Infrared Absorption Spectroscopy of Polycarbonate at High Pressure R. G. KRAUS,∗ E. D. EMMONS, J. S. THOMPSON, A. M. COVINGTON Physics Department and Nevada Terawatt Facility, MS 220, University of Nevada, Reno, Reno, Nevada 89557-0058

Received 16 October 2007; revised 18 December 2007; accepted 19 December 2007 DOI: 10.1002/polb.21405 Published online 4 February 2008 in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: High-pressure Fourier-transform infrared absorption spectroscopy has been performed on polycarbonate, using a diamond anvil cell to produce pressures up to ∼6 GPa. The frequencies of the vibrational modes have been measured as a function of pressure. Individual mode Grüneisen parameters have been determined for six vibrational modes. The data were fit to models that included both volume-dependent and -independent Grüneisen parameters. The vibrational frequency shifts as a function of pressure have been found to be consistent with those measured for similar types of bonds in other molecules. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 734–742, 2008

Keywords: compression; FTIR; high pressure; infrared spectroscopy; polycarbonate

INTRODUCTION Polycarbonate (PC) has a wide variety of industrial applications including bullet proof glass, compact discs, and common water bottles. A cursory inspection of a piece of PC shows that it is hard, lightweight, and transparent to visible light. These properties also make it useful for applications in research and development. An interesting application is as a window material in laser-driven shock wave experiments. A good description of this type of experiment and the uses of the backing window can be found in a recent publication by Swift et al.1 Under the conditions of this type of experiment, PC would reach high temperatures and pressures as dictated by the shock Hugoniot. PC has been previously studied with Raman spectroscopy at static pressures up to 35 kbar in ∗ Present address: University of Cambridge, Emmanuel College, Cambridge, CB2 3AP, UK Correspondence to: R. G. Kraus (E-mail: richardgkraus@ gmail.com) Journal of Polymer Science: Part B: Polymer Physics, Vol. 46, 734–742 (2008) © 2008 Wiley Periodicals, Inc.

734

a diamond anvil cell (DAC).2 The infrared absorption spectrum of PC has not previously been measured as a function of pressure. Data from these measurements can be used to calibrate ultrafast infrared reflection spectroscopy diagnostic techniques. These diagnostics are used in shockcompression experiments, as has been done in the case of nitrocellulose3 and poly(vinyl nitrate),4 to determine shock pressure and the effect of shock waves on chemical bonds. Only a limited number of vibrational spectroscopy experiments have been performed on polymers at static pressures typically achieved in a DAC. For a thorough literature review regarding vibrational spectroscopy of polymers at high pressure, see Emmons et al.5 We have measured the Fourier Transform infrared (FTIR) absorption spectrum of PC at high pressures up to ≈6 GPa in a DAC. The FTIR absorption spectrum of PC at room temperature and 1 bar of pressure has been studied previously, and the vibrational modes have been identified by Silverstein and Bassler6 and Schnell.7 Individual vibrational mode Grüneisen parameters have been determined under the assumption that they are volume-independent. In addition, the data

INFRARED ABSORPTION SPECTRA OF POLYCARBONATE

have been fit to a model where the mode Grüneisen parameter is assumed to be proportional to the fractional change in volume of the sample.2 During data analysis, particular emphasis was placed on the effects of the removal of free volume in the sample.

GRÜNEISEN PARAMETER ANALYSIS AND VIBRATIONAL ANHARMONICITIES Data from high-pressure vibrational spectroscopy experiments is typically analyzed to determine individual mode Grüneisen parameters. Bulk Grüneisen parameters are useful for calculating thermal energies in shock-compression experiments using the Mie-Grüneisen equation.8,9 The bulk Grüneisen parameter γ relates the bulk volume of the sample V , the heat capacity CV , the coefficient of thermal expansion β, and the bulk modulus B of a given material by the equation γ =

BV β . CV

(1)

The complete derivation for this relation can be found in Hook and Hall10 and a summary of the derivation follows. The volume coefficient for thermal expansion β is defined as



