Polymer Testing 29 (2010) 849–856
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Analysis Method
IR spectroscopy based thermal analysis of polymers Boris Zimmermann a, *, Domagoj Vrsaljko 1, b a b
Department of Organic Chemistry and Biochemistry, RuC er Boskovic Institute, Bijenicka 54, 10000 Zagreb, Croatia University of Zagreb, Faculty of Chemical Engineering and Technology, Marulicev trg 19, 10000, Zagreb, Croatia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 June 2010 Accepted 16 July 2010
Simple mid-infrared spectroscopy based methods for obtaining complete thermal characterization of polymers are proposed. In addition to some previously described structural transformations, such as melting and thermal decomposition, the proposed IR (transmittance and attenuated total reflectance) based thermal analyses can also determine glass transition temperatures. This innovative approach is extremely significant since the glass transition does not produce any vibrational band changes and is, therefore, completely undetectable by traditionally employed IR spectroscopy. The methods can be conducted with small amount of sample (approximately 1 mg) and with heating rates equivalent to those in DSC measurements. The method’s efficiency was corroborated by measuring the thermal transformations of various model polymers. Identification of glass transition, as well as other physical and chemical processes, obtained in a rapid and economical manner clearly demonstrates that IR spectroscopy can provide reliable and self-sufficient thermal characterization of polymers for analytical and quality control purposes. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: IR spectroscopy Thermal analysis Glass transition
1. Introduction Essential information on temperature dependent physical and chemical properties of materials is regularly provided by thermal analytical (TA) methods. Depending on the type of the measured information, TA methods can be separated into physical and structural state measurements. Physical measurements, such as differential scanning calorimetry (DSC) that measures the change in the heat capacity of the system, are traditionally more often applied than structural methods. The standard thermal analysis employs physical TA methods for rapid characterization of a compound in some temperature interval. Although physical measurements can detect the temperature of a thermal process, they can seldom disclose structural information accompanying that process. Therefore, structural measurements are regularly employed (X-ray
* Corresponding author. Tel.: þ385 1 4571 220; fax: þ385 1 4680 195. E-mail addresses:
[email protected] (B. Zimmermann),
[email protected] (D. Vrsaljko). 1 Tel.: þ385 1 4597 187; fax: þ385 1 4597 260. 0142-9418/$ – see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2010.07.009
diffraction, vibrational and nuclear magnetic resonance spectroscopy, thermal microscopy, etc.). The principal practical difference between these two groups of methods is the experimental acquisition time, which is quite short for physical measurements, and significantly longer for structural measurements. For example, typical acquisition in DSC or in differential thermal analysis (DTA) requires only a fraction of a second, therefore allowing fast heating rates (w10 K min1), excellent temperature resolution (several acquisitions per 1 C), wide thermal range (few hundred degrees Celsius) and relatively short overall measurement time. Obviously, typical acquisition of any structural information requires much more time, ranging from a few seconds for acquisition of a vibrational spectrum (infrared or Raman) to a few minutes for an X-ray diffractogram (X-ray powder diffraction). Since structural TA measurements are quite time consuming, they are often conducted only at some carefully designated temperatures (before and/or after the thermal transformation). Although acquisition of structural information can seem redundant, it is quite important for every thermal study to unambiguously provide identity of the measured system (structural
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information) at any given temperature. It must be stated that the conclusions based on separate physical and structural measurements can be misleading due to the decoupled experiments and, therefore, a rapid method that can simultaneously provide the temperature of phase transition and structural information on the phases involved would be of considerable value. Of the structural techniques, mid-infrared (MIR) spectroscopy is probably the most universal since it is widely available, inexpensive and easily applied. Although temperature dependent IR measurements can be routinely applied on their own it is still customarily to pair common TA methods, such as DSC, with IR spectrometry to obtain coupled physical and structural information [1]. Our previous work [2] has already demonstrated that IR spectroscopy can also be used on its own as a stand alone alternative to other TA methods, i.e., when it is necessary to quickly establish whether or not the substance of interest undergoes any structural transformation within the selected temperature range. The term baseline analysis was designated for this method due to utilization of uncorrected (absolute) baseline variations in temperaturedependent MIR transmittance spectra recorded for a KBr sample pellet. The method efficiency was corroborated by measuring various phase phenomena, including polymorphism (different ways of molecular packing in the solid state) and mesomorphism (liquid crystals), as well as chemical reactions such as oxidation. In this work we