Peer Reviewed: FTIR Images - Analytical Chemistry (ACS Publications)

Jie Liu , Mangilal Agarwal , Kody Varahramyan , Ernest S. Berney , Wayne D. .... Douglas L. Elmore , Mei-Wei Tsao , Simon Frisk , D. Bruce Chase , Joh...
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FTIR Images n most materials, compositional variation and physical organization at the microscopic level determine their ability to perform a desired function. In addition, knowing the microscopic chemical composition and how it correlates with macroscopic properties is useful in optimizing material performance. Conversely, the causes of poor performance or failure may be derived from microscopic chemical analysis techniques that provide spatially resolved chemical information. FTIR spectroscopy has been used for more than 30 years to study a host of chemical problems. Moreover, this classic technique has been successfully harnessed for microscopy. Now, with the recent introduction of focal plane array (FPA) detectors for FTIR microspectroscopy, rapid, comprehensive, and accurate microscopic chemical characterization has significantly improved (1, 2). In this article, we present a short introduction to FTIR microspectroscopy and discuss its required instrumentation and capabilities such as performing new applications for polymeric materials analysis.

A new technique produces images worth a thousand spectra.

Jack L. Koenig — Case Western Reserve University Shi-Qing Wang — University of Akron Rohit Bhargava — National Institutes of Health

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Defining FTIR microspectroscopy Coupling a microscope with an FTIR instrument has led to the collection of spatially resolved chemical information. Initial efforts at FTIR microscopy were limited to point-by-point analyses of microscopically small samples. With the advent of computer-controlled sampling stages, sample positioning could be accurately reproduced. Hence, large areas could be examined in a predetermined manner using apertures and systematic movement. FTIR mapping is point-by-point rastering across a sample to obtain spatially resolved information. FTIR mapping is used to study polymeric, biological, and inorganic materials. However, this microscopic technique suffers from numerous problems. Usually, sample areas are restricted to squares >15 µm on a side. Diffraction effects and stray light can compromise the accuracy of the data. Even with redundant aperturing, sensitive detectors, and high-speed computers, using the sequential mapping process on an area a fraction of a millimeter takes many hours. FTIR imaging using FPA detection provides a method of overcoming these limitations, although light diffraction effects

still occur (3). FPA detectors consist of a large number of small detectors, which we will call pixels, laid out in a grid pattern. Each pixel detector is capable of simultaneously collecting data from a specific sample area in the field of view. Thus, the whole field of view is illuminated by the source. This technique renders “snapshots”, or images, consisting of information collected from all areas at the same time, as opposed to the pointby-point examination of the sample area—hence the name FTIR imaging. Depending on the array and collection parameters, thousands of spectra can be acquired at near-diffractionlimited spatial resolution in a few minutes. A large area is imaged in approximately the same amount of time taken by a conventional spectrometer to collect a spectrum. It is now widely accepted that the most promising microspectroscopic IR instruments use FPA radiation detection (4).

Imaging instrumentation Figure 1 shows the general configuration of an FTIR imaging microspectrometer. It combines a step-scan spectrometer and an FPA mounted onto an attached microscope, with a synchronization board between the spectrometer and FPA. The FPA

CCD camera (optical) FT/ratio MCT 64 x 64 array

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FIGURE 1. Schematic of a typical FTIR imaging spectrometer. Radiation is diverted from a step-scan spectrometer onto an FPA detector using all-reflective optics. The same optical path can be used for visible microscopy by applying a visible light-sensitive CCD detector. Each pixel on the FPA yields a spectrum after appropriate processing. A frequency in the spectrum may be plotted for the whole array to yield a chemical image. Complementary images for other components may be obtained by plotting material-specific frequencies.

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Coupling a microscope with an FTIR instrument has led to the collection of spatially resolved chemical information.

