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Development of a Polystyrene Reference Material for Raman Spectrometer (NMIJ RM 8158-a)

The Raman shift is one of the most important parameters in Raman spectroscopy, and is calculated from the difference in the wavenumbers for excitation and for Raman scattering. Because the observed shifts are strongly dependent on the spectrometer and the measurement conditions, physically and chemically stable reference materials for Raman-shift validation are required. We reliably estimated the Raman shift and evaluated its uncertainty for peaks of a 4-mm-thick, 25-mm-diameter polystyrene disc by using a HeNe laser and Raman-scattered light calibrated with Ne/Ar emission lines. We considered uncertainties originating from the fitting, repeatability, and reproducibility of both the Ne/Ar emission lines and the Rayleigh/Raman-scattered lights, as well as the wavenumber of the unstabilised HeNe laser, and pixel and spectral resolutions. We also considered uncertainty originating from inhomogeneity among and within discs, as well as their long-term stability. The obtained Raman shifts of 11 peaks (reference values) were comparable to those described in ASTM E1840 with expanded uncertainty at 1.1 cm ‒1 or 1.2 cm ‒1 ( k = 2, coverage factor).


Introduction
The Raman shift originates from the difference between the energy of excitation and that of Raman scattering. 1-4 Although Raman shifts are theoretically independent of the Raman spectrometer that is used, in practice they are markedly dependent upon it. Consequently, users must calibrate individual Raman spectrometers by using references or protocols provided by manufacturers, because no standardized protocols are available for calibration.
Wavelengths/wavenumbers of elemental emission lines, such those of Ne and Ar, are suitable for accurate calibration of Raman spectrometers; however, they are not suitable for daily calibration of some Raman systems. For most applications of Raman systems, Raman-shift values of wellcharacterized materials provided in ASTM E1840 are more convenient and more easily handled. [1][2][3]5 However, Raman shifts of the materials provided in ASTM E1840 are not associated with the corresponding uncertainty information, which is essential for obtaining reliable values. 5,6 Polystyrene, which is described in ASTM E1840 and in which the Raman shifts of its 11 peaks are provided, 5 has been widely used as a reference material because it is not only physically and chemically stable, but is also free from any regulations related to chemical reagents. Polystyrene is therefore a suitable material to be developed as a reference material for the validation of Raman shifts in accord with ISO Guide 35:2017. 7 We have reliably estimated the Raman shift of the 11 peaks of polystyrene by using wavenumbers of a HeNe laser and Raman-scattered lights calibrated with Ne/Ar emission lines to develop a reference material (NMIJ RM 8158-a, Polystyrene for Raman spectrometer). We have also validated the reference values with other systems and by means of interlaboratory comparisons. Figure 1 shows the Raman spectrum of a polystyrene disc from 500 to 3200 cm -1 under the same spectral pixel resolutions with Raman shift values provided in ASTM E1840, 5 together with an assignment of the identities of the peaks used in this study. Although all peaks should be originated from polystyrene itself, we only evaluated 11 peaks which is provided in ASTM E1840. 5 To estimate the wavenumbers of the peaks, including the Rayleigh scattering of the HeNe laser, data were separately obtained in 12 spectral windows [see the Electric Supplementary Information (ESI), Figs. S1-S3]. After obtaining data for the Ne/Ar emission lines, data for the Rayleigh-and Raman-scattered lights were obtained without moving the grating. The grating was then moved and sets of data for the next spectral window were obtained. Detailed information on the measurements and the spectral windows are summarized in the ESI (Tables S1 and S2).

Experimental
A mixed Gaussian-Lorentzian function was used to estimate the wavenumbers of all the peak-tops for the Ne/Ar emission lines and for the Rayleigh-and Raman-scattered lights. Peaks F, J, and K were fitted as one bilaterally symmetric peak in each case, even though those peaks are bilaterally asymmetric (Fig. 1).
Changes in peak-top values for Peaks F, J and K, originating from different spectral resolutions, were evaluated by changing both the pinhole size (100, 200, 400, 600, 800, and 1000 μmφ) and the grating density (300, 600, 1200, and 1800 gr/mm) for a 532 nm laser. Uncertainty originating from changes in the spectral resolution were evaluated from the variance of peak-top values in 21 different spectral resolutions (spectral resolution range examined: 2.0-22 cm -1 ; spectral resolution at characterization: 3.7 cm -1 for the calcite peak at 1085 cm -1 ).

