Toward a practical method for measuring glass transition in polymers with low-frequency Raman spectroscopy

The glass transition is loosely defined by the temperature at which an amorphous material gains enough internal energy to overcome vitrification and begin to flow as a viscous liquid. As a result, the glass transition temperature T_g is one of the most important parameters when analyzing the structure–property–processing relationships in polymer science and engineering. While the melting point temperature of crystalline materials, at constant pressure, results from a clearly defined phase transition detectable by a discontinuity in extensive properties, such as volume, enthalpy, and entropy, the glass transition is a gradual process whereby the material slowly becomes less “glassy” and more “rubbery” as the temperature increases. Therefore, T_g is characterized as a rate-dependent quasi second order thermodynamic phase transition which can be identified by a change in the slope of volume, enthalpy, or entropy as a function of temperature.¹ Since it is challenging to directly measure these extensive quantities in the laboratory, T_g is traditionally measured indirectly by techniques, such as differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA).

The simpler of these two approaches is DSC, which measures the heat capacity (or heat flow) of a material as a function of temperature T. Since heat capacity is equal to the derivative of the enthalpy with respect to T, holding pressure or volume, and composition constant, a step change in the DSC curves can correlate with a glass transition. By contrast, DMA probes viscoelasticity by measuring the storage and loss moduli as functions of temperature. While DMA provides a more direct measurement of the “glassy” to “rubbery” transition, there is no universally accepted definition of the exact transition point, be it the onset temperature of the decrease in storage modulus E′, the temperature of the maximum in the loss modulus E″, or the temperature of the peak of the loss tangent E″/E′. Furthermore, there is rarely agreement among any of these various methods for determining T_g. For instance, one study reported T_g values for polystyrene measured at 2 °C/min ranging from 84.7 to 89.3 °C when determined from DSC measurements and ranging from 89.4 to 111.5 °C when ascertained from DMA results.² 

Both infrared and Raman spectroscopies have been explored as potential alternative methodologies for detecting the glass transitions in polymers.^3–6 Raman spectroscopy is of particular interest due to the high spatial resolution and inherent non-contact nature of laser-based techniques. However, most Raman-based approaches to measuring T_g have focused on detecting relatively small changes in either the intensity or position of peaks of bending or stretching modes which arise at T_g due to changes in steric hindrances.^5,7 Low-frequency Raman has been used to investigate the effects of aging and thermal history on amorphous polymers⁸ and as a normalization factor for determination of glass transition kinetics via quasi-elastic Rayleigh scattering (QERS).^9,10 Still, there seems to be no discussion in the literature around the direct use of low-frequency Raman to measure glass transition kinetics. Furthermore, previous studies in this area relied upon complex multi-grating monochromators and polarization sensitive collection optics.

In this work, we present a methodology which uses low-frequency Raman spectroscopy for determining T_g of polymers by using only a double volume-holographic-grating-based fiber optic Raman probe, with an unpolarized laser source and collection optics. The use of two gratings as a Rayleigh filter in a fiber optic Raman probe has been well demonstrated as a means of simulating a double monochromator providing access to low-frequency vibrational modes,^11–13 but there is still significant filter roll-off below ∼15 cm⁻¹, which can often make quantitation rather challenging. Here, we demonstrate the ability to determine T_g directly from the low-frequency Raman spectra, irrespective of the filter roll-off, and support with first principles modeling. This technique permits direct investigation of thermal–structural properties, in a contactless, nondestructive manner, and is inherently well suited for in situ or high spatial resolution applications. Furthermore, the high scattering efficiency in this region of the spectrum permits studies of relatively fast kinetics.