implemented this approach in measurements of various model polymers with intent to demonstrate the potential of the IR based thermal analysis of polymers. Alongside transmittance IR measurements, we also applied temperature dependent reflectance IR measurements (single reflection attenuated total reflectance mid-infrared spectroscopy (ATR)). The ATR technique is especially suitable for polymers since it enables spectrum acquisition without any sample preparation, but simply by pressing the sample into direct contact with the ATR crystal (diamond). In order to establish itself as a viable alternative to standard TA measurement of polymer, IR based TA has to be able to detect all thermal processes in a simple, rapid and economical way. Some of these processes, such as melting and thermal degradation, can be easily obtained, as was presented previously [2]. However, complete thermal characterization of polymer sample also includes determination of glass transition. Because the polymer transition from “glass” to a “rubber” state at the glass-transition temperature (Tg) results in a considerable change of its physical and mechanical properties, its value is of foremost importance in characterization of polymer materials. The glass transition of polymers is especially elusive for vibrational techniques because it is a dynamic phenomenon occurring between two amorphous states (the crystalline portion of polymer remains unaltered during the glass transition) and, consequently, molecular absorption (i.e. vibrational bands) should remain unaltered (however, some slight differences can be detected in the polarized spectra if an alteration of the orientation of the polymer chains is significant). For that reason, successful implementation of the IR based TA on polymeric systems represents quite a challenge.
2. Materials and methods 2.1. Materials Materials used in the study were commercial polymers: polystyrene E-678 (DIOKI, Croatia), polyvinyl chloride powder Mw ¼ 80000 (Aldrich), poly(methyl methacrylate) Plexiglas(R) EDGEFX (Altuglas International), polyethylene terephthalate Jade CZ-302 (Jiangsu Xingye Plastic, China), polycarbonate Makrolon (Bayer, Germany), low density polyethylene DOW LDPE 722 (Dow plastics), polypropylene Moplen HP 500 N (Basell Polyolefins), elastomeric polyurethane Desmocoll 176 (Bayer, Germany). 2.2. Methods Glass transition temperature of polymers was determined on a Mettler Toledo differential scanning calorimeter DSC 823e. Measurements were performed within the temperature range 20–250 C under nitrogen atmosphere and at different heating rates (2–10 K min1). Sample mass was 4–10 mg. The Tg values reported in this paper were obtained on second DSC heating at a scan rate of 10 K min1, and correspond to the half-height of the glass transition heat capacity jump. The KBr sample pellets were prepared by mixing 0.5– 2 mg of a sample with 100 mg of KBr. IR spectra were recorded at resolutions of 4–128 cm1 on an ABB Bomem MB102 single beam spectrometer, equipped with CsI optics and DTGS detector. Transmittance measurements were carried out with a Specac 3000 Series high stability temperature controller with heating jacket. Reflectance measurements were carried out with a Specac High Temperature Golden Gate ATR Mk II. Measurements were performed within the temperature range 20–250 C under atmospheric conditions and at different heating/cooling rates (2–10 K min1). Each single-beam spectrum collected in one temperature run was normalised to the single-beam spectrum of the sample-free setup (the reference spectrum) recorded immediately before starting the temperature-dependent measurements. The transmittance spectra were recorded with a total of 10 scans (temperature resolution of one spectrum per degree Celsius for all heating rates), while the reflectance spectra were recorded with either a total of 30 scans (spectral resolution of 4 cm1 and temperature resolution of one spectrum per 4 C for the heating rate of 2 Kmin1), or a total of 10 scans (spectral resolution of 128 cm1 and temperature resolution of one spectrum per degree Celsius for the heating rate of 10 Kmin1). After completing the heating, the measured KBr pellets were cooled and maintained at room temperature for at least 24 h. They were subsequently powdered with a pestle and mortar and recast into pellets for repeated measurements (unless decomposition occurred during the heating cycle). 2.3. Data treatment The baseline analysis designates an analysis of the baseline variations obtained from the raw (as-recorded data) temperature-dependent transmittance IR spectra at
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an arbitrarily chosen wavenumber assumed to be free of sample absorption (usually at around 2000 cm1). A simple plot showing transmittance (absorbance) at a given wavenumber versus temperature is found to be sufficient for obtaining phase transition temperatures. The 2D correlation analysis was performed by means of discrete Hilbert transformation (as defined by Ozaki and Noda [3]) implemented in a program written for Matlab 6.5 (The MathWorks, Inc., Natick, MA). Moving window (MW sic 2D IR) correlation maps were obtained as defined by Sa et al. [4] and the 2D contour plots were generated as described by Thomas and Richardson [5]. Detailed description of the 2D IR method and the baseline analysis can also be found in the previously published paper [2]. 