collects the data once the spectrometer mirrors are in a position to achieve a required retardation. The retardation is allowed to stabilize the step-scan mirror after the step is triggered, and the same pulse is used to trigger data collection by the FPA. At each retardation step, the FPA collects frames to co-add, and the voltage output is transmitted to a memory device. Hence, one step results in a single data point on the interferogram for each pixel. Step-by-step, the interferogram is built up for the array at successive spectrometer retardations. Most imaging spectrometers today use a Michelson-type interferometer-equipped spectrometer combined with FPA detection (5–7 ). Moderate-cost IR FPAs were originally developed by the military for imaging heat radiated over broad spectral ranges. More commonly used detectors include indium antimonide (InSb) and mercury–cadmium–telluride (MCT), but they range to the more exotic silicon arsenide (Si:As) (8) and uncooled barium strontium titanium (BST) (9). Mid-IR imaging with FPAs using MCT detectors has been the most popular technique because it accesses the mid-IR fingerprint region. The near-IR systems present advantages for sample preparation and high optical fidelity using InSb detectors; Si:As detectors provide a wide spectral range, and BST arrays do not need to be cooled. One of the primary requirements for FTIR imaging is that the FPA collects and co-adds enough image frames at each retardation for adequate S/N. This necessitates fairly constant retardation for the duration of the frame collection, which is readily achieved by step-scan spectrometers and then rapidly stepped to the next retardation. The total retardation and number of retardation points help determine spectral resolution over a spectral range. A single mirror may be stepped to achieve a new retardation, or two may be moved in tandem. One commercial instrument moves the single mirror at a constant velocity. The stationary mirror is moved a small distance to compensate for the continuous movement. Hence, the net retardation is constant for a period of time. A rapid-scan spectrometer coupled to an FPA-equipped microscope has also been recently used. In this case, it is estimated that the error in mirror position during the frame-collection process at a single retardation is of the same order of magnitude as the mirror position error in step-scan spectrometers. How-

ever, even in this case, the mirror movement is slower than a conventional microscopic instrument, and the FPA rate of data acquisition and readout is less than single-element detectors. Continuous scan allows for faster imaging and, hence, more time for averaging imaging data cubes, which are (x, y) spatial data collected at every frequency (10). Irrespective of the way retardation is achieved, a position is determined and requisite frames are collected. The collected frames are co-added and read out as an average snapshot at each retardation. The data obtained from the imaging spectrometer can be visualized in the form of a data cube consisting of a series of two-dimensional (2-D) arrays—images in which the third dimension is the voltage readout from the camera. This raw data cube is then synchronized with the spectrometer collection parameters to yield an interferometer data cube. Fourier transformation of the cube using appropriate spectroscopic analysis techniques of phase correction, zero filling, and apodization yields a single-beam image cube. This result may then be ratioed pixel-by-pixel against a similarly collected cube to yield an absorbance data cube useful for quantitative analysis. Compared with other FTIR spectroscopic techniques, the data processing involved in imaging takes most of the experimental time. Spatial inhomogeneities in the array are the result of uneven illumination, different individual detector element responses, and background sources. The response of each detector and its background may be determined by a two-point calibration. A determination of the two quantities with the maximum incident flux (at spectrometer zero path difference) and minimum flux (with spectrometer radiation blocked) allows calibration of each detector to a linear response model. This model assumes a linear readout signal, typically in millivolts, for incident intensity, with the slope (gain) and intercept (offset) of the line being determined. Figures of merit during this calibration are the mean high signal, mean low signal, the uniformity of the slope and offset, and mean deviations such as noise. Unmodulated background radiation, which is thermal emission in the wavelengths being monitored, is not expected to affect the measured signal, but it contributes to statistical noise and decreases the effective dynamic range of the spectrometer (11).

