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Photoacoustic infrared spectroscopy of polymer beads
Spectrochimica Acta Part A 73 (2009) 823–827
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa
Photoacoustic infrared spectroscopy of polymer beads Qing Wen, Kirk H. Michaelian ∗ CanmetENERGY, Natural Resources Canada, 1 Oil Patch Drive, Devon, Alberta T9G 1A8, Canada
a r t i c l e
i n f o
Article history: Received 25 November 2008 Received in revised form 19 March 2009 Accepted 15 April 2009 Keywords: Photoacoustic spectroscopy Infrared spectroscopy Phase spectra Saturation
a b s t r a c t Photoacoustic (PA) spectra of four types of polymer resin beads, ranging in size from 35 to 150 m, were acquired using a Fourier transform infrared spectrometer capable of both rapid- and step-scan mirror movement. Thermal diffusion lengths were on the order of the particle sizes of the beads. The PA magnitude spectra were similar to absorption spectra; both positive- and negative-going features occurred in the phase spectra. The frequency dependences of the total PA intensities of the polymer resins and carbon black differed by a factor of about f−0.30 . The intensities of the weak bands in the ratioed spectra (resin beads/carbon black) displayed a similar dependence. Partial saturation caused a more gradual variation for the stronger bands, where the intensity is proportional to ∼f−0.1 –f−0.2 . Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
1. Introduction Photoacoustic (PA) infrared spectra of condensed-phase samples are most commonly acquired using Fourier transform infrared (FT-IR) spectrometers and gas-microphone PA cells. The attributes and applications of the method have been reviewed in detail [1]. Significant advantages include the obviation of traditional sample preparation techniques and the capability for depth profiling. The former feature is invoked in the present study, a PA investigation of polymer resin beads with particle sizes in the ∼35–150 m range. These polymer beads are frequently utilized in the solid-phase industrial synthesis of peptides and other compounds. Interest in the PA investigation of these beads derives from two principal sources:
(2) The PA signal produced from a single particle has been reported to be greater than that of the corresponding bulk sample [9]. The current study of ∼10-mg samples will be followed by microsample experiments on single particles using either a thermal infrared source or synchrotron radiation. In this investigation, PA infrared spectra of the resin beads were obtained using both rapid- and step-scan mirror movements in an FT-IR spectrometer. A range of modulation frequencies existed in the rapid-scan experiments, while a single frequency was utilized in each step-scan measurement. Absorption bands were identified in both the magnitude and phase spectra. The dependence of PA intensity on f was studied and found to differ for strong and weak bands. 2. Experimental
(1) Their sizes are in the order of the thermal diffusion length [s = (˛/f)1/2 , where ˛ and f denote thermal diffusivity and modulation frequency, respectively]. The PA signal is strongly affected by the relative magnitudes of s (approximately equal to the sampling depth), the optical depth [ˇ = 1/ˇ, the inverse of the absorption coefficient], and the particle size (D). Several research groups have studied the effects of f and D on PA intensity [2–8]. The situation is complicated for fine particles because the interstitial gas gives rise to an additional pressure signal. The intensity of this signal is proportional to f−1 while the thermal contribution varies as f−n (n = 1–1.5) [4].
∗ Corresponding author. Tel.: +1 780 987 8646; fax: +1 780 987 8676. E-mail addresses: [email protected] (Q. Wen), [email protected] (K.H. Michaelian).