Traditional Raman spectroscopy provides a chemical fingerprint by probing the various vibrational modes of a molecule,¹⁴ but it is also sensitive to phonon modes which provide insight into the overall structure of the material.¹¹ Two common examples are the presence of c-Si (∼520 cm⁻¹) and a-Si (∼480 cm⁻¹) bands as well as the g (∼1582 cm⁻¹) and d (∼1380 cm⁻¹) bands in graphene, which are examples of optical phonons due to vibrations along a crystal axis. Raman spectroscopy is also sensitive to acoustic phonons, which arise from in-phase lattice vibrations, but due to their extremely low energy, their modes are incredibly close to the Rayleigh line. Until recently, this made it challenging to measure them without the use of a double or triple monochromator.^15–23 

The tendency of phonon modes to redshift and broaden is a universal feature of amorphous materials. Therefore, $I R ν$ can be considered as the disorder band of the polymer, analogous to the a-Si band or the d band in graphene. The primary difference is that the extremely soft nature of polymers shifts the disorder band into the low-frequency region of the Raman spectrum. We propose a method of using this disorder band to monitor the change in the phonon density of states as a function of temperature to determine T_g of a polymer.

We utilized polystyrene pellets (CAS# 9003-53-6) with an approximate molecular weight of 210 000 g/mol purchased from Scientific Polymer Products, Inc. We also used polylactic acid (PLA) pellets (CAS# 26100-51-6) with an approximate molecular weight of 160 000 g/mol purchased from IC3D Industries and poly(methyl methacrylate) (PMMA) pellets (CAS# 9011-14-7) with unknown manufacturer and molecular weight. The samples were placed in a THMS600 temperature-controlled microscope stage from Linkam, allowing T to be controlled with an accuracy of <0.01 °C. The stage was sealed, and measurements were taken through the lid window. No extra efforts were taken to control the internal environment. Liquid nitrogen was utilized to stabilize the heating rate even though the samples were never cooled below 20 °C. The Raman measurements were made with an 808-nm CleanLine laser and TR-PROBE from Coherent coupled with an 8-mm working distance focusing lens. The TR-PROBE is a fiber-coupled Raman probe capable of measuring both Stokes and anti-Stokes Raman scattering to within approximately ±7 cm⁻¹ of the Rayleigh line. The scattered light was then fiber coupled directly into a HORIBA LabRAM HR Evolution spectrometer. It is important to note that a fixed grating modular spectrometer would have provided sufficient sensitivity and resolution, but the LabRAM HR evolution was used because it interfaced with the THMS600 temperature stage.

Heat flow measurements were conducted by DSC with a TA Instruments Discovery Series DSC 2500; 5–10 mg samples were sealed in aluminum pans with hermetic lids and heated at various temperature rates. All DSC measurements were conducted under nitrogen with a 50 ml/min flow rate. All DSC thermograms were smoothed with a Gaussian window function and scaled with MATLAB. The T_g values were determined by the built-in analysis function in the TA Instruments TRIOS software package to determine the midpoint temperature. Typically heat-cool-heat experiments are used, which erase the thermal history of the sample with an initial heating ramp, impart a known thermal history with a cooling ramp, and heat the sample again with the result from the second heating ramp being reported. However, because the spectral analysis was performed with a single temperature ramp, we only focused on the initial DSC ramp. Polystyrene and PMMA were measured at a 10 °C/min heating rate, and PLA was measured at a 5 °C/min heating rate.

Initially, we measured the Raman spectra of polystyrene using a 600 lines/mm diffraction grating and a 5 s integration time from −1100 to 1700 cm⁻¹ with a total measurement time of 30 s per spectrum. The sample was heated from 70 to 150 °C with a 2 °C step size, and accounting for spectral acquisition time, this corresponded to an average ramp rate of ∼4 °C/min. Figure 1(a) shows an overlay of the 41 spectra acquired over the temperature range, with the inset highlighting the disorder band increase as a function of T. Figures 1(b) and 1(c) show the normalized intensity of the Stokes and anti-Stokes shifted disorder band, $ζ D T$ with a clear change in slope at ∼92 °C. Next, we measured polystyrene over a spectral range of −1060 to 1060 cm⁻¹ with an 1800 lines/mm grating and an integration time of 30 s, resulting in a total acquisition time of 457 s per spectrum. The sample was heated from 20 to 198 °C with a 2 °C step size. Taking into account for spectral acquisition time, this corresponded to an average ramp rate of ∼0.25 °C/min. This provided an increase in both spectral and temperature resolution. The results shown in Figs. 2(a) and 2(b) again demonstrate an apparent change in slope in $ζ D T$ around ∼90 °C, which correlates with the T_g midpoint of ∼91 °C found by DSC [Fig. 2(c)].

