig. 1. The refraction
and absorption
spectra
(cm-l) of polypropylene
at 290 K.
FIR optical constants of polypropylene, FTFE and polystyrene
35
alternative to polyethylene for spectroscopy involving the 70-8Ocm-’ region. This would avoid absorption losses due to the 73 cm-’ band of polyethylene, although, of course, the same objective could be achieved through the use of the lower loss polymer TPX. The refraction and absorption spectra of the polypropylene specimen studied in the present work are shown in Fig. 1. The absorption spectrum has five discrete absorption bands superimposed on a background that rises monotonically with increasing wavenumber. These bands are at 111, 170, 250, 320 and 398 cm-“, the first four of which agree with those found by Chantry et a/.(“) in a study from 20 to 400 cm”‘. Their absorption spectrum does not show the 398 cm-’ band found in the present work. The 111 cm-’ band is considerably wider than the other bands as it is the envelope of a doublet that only becomes clearly resolved when the temperature is reduced to 77 IL@‘) In the refraction spectrum one finds the corresponding dispersion associated with the five discrete absorption bands. The overall level of the refraction spectrum falls with increasing wavenumber up to about 300 cm-‘, as one would expect, and then begins to rise, showing the onset of the underlying dispersion due to the broad mid-infrared feature that the absorption spectrum is rising towards. The mean value of the refractive index over this spectra1 region is about 1.4975, and this agrees reasonably well with unpublished results@‘)reported by Chantry and Chamberlain’**) which show a value of about 1.505, given the known variablity of polymer specimens from different sources. 1.480
50
50
100
loo
150
200
250
300
350
400
450
150
200
250
300
350
400
450
Wavenumber (cm-11 Fig. 2. The refraction and absorption spectra of polytetrafl~oroethyIene
at 290 K.
J. R. BIRCH
36
Polytetrajuorethylene
At near millimetre wavelengths PTFE is about as transparent as polyethylene and TPX,“) and has consequently been used in lens and window applications in that spectral region. It has, in particular, been used in such applications for liquid studies as its relatively inert character renders it safe from corrosion and adsorption problems. However, as one moves out of the near millimetre region to higher wavenumbers the absorption in PTFE increases rapidly due to a strong absorption band at 202 cm-‘, which is due to vibrations of neighbouring CF, groups. The material becomes sufficiently lossy that by the 50-100 cm-’ region it is unsuitable for use in transmission optics. The measured refraction and absorption spectra of the 2 mm thick PTFE specimen in the 5&190 cm-’ region are shown in Fig. 2. Although the background spectrum of the empty interferometer contained intensity from 50 to 500 cm-‘, measurements on the PTFE specimen were only possible below 190cm-‘. Above 190cm-’ the power levels transmitted through the specimen were indistinguishable from zero within the limits implied by the random noise levels, with the exception of a 10 cm-’ wide region centred on 355 cm-‘. In this band the specimen became sufficiently transparent to achieve a peak fractional transmission coefficient of 0.05. The measured absorption spectrum increases rapidly from values -2 cm-’ at wavenumbers in the 50 cm-’ region to reach values close to 30 cm-’ by 190 cm-‘. Chamberlain and Gebbie (‘v have made DFTS studies on films of PTFE sufficiently thin to allow measurements to be made out to 300 cm-‘. These reveal the full
l&O0 I------
150
200
250
Wavenumber Fig. 3. The refraction
and absorption
spectra
300
350
400
(cm-‘) of polystyrene
at 290 K
450
FIR optical
constants
of polypropylene,
PTFE
and polystyrene
37
extent of the 202 cm-’ band, showing it to have a peak absorption value of about 220 cm-‘. In the region of overlap between the two measurements the absorption spectrum of Chamberlain and Gebbie is systematically higher than the present one. At 190 cm-‘, for example, their absorption coefficient is about 50 cm-’ compared to the present value of 30 cm-‘. This difference could be due to the different specimens used, thin film and bulk material. It is well known that the rolling or stretching used to produce thin polymer films induces birefringence and dichroism into their optical properties. Thus, the difference, although large, may not be significant, in that one is not comparing like with like. The measured refraction spectrum is dominated by the onset of dispersion across the intense 202 cm-’ band. It rises by 0.04 over the measured range, a very large amount compared to the values seen in the other specimens. In polypropylene, for example, the typical dispersion across its much weaker discrete absorption features was -0.0005. The overall level of the present refraction spectrum is somewhat above that found by Chamberlain and Gebbie (1.38),‘13’but is in reasonable agreement with near millimetre wavelength values,“” and the previous comments about the different character of the specimens apply. Polystyrene
At near millimetre wavelengths polystyrene is intermediate in the level of its absorption between the genuinely low loss spectra of LDPE, HDPE, TPX and PTFE, lying a factor of h- 3 above these and a factor of w 8 below the considerably more lossy spectra of nylon and perspex.“’ It does not appear to have found wide useage as a lens material for this reason, although Chantry and Chamberlain(22’ suggest that it could be a useable material for wavenumbers below 30 cm-‘. This seems somewhat unlikely, given the ready availability of polyethylene and TPX, unless polystyrene has other properties which would make it well-suited to a particular application. The refraction and absorption spectra of the polystyrene specimen are shown in Fig. 3. The absorption spectrum is dominated by a very broad feature centred on 220 cm-‘, with other features at 84, 247, 293, 324, 375, 405 and 432 cm-‘. The refraction spectrum has a mean level of about 1.59, in good agreement with its near millimetre wavelength value,(5’ and clearly shows the expected regions of dispersion associated with the stronger absorption bands.