Four types of resin beads (Polystyrene, PS; Acetyl Polystyrene SS, APSS; Isocyanate, ISO; TentaGel S COOH SS, TGS) manufactured by Advanced ChemTechTM were analyzed in this study. The structures and particle sizes of the beads are shown in Table 1. Experiments were performed using a Bruker IFS 88 FT-IR spectrometer and an MTEC 200 PA cell. The volume of the sample chamber in this cell is approximately 0.9 mL [10]. Sample cups, with diameters of 5 mm and depths of 2 mm, were completely filled as each type of bead was analyzed. Thus the sample volumes (∼0.04 mL) were much smaller than the cell volume, and the exact quantity of sample had little effect on the cell geometry. Rapid-scan spectra of the resins were recorded at four different mirror velocities, corresponding to He–Ne laser modulation frequencies of 1.6, 2.2, 3.0 and 4.0 kHz, respectively. The nominal resolution of these spectra is 6 cm−1 . Carbon black powder was used
1386-1425/$ – see front matter Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2009.04.004
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Q. Wen, K.H. Michaelian / Spectrochimica Acta Part A 73 (2009) 823–827 Table 1 Structures and particle sizes of resin beads. Name
Structure
Particle size (m)
Polystyrene (PS)
37–74
Acetyl Polystyrene SS (APSS)
74–149
Isocyanate (ISO)
74–149
TentaGel S COOH SS (TGS)
90
to obtain reference (background) spectra. At each velocity, 20 50scan spectra were averaged for the resins and 10 50-scan spectra were averaged for carbon black. All measurements were performed within two days so as to minimize any intensity drifts due to gradual changes in optical alignment or humidity variations in the instrument. The PA intensities measured in this manner are generally quite reproducible, with experimental errors less than the thickness of the plotted curves in the spectra shown below. The spectrometer was purged with dry N2 to reduce absorption by ambient water vapour and CO2 during these measurements. Step-scan spectra were acquired using amplitude modulation at frequencies of 50, 100 and 200 Hz, and a spectrum resolution of 15 cm−1 . Spectra obtained at higher resolution were rather noisy due to mechanical vibrations, making identification of features difficult. An EG&G 5206 lock-in amplifier was used to recover the real (Re) and imaginary (Im) interferograms. The magnitude [M = (Re2 + Im2 )1/2 ] and phase [ = tan−1 (Im/Re)] spectra were calculated after Fourier transformation. Data for resins and carbon black were collected under like conditions.
agree well with published data from transmission measurements [11]. 3.2. Step-scan phase spectra Convenient retrieval of the PA phase is an important feature of step-scan data [12,13]. The Re and Im components, acquired simultaneously using a two-phase lock-in amplifier, have the same instrument phase. The PA phase can therefore be completely separated from the instrument phase through division.
3. Results and discussion The results obtained for the resin beads using both rapid- and step-scan operation of the spectrometer are presented in the following three sections. Magnitude spectra, step-scan phase spectra, and the variation of PA intensity with modulation frequency, are discussed in these sections. 3.1. Rapid- and step-scan magnitude spectra Rapid- and step-scan magnitude spectra of the resin beads, ratioed against appropriate carbon black spectra, are shown in Figs. 1 and 2, respectively. The low-wavenumber limit is dictated by the Ge/KBr beamsplitter, while the upper limit was chosen because of the absence of well-defined features above ∼3500 cm−1 . The rapid-scan spectra display a number of prominent fundamental bands in the 500–1800 and 2800–3200 cm−1 regions for each resin. In addition, weak features due to combination (∼2000 cm−1 ) and overtone (∼2700–2740 cm−1 for TGS) transitions were also observed. Some of the bands are not well defined in the step-scan spectra because of their lower resolution. The bands observed for PS
Fig. 1. Rapid-scan PA spectra of the resin beads obtained at a laser modulation frequency of 1.6 kHz and ratioed against a carbon black spectrum acquired under like conditions. The spectra of ISO, APSS, and PS are shifted along the intensity axis by successive increments of ∼0.2 intensity units for clarity. The intensities of the highwavenumber bands are reduced compared to the low-wavenumber ones because of the f−0.3 dependence (see text).
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Fig. 3. Phase spectra of ISO calculated from step-scan Re and Im spectra obtained at 50 Hz. The Im spectra used to obtain the phase spectra in (a) and (b) were calculated, using the standard Mertz and Mertz/stored-phase procedures, respectively. The asterisks indicate bands at 1450, 1499, 1548, 1597, 1675, 2264, 2853, 2922, 3023, and 3055 cm−1 .
Fig. 2. Step-scan PA spectra of the resin beads obtained at fixed f (100 Hz). The spectra have been ratioed against a carbon black spectrum acquired at the same frequency. The spectra of ISO, APSS, and PS are shifted along the intensity axis by successive increments of ∼0.2 intensity units for clarity.
The PA phase spectra contain many of the absorption features and can facilitate band identification, since the phase tends to vary linearly with absorption even when the magnitude exhibits partial saturation. The Re and Im spectra used to calculate the PA phase are obtained by Fourier transformation of the corresponding interferograms. In FT-IR spectroscopy, phase correction and Fourier transformation are usually performed automatically in software. In the well-known Mertz algorithm [14], the phase (mainly due to the instrument) is calculated using a narrow region of the interferogram with an equal number of points on either side of the centreburst. The phase spectrum is interpolated so that the spacing between successive points is the same as that in the spectra calculated from the entire interferogram. Point-by-point multiplication of the real (imaginary) spectrum by the cosine (sine) of the phase produces spectra without instrumental phase errors. It should be noted that correction for the instrument phase is optional in the present context since this phase affects both Re and Im spectra in the same way [12,13]. In situations where an interferogram is particularly noisy or its centreburst is weak, an appropriate instrument phase calculated under more favourable circumstances can be utilized in the calculation. For example, the phase obtained for the Re spectrum was frequently used during calculation of the corresponding Im spectrum in the present work. This strategy is referred to as the Mertz/stored-phase method in Bruker software. Fig. 3 shows the PA phase spectra obtained for ISO using these two variations of the Mertz method. Prominent bands that also occur in the magnitude spectrum (Fig. 2) are labelled with asterisks and listed in the caption of Fig. 3. Several weak features in the phase spectra, such as those located between about 2500 and 2800 cm−1 , may suggest the existence of weak bands not visible in Fig. 2.