 ∂p 1 ∂V 1 ∂V 1 ∂p β= =− = , V ∂T p V ∂p T ∂T V B ∂T V (2) wherein the pressure is determined by the following relation,
 1 dEpot  dνi 1 − + h p=− dV dV 2 exp(hνi /kB T) − 1 i (3) with the summation over each individual mode at frequency νi . Epot is the temperature-independent potential energy associated with the interatomic interactions. A simple assumption can be made that νi = V −γi . (4) where γi is the individual mode Grüneisen parameter. It is possible to show that the Grüneisen parameter can be written as 
d ln(νi ) V dνi γi = − =− . (5) d ln(V ) νi dV Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb

735

Using this expression and assuming that the individual mode Grüneisen parameter, γi , is independent  γi is the slope of the plot of  ofvolume, then νi (P) (0) . ln ν (0) versus ln VV (P) i A substitution can then be made for dνi /dV in eq 3 so that
 1 1  1 dEpot γi hνi + + . p=− dV V i 2 exp(hνi /kB T) − 1 (6) The summation can then be done over the individual modes, leaving p=−

γ Emodes dEpot + , dV V

(7)

where γ is now the bulk Grüneisen parameter. Substituting back into eq 1, one can see that
 γ CV δEmodes γ = . (8) β= BV δT BV V Bulk Grüneisen parameters are extremely important in modeling the mechanical properties of solids and liquids; much of the error in using the Mie-Grüneisen equation of state is in the knowledge of the bulk Grüneisen parameter.11 Note that in this IR absorption experiment the bulk Grüneisen parameter was not calculated. The complete set of individual mode Grüneisen parameters must first be found and then the bulk Grüneisen parameter can be determined through the summation of individual mode Gruüneisen parameters in eq 6. In practice, this type of determination of the bulk Grüneisen parameter is difficult because of the high number of vibrational modes in most polymers. (0) To determine the value for VV (P) one can use the equation for the bulk compressibility of PC determined empirically by Zoeller,12
 −1 V (0) P(GPa) = 1 − (0.0894) ln +1 , (9) V (P) B(T) where B(T) is the Tait parameter12 in GPa with the temperature in K given by B(T) = (0.3878) exp[−0.002609T].

(10)

Information about the intermolecular potentials and the nature of the compression can be determined through the value of the mode Grüneisen parameter. For example, the mode

736

KRAUS ET AL.

Grüneisen parameter can be dependent on or independent of the volume If   of the sample.   the slope νi (P) V (0) of the plot of ln ν (0) versus ln V (P) is a coni stant, then the mode can be considered to be volume independent. In contrast, if the slope is not constant, then the mode Grüneisen parameter is considered to be volume dependent. Flores and Chronister2 assumed a volume-dependent mode Grüneisen parameter to have the form,

 V V (P) γi = m =m 1− , (11) V (0) V (0) for some Raman active modes of PC, where m is a parameter that determines the volume dependence and V is defined as V (0) − V (P). Emmons et al.5 and Dattelbaum et al.9 found that most volume-dependent modes will reach a critical value of the compression and thereafter the mode will appear volume independent. An amorphous solid is usually of lower density than a crystalline solid of the same polymer, because the random orientations of the polymer chains cause void spaces to form. The first stage of compression of an amorphous polymer takes up these void spaces and has little effect upon bond lengths. Once the majority of void spaces are removed, the compression of the polymer will start to look more like that of a crystalline polymer, where the chains are moving closer together and the bonds decrease in length with compression. A more thorough explanation of this phenomena can be found in a previous study by Emmons et al.5 The model of Sherman13,14 predicts that if the bond lengths decrease by 1%, for typical potentials the vibrational frequencies will increase by an amount on the order of 10%. As will be shown later, for the final pressures of around ≈6 GPa in the present experiment, the mode frequencies of PC shifted by an amount on the order of 1% from the zero-pressure values. Thus, the changes in bond lengths for the stretching modes were of the order of 0.1%. In contrast, the volume changes of the sample were ≈25%. Clearly, the change in the volume must be primarily because of the removal of free volume and compression of the interchain bonds, and not to compression of the intramolecular bond lengths.13 Generally, vibrational bands decrease in intensity and shift to higher frequency as the pressure is increased. For a purely harmonic potential, the vibrational frequency is independent of pressure and density changes,13,14 so pressure-induced shifts of the vibrational frequencies indicate bond