CONCLUSIONS
The results of the determination of the optical constants of polypropylene, PTFE and polystyrene in the far-infrared spectral region between about 50 and 500 cm-’ at 290 K have been presented. The measurement accuracy was such that the small scale refractive index dispersion associated with the various observed absorption bands was fully resolved. It is well known that the optical constants of polymers can be very sensitive to the particular details of their manufacturing process and previous history. It is intended that the present spectra provide a guide to the typical values that can be expected. An internal report(‘7’ containing a full tabulation of the spectral variation of the refractive index, absorption coefficient, real and imaginary parts of the complex relative permittivity and the loss tangent is available. REFERENCES 1. J. R. Birch and T. J. Parker, Infrared and Millimefer Waves (Edited by K. J. Button), Chap. 3, Vol. 2. Academic New York (1979). 2. J. R. Birch, Proc. SPIE 289, 362 (1981). 3. J. R. Birch, Mikrochimica Acfa (Wien) III, 105 (1987). 4. T. J. Parker, Contemp. Phys. 31, 335 (1990). 5. J. R. Birch, J. D. Dromey and J. Lesurf, Infrared Phys. 21, 225 (1981). 6. J. R. Birch and F. P. Kong, Infrared Phys. 24, 30 (1984). 7. M. N. Asfar, IEEE Trans. Microwave Theory Tech. MTT-33, 1410 (1985). 8. J. R. Birch and F. P. Kong, Infrared Phys. 26, 131 (1986). 9. M. N. Afsar, IEEE Trans. instrum. Meas. IM-36, 530 (1987). 10. J. R. Birch and J. Lesurf, Infrared Phys. 27, 423 (1987). 11. P. B. Whibberley and J. R. Birch, Infrared Phys. 29, 995 (1989). 12. C. Meny, J. LBotin and J. R. Birch, Infrared Phys. 31, 211 (1991). 13. J. E. Chamberlain and H. A. Gebbie, Appl. Opt. 5, 393 (1966). 14. M. N. Afsar and G. W. Chantry, IEEE Trans. Microwave Theory Tech. MTT-25, 509 (1977).
Press,
38
J. R.
BIRCH
15. J. R. Birch and E. A. Nicol, Infrared Phys. 24, 573 (1984). 16. J. R. Birch. Infrared Phvs. 30, 195 (1990). 17. J. R. Birch, NPL Report DES 111, June’ (1991). 18. D. H. Martin and E. hDktt. Infrared Phvs. 10. 105 0970).
19. 20. 21. 22.
J. R. Birch, J. Phys. E. i3, 716 i1980). . . ’ G. W. Chantry, J. W. Fleming, G. W. F. Pardoe, W. Reddish and H. A. Willis, Infrared Phys. 11, 109 (1971). G. J. Davies, unpublished. G. W. Chantry and J. Chamberlain, Polymer Science (Edited by A. D. Jenkins), Chap. 20, Vol. 2. North Holland, Amsterdam (1972).