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puter tasks. Today’s immense data sets, ranging from a few to hundreds of It has been predicted that megabytes, require fast comthe maximum achievable 0.6 puters for rapid computaS/N of an imaging spections. Performing mathetrometer is higher than that 0.4 matical operations and of a single-element microstorage is simpler if the data scope–spectrometer using set is truncated to subsets apertures (10). In practice, 0.2 based on the wavelengths of the S/N of individual specinterest. tra from pixels in FPAs is 0.0 Collecting and processbelow the predicted theo0.0 0.1 0.2 0.3 0.4 0.5 i n g S/N data. Analyzing retical limits, and it is usualAbsorbance (C=CH) noise determines the acculy comparable with spectral racy of measurements. A S/Ns from single-element FIGURE 2. (a) FTIR image of a blend. (b) False-color composite of good criterion for data quansystems, which are limited absorbance distribution for the blend image. (c) Scatter plot of abtification has been proposed: by noise equivalent power sorbance against a specific peak. (Reproduced with permission For spectroscopic imaging, (NEP) noise. NEP is due to from Ref. 27.) the detection limits are taken reduced efficiency of data to be three times the peakcollection in imaging systems and the unique sources of noise in an FPA. Detector to-peak baseline noise, whereas quantification limits are set at noise is typically the major contributor to spectral noise and 10 times the baseline noise. For raw data collected in a matovershadows other sources from the spectrometer and optics. ter of minutes, the S/N is ~10–50, yielding the highest quanCommon detector features leading to noise include nonuni- tification levels only in the tens of percentage points (14). Alformity in pixel response arising from manufacturing prob- though these levels may be lowered by modifications in the lems, cross talk between individual pixels, pixel shorting and data collection, processing and mathematical means have also other electrical faults, and readout noise. The analog-to-digital been suggested to improve the S/N. The first approach is to increase the number of co-added converter is also usually only 12 or 14 bits, which further limits the dynamic range. These deficiencies will improve with bet- frames per spectrometer step. This method is closely linked to ter detector manufacturing and more sophisticated electronics. two other variables—frame rate and data collection time. The The sample also introduces optical complications in the im- frame rate determines the total staring (collection) time of the ages. A sudden change in the refractive index of a sample leads array for each frame. The smaller the frame rate, the larger the to scattering at the boundary (12). As a consequence, an ex- staring time and more integrated the signal measured by the cess absorbance may be seen in the images, which makes ac- detector. Very low frame rates may lead to pixel saturation curate data analysis difficult (13). This “error” may be used to even at low illumination levels because the intensity is simply detect the presence of interfaces without the use of an absorb- integrated. Thus, for high-IR intensities, a higher frame rate is ing or component-specific wavelength. For example, it has been used. Once a useful frame rate is fixed, the number of frames used to study the interface evolution during the formation of a collected per data step is increased to improve the S/N. The class of polymer composites. benefits of increasing co-added frames are limited because the Data processing and quantification. Although the first S/N has almost reached a plateau (9). Beyond a certain level, applications of FTIR imaging were qualitative, the utility and increasing co-added frames increases collection time without power of the new instrumentation have improved with the any additional S/N. Thus, an optimum number of co-adds application of statistical analysis and image-processing meth- should be chosen such that the benefits of increased S/N are ods. In many respects, processing spectroscopic imaging data significant compared with the increased experimental time. is a unique strategy. The basic spectral operations like Fourier Another effective approach to increasing the S/N is timetransformation, conversion to absorbance, baseline correction, averaging the collected images (10). Additional background and peak height ratios are common and relatively simple com- single-beam images can be collected at an optimum frame Absorbance (CN)

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ing spectra and varies as √n, where n is the number of co-added pixels. The major benefit of such an approach is that there is no increase in collection time. However, it reduces the 2-D plot of absorbance (x–y scale) to a number of low-noise 1-D representations (z- or wave number scale). For better image visualization, mathematical methods can reduce noise (14). The philosophy is to transform the data set into another set of coordinates that is ordered in terms of components with progressively increasing noise contribution. A certain number of these components are selected, and the inverse transform is obtained. Although mathematical noise reduction yields much higher quality images, the spectral content is only a best estimate and may not reflect the subtleties in small features, which are required for some sophisticated studies. Thus, knowing what information is required from a sample is important input toward determining the best strategy for attaining satisfactory S/N data. Data extraction. To display an experimental image so that it provides spatial information, each spectrum in the image is reduced to a singlefrequency intensity, which is plotted as a function of location. Each data point represents the intensity at a single wavelength or the integrated intensity of an absorption band. This reduction of a spectrum to a single frequency is called “profiling” and is particularly valuable for fine structural contrasts that are too small in size (too few pixels) or too weak to be seen (only a few intensity levels strong). Digital zoom and contrast segmentation can help overcome these limitations. More often, peak absorbance ratios from different components are used because they correct variations in thickness and enhance contrast at the same time. Another representation that is popular for two or more populations is n-dimensional visualization. For example, for a two-component system, the absorbance of a peak specific to one component is plotted against another to give a 2-D visualization scatter plot. A scatter plot of this type is shown in Figure 2c, and the data from the same experimental set are plotted as a ratio of the two peaks’ absorbances in Figure 2b. Although it is apparent from Figure 2a that there are two distinct phases, the absorbance of each phase can be read off the plot in Figure 2c. Creating a false

The utility and power of the new instrumentation have improved with the application of statistical analysis and image-processing methods.