Phase spectra of the other three resins are illustrated in Fig. 4. The Mertz/stored-phase method was used to calculate the Im spectra in all three cases. The TGS phase spectrum contains most of the features in the magnitude spectrum, a result similar to that described above for ISO. Despite the considerable noise in the phase spectra of PS and APSS, a number of strong bands can still be recognized. These bands are indicated by asterisks in Fig. 4. It should be noted that the bands in the phase spectra can be either positive- or negative-going with regard to the phase in regions where absorption is minimal [12,13]. The same bands were also identified in phase spectra calculated from rapid-scan, double-sided interferograms recorded in a separate experiment; however, the PA phase is partly obscured by the instrument phase in that case.
Fig. 4. Step-scan phase spectra of PS, APSS, and TGS obtained at 50 Hz. The Im spectra, used to calculate the phase spectra were obtained from the Mertz/stored-phase procedure. The asterisks indicate bands identified in magnitude spectra of the three polymers.
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Fig. 5. Variation of interferogram peak amplitude with f (log–log scale) for PS and carbon black. The frequency is specified at the He–Ne laser wavenumber (15,800 cm−1 ). The peak amplitudes are normalized to unity at 1.6 kHz, the lowest frequency. The straight lines are least-square fits of the data and have slopes of −0.85 and −1.15 for carbon black and PS, respectively.
3.3. Variation of the PA intensity with modulation frequency Rapid-scan spectra of the resin beads were ratioed against carbon black spectra recorded under similar conditions. Data obtained at the four frequencies reveal different behaviours for the PS beads and carbon black (Fig. 5). The integrated carbon black PA intensity (represented by the interferogram centreburst amplitude) is proportional to f−0.85 , reasonably close to the f−1 dependence predicted for an optically opaque, thermally thin solid [15]. The PS intensity exhibits a stronger, f−1.15 dependence; the other three resins show similar trends. The ratioed spectra (polymer resin/carbon black), as a result, vary approximately as f−0.30 . This behaviour was observed in multiple repeated measurements. Experiments that employed two other sample-filling strategies (half-full sample cup, or a very thin layer of sample in the cup) were also performed; the same frequency dependence was observed in these cases. The difference between the f dependences of the polymers and carbon black can be attributed to the fact that the PA signal originates from within the beads, while absorption occurs near the surface for carbon black [15,16]. The frequency dependence of the PA signal was also studied for individual bands or groups of bands. For each compound, four or five bands were chosen from various spectral regions; both strong and weak features were selected. The peak intensities, represented as the area of each band (or group of bands), are plotted against f in Fig. 6. To facilitate interpretation of the data, the intensity is normalized to unity at the lowest f value for each band. As the frequency increases, the intensities of all the bands decrease, although at different rates. Specifically, the intensities of the strong bands were found to diminish more slowly than those of the weak ones. The strong peaks [APSS, 1606 and 1684 cm−1 ; ISO, 1670 and 1684 cm−1 ; TGS, 2887 and the 1010–1213 cm−1 group; all compounds, 702 cm−1 ] show intensity reductions with slopes between −0.1 and −0.2. By contrast the slopes are approximately −0.3 for the weaker bands. The latter result is consistent with the f−0.30 dependence of the ratioed spectra mentioned above. The relative dimensions of s , ˇ , and D must be considered in order to interpret these results properly. s can be estimated using the value of ˛ (0.00082 cm2 /s) reported [17] for PS. In conventional rapid-scan FT-IR spectroscopy, f is related to both infrared wavenumber () and mirror velocity (V) through the relationship f = 2V. For the spectrometer used in this study, in the mid-infrared region ( = 500–3500 cm−1 ) f varies from about 50 to 350 Hz at the
Fig. 6. Variation of rapid-scan PA intensity with f (log–log scale) for various bands and band groups in spectra of PS, APSS, ISO, and TGS (top to bottom, respectively). The legends indicate approximate band positions and ranges. A band common to more than one compound is denoted by the same symbol, with its position given on first usage. PA intensities are normalized to unity at the lowest applicable frequency.