3. Results and discussion The evaluation of the proposed method was conducted by the measuring thermal behaviour of eight common polymers: polystyrene (PS), polyvinyl chloride (PVC), poly (methyl methacrylate) (PMMA), polyethylene terephthalate (PET), polycarbonate (PC), low density polyethylene (PELD), polypropylene (PP) and polyurethane (PU). The primary objective was determination of glass transition temperature of polymers (PS, PMMA, PET, PC and PVC) with IR spectroscopy, while other phenomena, such as melting and thermal degradation were merely collateral to this primary goal since the detection of such processes had already been assessed [2]. It is important to note that the exact value of Tg for a given polymer sample can vary depending on the test conditions because the glass phase is not at thermodynamic equilibrium. The measured value will depend on the molecular weight of the polymer, on its thermal history and age, on the measurement method, and on the rate of heating and cooling. Since the most frequently used TA method for characterization of polymers is DSC, we correlated all our temperature dependent IR measurements with the DSC measurements.
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88 C (PS), 112 C (PMMA), 76 C (PET) and 147 C (PC). Transmittance IR measurements of the KBr sample pellets are showing significant baseline variations at these temperatures indicating that glass transitions influence optical properties of measured KBr pellets in a similar way as was the case with the other previously reported phase transitions [2]. The temperature values corresponding to the start of the baseline variation are as follow: 88 C (PS),118 C (PMMA), 74 C (PET) and 146 C (PC) (Fig. 1). Experimental reproducibility and the influence of thermal history on measured polymers are illustrated with results of the repeated measurements on PS samples (Fig. 2). While the actual baseline varies from the first to the subsequent heating runs, it will always indicate the same phase transition temperature. Taking into account our previous measurements of organic compounds, it is reasonable to conclude that changes in volume thermal expansion accompanying glass transition of polymer induce irreversible disintegration of the sample pellet. This, and to some extent the change in the refractive index, leads to alteration in transmission, reflection and scattering of IR light, that finally results in detection of Tg.
3.1. The baseline analysis As opposed to other TA infrared spectroscopies that are based solely on vibrational band changes, baseline analysis monitors temperature-dependent baseline variations in the IR spectral data set. Hence, it uses only those parts of an IR spectrum that are free of molecular absorptions. Seeing that spectral resolution is not imperative, it is possible to make spectral acquisition times shorter by applying faster heating rates equivalent to those in DSC experiments, without the loss of temperature resolution (the temperature resolution in this study was one spectrum per degree Celsius). If some structural transformation is determined within the available temperature range, more thorough IR search for structural information can be made by applying better spectral resolution. However, as already stated, in the case of glass transition it is highly unlikely that any meaningful change in appearance of vibrational bands will be present during the transformation from one amorphous phase to another. According to the DSC measurements, the glass transitions of polymer samples occur at the following temperatures:
Fig. 1. Spectral baseline variations at 2000 cm1 of sample pellets containing (top) PMMA and PC (bottom) PS and PET. Heating rate: 4 K min1, spectral resolution: 32 cm1. For better viewing the transmittance values are scaled.
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the absolute absorbance values while the relative absorbance values, band positions and bandwidths remain unchanged. This spectral constancy is demonstrated by the two spectra of PS (Fig. 3) that were recorded before and after the glass transition. As can be seen, these spectra can be interconverted by simple scaling, proving that molecular structure (and its adjacent surrounding) remained unchanged. Precisely this consistency in vibrational band relative intensities and positions is sufficient evidence that a particular sample is undergoing a glass transition, given that all other phase transitions (such as crystal-to-crystal or solid-to-liquid) result in more extensive spectral change. This changeless appearance of the IR spectra during the glass transition has an important consequence on the measurement conditions. Since spectral resolution is irrelevant, it is possible (analogous to the baseline analysis) to make spectral acquisition times shorter by lowering the spectral resolution and by applying faster heating rates equivalent to those in DSC experiments, without the loss of temperature resolution. Although glass transition temperature can be obtained by a simple plot showing transmittance (absorbance) values at a wavenumber of a maximum absorption, it is more sensible to perform analysis of the overall spectral intensity change. The determination of glass transition temperatures from huge spectral data sets is facilitated by the implementation of MW 2D-IR data representation. A MW contour map shows temperature-ordered spectral changes and thus presents temperatures of phase transitions and associated structural information. It is important to emphasize that signals in the contour map are directly related to spectral Fig. 2. Spectral baseline variations at 2000 cm1 (top) of the first heating run of three different KBr PS sample pellets, and (bottom) of the second, third and forth heating run of the same PS sample. Heating rate: 4 K min1, spectral resolution: 32 cm1. For better viewing the transmittance values are scaled and offset.