Overview of Characterization of Raman Shift Values and Their Uncertainty
For a reliable estimation of the wavenumbers of the HeNe laser and the Raman-scattered lights, we applied the following procedure and we considered several factors for the evaluation of the expanded uncertainty. Here, we also used the estimated wavenumber of the HeNe laser with Ne emission lines as Raman-scattered lights, because possible systematic changes in measurements can be cancelled out by using the wavenumbers obtained under the same calibration conditions. 1. The wavenumbers of Ne and Ar emission lines, together with their uncertainty, reported in the literature [10][11][12] were used to calibrate wavenumbers and to evaluate their uncertainty. We also considered the uncertainty of the peak fitting, the repeatability and reproducibility of the peak-top estimation separately evaluated by 5 iteration for each peak at each window, and differences in regions of the spectral window and in the spectral and pixel resolutions, as well the as uncertainty for the wavenumber of the HeNe laser.

Homogeneity and Stability
The homogeneity among the polystyrene discs was assessed by estimating the Raman shifts at two points for ten discs, hierarchical-randomly selected from among 1900 discs according to ISO Guide 35:2017. 7 The homogeneity within a disc was also assessed by measuring at ten randomly selected points on the disc and calculating the standard deviations of the measurements for these points. The long-term stability of polystyrene discs stored at 15 °C to 25 °C in darkness was assessed by estimating the Raman shifts of all peaks for two points on each disc at 1, 2, 4, 6, 8, and 9.5 months.
More details are given in the ESI.

Validation of the Raman-Shift Characterization and Reference Values
We used an acetaminophen [GBW 3654; paracetamol, N-(4-hydroxyphenyl)acetamide] certified reference material (CRM) obtained from the National Metrology Institute of China (NIM), 13 and we examined 17 peaks between 500 and 3100 cm -1 to validate the Raman-shift values obtained by our characterization method (ESI; Table S3).
Raman shifts of polystyrene peaks were also estimated in the following four ways, and their values were used for additional validation of the reference values:

Results and Discussion
Observed wavenumbers of the HeNe laser and the Raman-Scattered Lights To obtain reliable estimates of the wavenumbers of the HeNe laser and the Raman-scattered lights, we measured 10 discs for characterization and obtained wavenumber in air for each peak at each window and evaluated each reproducibility. Table 1 shows the observed wavenumbers of the HeNe laser and the Raman-scattered lights for each spectral window. Here, the uncertainty (u) was estimated from the standard deviation divided by √10 because ten samples were used in the characterization. The uncertainty (u) of the wavenumber for each window was ranged from 0.0362 cm -1 to 0.2215 cm -1 , and differences in the observed wavenumbers for each window ranged from 0.0128 cm -1 to 0.1457 cm -1 . Our results suggested that the reproducibility of the observed wavenumbers of the HeNe laser and the Raman-scattered light for each window was good and that differences in the wavenumbers measured in different region of the grating (spectral window) were small.

Evaluation of the Third-Polynomial Calibration Curve and its Uncertainty by Using Wavenumbers of the Ne/Ar Emission Lines
To estimate the wavenumbers of the HeNe laser and the Raman-scattered lights in vacuum, third-polynomial calibration curves were obtained from the wavenumbers of the Ne/Ar emission lines provided in the literature (in vacuum) and those observed with our system (in air). [10][11][12] The thirdpolynomial calibration curve at each window and its uncertainty was estimated from Eq. 1 below: .,  Table 1).