rate and co-added to the frames. These background images are averaged and compared against an image obtained by averaging nI, the number of single-beam images of the sample collected in a similar manner. The S/N scales are √nI. The distribution of absorbances for a uniform sample narrows with increasing co-adds. The width of the distribution, as characterized by the standard deviation, indicates a reduction in noise. However, the time required for data set collection scales is 2nI. Thus, the gains achieved by the procedure diminish as a function of increasing time. For very large co-addition times, the temporal stability of the spectrometer may also be in question. Hence, while this procedure is very useful for obtaining high-fidelity images, it does not lend itself to the rapid analysis of a large number of samples. For such applications, one approach is to use a large number of backgrounds to generate “pseudo” data sets. A number of background single-beam images are collected and stored. A single sample using a single beam is then collected. A systematic ratio is calculated between the image and each background, thereby creating several absorbance images from the same sample data set. These images can then be averaged to obtain one with lower noise. The benefits of this method are limited, and the noise inherent in the single-image data set soon starts to dominate. The achievable gain in S/N is ~40%. Often, high-fidelity spectral information is desired from a large number of pixels that have the same chemical composition, which is systematically changing with time, as is the case in diffusion, swelling, and dissolution studies. For these cases, a number of within-image co-addition strategies are suggested. These strategies call for the co-addition of pixels in a line, area, or material phase delineated by the initial image analysis. For example, the 1-D change in concentration of a species (e.g., diffusion) may be analyzed for pixels in a direction perpendicular to the diffusion. Similarly, pixels may be delineated by phase in a multiphase system. The spectrum extracted from this phase average is better than the spectrum from a single pixel. Because pixel-to-pixel noise for any randomly selected pixels is predominantly uncorrelated, the scaling of within-image co-addition is the same as that of time-averag-

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possible for many years, and numerous reports have appeared (16, 17 ). The applications reported next are representative of the types of issues resolvable by FTIR imaging. Moreover, given its speed of data acquisition, FTIR imaging allows for the examination of many samples quickly or CN absorbance many processes in real time. 0.0 0.7 Polymer laminates. Chemical imaging helps identify the polymers forming the (c) different layers of a laminate for quality assurance. Laminate images also demon1.0 strate the spatial and spectral sensitivity and 0.8 the fidelity of the spectroscopic measure0.6 OH ment. Hence, laminates are a popular CN model system for demonstrating the capaCO 0.4 bilities of a spectroscopic imaging or pro0.2 DAR = DA1 2+ DA2 2 filing technique. For example, co-extruded AR A1 A2 0.0 tubes of polyethylene layers differing by 0 10 20 30 40 50 60 70 the concentration of methyl end groups— Pixel number where ⌬A1 and ⌬A2 are determined from 6 compared with 25 per 1000—have readthe axes of the ellipses in plots similar to FIGURE 3. Imaging dissolution of polyily discernable layers (18). Careful examination of the images revealed the presence Figure 2c. Whatever the method of data mers by solvents. of a likely inorganic contaminant. Anothextraction, it is clear that imaging offers (a) Two materials are brought into contact er study examined a laminate of the advantage of obtaining statistically sig- and allowed to diffuse across the interface. The diffusion region develops over time. poly(ethylene terephthalate), ethylene alnificant data in a short time. Data visualization. Once the image is (b) An image is obtained by monitoring radiacohol copolymer, and low-density polytion passing through the sample at a direcobtained using predetermined constraints, tion perpendicular to the diffusion direction. ethylene layers (19). With fairly simple sample preparation, laminates may be anathe presentation of the desired information (c) Concentration profiles for three different lyzed to identify components or impurities may be enhanced in several ways. Contrast functional groups obtained from the same sample as in (b) (diffusion of a liquid crystal is enhanced by multiplying images by them- monomer at 265 K for 3 h). (3b reproduced and imaged for routine quality control selves or using various filters. Mathemati- with permission from Ref. 24.) studies. Semicrystalline polymers and their cal transform techniques such as principal blends. Various microscopic, spectroscopic, components analysis and maximum/minimum noise fractions are useful to visualize various and scattering techniques have been used to probe the struccomponents and the structure of noise and to obtain low- ture of semicrystalline polymers and their blends. FTIR imnoise images. Different techniques are used to obtain the best aging is a unique method for studying the local chemical comcontrast, the highest sensitivity, or greatest dynamic range vi- position, crystallinity, degree of orientation, morphology, or sualizations. spatial distribution of these polymers. The morphology of poly(ethylene glycol) and its blends was studied using imaging Applications of imaging (20). Images are collected using incident radiation polarized Applications of FTIR imaging can be divided into two broad in two perpendicular planes on the sample plane. The two imareas—biological and materials analysis. Here, we examine ages are then ratioed pixel-by-pixel and calculated between the FTIR imaging of synthetic polymeric materials, because re- two images of the sample area to yield a dichroic ratio image. views of the biological area are available (15). Additionally, a population distribution of the dichroic ratio Materials analysis and characterization. Microspectro- for the image may be obtained. scopic FTIR characterization of polymeric samples has been Images of blends revealed the phase-exclusion of added color composite, as shown in Figure 2b, can highlight the individual regions. The major axes of the ellipses can be used to estimate the spread of data and the error in absorbance determination. The intersection of the major axes determines the most probable absorbance, which is read off the ordinate and abscissa, and the absorbance ratio is determined for each phase. Using pure components, a calibration curve is constructed based on peak ratios. The most probable absorbance ratio and its error are determined from 2D scatter plots. The error in the peak absorbance ratio (⌬AR) for two materials’ absorbances, A1 and A2, is estimated to be