anharmonicities. From models such as that of Sherman,13,14 involving fairly general potentials, the potential gradients tend to increase as the internuclear distance is decreased. This explains the tendency for the corresponding vibrational frequencies to increase with compression.

EXPERIMENTAL Experiments were performed using a Bruker Hyperion 2000 infrared microscope coupled to a Tensor 27 FTIR spectrometer. IR radiation was produced in a globar lamp. A reflecting condenser was used to focus the IR radiation on the sample, and knife edge apertures were used to truncate light to the area of interest. A second objective, identical to the first reflecting condenser, is used above the sample to recollimate the transmitted light; the light is then passed to the FTIR spectrometer. The spectrometer was operated in 4 cm−1 resolution mode in the 500–4,000 cm−1 region; the scan was repeated 1000 times at each pressure to improve statistics. A liquid nitrogen cooled mercury cadmium—telluride detector was used to detect the radiation. The DAC used was a four-post high-pressure cell (High Pressure Diamond Optics, Tucson, AZ) designed for performing Raman and FTIR absorption measurements at moderate pressures. The culet diameter is 0.6 mm, and the sample chamber was a hole of ∼250 µm diameter drilled in an Inconel gasket. The standard ruby fluorescence technique was used to measure the pressure, where AgCl was used as the pressure medium. As opposed to KBr, which was used as the pressure transmitting medium in ref. 5, AgCl was chosen because the index of refraction (2.07) is more closely matched to diamond (2.37) than that of KBr (1.53), thus effectively eliminating the etaloning effect seen by Emmons et al.5 These indices were measured at 2.0 µm (5000 cm−1 ).15 AgCl has been used as early as 1965 as a pressure medium in compressible gasket devices.16 It has been noted by Jayaraman et al.17 that AgCl is hydrostatic up to 5.5 GPa and the hydrostatic nature of AgCl has been explicitly and thoroughly studied by Piermarini et al.18 and was found to be qualitatively hydrostatic up to 7 GPa. The nature of the stresses in a pressure medium can be determined by examining the spacing and widths of the ruby R1 and R2 lines, as described by Chai and Brown.19 The shift of the R2 line depends only on the mean stress (pressure), while Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb

INFRARED ABSORPTION SPECTRA OF POLYCARBONATE

Figure 1. Chemical structure of the monomer of PC. The mass of the monomer is 254, and the average mass of a polymer chain is 198,000.

737

temperature, melting point, and free volume content. PC of this type typically has a glass transition temperature of ≈145 ◦ C and a melting point of ≈233 ◦ C.22 The PC used in the high-pressure Raman spectroscopy study by Flores and Chronister2 was likely similar. Further characterization was not given by Flores and Chronister.