lowest mirror velocity, and from 125 to 885 Hz at the highest velocity. These data yield approximate s values that vary between 23 and 5.5 m. Thus the particle sizes D, which are in the ∼35–150 m range, are similar to or larger than s . In this regime, the thermal term dominates the PA signal and the pressure signal due to the interstitial gas is not expected to play an important role [4,8]. Hence the different frequency dependences of the pressure and thermal signals are not the likely cause of the different f dependencies for strong and weak bands. Pandurangi and Seehra [8] described the effects of D and f on the PA intensity in spectra of silica particles. The role of saturation and the probable relations ˇ < s (strong bands) and ˇ > s (weak bands) were noted for large particles. Similar relations may also occur for the beads studied in this work. The strong bands are partially saturated such that the relationship ˇ < s applies. As f increases, their intensities decrease more slowly than those of the unsaturated bands. As the limit of full saturation is approached, the dependence of PA intensity on f goes to zero and may even become positive [8]. The results in the step-scan spectra support the above interpretation; as expected, the frequency dependences of the interferogram centreburst amplitudes for the polymer beads and carbon black are similar to those in the corresponding rapid-scan data. In general, the intensity diminishes rapidly for weak bands but more gradually for strong bands because the latter are partially saturated. For some of the strong bands, the degree of saturation differs from that in the rapid-scan spectra because different modulation frequencies (and therefore different s ) apply. Fig. 7 shows results for TGS. The 702-cm−1 band has not been included because the noise in the 50-Hz spectrum precludes accurate calculations. The other four bands can be divided into two groups according to the slope of the frequency dependence. The strong bands [2887
Q. Wen, K.H. Michaelian / Spectrochimica Acta Part A 73 (2009) 823–827
827
tion spectra. Fewer bands are identifiable in the phase spectra, where both positive- and negative-going features occur. Most of the PA signal originated from within the beads, whereas absorption occurred near the surface for the reference carbon sample. The frequency dependence of the total PA intensities of the polymer resins and carbon black differed by a factor of about f−0.30 . The intensities of the weak bands in the ratioed spectra (polymer resin/carbon black) varied approximately as this factor. Partial saturation caused a more gradual variation for the stronger bands, where the intensity is proportional to ∼f−0.1 –f−0.2 . Acknowledgement Qing Wen would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) visiting fellowship program for funding. Fig. 7. Variation of step-scan PA intensity with f (log–log scale) for various TGS bands. The legend shows the positions of the bands and band group that were analyzed. PA intensities are normalized to unity at 50 Hz.
and the 1010–1213 cm−1 group)] decrease in intensity more gradually while the intensities of the weak (1601 and 1736 cm−1 ) bands decrease more quickly. These findings are consistent with those in the rapid-scan spectra (Fig. 6). 4. Summary Rapid- and step-scan mid-infrared PA spectra of four types of polymer resin beads (Polystyrene, Acetyl Polystyrene SS, Isocyanate, and TentaGel S COOH SS), ranging in size from 35 to 150 m, are discussed in this article. Approximately 25–40 bands were identified in each rapid-scan magnitude spectrum, whereas about 15 bands were observed in the lower resolution step-scan spectra. The PA magnitude spectra resemble conventional absorp-
References [1] K.H. Michaelian, Photoacoustic Infrared Spectroscopy, Wiley, New Jersey, 2003. [2] N.L. Rockley, M.K. Woodard, M.G. Rockley, Appl. Spectrosc. 38 (1984) 329–334. [3] J.-P. Monchalin, L. Bertrand, G. Rousset, F. Lepoutre, J. Appl. Phys. 56 (1984) 190–210. [4] S.J. McGovern, B.S.H. Royce, J.B. Benziger, J. Appl. Phys. 57 (1985) 1710–1718. [5] C.Q. Yang, W.G. Fateley, J. Mol. Struct. 141 (1986) 279–284. [6] C.Q. Yang, W.G. Fateley, J. Mol. Struct. 146 (1986) 25–39. [7] P.S. Belton, R.H. Wilson, A.M. Saffa, Anal. Chem. 59 (1987) 2378–2382. [8] R.S. Pandurangi, M.S. Seehra, Anal. Chem. 62 (1990) 1943–1947. [9] E.Y. Jiang, Appl. Spectrosc. 53 (1999) 583–587. [10] R.W. Jones, J.F. McClelland, Appl. Spectrosc. 55 (2001) 1360–1367. [11] C.Y. Liang, S. Krimm, J. Polym. Sci. 27 (1958) 241–254. [12] R.A. Palmer, C.J. Manning, J.M. Widder, R.M. Dittmar, P.J. Thomas, J.L. Chao, in: J.C. Murphy (Ed.), Photoacoustic and Photothermal Phenomena II, Springer, Berlin, 1990, pp. 529–532. [13] C.J. Manning, R.M. Dittmar, R.A. Palmer, Infrared Phys. 33 (1992) 53–62. [14] L. Mertz, Infrared Phys. 7 (1967) 17–23. [15] A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy, Wiley, New Jersey, 1980. [16] H.S. Bennett, R.A. Forman, J. Appl. Phys. 48 (1977) 1432–1436. [17] K.N. Madhusoodanan, M.R. Thomas, J. Philip, J. Appl. Phys. 62 (1987) 1162–1166.