Infrared Phys. Vol. 33, No. 1, pp. 33.--38, 1992 Printed in Great Britain
THE FAR-INFRARED OPTICAL CONSTANTS OF POLYPROPYLENE, PTFE AND POLYSTYRENE J. R. BIRCH Division of Electrical Science, National Physical Laboratory, Teddington, Middlesex lWl1
OLW, U.K.
(Receitfed 29 July 199i) Abstract-The
far-infrared optical constants of polypropylene, PTFE and polystyrene have been determined in the spectral region between 50 and 500 cm-’ at a temperature of 290 K by the method of dispersive Fourier transform spectroscopy.
INTRODUCTION Low loss polymers are widely used for the construction of lenses and windows throughout the far-infrared spectral region. There consequently exists a considerable body of info~ation on their transmission spectral properties. There is, however, substantially less information available about the detailed spectral variation of both optical constants, the refractive index and the absorption coefficient, of such materials. In addition, such info~ation as is available on the refractive index is often limited by random uncertainties at the percent or so level. This can result in constant values being assigned to the far infrared refractive indices of such materials. While information at this level of uncertainty is generally adequate for most optical element design purposes, it does obscure both any local dispersion across an absorption band and any underlying larger scale dispersion due to distant strong loss processes, thereby inhibiting detailed studies of the microscopic dynamics of the polymers. A notable exception to this is provided by the measurement method of dispersive Fourier transform spectroscopy (DFTS). (I+ This allows the spectral variation of both the absorption coefficient and the refractive index of a material to be determined from a measurement of the attenuation and phase shift imposed on an electromagnetic wave by its interaction with a specimen, either in transmission or reflection. Present instrumentation allows the refractive index spectrum of a reasonably transparent polymer specimen to be determined with an accuracy of between parts in 10’ and 106, and a precision that can be as large as parts in 104. This difference between accuracy and precision arises from the difficulty of producing polymer specimens with a sufficiently well-defined optical thickness to allow the very high accuracy of the phase measurement to be carried over into the refractive index calculation. The method has been used to study the optical constants of a number of polymers and polymer-based composite materials in the technologically important near millimetre wavelength spectral region from N 3 to 40 cm--’ ( -90 to 1200 GHz), (*-“) but has only been used to study relatively few such materials in the far-infrared.““‘@ In the present work this sparce data base is extended with the report of the results of DFTS studies in the 50-500 cm-’ spectral region on polypropylene, polytetrafluoroethylene and polystyrene at 290 K.
EXPERIMENTAL The refraction and absorption spectra of each specimen were calculated from its phase shift and attenuation spectra as determined by the technique of dispersive Fourier transform spectroscopy in the spectral region between 50 and 500 cm-‘. This was done using two interferometers.(17) One of these interferometers was based on the Martin-Fuplett polarising wire grid configuration,@) and was used with a quartz-window Golay cell for measurements in the spectral region below 110 cm-‘. The second instrument was a conventional two beam interferometer with a thin film melinex beamdivider, and was used with a diamond-window Golay cell to cover the spectral region above Q Controller, Her Majesty’s Stationery Of&e, 1991. 33
J. R. BIRCH
34
110 cm-‘. In both instruments the specimen holder had a load lock construction so that a specimen could be inserted into, and removed from, the interferometer without affecting its vacuum environment.(‘g’ Thus, the mechanical stability of the instrument was unaffected by specimen changing, thereby avoiding the requirement for a stabilisation period after each change of specimen. All of the measurements were made at a temperature of 290 K and with a spectral resolution of -4 cm-‘. The specimens were all 50 mm diameter discs, with thicknesses of 3.1 mm (polypropylene), 2.1 mm (PTFE) and 2.0 mm (polystyrene). RESULTS The refraction and absorption spectra of all the specimens used in this study are presented in Figs l-3. Each spectrum is the average of four independent determinations. The reproducibility of these was such as to suggest a level of random uncertainty in the refraction spectra of about 10m5 above 110 cm-’ and a few times lo-’ at lower wavenumbers. In the absorption spectra the random uncertainties were typically of the order of 0.05 cm-‘. Polypropylene Polypropylene is not widely used as a lens material as it has a somewhat higher level of absorption than is found in polyethylene or TPX. Chantry et al., (*O)however, suggest its use as an
‘.4g85 I 1.4960 z -0 .c .-t z
1.4975 -
s n” 1.4970 -
I,..,I..,.I..,,I.,.,l...,l.,.,l..,.I,...I, 100 150 200
50
50
100
150
200
250
300
350
400
45c
250
300
350
400
450
Wavenumber Fig. 1. The refraction
and absorption
spectra
(cm-l) of polypropylene
at 290 K.
