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On the temperature dependence of infrared emission bands
239
Journal of Molecular Structure, 294 (1993) 239-242 Elsevier Science Publishers B.V., Amsterdam
ON THETEMPERATURE DEPENDENCE OFINFRARED EMISSION BANDS S.
V. Ribnikar
Institute Belgrade,
and Z. Radak-Jovanovic
of Physical Chemistry, Faculty of Science, P.O.Box 137, YU-11001 Belgrade, Yugoslavia
University
of
The emission intensity of the infrared band of polyethylene at 721 cm-* was measured in the interval if 80° to -7’C. The temperature dependence of the intensity corresponds to a true Boltzmann distribution, which lead to a reconsideration of previously proposed theoretical dependence. 1. INTRODUCTION In contrast to the absorption infrared spectroscopy, which dates back to the early years of the 20th century and becoming a widespread laboratory analytical method after the nineteen-forties, its analogue, the emission IR spectroscopy is a rather recent development. The main topics of it are covered by two review articles [l, 21. infrared Emission of discrete bands from condensed systems was for obviously, tacitly a long time assumed to be practically nonexistent. The reasons are, firstly, because of a much faster vibrational-translational relaxation of the received energy compared to the emission probability, and secondly, because of the reabsorption of the emitted radiation which occurs at the same wavelength of the emission (in contrast to luminescence where the wavelengths generally differ). A number of works, mentioned in the two above reviews, shows that condensed-phase emissions are a full reality. The emission intensity of a molecular system should depend on the population of a given energy 0022-2860/93/$06.00
0 1993 Elsevier Science Publishers B.V.
level of the molecules, i.e. on the for the given Boltzmann factor energy. Concerning the infrared emission intensity of molecular emission, one of the present authors [33 proposed that a dependence on l/b at first approximation, and on l/b( b -1) in a second one should be applicable in the composite spectra, with b = exp( hcu/kT) where h is the Planck constant, c the velocity oC light, v the frequency (in cm ), k the Boltzmann constant and T the absolute temperature. When recording emission with an infrared spectrophotometer the intensity of the recorded signal from the emitting sample will equal zero when the temperatures of the sample and detector are equal. Measurable signals are obtained when the sample is either warmer or colder than the detector. In order to establish the radiant net emitted energy s the recorded signals should be corrected for the difference AT = T - To, the latter temperature referring to the detector. Therefore, the recorded temperature dependence of the emisAll rights reserved.
240
sion should follow
a
I
2. EXPERIMENTAL
equations:
$-,
or
I Ocb(b
AT
- 1)
The situation Fig.1. 0.75
(2)
’
is
illustrated
I
in
1
A . f
0.50 3
1
0.25
.
S
s
. . W
0.00 _--___-@
-O.ZS[““‘““‘““‘“” 0 100
200
Tompmmture
7
00
K
400
Fig. 1. Expected emission intensities as a function of temperature for a detector at 298 K and alvibrational frequency of 721 cm . 1 according to Eq. 1, 2 - Eq. 2, 3 scale is not Eq. 3. The ordinate quantitative. To our knowledge, there are no systematic published data on the temperature dependence of the infrared emission band intensities, particularly on ones below ambient temperature. The most sensitive region for testing the above mentioned alternatives is the one below ambient (detector) temperature, as seen from The normally “positive” Fig. 1. emission bands should there appear i. e. present missing as “negative”, gaps in the emission continuum.
As the emitting object a polyethylene foil of a thickness of 50 pm was uti-ll ized. Its emission band at 721 cm was chosen both because of its greatest intensity and the absence of instrumental distortions in this region. The foil was attached to a box with a copper sheet side, which was connected to a thermostat enabling circulation of a cooled or heated fluid through it. The temperature was monitored by a thermocouple inserted into an extension of the backing copper sheet. A Perkin-Elmer 983G spectrophotometer was used in its emission mode. The effe$ive slit width was kept at 10.5 cm . The cell, fixed by a common cell holder, was inserted into the sample beam, while the reference beam contained a bright copper plate of the same quality as the backing in the emitting cell. The instrument was flushed by dry nitrogen; the gas emerging through the instrument sample opening prevented wetting or icing of the emitting surface at subzero temperatures. The plate in the reference beam was at ambient temperature. The reported intensities refer to peak heights above the continuum background, even though the latter amounted only to a small fraction compared to the peak height. The output of the instrument in its emission mode appears to be analogous to a per cent transmittance scale, i.e. not proportional to absorbance or energy of emission. However, since all the data refer to values below l%, a linear relationship should be greatly fulfilled. The ‘ambient’ temperature refers to the temperature of the detector, being normally one to two degrees above room temperature.