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa
Photoacoustic infrared spectroscopy of polymer beads Qing Wen, Kirk H. Michaelian ∗ CanmetENERGY, Natural Resources Canada, 1 Oil Patch Drive, Devon, Alberta T9G 1A8, Canada
a r t i c l e
i n f o
Article history: Received 25 November 2008 Received in revised form 19 March 2009 Accepted 15 April 2009 Keywords: Photoacoustic spectroscopy Infrared spectroscopy Phase spectra Saturation
a b s t r a c t Photoacoustic (PA) spectra of four types of polymer resin beads, ranging in size from 35 to 150 m, were acquired using a Fourier transform infrared spectrometer capable of both rapid- and step-scan mirror movement. Thermal diffusion lengths were on the order of the particle sizes of the beads. The PA magnitude spectra were similar to absorption spectra; both positive- and negative-going features occurred in the phase spectra. The frequency dependences of the total PA intensities of the polymer resins and carbon black differed by a factor of about f−0.30 . The intensities of the weak bands in the ratioed spectra (resin beads/carbon black) displayed a similar dependence. Partial saturation caused a more gradual variation for the stronger bands, where the intensity is proportional to ∼f−0.1 –f−0.2 . Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
1. Introduction Photoacoustic (PA) infrared spectra of condensed-phase samples are most commonly acquired using Fourier transform infrared (FT-IR) spectrometers and gas-microphone PA cells. The attributes and applications of the method have been reviewed in detail [1]. Significant advantages include the obviation of traditional sample preparation techniques and the capability for depth profiling. The former feature is invoked in the present study, a PA investigation of polymer resin beads with particle sizes in the ∼35–150 m range. These polymer beads are frequently utilized in the solid-phase industrial synthesis of peptides and other compounds. Interest in the PA investigation of these beads derives from two principal sources:
(2) The PA signal produced from a single particle has been reported to be greater than that of the corresponding bulk sample [9]. The current study of ∼10-mg samples will be followed by microsample experiments on single particles using either a thermal infrared source or synchrotron radiation. In this investigation, PA infrared spectra of the resin beads were obtained using both rapid- and step-scan mirror movements in an FT-IR spectrometer. A range of modulation frequencies existed in the rapid-scan experiments, while a single frequency was utilized in each step-scan measurement. Absorption bands were identified in both the magnitude and phase spectra. The dependence of PA intensity on f was studied and found to differ for strong and weak bands. 2. Experimental
(1) Their sizes are in the order of the thermal diffusion length [s = (˛/f)1/2 , where ˛ and f denote thermal diffusivity and modulation frequency, respectively]. The PA signal is strongly affected by the relative magnitudes of s (approximately equal to the sampling depth), the optical depth [ˇ = 1/ˇ, the inverse of the absorption coefficient], and the particle size (D). Several research groups have studied the effects of f and D on PA intensity [2–8]. The situation is complicated for fine particles because the interstitial gas gives rise to an additional pressure signal. The intensity of this signal is proportional to f−1 while the thermal contribution varies as f−n (n = 1–1.5) [4].
∗ Corresponding author. Tel.: +1 780 987 8646; fax: +1 780 987 8676. E-mail addresses: [email protected] (Q. Wen), [email protected] (K.H. Michaelian).