poly(vinyl acetate) to the interspherulitic region. Similar segregation was observed for noncrystallizable, low-molecularweight oligomers blended with poly(ethylene oxide) (21). An image of the OH stretching mode vibrational peak absorbance shows the presence of low-molecular-weight species at the boundaries of the spherulite, or crystalline morphological unit. The image contrast indicates the strength of the dichroic ratio, while the image structure indicates relative spatial orientation of the functional groups. Polymer–liquid systems. Polymers blended with other polymers or liquids separate into phases because of thermodynamic considerations. For example, a mixture of diallyl phthalate and polybutadiene phase separates; however, the resultant structures are difficult to observe using light microscopy. FTIR imaging provided visualization based on functional group vibrational absorption differences (22). The dispersed morphology could readily be seen and quantitatively characterized immediately and after 24 hours. Interestingly, curing the network system led to the appearance of a micrometer-scale homogeneous matrix.

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The dissolution of polymers by solvents interests the lithography industry, among others. Often, a mixture of solvents is used in dissolution processes. FTIR imaging is an excellent noninvasive method for studying the dynamics of each solvent in a multicomponent system as part of the same experiment. Two substances, of which at least one is a liquid, are brought into contact between two IR transparent substrates. This is schematically shown in Figure 3a. The two interdiffuse, and this region of contact is imaged over time. An image of the interface region reveals the distribution of absorbance for a component (Figure 3b). By extracting the absorbance profiles, the concentration can be determined separately for each component as a function of distance (Figure 3c). A study examining the effects of using mixed solvents for the dissolution of low-molecular-weight polymers showed dissolution rates to be proportional to the solvent fraction. Solvent segregation was not observed when the two solvents were of the same quality (23). Individual concentration profiles of each solvent and polymer can be obtained. The concentration profile of the polymer could be used to determine the dissolution rate

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FIGURE 4. FTIR images of the dissolution of poly(␣-methylstyrene) with a mole weight of 31,000 as a function of time with a good solvent methyl isobutyl ketone and a nonsolvent (C6D12).

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The main advantages are noninvasiveness, fast data collection, and the ability to create visually appealing displays.

of the polymer. There are some interesting results when the polymer is studied above its entanglement molecular weight. As demonstrated in Figure 4, the polymer interface of poly(␣-methyl styrene), with a molecular weight of 31,000, is quite complex as a function of dissolution time in a mixture of a solvent and nonsolvent. In this case, a number of kinetic processes—diffusion, dissolution, and reptation (movement of polymer molecules)—compete as the dissolved polymer diffuses from the interface. Solvent segregation is observed in cases where the quality of the two solvents was very different. Reprecipitation of the polymer was observed in solution where the concentration of the nonsolvent was high. Polymer–liquid crystal systems. Polymer dispersed liquid crystals (PDLCs) are a class of polymer composites with potential applications in electro-optic devices. Microscopically, PDLCs are rich in domains of liquid crystal (LC) dispersed in a polymer matrix. These rod-shaped LC molecules are anisotropic in their refractive index. In one configuration, the refractive index along the major axis of the LC is matched to the polymer, and the refractive index along the minor axis is different. Hence, randomly oriented LC molecules in the dispersed domains scatter light at the domain boundaries because of a refractive index mismatch, which makes the window opaque. The LC can be oriented by applying an electric field to match its refractive index to the polymers, which renders the window transparent. As a result of these properties, light scatters at the domain interface and results in baseline offsets that produce the features in FTIR images. Applying appropriate voltage across the film orients the LC and matches the refractive index between the LC-rich domain and the polymer-rich matrix. This matching of refractive indices results in the loss of the baseline offset, and the image features disappear. From such an experiment, it was observed that significantly higher voltages are required to switch the LC at the boundary than are requried to switch the LC in the bulk of the phase. Such an approach can be readily used to examine refractive index matching and optimize its voltage at specific wavelengths across a broad wavelength range. Ideally, phase separation to form PDLCs yields two phases—pure LC and pure polymer. However, temperature-dependent limited miscibility exists, and the two phases are ac-