Evaluation of Uncertainty for the Combined Wavenumber of Each Peak
Wavenumbers of peaks obtained at three or four windows were combined with the weighted means by using 1/ui, where ui is the uncertainty of each window, as the weighting factor. The uncertainty in the between-window variance ( ) was calculated by performing an analysis of variance (ANOVA) on the results listed in Table 1, and this was taken into consideration if significant.
The combined standard uncertainties ( ) obtained from different windows ( ) and are summarized in Table 4. Eight peaks among the 12 peaks including the HeNe laser were significant and their was taken into consideration in their combined standard uncertainty.
For the combined wavenumbers of peaks, we also considered uncertainty originating from the wavenumber of the HeNe laser itself ( ) and from the pixel and spectral resolutions ( and ). The uncertainty given by the CIPM (relative uncertainty: 1.5 × 10 -6 ) was used for the uncertainty of the wavenumber of the HeNe laser itself. 8,9 Because peak-top wavenumbers were estimated by using the mixed Gaussian-Lorentzian function, their reliability was also dependent on the pixel resolution. We therefore also considered the pixel resolution for all peaks, although this might be an overestimation for the standard uncertainty.
Uncertainty originating from the pixel resolution ( ) was evaluated from the rectangular distributions of the half-width of two points (e.g., pixel resolution at the HeNe laser: 1.295 cm -1 ÷ 2 ÷ √3 = 0.3738 cm -1 ), because the pixel resolution can be taken as the point-to-point resolution. The resulting values of ranged from 0.2401 to 0.3738 cm -1 (Table 4).
We also considered the spectral resolutions of asymmetric peaks that probably consisted of several sub-peaks, such as Peaks F, J, and K (Fig. 1), not only because these are probably dependent on such measurement conditions as the wavelength of the laser, the grating density, the focal length, the objective lens, and the pinhole/slit sizes, but also because we regarded these peaks as symmetrical peaks for the mixed Gaussian-Lorentzian function. To evaluate the uncertainty originating from changes in the spectral resolution ( ), we examined the variance of spectral resolutions by using 21 different analytical conditions. The resulting uncertainties were 0.1021 cm -1 , 0.0982 cm -1 , and 0.0671 cm -1 for Peaks F, J, and K, respectively, which are much smaller than that of ( Table 4).

Estimation of the Raman Shift for Each Peak and Its Expanded Uncertainty
The Raman shift for each peak can be calculated from the differences in the wavenumbers of HeNe laser and Raman-scattered light, and uncertainty of Raman shift can also be calculated from wavenumbers' uncertainties of the HeNe laser and Raman-scattered lights in Table 4.
ISO Guide 35:2017 specifies that uncertainties in CRMs should be evaluated from the standard uncertainty due to characterization , homogeneity of the material , standard uncertainty due to long-term instability , and short-term instability (instability during transportation) . 7 In the present case, we also considered inhomogeneity within a disc , because the point size for characterization (~10 μm) was considerably smaller than the disc size (25 mm diameter), and there is a possibility of inhomogeneity over a disc. Uncertainty related to longterm stability ( ) was evaluated by ANOVA as , because linearity regression was insignificant.
The combined standard uncertainty was calculated by using Eq. 3:   Table S4). We therefore believe that the reference values are reasonable and reliable.
We also examined the consistency of the reference values with those described in ASTM E1840 5 by using the following equation: where is the reference value of the reference material, is the Raman shift value given in ASTM E1840, is the expanded uncertainty (coverage factor k = 2) of , and is the expanded uncertainty (coverage factor k = 2) of , which is the twice the standard deviation described in ASTM E1840. 5 This evaluation showed that the difference is insignificant when ≤ 1. The values obtained ranged from 0.10 to 0.67, and only the value of 1.3 for Peak F was greater than 1 (ESI; Table S5); this was attributed to the method used to decide the peak top (obtained by using the mixed Gaussian-Lorentzian function for this asymmetric peak). Because the reference values for 10 of the 11 peaks were consistent with the ASTM values, it can be considered that the reference values and the ASTM values are consistent with one another.

Conclusions
A polystyrene disc reference material for Raman spectrometer has been developed by using   Uncertainty budget in the relative standard uncertainty for Raman shift of each peak. Value in the parenthesis is Raman shift (cm -1 ) of each peak.       Uncertainty budget in the relative standard uncertainty for Raman shift of each peak. Value in the parenthesis is Raman shift (cm -1 ) of each peak.