Four types of resin beads (Polystyrene, PS; Acetyl Polystyrene SS, APSS; Isocyanate, ISO; TentaGel S COOH SS, TGS) manufactured by Advanced ChemTechTM were analyzed in this study. The structures and particle sizes of the beads are shown in Table 1. Experiments were performed using a Bruker IFS 88 FT-IR spectrometer and an MTEC 200 PA cell. The volume of the sample chamber in this cell is approximately 0.9 mL [10]. Sample cups, with diameters of 5 mm and depths of 2 mm, were completely filled as each type of bead was analyzed. Thus the sample volumes (∼0.04 mL) were much smaller than the cell volume, and the exact quantity of sample had little effect on the cell geometry. Rapid-scan spectra of the resins were recorded at four different mirror velocities, corresponding to He–Ne laser modulation frequencies of 1.6, 2.2, 3.0 and 4.0 kHz, respectively. The nominal resolution of these spectra is 6 cm−1 . Carbon black powder was used
1386-1425/$ – see front matter Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2009.04.004
824
Q. Wen, K.H. Michaelian / Spectrochimica Acta Part A 73 (2009) 823–827 Table 1 Structures and particle sizes of resin beads. Name
Structure
Particle size (m)
Polystyrene (PS)
37–74
Acetyl Polystyrene SS (APSS)
74–149
Isocyanate (ISO)
74–149
TentaGel S COOH SS (TGS)
90
to obtain reference (background) spectra. At each velocity, 20 50scan spectra were averaged for the resins and 10 50-scan spectra were averaged for carbon black. All measurements were performed within two days so as to minimize any intensity drifts due to gradual changes in optical alignment or humidity variations in the instrument. The PA intensities measured in this manner are generally quite reproducible, with experimental errors less than the thickness of the plotted curves in the spectra shown below. The spectrometer was purged with dry N2 to reduce absorption by ambient water vapour and CO2 during these measurements. Step-scan spectra were acquired using amplitude modulation at frequencies of 50, 100 and 200 Hz, and a spectrum resolution of 15 cm−1 . Spectra obtained at higher resolution were rather noisy due to mechanical vibrations, making identification of features difficult. An EG&G 5206 lock-in amplifier was used to recover the real (Re) and imaginary (Im) interferograms. The magnitude [M = (Re2 + Im2 )1/2 ] and phase [ = tan−1 (Im/Re)] spectra were calculated after Fourier transformation. Data for resins and carbon black were collected under like conditions.
agree well with published data from transmission measurements [11]. 3.2. Step-scan phase spectra Convenient retrieval of the PA phase is an important feature of step-scan data [12,13]. The Re and Im components, acquired simultaneously using a two-phase lock-in amplifier, have the same instrument phase. The PA phase can therefore be completely separated from the instrument phase through division.
3. Results and discussion The results obtained for the resin beads using both rapid- and step-scan operation of the spectrometer are presented in the following three sections. Magnitude spectra, step-scan phase spectra, and the variation of PA intensity with modulation frequency, are discussed in these sections. 3.1. Rapid- and step-scan magnitude spectra Rapid- and step-scan magnitude spectra of the resin beads, ratioed against appropriate carbon black spectra, are shown in Figs. 1 and 2, respectively. The low-wavenumber limit is dictated by the Ge/KBr beamsplitter, while the upper limit was chosen because of the absence of well-defined features above ∼3500 cm−1 . The rapid-scan spectra display a number of prominent fundamental bands in the 500–1800 and 2800–3200 cm−1 regions for each resin. In addition, weak features due to combination (∼2000 cm−1 ) and overtone (∼2700–2740 cm−1 for TGS) transitions were also observed. Some of the bands are not well defined in the step-scan spectra because of their lower resolution. The bands observed for PS
Fig. 1. Rapid-scan PA spectra of the resin beads obtained at a laser modulation frequency of 1.6 kHz and ratioed against a carbon black spectrum acquired under like conditions. The spectra of ISO, APSS, and PS are shifted along the intensity axis by successive increments of ∼0.2 intensity units for clarity. The intensities of the highwavenumber bands are reduced compared to the low-wavenumber ones because of the f−0.3 dependence (see text).
Q. Wen, K.H. Michaelian / Spectrochimica Acta Part A 73 (2009) 823–827
825
Fig. 3. Phase spectra of ISO calculated from step-scan Re and Im spectra obtained at 50 Hz. The Im spectra used to obtain the phase spectra in (a) and (b) were calculated, using the standard Mertz and Mertz/stored-phase procedures, respectively. The asterisks indicate bands at 1450, 1499, 1548, 1597, 1675, 2264, 2853, 2922, 3023, and 3055 cm−1 .