FIR optical constants of polypropylene, FTFE and polystyrene
35
alternative to polyethylene for spectroscopy involving the 70-8Ocm-’ region. This would avoid absorption losses due to the 73 cm-’ band of polyethylene, although, of course, the same objective could be achieved through the use of the lower loss polymer TPX. The refraction and absorption spectra of the polypropylene specimen studied in the present work are shown in Fig. 1. The absorption spectrum has five discrete absorption bands superimposed on a background that rises monotonically with increasing wavenumber. These bands are at 111, 170, 250, 320 and 398 cm-“, the first four of which agree with those found by Chantry et a/.(“) in a study from 20 to 400 cm”‘. Their absorption spectrum does not show the 398 cm-’ band found in the present work. The 111 cm-’ band is considerably wider than the other bands as it is the envelope of a doublet that only becomes clearly resolved when the temperature is reduced to 77 IL@‘) In the refraction spectrum one finds the corresponding dispersion associated with the five discrete absorption bands. The overall level of the refraction spectrum falls with increasing wavenumber up to about 300 cm-‘, as one would expect, and then begins to rise, showing the onset of the underlying dispersion due to the broad mid-infrared feature that the absorption spectrum is rising towards. The mean value of the refractive index over this spectra1 region is about 1.4975, and this agrees reasonably well with unpublished results@‘)reported by Chantry and Chamberlain’**) which show a value of about 1.505, given the known variablity of polymer specimens from different sources. 1.480
50
50
100
loo
150
200
250
300
350
400
450
150
200
250
300
350
400
450
Wavenumber (cm-11 Fig. 2. The refraction and absorption spectra of polytetrafl~oroethyIene
at 290 K.
J. R. BIRCH
36
Polytetrajuorethylene
At near millimetre wavelengths PTFE is about as transparent as polyethylene and TPX,“) and has consequently been used in lens and window applications in that spectral region. It has, in particular, been used in such applications for liquid studies as its relatively inert character renders it safe from corrosion and adsorption problems. However, as one moves out of the near millimetre region to higher wavenumbers the absorption in PTFE increases rapidly due to a strong absorption band at 202 cm-‘, which is due to vibrations of neighbouring CF, groups. The material becomes sufficiently lossy that by the 50-100 cm-’ region it is unsuitable for use in transmission optics. The measured refraction and absorption spectra of the 2 mm thick PTFE specimen in the 5&190 cm-’ region are shown in Fig. 2. Although the background spectrum of the empty interferometer contained intensity from 50 to 500 cm-‘, measurements on the PTFE specimen were only possible below 190cm-‘. Above 190cm-’ the power levels transmitted through the specimen were indistinguishable from zero within the limits implied by the random noise levels, with the exception of a 10 cm-’ wide region centred on 355 cm-‘. In this band the specimen became sufficiently transparent to achieve a peak fractional transmission coefficient of 0.05. The measured absorption spectrum increases rapidly from values -2 cm-’ at wavenumbers in the 50 cm-’ region to reach values close to 30 cm-’ by 190 cm-‘. Chamberlain and Gebbie (‘v have made DFTS studies on films of PTFE sufficiently thin to allow measurements to be made out to 300 cm-‘. These reveal the full
l&O0 I------
150
200
250
Wavenumber Fig. 3. The refraction
and absorption
spectra
300
350
400
(cm-‘) of polystyrene
at 290 K
450
FIR optical
constants
of polypropylene,
PTFE
and polystyrene
37