241
3. RESULTSANDDISCUSSION Several
series of intensity measmade in the interval of 80’ to -7OC. With runs restricted to the above-ambient temperatures, recorded signals appeared proportional to the temperature difference no curvature could be esAT, i.e. tablished within the experimental scatter of data. Runs at lower temto show peratures were expected curvatures (cf. Pig. 1)) greater which proved to be true. Transition through the ambient temperature of the instrument showed clearly an inversion of the sense of emission, as illustrated in Fig. 2. In order to eliminate the overwhelming influence of AT on the the obtained emission intensity, data were divided by the corresponding known values of AT to get a plain dependence on f ( b) as defined by Eqs. 1 or 2. Since in our case !! B 1, Eq. 2 reduces to I/AT * l/b . By taking logarithms of both sides of the equations, the following dependences are expected
urement
In (I/AT)
were
= -a/T
or In (I/AT)
=
-24T,
.
linear plots in coordinates ii”; I/AT) VS. 1/T, where a represents hcu/k = 1.4387 x v. Since in
27.25
Fig.
25.25
our case u = 721 cm-I, the value of the slope should be either 1037 K or twice as much, depending on the above assumed dependences.
-1
0.0034
0.0036
0.0038
l/r
Fig. 3. The plot of ln(I/AT) VS. l/T for a run between 17O and -7OC. Figure 3 shows a plot of exgerimental data recorded between 17 and -7OC. A linear least squares treatment yields -a = 1039 f 79 K. Two other experiments yielded for -a values of 1090 f 156 K and 990 f 188 K, The composite weighted average amounts to -a = 1042 f 66 K, This datum corresponds to a plain Boltzmann emission (Eq. 1). The values of the ordinate intercept, signifying a proportionality constant, vary somewhat, which can be explained by differing experimental and geometrical conditions of the measurements.
23.15
20.75
19.75
2. Recorded emission bands in the vicinity of the detector temperature1 Figures show temperatures in OC. Scanned were regions 900 - 600 cm .
242 It is obvious that the value of the slope does not reproduce the quantity of 2074 K, excluding thus the dependence on Eq. 2. Formulae 1 and 2, whichever being closer to truth, are to some extent approximate for treating the present The reason is experimental data. that the recorded signal presents actually the difference between the sample and reference beams (despite the fact that the instrument is of the ratio-recording type). Next to that, in the present experiments the reference plate was always at ambiwhile the sample ent temperature, system was exposed to widely varying When these facts are temperatures. taken into account (with some simit can be plifying assumptions), shown that the recorded emission intensity should follow the expression f
em
where b was defined above, b is its value at the ambient tempera ? ure, To, and c being a proportionality factor. It is noticeable that the term aT does not appear in Eq. 3, but that the curve, nevertheless, passes zero at the temperature of To. The curve is shown in Fig, 1 (3). The greatest difference , compared to Eqs 1 and 2 (curves 1 and 2), is at the lowest temperatures where it tends to a constant negative value, presenting the uncompensated emission of the reference plate i.e. to -c/(b,-1). Equation (3) may be developed into a series around the point To , making the quantity AT appear: I
em
=
g [A-AT - &(AT)’
with A = a bo/r((b,-
+ . ..I
1)l ad
(4)
B = (2aTo + a2)bo/12T~(bo-1)I.
As expected, the validity of Eq. 4 with only two terms of the series extends only in a span of some 3: 30 degrees. The experimental points could be well fitted to Eqs 3 and 4, both with variation of two or three constants. In the latter case the constant representing the slope, a, reproduces simultaneously the value of -1037 K within the normally expected uncertainty. This method does not suffer from the disadvantage encountered when treating quantities I/AT in the vicinity of To, where small values of AT produce great positive or negative excurs ions. 4. INCLUSIONS The intensity of infrared emission bands follows obviously the Boltzmann factor for the given frequency excluding thus the previously proposed dependence. The expected appearance of negative emission bands proved true. REFERENCES 1. P. V. Huong,
Infrared emission spectroscopy, in Advances in Infrared and Raman Spectroscopy, VO1.4.) edited by R.J.H,Clark and R.E.Hester, pp. 85-107, Heyden, London, 1978,
2.
P. Baraldi, Infrared emission spectroscopy (IRES): a tool in research and application, Chimica Oggi (Chemistry Today), May 1990, pp. 53-57.
3. S,V.Ribnikar, (1988) 363.
J.Serb.Chem.Soc.