Fig. 2. Step-scan PA spectra of the resin beads obtained at fixed f (100 Hz). The spectra have been ratioed against a carbon black spectrum acquired at the same frequency. The spectra of ISO, APSS, and PS are shifted along the intensity axis by successive increments of ∼0.2 intensity units for clarity.
The PA phase spectra contain many of the absorption features and can facilitate band identification, since the phase tends to vary linearly with absorption even when the magnitude exhibits partial saturation. The Re and Im spectra used to calculate the PA phase are obtained by Fourier transformation of the corresponding interferograms. In FT-IR spectroscopy, phase correction and Fourier transformation are usually performed automatically in software. In the well-known Mertz algorithm [14], the phase (mainly due to the instrument) is calculated using a narrow region of the interferogram with an equal number of points on either side of the centreburst. The phase spectrum is interpolated so that the spacing between successive points is the same as that in the spectra calculated from the entire interferogram. Point-by-point multiplication of the real (imaginary) spectrum by the cosine (sine) of the phase produces spectra without instrumental phase errors. It should be noted that correction for the instrument phase is optional in the present context since this phase affects both Re and Im spectra in the same way [12,13]. In situations where an interferogram is particularly noisy or its centreburst is weak, an appropriate instrument phase calculated under more favourable circumstances can be utilized in the calculation. For example, the phase obtained for the Re spectrum was frequently used during calculation of the corresponding Im spectrum in the present work. This strategy is referred to as the Mertz/stored-phase method in Bruker software. Fig. 3 shows the PA phase spectra obtained for ISO using these two variations of the Mertz method. Prominent bands that also occur in the magnitude spectrum (Fig. 2) are labelled with asterisks and listed in the caption of Fig. 3. Several weak features in the phase spectra, such as those located between about 2500 and 2800 cm−1 , may suggest the existence of weak bands not visible in Fig. 2.
Phase spectra of the other three resins are illustrated in Fig. 4. The Mertz/stored-phase method was used to calculate the Im spectra in all three cases. The TGS phase spectrum contains most of the features in the magnitude spectrum, a result similar to that described above for ISO. Despite the considerable noise in the phase spectra of PS and APSS, a number of strong bands can still be recognized. These bands are indicated by asterisks in Fig. 4. It should be noted that the bands in the phase spectra can be either positive- or negative-going with regard to the phase in regions where absorption is minimal [12,13]. The same bands were also identified in phase spectra calculated from rapid-scan, double-sided interferograms recorded in a separate experiment; however, the PA phase is partly obscured by the instrument phase in that case.
Fig. 4. Step-scan phase spectra of PS, APSS, and TGS obtained at 50 Hz. The Im spectra, used to calculate the phase spectra were obtained from the Mertz/stored-phase procedure. The asterisks indicate bands identified in magnitude spectra of the three polymers.
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Fig. 5. Variation of interferogram peak amplitude with f (log–log scale) for PS and carbon black. The frequency is specified at the He–Ne laser wavenumber (15,800 cm−1 ). The peak amplitudes are normalized to unity at 1.6 kHz, the lowest frequency. The straight lines are least-square fits of the data and have slopes of −0.85 and −1.15 for carbon black and PS, respectively.