RESULTS the splitting of the two lines varies depending on whether the ruby crystal is being compressed parallel to the c-axis or the a-axis. Broadening of the ruby lines is due to spatial variations of the mean stress across the ruby chip. Uncertainty in determining the average pressure within the sample volume can be due to a quasihomogeneous pressure distribution across the diamond culet. This could be caused by a heterogeneous distribution of the pressure medium within the sample chamber, as the size and positioning of the AgCl slabs was not well controlled, for they were cut and positioned manually. In the present study using AgCl as a pressure medium, the maximum pressures obtained were ∼6 GPa. By observing ruby line broadening, changes in splitting, and different ruby crystals within the sample volume, the estimated errors in the pressure are ∼5%, with contributions from the three effects described earlier. Type IIa diamonds were used in the DAC in order to minimize impurity induced one-phonon absorption.20 The range from 1900 to 2300 cm−1 could not be studied because of strong absorption, with the production of two phonons that is present in a perfect diamond lattice.20 Fortunately, PC contains no vibrational modes in this range.21 The PC samples (Sigma-Aldrich, average molecular weight 198,000) consisted of a variety of thin film thicknesses. PC was put into solution by dissolving small amounts of the material in dichloromethane (CH2 Cl2 ), and thin films were formed across the sample chamber of the inconel gasket. The thickness of the films varied between ∼5 and 100 µm, as determined by comparison to the thickness of the gasket. AgCl was then used to fill the remaining volume of the sample chamber. Thicker films were studied to examine the weaker absorption bands while thinner films were studied to prevent the stronger absorbing peaks from saturating. The PC sample was not characterized to determine properties such as the glass transition Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb

The chemical structure of the repeating PC monomer unit is illustrated in Figure 1. The infrared absorption spectrum of PC at ambient temperature and pressure is shown in Figure 2. This spectrum was obtained by casting a thin film of PC using dichloromethane (CH2 Cl2 ) as a solvent. The 1800–2700 cm−1 region has been omitted because of overcompensation of the diamond absorption background subtraction. Identification of several infrared modes studied under high pressure is given in Table 1. The mode labels given in Table 1 correspond to those shown in Figure 2. Representative infrared absorption spectra of PC as a function of pressure for the vibrational modes in the range of 800–1600 cm−1 are shown in Figure 3. Similarly, the infrared absorption spectrum in the region of the O–C–O stretch mode from 950 to 1060 cm−1 is shown in Figure 4. All of the vibrational modes inhomogeneously broaden, shift to higher frequency, and decrease in intensity as the pressure is increased. Schoonover et al.23 attributed the broadening of the peaks to pressure

Figure 2. Spectrum of PC at ambient pressure and temperature. The 1800–2600 cm−1 region has been removed because there are no vibrational modes in this spectral region. The labels above several of the peaks are references to their mode descriptions in Table 1.

738

KRAUS ET AL.

Table 1. Table of Infrared-Active Vibrational Modes Analyzed at High Pressure Label

Frequency (cm−1 ) at Ambient Pressure

1 2 3 4 5 6

831 1015 1080 1505 1772 2970

Assignment Out of plane (C H) def. νs (O C O) γ (C C C) Ring ν(C C) ν(C O) Methyl νa (C H) combination

The assignments were found by Silverstein and Bassler6 and Schnell.7 The symbol ν refers to stretching modes; γ and def. (deformation) refer to bending modes.

variations within the DAC and to the molecules being locked into different bond lengths, bond angles, and local environments as the pressure is increased. Because of the increased interchain interactions at high pressure, the frequency differences become accentuated. In the present experiment, pressure variations within the DAC also contribute to the peak broadening. Mode Grüneisen parameters were found for several of the infrared active modes of PC. A plot of the infrared absorption data for the 2970 cm−1 methyl antisymmetric C H stretch is shown in Figure converted to units of  5. Plots of the  data  νi (P) V (0) ln ν (0) versus ln V (P) for several other modes i are shown in Figure 6. Parameters for both the volume-independent and volume-dependent models of the Grüneisen parameters are given in

Figure 3. Infrared absorption spectrum of PC as a function of pressure for the range 800–1600 cm−1 . The intensity of all the vibrational modes monotonically decrease in absorbance as the pressure is increased.

Figure 4. Infrared absorption spectra of PC for a symmetric O–C–O stretching mode. This figure shows the decrease in intensity, increase in width, and shift to higher frequency of the mode with increasing pressure.