3.2. The ATR measurements and the 2D-IR analyses As already stated, the ATR technique is the preferred method in IR measurement of polymers since it enables spectrum acquisition simply by pressing the sample into direct contact with the ATR crystal. Sudden change of polymer physical properties accompanying glass transition (changes of the volume thermal expansion and the refractive index) will also affect the appearance of ATR spectra. Good optical contact between the sample and the ATR crystal, essential for acquisition of spectrum of high quality, is achieved by constant pressure upon the sample by the ATR anvil. Above the glass transition temperature the mechanical properties of polymers are significantly altered, adherence of polymer on the ATR crystal is improved by softening of the sample and, consequently, IR spectral intensities increase. This noticeable non-linear increase (as a function of temperature) of vibrational band absorptions is a good indication that the sample undergoes a glass transition. It should be emphasized that molecular absorptions (i.e. vibrational bands) are essentially unaltered due to the negligible structural changes during the glass transition. In other words, glass transition affects only
Fig. 3. ATR spectra of PS before (middle, 80 C) and after the glass transition (bottom, 100 C). (Top) The difference spectrum of spectrum at 100 C and the 20% scaling up of spectrum at 80 C (resolution: 4 cm1; number of scans per spectrum: 30). For better viewing the transmittance values are offset.
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changes. In other words, the temperature interval devoid of spectral changes is present as a blank area, hence indicating the temperature range of the presence of only one phase. In contrast, peaks on the contour map are found at temperatures where the largest spectral variations occur, therefore revealing the presence of a phase transition (or a chemical reaction). The MW contour map of the spectral data belonging to the PS heating run, recorded with 10 K min1 heating run and with the minimal spectral resolution of only 128 cm1, is depicted in Fig. 4. The glass transition is evidently detected although the IR spectra are of extremely low resolution (the effect of the spectral resolution on recorded spectra is evident by comparing the analogous PS spectra from Figs. 3 and 4). The same data set can be presented as a temperature– temperature diagram (TT contour map) (Fig. 4.). Any plateau that might occur in a TT contour map indicates similarity of the two spectra, while the increase or decrease of the covariance coefficient between the two spectra indicates rising dissimilarities due to change in molecular and/or phase structure. By fixing one of the temperatures (in this case the starting temperature) a slice is defined along the second temperature illustrating (dis)similarities between the IR spectrum at the starting temperature and the spectra obtained at any other temperature within the temperature range. The slice spectra along the referent temperature (30 C) of the TT correlation spectra of PS (Fig. 4) is shown in Fig. 5, together with analogous slice spectra of the PMMA and PC samples. It is evident that the PS spectra within the 30–80 C temperature range were mutually similar, highlighting the thermal interval of the first phase (“glass”). The sudden spectral dissimilarity appeared in the 80–100 C interval indicating the phase transition, followed by renewed spectral consistency of the
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second phase (“rubber”). Comparing the results of transmittance and reflectance IR measurements with the well established DSC method (Figs. 1 and 5) it is obvious that temperature dependent IR spectroscopy can provide temperature values of glass transition. When analyzing temperature dependent ATR spectra one should also take into consideration the thermal variations of the diamond (i.e. ATR crystal) absorptions in the 2600–1650 cm1 region that seriously hinder any exact analysis of sample vibrational bands in this spectral region (the spectral anomalies and noise are clearly present in the mentioned spectral region of the PS spectra in Fig. 3.). For that reason, the spectral region of diamond absorptions was excluded in all 2D IR analyses. 3.3. Determination of melting point Previously published results addressed the issue of determining melting points by means of transmittance measurements of KBr sample pellets [2]. Optical properties of the entire pellet are mainly affected by the significant difference in the volume thermal expansion of the solid KBr and the melted sample. This probably leads to pressureinduced strains within the pellet and, consequently, to its irreversible degradation. The pellet breakage results in decreased transparency that can be easily detected by means of the baseline analysis. As opposed to glass transition, melting of polymers can also result in detectable changes of their IR spectra. Detectable broadening of spectral bands and shifting of band position can accompany the melting process as a direct consequence of transformation of crystalline structure into less ordered liquid phase, characterized by lack of long-range periodicity. However, since polymers are essentially a combination of
Fig. 4. 2D IR correlation analysis of the temperature dependent ATR spectral data of PS sample: (top left) IR spectra of PS before (80 C) and after the glass transition (100 C), (bottom left) MW contour map, and (right) temperature–temperature (TT) contour map. Analyzed spectral region: 679–3517 cm1 (excluding 1542–2653 cm1); window size: 10 spectra; window step: 1 spectrum; heating rate: 10 K min1; resolution: 128 cm1; number of scans per spectrum: 10.