To demonstrate the broad applicability of this method, we also studied two additional polymers, such as PLA and PMMA. For PLA, we used a spectral range of −300 to 300 cm⁻¹, and an 1800 lines/mm grating with a 30-s integration time with a total measurement time of 129 s per spectrum, leading to an average ramp rate of ∼0.32 °C/min for 1 °C step size. There is a kink in $ζ D T$ at ∼62 °C [Figs. 2(d) and 2(e)]. This correlates with the PLA T_g midpoint of ∼62 °C found by DSC [Fig. 2(f)]. For the PMMA sample, we used a spectral range of −330 to 330 cm⁻¹, an 1800 line/mm grating with a 60-s integration time, resulting in a total measurement time of 312 s per spectrum, with an average ramp rate of ∼0.18 °C/min. The PMMA did not exhibit a strong kink in $ζ D T$ as observed in the other samples, but there is still a discernable change in slope at ∼101 °C, as seen in Figs. 2(g) and 2(h). This agrees with the PMMA T_g midpoint of ∼101 °C determined by DSC [Fig. 2(i)]. It is interesting to note that the relatively weak inflection in $ζ D T$ coincides with the DSC results where the transition is so weak that it was undetectable for heating rates below 10 °C/min.

The Boson peak is defined as the maxima of the normalized phonon density of states, $g ν ν 2$⁠. While the origins of this feature are still debated in the community, extensive experimental evidence and more recent modeling have shown this feature to be extremely sensitive to sound velocity.^24,38–44 The van Hove peak in $g ν$ originates from singularities that arrive at critical points in the Brillouin zone and is far less sensitive to sound velocity changes than the Boson peak.^15,24,45,46 In addition to the pure Raman signal, there is also an additional contribution in the disorder band due to QERS.⁴⁷ The QERS arises from the translational energy associated with the molecules in the sample, resulting in a broadening of the Rayleigh band and can be modeled as a Lorentzian function centered at 0 cm⁻¹.

Based on an observed Rayleigh filter cut-on of ±7 cm⁻¹ after intensity correction, we digitally applied a notch filter to both the measured spectrum and intensity fitting function [Eq. (3)]. Since most of the QERS is contained within ±7 cm⁻¹, fitting its contribution outside this region is inherently difficult so the upper bound of $Δ ν QERS$ was set to 0.5 cm⁻¹ to ensure physically relevant results. The $γ$ term was also bound between 0.5 and 2. All other fit parameters were unconstrained. Four representative fitted spectra of polystyrene (two measured below and two above T_g) are shown in Fig. 3, with Boson peak positions of 11.7, 11.5, 9.8, and 8.7 cm⁻¹ at 50, 60, 120, and 130 °C, respectively.

The disorder band feature in Raman spectra of amorphous materials is a combination of QERS and the Boson peak. While it is known that this disorder band increases as a material softens, we have demonstrated the ability to use this phenomenon to directly measure glass transition behavior using a compact fiber coupled Raman probe without the need for advanced spectral processing. Rigorous analysis of the temperature dependent spectra can accurately identify T_g of polymers but so too can simply monitoring the temperature dependence of the integrated intensity near the apparent spectral peak (∼15 cm⁻¹) normalized to that of the shoulder (∼65 cm⁻¹).

The improved signal-to-noise in the low-frequency region of the Raman spectrum makes it far more promising for mainstream polymer characterization applications compared to conventional Raman focused on the chemical fingerprint region. Furthermore, the non-contact and high spatial resolution nature of Raman spectroscopy makes this technique ideal for both micro-analysis and in situ process control applications. This is in stark contrast to DSC and DMA, neither of which are particularly suited for in-line process measurements or analysis of fibers and films. While this methodology produces similar results as those previously shown by Novikov et al. when they monitored the intensity of the QERS normalized to the low-frequency Raman scatter,⁹ the use of the shoulder of the disorder band as a normalization for the low-frequency scattering greatly simplifies the instrumentation requirements representing a major step toward widespread implementation of the technique.