53
Journal of Molecular Structure, 294 (1993) 239-242 Elsevier Science Publishers B.V., Amsterdam
ON THETEMPERATURE DEPENDENCE OFINFRARED EMISSION BANDS S.
V. Ribnikar
Institute Belgrade,
and Z. Radak-Jovanovic
of Physical Chemistry, Faculty of Science, P.O.Box 137, YU-11001 Belgrade, Yugoslavia
University
of
The emission intensity of the infrared band of polyethylene at 721 cm-* was measured in the interval if 80° to -7’C. The temperature dependence of the intensity corresponds to a true Boltzmann distribution, which lead to a reconsideration of previously proposed theoretical dependence. 1. INTRODUCTION In contrast to the absorption infrared spectroscopy, which dates back to the early years of the 20th century and becoming a widespread laboratory analytical method after the nineteen-forties, its analogue, the emission IR spectroscopy is a rather recent development. The main topics of it are covered by two review articles [l, 21. infrared Emission of discrete bands from condensed systems was for obviously, tacitly a long time assumed to be practically nonexistent. The reasons are, firstly, because of a much faster vibrational-translational relaxation of the received energy compared to the emission probability, and secondly, because of the reabsorption of the emitted radiation which occurs at the same wavelength of the emission (in contrast to luminescence where the wavelengths generally differ). A number of works, mentioned in the two above reviews, shows that condensed-phase emissions are a full reality. The emission intensity of a molecular system should depend on the population of a given energy 0022-2860/93/$06.00
0 1993 Elsevier Science Publishers B.V.
level of the molecules, i.e. on the for the given Boltzmann factor energy. Concerning the infrared emission intensity of molecular emission, one of the present authors [33 proposed that a dependence on l/b at first approximation, and on l/b( b -1) in a second one should be applicable in the composite spectra, with b = exp( hcu/kT) where h is the Planck constant, c the velocity oC light, v the frequency (in cm ), k the Boltzmann constant and T the absolute temperature. When recording emission with an infrared spectrophotometer the intensity of the recorded signal from the emitting sample will equal zero when the temperatures of the sample and detector are equal. Measurable signals are obtained when the sample is either warmer or colder than the detector. In order to establish the radiant net emitted energy s the recorded signals should be corrected for the difference AT = T - To, the latter temperature referring to the detector. Therefore, the recorded temperature dependence of the emisAll rights reserved.
240
sion should follow
a
I
2. EXPERIMENTAL
equations:
$-,
or
I Ocb(b
AT
- 1)
The situation Fig.1. 0.75
(2)
’
is
illustrated
I
in
1
A . f
0.50 3
1
0.25
.
S
s
. . W
0.00 _--___-@
-O.ZS[““‘““‘““‘“” 0 100
200
Tompmmture
7
00
K
400
Fig. 1. Expected emission intensities as a function of temperature for a detector at 298 K and alvibrational frequency of 721 cm . 1 according to Eq. 1, 2 - Eq. 2, 3 scale is not Eq. 3. The ordinate quantitative. To our knowledge, there are no systematic published data on the temperature dependence of the infrared emission band intensities, particularly on ones below ambient temperature. The most sensitive region for testing the above mentioned alternatives is the one below ambient (detector) temperature, as seen from The normally “positive” Fig. 1. emission bands should there appear i. e. present missing as “negative”, gaps in the emission continuum.
As the emitting object a polyethylene foil of a thickness of 50 pm was uti-ll ized. Its emission band at 721 cm was chosen both because of its greatest intensity and the absence of instrumental distortions in this region. The foil was attached to a box with a copper sheet side, which was connected to a thermostat enabling circulation of a cooled or heated fluid through it. The temperature was monitored by a thermocouple inserted into an extension of the backing copper sheet. A Perkin-Elmer 983G spectrophotometer was used in its emission mode. The effe$ive slit width was kept at 10.5 cm . The cell, fixed by a common cell holder, was inserted into the sample beam, while the reference beam contained a bright copper plate of the same quality as the backing in the emitting cell. The instrument was flushed by dry nitrogen; the gas emerging through the instrument sample opening prevented wetting or icing of the emitting surface at subzero temperatures. The plate in the reference beam was at ambient temperature. The reported intensities refer to peak heights above the continuum background, even though the latter amounted only to a small fraction compared to the peak height. The output of the instrument in its emission mode appears to be analogous to a per cent transmittance scale, i.e. not proportional to absorbance or energy of emission. However, since all the data refer to values below l%, a linear relationship should be greatly fulfilled. The ‘ambient’ temperature refers to the temperature of the detector, being normally one to two degrees above room temperature.