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Fig. 5. TA (second run, heating rate: 10 K min1) of (left) PS, (middle) PMMA and (right) PC samples: (top) DSC thermograms, (down) slice spectra of the corresponding TT contour maps along the lines T ¼ T0. (HF ¼ heat flow, CI ¼ covariance intensity).
amorphous and crystalline phases, detectable changes in spectral appearances will be present only during the measurement of a polymer with a significant crystalline part. Fig. 6 depicts ATR IR spectra of PELD acquired before and after the melting point and, as can be seen, a simple scaling procedure cannot interconvert spectra recorded at different temperatures. The reason for this is the different thermal behaviour of absorption bands that includes not only different relative intensity change but also broadening
of bands and shifting of peaks. Implementation of the 2D IR analysis on the spectral measurements of melting transitions of polymers results in unambiguous detection of melting temperatures (Fig. 7). 3.4. Thermal degradation of PVC The PVC sample was measured in order to demonstrate applicability of the transmittance IR TA for complete thermal characterization of polymers. The IR spectra of the KBr sample pellets of PVC powder were acquired not only in the thermal region of glass transition (80 C), but also above the degradation temperature of PVC (>100 C). Fig. 8 shows DSC thermograms and spectral baseline variations of the PVC sample. Both methods detect glass transition in the 70–90 C region. However, DSC is much less sensitive, compared to the IR method, in detecting the slow degradation of PVC in the 140–220 C interval. Thermal degradation of PVC has several mechanisms: dehydrochlorination, creation of long polyene chains and possible crosslinking. Every one of these mechanisms can produce pressure-induced strains within the pellet and lead to its irreversible degradation and pellet breakage, which finally results in decreased transparency detected by the baseline analysis. After reaching 225 C, both methods register fast dehydrochlorination, after which the sample completely degrades. This degradation is apparent in the IR spectrum as significant decrease of band intensities, especially those attributed to carbon-chlorine stretching vibrations (600– 700 cm1). Since the IR method detected even small changes in the sample during degradation, we can conclude that it gives additional information compared to the standard DSC method. 3.5. Assessment of transmittance and reflectance methods
Fig. 6. ATR spectra of PE before (middle, 100 C) and after the melting point (bottom, 120 C). (Top) The difference spectrum of spectrum at 100 C and the 50% scaling up of spectrum at 120 C (resolution: 4 cm1; number of scans per spectrum: 30). For better viewing the transmittance values are offset, and the spectral range of diamond absorptions is omitted.
It is well known that an IR spectrum of a sample reflects not only its chemical structure but also its physical state (phase) and the state of its environment at the time the spectrum is recorded. Although phase transition can result
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Fig. 7. TA (second run, heating rate: 10 K min1) of (left) PE and (right) PP samples: (top) DSC thermograms, (down) slice spectra of the corresponding TT contour maps along the lines T ¼ T0. (HF ¼ heat flow, CI ¼ covariance intensity).
in substantial change of the molecular structure (for example, melting), some structural differences between phases are quite small (or well within experimental and/or instrumental error), resulting in negligible differences in
Fig. 8. (top) DSC thermograms of PVC and (bottom) spectral baseline variations at 2000 cm1 of PVC sample pellets. Heating rates 2 (black), 4 (gray) and 10 K min1 (light gray). For better viewing the transmittance values are normalized to unity and offset.
their MIR spectra. As already stated, the glass transition of polymers is especially elusive for vibrational techniques because molecular absorptions are almost completely unaltered by this transformation. Although this is true in ideal conditions, in the real world the recorded IR spectrum is always a combination of molecular and macroscopic properties of a measured specimen. The polymer transition from “glass” to “rubber” state at the glass-transition temperature (Tg) results in a considerable change of its physical and mechanical properties that will certainly have an effect on spectral appearance. Baseline analysis, for instance, is primarily based on monitoring optical properties of the KBr sample pellet (although one can also depict structural information by careful analysis of these temperature dependent IR spectra). Therefore, the abrupt change of the refractive index of polymer as well as pellet breakage (due to pressure-induced strains within the pellet) will be detected in the transmittance IR measurement as noticeable spectral variation. Needless to say, an analogous argument is also valid for ATR IR measurements. These temperature dependent property variations result in significant spectral change that can mislead (especially if the baseline correction is not done with a proper care) into erroneous conclusion that glass transition causes vibrational band shifting. However, careful examination of the IR spectral data reveals that molecular absorptions are essentially unaltered, and that all of the changes in bands positions and intensities can be attributed either to the baseline variations (and subsequent baseline correction) or to the change in overall absorbance. Although our IR TA measurements are novel in thermal characterization of polymers, it must be stated that these IR methods only exploit in an innovative approach some well known thermal properties of compounds. For instance, the change in volume and refractive index of polymer as a function of temperature is already exploited by dilatometry and measurement of refractive index. Also, similar to dynamic mechanical analysis, the IR method is following the change in the modulus as a function of temperature.
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4. Conclusions This research demonstrated the applicability of IR spectroscopy in complete thermal characterization of polymers. In addition to some previously described structural transformations, such as melting and thermal decomposition, the IR based TA can also detect glass transition temperatures. Taking into account that measurement can be conducted with a small amount of sample (approximately 1 mg), with heating rates equivalent to those in DSC, and that the sample can be in various forms (powder, chip or granule), it is quite obvious that the value of the IR TA approach is considerable. Vibrational band changes in an IR spectrum can provide straightforward structural information regarding various physical and chemical transformations. However, glass transition does not produce any vibrational band changes and is, therefore, completely undetectable by traditionally employed IR spectroscopy. The methods described in this report are merely using an IR spectrometer as a detector for observing changes in physical properties induced by glass transition. As such, temperature dependent transmittance and ATR IR measurement are completely independent methods that differently detect physical manifestations surrounding the glass transition (change in refractive index, volume and modulus), even though they both utilize an IR spectrometer as a detector. Since these IR methods are unconnected, one can obtain verification and re-examination
by conducting the measurement with both methods, thus making the analysis more tolerant of error. Identification of glass transition, as well as other physical and chemical processes, obtained in a rapid and economical manner clearly demonstrates that IR spectroscopy can provide reliable and self-sufficient thermal characterization of polymers for analytical and quality control purposes. Acknowledgments This work was supported by the Ministry of Science, Education and Sports of the Republic of Croatia (grant numbers: 0982904-2927 and 125-1252971-2575). References [1] J.W. Hellgeth, Thermal analysis-IR methods. in: J.M. Charmels, P.R. Griffiths (Eds.), Handbook of Vibrational Spectroscopy, vol. 2. Wiley, Chichester, 2002, pp. 1699–1714. [2] B. Zimmermann, G. Baranovi c, Determination of phase transition temperatures by the analysis of baseline variations in transmittance infrared spectroscopy, Appl. Spectrosc. 63 (2009) 1152. [3] Y. Ozaki, I. Noda, Two-dimensional Correlation Spectroscopy. John Wiley and Sons, Chichester, 2004. si [4] S. Sa c, Y. Katsumoto, H. Sato, Y. Ozaki, Applications of moving window two-dimensional correlation spectroscopy to analysis of phase transitions and spectra classification, Anal. Chem. 75 (2003) 4010. [5] M. Thomas, H.H. Richardson, Two-dimensional FT-IR correlation analysis of the phase transitions in a liquid crystal, 4’-n-octyl-4cyanobiphenyl (8CB), Vib Spectrosc. 24 (2000) 137.