3.3. Variation of the PA intensity with modulation frequency Rapid-scan spectra of the resin beads were ratioed against carbon black spectra recorded under similar conditions. Data obtained at the four frequencies reveal different behaviours for the PS beads and carbon black (Fig. 5). The integrated carbon black PA intensity (represented by the interferogram centreburst amplitude) is proportional to f−0.85 , reasonably close to the f−1 dependence predicted for an optically opaque, thermally thin solid [15]. The PS intensity exhibits a stronger, f−1.15 dependence; the other three resins show similar trends. The ratioed spectra (polymer resin/carbon black), as a result, vary approximately as f−0.30 . This behaviour was observed in multiple repeated measurements. Experiments that employed two other sample-filling strategies (half-full sample cup, or a very thin layer of sample in the cup) were also performed; the same frequency dependence was observed in these cases. The difference between the f dependences of the polymers and carbon black can be attributed to the fact that the PA signal originates from within the beads, while absorption occurs near the surface for carbon black [15,16]. The frequency dependence of the PA signal was also studied for individual bands or groups of bands. For each compound, four or five bands were chosen from various spectral regions; both strong and weak features were selected. The peak intensities, represented as the area of each band (or group of bands), are plotted against f in Fig. 6. To facilitate interpretation of the data, the intensity is normalized to unity at the lowest f value for each band. As the frequency increases, the intensities of all the bands decrease, although at different rates. Specifically, the intensities of the strong bands were found to diminish more slowly than those of the weak ones. The strong peaks [APSS, 1606 and 1684 cm−1 ; ISO, 1670 and 1684 cm−1 ; TGS, 2887 and the 1010–1213 cm−1 group; all compounds, 702 cm−1 ] show intensity reductions with slopes between −0.1 and −0.2. By contrast the slopes are approximately −0.3 for the weaker bands. The latter result is consistent with the f−0.30 dependence of the ratioed spectra mentioned above. The relative dimensions of s , ˇ , and D must be considered in order to interpret these results properly. s can be estimated using the value of ˛ (0.00082 cm2 /s) reported [17] for PS. In conventional rapid-scan FT-IR spectroscopy, f is related to both infrared wavenumber () and mirror velocity (V) through the relationship f = 2V. For the spectrometer used in this study, in the mid-infrared region ( = 500–3500 cm−1 ) f varies from about 50 to 350 Hz at the
Fig. 6. Variation of rapid-scan PA intensity with f (log–log scale) for various bands and band groups in spectra of PS, APSS, ISO, and TGS (top to bottom, respectively). The legends indicate approximate band positions and ranges. A band common to more than one compound is denoted by the same symbol, with its position given on first usage. PA intensities are normalized to unity at the lowest applicable frequency.
lowest mirror velocity, and from 125 to 885 Hz at the highest velocity. These data yield approximate s values that vary between 23 and 5.5 m. Thus the particle sizes D, which are in the ∼35–150 m range, are similar to or larger than s . In this regime, the thermal term dominates the PA signal and the pressure signal due to the interstitial gas is not expected to play an important role [4,8]. Hence the different frequency dependences of the pressure and thermal signals are not the likely cause of the different f dependencies for strong and weak bands. Pandurangi and Seehra [8] described the effects of D and f on the PA intensity in spectra of silica particles. The role of saturation and the probable relations ˇ < s (strong bands) and ˇ > s (weak bands) were noted for large particles. Similar relations may also occur for the beads studied in this work. The strong bands are partially saturated such that the relationship ˇ < s applies. As f increases, their intensities decrease more slowly than those of the unsaturated bands. As the limit of full saturation is approached, the dependence of PA intensity on f goes to zero and may even become positive [8]. The results in the step-scan spectra support the above interpretation; as expected, the frequency dependences of the interferogram centreburst amplitudes for the polymer beads and carbon black are similar to those in the corresponding rapid-scan data. In general, the intensity diminishes rapidly for weak bands but more gradually for strong bands because the latter are partially saturated. For some of the strong bands, the degree of saturation differs from that in the rapid-scan spectra because different modulation frequencies (and therefore different s ) apply. Fig. 7 shows results for TGS. The 702-cm−1 band has not been included because the noise in the 50-Hz spectrum precludes accurate calculations. The other four bands can be divided into two groups according to the slope of the frequency dependence. The strong bands [2887
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tion spectra. Fewer bands are identifiable in the phase spectra, where both positive- and negative-going features occur. Most of the PA signal originated from within the beads, whereas absorption occurred near the surface for the reference carbon sample. The frequency dependence of the total PA intensities of the polymer resins and carbon black differed by a factor of about f−0.30 . The intensities of the weak bands in the ratioed spectra (polymer resin/carbon black) varied approximately as this factor. Partial saturation caused a more gradual variation for the stronger bands, where the intensity is proportional to ∼f−0.1 –f−0.2 . Acknowledgement Qing Wen would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) visiting fellowship program for funding. Fig. 7. Variation of step-scan PA intensity with f (log–log scale) for various TGS bands. The legend shows the positions of the bands and band group that were analyzed. PA intensities are normalized to unity at 50 Hz.
and the 1010–1213 cm−1 group)] decrease in intensity more gradually while the intensities of the weak (1601 and 1736 cm−1 ) bands decrease more quickly. These findings are consistent with those in the rapid-scan spectra (Fig. 6). 4. Summary Rapid- and step-scan mid-infrared PA spectra of four types of polymer resin beads (Polystyrene, Acetyl Polystyrene SS, Isocyanate, and TentaGel S COOH SS), ranging in size from 35 to 150 m, are discussed in this article. Approximately 25–40 bands were identified in each rapid-scan magnitude spectrum, whereas about 15 bands were observed in the lower resolution step-scan spectra. The PA magnitude spectra resemble conventional absorp-
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