Table 2. An analysis technique similar to that of Dattelbaum et al.9 was used. This technique assumes that there are two different regimes involved in the compression. The infrared absorption data from a C C C deformation are shown in Figure 7, and this absorption feature clearly exhibits low-pressure volume dependence and high-pressure volume independence to its mode Gruneisen parameter. In the low-pressure regime, the compression mainly involves the removal of free volume. In the high-pressure regime, the polymer chains are pushed closer together and the

Figure 5. Plot of shift in frequency with pressure for methyl antisymmetric C–H stretch. The peak position was determined by the peak maxima method, and estimated error bars are shown to within ±2 cm−1 and 5% of the pressure. Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb

INFRARED ABSORPTION SPECTRA OF POLYCARBONATE

bond lengths are starting to decrease. To determine the volume-independent Grüneisen parameters, the data points below a particular pressure were excluded from the fits, since for some modes the initial compression caused a decrease in void space and not bond length. This particular pressure was often around 1.5 GPa, although it varies from mode to mode. All of the modes were found to have volume-independent Grüneisen parameters in the higher pressure regime, consistent with the measurements of Dattelbaum et al. for 9 a crosslinked poly(dimethylsiloxane). The inter  V (0) cepts of the linear fits with the ln V (P) axis are also listed in Table 2. These give a relative indication of the pressure where the free volume in the polymer is removed.9 For absorption peaks in regions of low mode density, the peak centroid could be found by fitting the data to a Voight profile function. Infrared absorption features are nominally Lorentzian in shape; however, they often broaden to show Gaussian features when the sample is pressurized nonuniformally. For regions of high mode density, use of a fitting function was not practical owing to large number of peaks and etaloning around the absorption feature of interest. To determine the frequency of the peak by a fit function, one would have to use a large number of parameters to fit the complicated spectra, increasing the uncertainty beyond that which is acceptable. In these regions, the peak position was determined by finding the frequency of the peak maximum. This method was determined to be viable based upon comparisons made on peaks in which both methods were possible; the peak

    (0) Figure 6. Plot of ln ννi (P) versus ln VV (P) for all peaks (0) i analyzed. This graph shows the tendency for certain vibrational modes to exhibit both volume-independent and -dependent mode Grüneisen parameters. Peaks which exhibit volume-dependent mode Grüneisen parameters are fit as shown with the dashed line, and the high pressure fit to a linear slope is shown by a solid line.

Table 2. Table of Volume-Independent Grüneisen Parameters, γi , and Volume-Dependent Parameters, m Label

γi

m

ν/P (cm−1 /GPa)

Pressure (GPa)

1 2 3 4 5 6

0.047 ± 0.001 0.056 ± 0.004 0.062 ± 0.006 0.041 ± 0.006 0.027 ± 0.003 0.095 ± 0.006

– 0.155 ± 0.003 0.169 ± 0.003 0.117 ± 0.004 – 0.218 ± 0.004

1.7 ± 0.1 1.9 ± 0.1 2.3 ± 0.1 2.2 ± 0.1 2.2 ± 0.2 8.7 ± 0.2

0 0.7 ± 0.2 0.7 ± 0.3 0.7 ± 0.5 0 1.0 ± 0.3

Uncertainties result from fitting the volume-dependent and -independent fitting functions to the     V (0) ln ν(P) versus ln data. The labels correspond to the modes listed in Table 1. Values of the ν(0) V (P) volume-dependent parameter m were not calculated for modes that are obviously volume independent. The value of ν/P measured between   ∼ 6 GPa and ambient pressure is also listed. The final (0) column lists the intercept with the ln VV (P) -axis of the volume-independent fit, converted back to pressure units.

Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb

739

740

KRAUS ET AL.