extent of the 202 cm-’ band, showing it to have a peak absorption value of about 220 cm-‘. In the region of overlap between the two measurements the absorption spectrum of Chamberlain and Gebbie is systematically higher than the present one. At 190 cm-‘, for example, their absorption coefficient is about 50 cm-’ compared to the present value of 30 cm-‘. This difference could be due to the different specimens used, thin film and bulk material. It is well known that the rolling or stretching used to produce thin polymer films induces birefringence and dichroism into their optical properties. Thus, the difference, although large, may not be significant, in that one is not comparing like with like. The measured refraction spectrum is dominated by the onset of dispersion across the intense 202 cm-’ band. It rises by 0.04 over the measured range, a very large amount compared to the values seen in the other specimens. In polypropylene, for example, the typical dispersion across its much weaker discrete absorption features was -0.0005. The overall level of the present refraction spectrum is somewhat above that found by Chamberlain and Gebbie (1.38),‘13’but is in reasonable agreement with near millimetre wavelength values,“” and the previous comments about the different character of the specimens apply. Polystyrene
At near millimetre wavelengths polystyrene is intermediate in the level of its absorption between the genuinely low loss spectra of LDPE, HDPE, TPX and PTFE, lying a factor of h- 3 above these and a factor of w 8 below the considerably more lossy spectra of nylon and perspex.“’ It does not appear to have found wide useage as a lens material for this reason, although Chantry and Chamberlain(22’ suggest that it could be a useable material for wavenumbers below 30 cm-‘. This seems somewhat unlikely, given the ready availability of polyethylene and TPX, unless polystyrene has other properties which would make it well-suited to a particular application. The refraction and absorption spectra of the polystyrene specimen are shown in Fig. 3. The absorption spectrum is dominated by a very broad feature centred on 220 cm-‘, with other features at 84, 247, 293, 324, 375, 405 and 432 cm-‘. The refraction spectrum has a mean level of about 1.59, in good agreement with its near millimetre wavelength value,(5’ and clearly shows the expected regions of dispersion associated with the stronger absorption bands.
CONCLUSIONS
The results of the determination of the optical constants of polypropylene, PTFE and polystyrene in the far-infrared spectral region between about 50 and 500 cm-’ at 290 K have been presented. The measurement accuracy was such that the small scale refractive index dispersion associated with the various observed absorption bands was fully resolved. It is well known that the optical constants of polymers can be very sensitive to the particular details of their manufacturing process and previous history. It is intended that the present spectra provide a guide to the typical values that can be expected. An internal report(‘7’ containing a full tabulation of the spectral variation of the refractive index, absorption coefficient, real and imaginary parts of the complex relative permittivity and the loss tangent is available. REFERENCES 1. J. R. Birch and T. J. Parker, Infrared and Millimefer Waves (Edited by K. J. Button), Chap. 3, Vol. 2. Academic New York (1979). 2. J. R. Birch, Proc. SPIE 289, 362 (1981). 3. J. R. Birch, Mikrochimica Acfa (Wien) III, 105 (1987). 4. T. J. Parker, Contemp. Phys. 31, 335 (1990). 5. J. R. Birch, J. D. Dromey and J. Lesurf, Infrared Phys. 21, 225 (1981). 6. J. R. Birch and F. P. Kong, Infrared Phys. 24, 30 (1984). 7. M. N. Asfar, IEEE Trans. Microwave Theory Tech. MTT-33, 1410 (1985). 8. J. R. Birch and F. P. Kong, Infrared Phys. 26, 131 (1986). 9. M. N. Afsar, IEEE Trans. instrum. Meas. IM-36, 530 (1987). 10. J. R. Birch and J. Lesurf, Infrared Phys. 27, 423 (1987). 11. P. B. Whibberley and J. R. Birch, Infrared Phys. 29, 995 (1989). 12. C. Meny, J. LBotin and J. R. Birch, Infrared Phys. 31, 211 (1991). 13. J. E. Chamberlain and H. A. Gebbie, Appl. Opt. 5, 393 (1966). 14. M. N. Afsar and G. W. Chantry, IEEE Trans. Microwave Theory Tech. MTT-25, 509 (1977).
Press,
38
J. R.
BIRCH
15. J. R. Birch and E. A. Nicol, Infrared Phys. 24, 573 (1984). 16. J. R. Birch. Infrared Phvs. 30, 195 (1990). 17. J. R. Birch, NPL Report DES 111, June’ (1991). 18. D. H. Martin and E. hDktt. Infrared Phvs. 10. 105 0970).
19. 20. 21. 22.
J. R. Birch, J. Phys. E. i3, 716 i1980). . . ’ G. W. Chantry, J. W. Fleming, G. W. F. Pardoe, W. Reddish and H. A. Willis, Infrared Phys. 11, 109 (1971). G. J. Davies, unpublished. G. W. Chantry and J. Chamberlain, Polymer Science (Edited by A. D. Jenkins), Chap. 20, Vol. 2. North Holland, Amsterdam (1972).