241
3. RESULTSANDDISCUSSION Several
series of intensity measmade in the interval of 80’ to -7OC. With runs restricted to the above-ambient temperatures, recorded signals appeared proportional to the temperature difference no curvature could be esAT, i.e. tablished within the experimental scatter of data. Runs at lower temto show peratures were expected curvatures (cf. Pig. 1)) greater which proved to be true. Transition through the ambient temperature of the instrument showed clearly an inversion of the sense of emission, as illustrated in Fig. 2. In order to eliminate the overwhelming influence of AT on the the obtained emission intensity, data were divided by the corresponding known values of AT to get a plain dependence on f ( b) as defined by Eqs. 1 or 2. Since in our case !! B 1, Eq. 2 reduces to I/AT * l/b . By taking logarithms of both sides of the equations, the following dependences are expected
urement
In (I/AT)
were
= -a/T
or In (I/AT)
=
-24T,
.
linear plots in coordinates ii”; I/AT) VS. 1/T, where a represents hcu/k = 1.4387 x v. Since in
27.25
Fig.
25.25
our case u = 721 cm-I, the value of the slope should be either 1037 K or twice as much, depending on the above assumed dependences.
-1
0.0034
0.0036
0.0038
l/r
Fig. 3. The plot of ln(I/AT) VS. l/T for a run between 17O and -7OC. Figure 3 shows a plot of exgerimental data recorded between 17 and -7OC. A linear least squares treatment yields -a = 1039 f 79 K. Two other experiments yielded for -a values of 1090 f 156 K and 990 f 188 K, The composite weighted average amounts to -a = 1042 f 66 K, This datum corresponds to a plain Boltzmann emission (Eq. 1). The values of the ordinate intercept, signifying a proportionality constant, vary somewhat, which can be explained by differing experimental and geometrical conditions of the measurements.
23.15
20.75
19.75
2. Recorded emission bands in the vicinity of the detector temperature1 Figures show temperatures in OC. Scanned were regions 900 - 600 cm .
242 It is obvious that the value of the slope does not reproduce the quantity of 2074 K, excluding thus the dependence on Eq. 2. Formulae 1 and 2, whichever being closer to truth, are to some extent approximate for treating the present The reason is experimental data. that the recorded signal presents actually the difference between the sample and reference beams (despite the fact that the instrument is of the ratio-recording type). Next to that, in the present experiments the reference plate was always at ambiwhile the sample ent temperature, system was exposed to widely varying When these facts are temperatures. taken into account (with some simit can be plifying assumptions), shown that the recorded emission intensity should follow the expression f
em
where b was defined above, b is its value at the ambient tempera ? ure, To, and c being a proportionality factor. It is noticeable that the term aT does not appear in Eq. 3, but that the curve, nevertheless, passes zero at the temperature of To. The curve is shown in Fig, 1 (3). The greatest difference , compared to Eqs 1 and 2 (curves 1 and 2), is at the lowest temperatures where it tends to a constant negative value, presenting the uncompensated emission of the reference plate i.e. to -c/(b,-1). Equation (3) may be developed into a series around the point To , making the quantity AT appear: I
em
=
g [A-AT - &(AT)’
with A = a bo/r((b,-
+ . ..I
1)l ad
(4)
B = (2aTo + a2)bo/12T~(bo-1)I.
As expected, the validity of Eq. 4 with only two terms of the series extends only in a span of some 3: 30 degrees. The experimental points could be well fitted to Eqs 3 and 4, both with variation of two or three constants. In the latter case the constant representing the slope, a, reproduces simultaneously the value of -1037 K within the normally expected uncertainty. This method does not suffer from the disadvantage encountered when treating quantities I/AT in the vicinity of To, where small values of AT produce great positive or negative excurs ions. 4. INCLUSIONS The intensity of infrared emission bands follows obviously the Boltzmann factor for the given frequency excluding thus the previously proposed dependence. The expected appearance of negative emission bands proved true. REFERENCES 1. P. V. Huong,
Infrared emission spectroscopy, in Advances in Infrared and Raman Spectroscopy, VO1.4.) edited by R.J.H,Clark and R.E.Hester, pp. 85-107, Heyden, London, 1978,
2.
P. Baraldi, Infrared emission spectroscopy (IRES): a tool in research and application, Chimica Oggi (Chemistry Today), May 1990, pp. 53-57.
3. S,V.Ribnikar, (1988) 363.
J.Serb.Chem.Soc.
53