    (0) Figure 7. Plot of ln ννi (P) versus ln VV (P) for C–C–C (0) i deformation. This graph shows the tendency for certain vibrational modes to exhibit both independent and dependent mode Grüneisen parameters. Representative error bars are also shown (see text for details).

maxima method was found to consistently agree to within the fitting errors of the Voight fitting function. Figure 5 shows the shift of peak position with pressure for a methyl antisymmetric C–H stretch in which the peak positions were determined by the peak maxima method. Calculating the uncertainty in centroid position for those peak positions which were determined by the peak maxima method is a bit subjective; however, reasonable assumptions were made, based on the width of the absorption feature, as to how accurate one could be in determining the centroid position. For those peaks that were fit to a Voight fitting function, the uncertainty in the peak position was determined from the fitting error itself. The relative uncertainty in the pressure measurement was determined to be about 5%, based upon a test run in which multiple ruby chips were placed at different locations that spanned the sample chamber. The pressure measurements from each of the ruby chips were compared after increasing the pressure and found to agree within ≈5%.

DISCUSSION Amorphous polymers contain a significant amount of free volume because of inefficient packing of chains in the solid. The effect of high pressure on the free volume is of fundamental interest and has received attention in several studies. Free volume is connected to the glass transition, since above

the glass transition temperature there is enough free volume in the polymer to allow the coordinated motion of polymer chains. Skorodumov and Godovskii24 measured the glass transition temperature of PMMA as a function of pressure. It was found that the glass transition temperature asymptotically approached a limiting temperature of 485 K as the pressure was increased. This is qualitatively in agreement with the GibbsDiMarzio theory, and in contradiction to the free volume theory, which predicts that the glass transition temperature should increase indefinitely as pressure is increased.24 The molecular weight of a polymer effects the fractional free volume, and thus the glass transition temperature, as described by Sperling.25 Materials with higher molecular weight have fewer end groups, and consequently less free volume. As a result, the glass transition temperature generally increases with increasing molecular weight. Due to decrease of free volume with increasing molecular weight, it would also be expected that the equation of state is a function of molecular weight. Higher molecular weight materials would be less compressible at low pressures than low-molecular-weight materials, where compression of the free volume is important. For higher molecular weight samples with less free volume, the mode Grüneisen parameters would be expected to have a smaller volume dependence. The fractional free volumes of the samples used in the present study, and those used by Zoeller,12 from which the equation of state was obtained, were not known, however. Measurements of samples of different molecular weights where the fraction of free volume has also been characterized by a technique such as positron annihilation lifetime spectroscopy would be helpful in elucidating these effects. Other studies of the free volume as a function of pressure have also been performed. Flores and Chronister performed Raman spectroscopy of PMMA and PC at high pressure in a DAC.2 For the modes measured, it was found that modes off the polymer backbone had volume-independentmode Gruneisen parameters, while those on the polymer backbone had volume-dependent parameters. This was interpreted to be due to shielding of the modes on the polymer backbone from the initial stage of the compression, where the main process is removal of the free volume. However, Dattelbaum et al.9 and Emmons et al.5 found that this does not hold for all the vibrational modes of polymers. Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb

INFRARED ABSORPTION SPECTRA OF POLYCARBONATE

Wu et al.26 pointed out that the arrangement of polymer chains in a solid can also contribute to variations in measured values of Gruneisen parameters. Variations in samples such as differences in the percent crystallinity or the fraction of free volume in the amorphous phase will change the measured value of the Gruneisen parameter, since the equation of state will change. In general, the equation of state and pressure-induced vibrational frequency shifts could depend on the sample pedigree. Four out of the six vibrational modes analyzed in this experiment, peaks 2, 3, 4, and 6 from Table 1 were found to show some volume dependence. The mode Grüneisen parameter related to peak 6, in the volume-independent region (0.095 ± 0.006), is nearly double that of the other modes which exhibited initially volume-dependent Grüneisen parameters. This could be caused by a greater anharmonicity of the potential surface or a larger local compression of the methyl antisymmetric C–H stretch. In this instance, it is plausible that the methyl antisymmetric C–H stretch sees a larger local compression because of the relatively large distance of this mode from the polymer backbone (see Fig. 1), this phenomena was also noticed by Schoonover et al.23 Some of these results are inconsistent with the explanation provided by Flores and Chronister2 that vibrational modes off the polymer backbone are often volume independent. For example, the methyl antisymmetric C–H stretch is relatively far from the backbone and would not be shielded from the initial compression, yet it shows a strong volume dependence. However, peaks 2, 3, and 4 are close to or on the backbone and might be shielded from the initial compression, which is in agreement with the analysis done by Flores and Chronister.2 Two of the six vibrational modes analyzed, modes 1 and 5, were found to have purely volumeindependent mode Grüneisen parameters. Both of these modes can be considered off the backbone and thus is in agreement with the conclusions made by Flores and Chronister.2 The value of the volume-independent Grüneisen parameter for each mode is significantly different (0.047 ± 0.001 for mode 1, 0.027 ± 0.003 for mode 5). As stated earlier, this could be caused by a greater anharmonicity of the local potential surface or a larger local compression for mode 1. Because there is no large difference in distance between the backbone and these modes, it is possible that the local potential surface for mode 1 shows a greater Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb

741

anharmonicity than that of mode 5. It is also possible that the difference in Grüneisen parameter between modes 1 and 5 could be due to the inherent difference in the type of vibration: mode 5 is a double-bond stretch, whereas mode 1 is an out-of-plane deformation. Under compression, it is difficult to say how these vibrations will act and there is very little theoretical support for this type of experiment. It is also useful to compare the pressureinduced shifts of the vibrational modes in PC to similar modes in other polymers, to see if general trends can be established. Some care must be used, however, since the modes are not pure vibrations and the nature of the polymeric material will also play a role. The 2970 cm−1 methyl C–H combination stretching mode exhibits a shift with pressure of 8.72 cm−1 /GPa, and this is greater than the pressure-induced shift of 6.1 cm−1 /GPa for a methyl C–H stretch of PMMA.5 However, it is within the range of pressure-induced shifts of a C–H stretch in polyurethane, polyester, estane, and degraded estane which where found by Schoonever et al.23 to shift by 12, 6, 10, and 10 cm−1 /GPa, respectively. The 1772 cm−1 C O stretch was found to exhibit a shift with pressure of 2.18 cm−1 /GPa. This is in agreement with the pressure-induced frequency shift for a C O stretch in polyurethane, polyester, estane, and degraded estane (3, 2, 2, 3 cm−1 /GPa, respectively) found by Schoonever et al.23 The 1015 cm−1 O–C– O stretch was found to have a volume-dependent parameter, m, equal to 0.155. Flores and Chronister2 found m to have a value of 0.191 for the Raman active O–C–O stretching mode in PC.

CONCLUSIONS The frequencies of the infrared absorption modes of PC have been measured as a function of pressure in order to determine mode Grüneisen parameters. Data of this type on scientifically and technologically important materials is helpful for benchmarking theoretical models of the materials under pressure and interpreting the results of shock-compression experiments. Most of the analyzed vibrational modes of PC have volumedependent Grüneisen parameters, and it has been shown that using a model in which the Grüneisen parameter is proportional to the fractional change in volume gives a better fit to the experimental data in these cases. The data indicate that most of the polymer free volume is removed after

742

KRAUS ET AL.

compression to 1.0 GPa. The pressure-dependent shifts in the vibrational frequencies were generally found to be consistent with those measured for similar bonds in other polymers. Although they cannot be definitively ruled out, there is no evidence for any phase transitions such as crystallization in the measured experimental data, as might be indicated by peak splittings or discontinuous changes in the frequencies or in dν/dP as a function of pressure.27 Static high-pressure data of this type is particularly valuable for analyzing experiments using ultrafast vibrational spectroscopy as a diagnostic during shock-compression experiments. As the shock pressures become higher, sample heating will also become more important, and it will be necessary to perform static measurements as a function of both pressure and temperature. Raman spectroscopy is a common ultrafast in situ diagnostic technique for shock-compression experiments, but ultrafast infrared reflection measurements have been performed as well. This technique has been used to study nitrocellulose3 and poly(vinyl nitrate)4 under shock compression. Poly(vinyl nitrate) was observed to undergo a chemical reaction on picosecond time scales during shock compression to ≈18 GPa. Static data of the type measured in the present study would be useful for benchmarking these shockcompression diagnostics. Overall, there has been increased interest in recent years regarding the high-pressure properties of polymers and energetic materials, especially those commonly used in shock-compression experiments.3,4,9,28 This work was supported by the Honors Undergraduate Research Award at the University of Nevada, Reno, and the US DOE under Grant no. DE-FC52-06NA27616 at UNR. We sincerely thank Dr. Tim Darling for many fruitful discussions. We also thank the UNR physics department electrical and mechanical technicians B. Brinsmead, W. Cline, D. Meredith, and W. Weaver for technical assistance.