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tually LC-rich and polymer-rich. All methods of PDLC formation resulted in highLC solubility in the polymer-rich phase, characterized at typically >30%, and lower polymer solubility in the LC-rich phase. A new method has been proposed to reduce LC solubility by cooling a homogeneous LC–precursor mixture into the two-phase regime followed by fast matrix polymerization. The procedure was tested by imaging PDLCs from a well-studied system (24). Solubilities determined by using statistical methods on image data revealed sharply reduced solubility by this method. Residual solubility of the LC in the polymer and matrix material in LC domains was decreased. Imaging studies also demonstrated that, while maintaining the same phase composition, the cooling method allowed tailoring of the dispersion size. Samples made by this method were used as models for analyzing data enhancement strategies for FTIR imaging. Thermoplastic polymers and LCs were also used as model study systems in another application comparing FTIR microspectroscopic instrumentation. The electro-optical properties of a PDLC could also be analyzed using imaging. FTIR imaging, combined with statistical methods, is thus shown to be a valuable tool for determining phase composition in multiphase systems and simultaneously observing morphological changes. The diffusion of LCs in polymers is also an important phenomenon in the formation of composites. The diffusion of LC 4-pentyl-4´-cyanobiphenyl (5CBI) into polymer poly(butyl methacrylate) (PBMA) was studied (25). In another study (26), the diffusion of 5CB into PBMA (Tg ~32 °C) was examined as a function of temperature. When examined as a function of time at a given temperature, the diffusion process was found to be non-Fickian. The diffusion process was identified as anomalous, and it was pointed out that this distinction might not be possible without specific concentration profiles obtained by FTIR imaging. Determining phase diagrams. Phase compositions are determined using FTIR imaging coupled to thermal control of the sample. A single composition is held in the two-phase region and quenched to different temperatures. The sample is imaged continuously when hydrodynamic and coarsening equilibrium are attained for a few minutes. Subsequent quantita-

tive analysis yields the phase composition of the two phases at the quenching temperature. Thus, the two points of the coexistence curve at the quenching temperature are simultaneously determined. Now, the sample can be subjected to higher temperatures and allowed to equilibrate, and the phase diagram can be determined by sequentially stepping back to the single-phase temperature. A calibration curve was independently determined by starting at high temperatures. The average spectrum at each temperature was taken to indicate phase composition. There is a minor temperature effect for some cases, with a major change only occurring after phase separation.

A thousand spectra The development and applications of FTIR imaging to polymeric materials have increased rapidly over the past five years. Numerous applications, ranging from simple visualization of the distribution of a chemical entity to complex analysis of multiphase systems, have been reported. The emphasis on analysis has shifted from qualitative visualization of spatial distribution to obtaining quantitative results. Another trend has been to obtain these results faster with greater accuracy. These developments portend a proliferation of applications and newer, multivariate techniques to analyze data. The applications reviewed here highlight some areas where this technique has proven valuable. The main advantages are noninvasiveness, fast data collection, and the ability to create visually appealing displays. FTIR imaging not only provides new scientific capabilities, but it is also a compact yet informative way to present results. Indeed, a picture is worth a thousand words, or in this case, we should say a thousand spectra!

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The authors want to acknowledge the financial support of the NSF-sponsored ALCOM Center, the Ohio Board of Regents, the Digilab Division of BioRad, and Beth Miller’s contribution to Figure 4.

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Jack Koenig is a professor at Case Western Reserve University with research interests including polymer characterization. Shi-Qing Wang is a professor at the University of Akron with research interests including polymer rheology. Rohit Bhargava is a research associate in the Laboratory of Chemical Physics, NIDDK at the National Institutes of Health, with research interests including materials characterization. Address correspondence to Koenig at Case Western Reserve University, Department of Macromolecular Science, Kent Hale Smith Bldg., Rm. 212, 10900 Euclid Ave., Cleveland OH 441067202 or [email protected].

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