REFERENCES AND NOTES 1. Swift, D. C.; Niemczura, J. G.; Paisley, D. L.; Johnson, R. P.; Luo, S.-N.; Tierney, T. E. IV. Rev Sci Instrum 2005, 76, 093907.

2. Flores, J. J.; Chronister, E. L. J Raman Spectrosc 1996, 27, 149. 3. Moore, D. S.; McGrane, S. D.; Funk, D. J. Appl Spectrosc 2004, 58, 491. 4. McGrane, S. D.; Moore, D. S.; Funk, D. J. J Phys Chem A 2004, 108, 9342. 5. Emmons, E. D.; Kraus, R. G.; Duvvuri, S. S.; Thompson, J. S.; Covington, A. M. J Polym Sci Polym Phys Ed 2007, 45, 358. 6. Silverstein, R.; Bassler, G. Spectrometric Identification of Organic Compounds; Wiley: New York, 1963. 7. Schnell, H. Chemistry and Physics of Polycarbonate; Interscience: New York, 1964. 8. Zel’dovich, Y. B.; Raizer, Y. B. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena; Dover: Mineola, New York, 2002. 9. Dattelbaum, D. M.; Jensen, J. D.; Schwendt, A. M.; Kober, E. M.; Lewis, M. W.; Menikoff, R. J Chem Phys 2005, 122, 144903. 10. Hook, J. R.; Hall, H. E. Solid State Physics; Elsevier: New York, 1991. 11. Swift, D. C. Private communication, 2007. 12. Zoeller, P. J Polym Sci Polym Phys Ed 1982, 20, 1453. 13. Sherman, W. F. J Phys C Solid State Phys 1980, 13, 4601. 14. Sherman, W. F. J Phys C Solid State Phys 1982, 15, 9. 15. http://infrared.als.lbl.gov/IRwindows.html. 16. King, J. H. J Sci Instrum 1965, 42, 374. 17. Jayaraman, A.; Narayanamurti, V.; Bucher, E.; Maines, R. G. Phys Rev Lett 1970, 25, 368. 18. Piermarini, G. J.; Block, S.; Barnett, J. D. J Appl Phys 1973, 44, 5377. 19. Chai, M.; Brown, J. M. Geophys Res Lett 1996, 23, 3539. 20. Walker, J. Rep Prog Phys 1979, 42, 1605. 21. Willis, H. A.; Zichy, V. J. I.; Hendra, P. J. Polymer 1968, 10, 737. 22. http://www.polymersdatabase.com. 23. Schoonover, J. R.; Dattelbaum, D. M.; Osborn, J. C.; Bridgewater, J. S.; Kenney, J. W. III. Spectrochim Acta 2003, 59, 309. 24. Skorodumov, V. F.; Godovskii, Y. K. Polym Sci USSR 1987, 29, 127. 25. Sperling, L. H. Introduction to Physical Polymer Science, 4th ed.; Wiley: Hoboken, New Jersey, 2006. 26. Wu, C.-K.; Jura, G.; Shen, M. J Appl Phys 1972, 43, 4348. 27. Wu, C.-K.; Nicol, M. Chem Phys Lett 1973, 21, 153. 28. Bourne, N. K.; Gray, G. T. III. J Appl Phys 2003, 93, 8966.

Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb