Estimating Percent Crystallinity of Polyethylene as a Function of

Feb 7, 2017 - Under this circumstance, a simple two-state model may not be adequate and we describe the modifications required to treat such systems, ...
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Estimating Percent Crystallinity of Polyethylene as a Function of Temperature by Raman Spectroscopy Multivariate Curve Resolution by Alternating Least Squares Ashok Zachariah Samuel,† Bo-Han Lai,‡ Shih-Ting Lan,‡ Masahiro Ando,§ Chien-Lung Wang,‡ and Hiro-o Hamaguchi*,† †

Department of Applied Chemistry and Institute of Molecular Science and ‡Department of Applied Chemistry, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 30010, Taiwan § Waseda University, Consolidated Research Institute for Advanced Science and Medical Care, 513 Wasedatsurumaki-cho, Shinjuku-ku, Tokyo 162-0041, Japan S Supporting Information *

ABSTRACT: We have recently demonstrated a methodology to estimate the percent crystallinity (PC) of polymers directly with Raman spectroscopy and multivariate curve resolution (MCR) by alternating least-squares (ALS). In the MCR-ALS methodology, the Raman spectrum of a semicrystalline polymer is separated into two constituent components (crystalline and molten/amorphous) and their corresponding concentrations. The methodology necessitates that the Raman spectrum at any temperature be a linear combination of two MCR spectral components (one molten and one crystalline). This is true in the case of simple systems such as crystalline pendant alkyl domains in polymers (Samuel et al. Anal. Chem. 2016, 88, 4644). However, in the case of main chain polymer crystals (e.g., polyethylene), the situation can be complicated owing to several molecular changes in the lattice in addition to conformational reorganizations during melting. Under this circumstance, a simple two-state model may not be adequate and we describe the modifications required to treat such systems, keeping the basic principles of the proposed methodology unchanged. A comparative study with wide-angle X-ray scattering (WAXS) and Raman spectroscopy is also performed to substantiate our findings. In addition to estimating percent crystallinity (PC), our methodology is capable of revealing additional information, such as interchain interactions in crystal lattice, that in principle will help distinguishing polymorphic transformations, subtle changes in lamellar lattice dimensions, and other phase changes in polymers.

D

dimensional grazing incidence X-ray diffraction (2D-GIXD) to detect lamellar orientation on surface,16 and Raman-MCR-ALS methodology to detect the crystallinity of semicrystalline polymers.17 The performance of polymeric materials and devices significantly depends on the crystallinity. For instance, high crystallinity has been shown to enhance the carrier mobility and hence the performance of photovoltaic devices.18−21 Determination of crystallinity of semicrystalline polymers requires precise estimation of crystalline and amorphous contents. Spectroscopic determination of these quantities necessitates spectral signatures specific to molecules that exist in crystalline or amorphous domains. For instance, the terminal CH3 groups of hexyl chains in regioregular poly(3-hexylthiophene) (P3HT) give specific 13C NMR signals for polymer chains existing in

uring crystallization, polymer chains undergo numerous conformational restructuring and folding to organize into a regular crystal lattice to form lamellar structures.1−5 In the case of polyethylene, a minimum of 150 CH2 units exist in a straight all-trans segment before the chain fold back into lamella.6−14 The re-entry into the lattice can be adjacent or random.11,13,14 Owing to this unique crystallization mechanism, energetics and structural characteristics of polymer crystallization are fundamentally intriguing.1,5 Several molecular properties, such as conformation of polymer chain, symmetry of crystal lattice, magnetic and dipolar interactions between neighboring units, etc., are characteristic of specific lamellar organization, which can be explored using various advanced spectroscopic tools to understand the details of polymer crystal formation and melting. For instance, 13C−13C dipolar-based DQ NMR experiments to detect the re-entry of chain into crystal lattice,13,14 Raman spectroscopy to understand mechanism of restructuring of helical chain configuration,15 infrared reflection−absorption spectroscopy (IR-RAS) along with two© 2017 American Chemical Society

Received: November 30, 2016 Accepted: February 7, 2017 Published: February 7, 2017 3043

DOI: 10.1021/acs.analchem.6b04750 Anal. Chem. 2017, 89, 3043−3050

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Analytical Chemistry crystalline and amorphous domains.22 Hence, it was possible to estimate the percent crystallinity of regioregular P3HT using solid-state 13C single pulse excitation (SPE) NMR spectroscopy. X-ray diffraction technique can also be used to estimate percent crystallinity of polymers. The relative integration area of the scattering peaks from the amorphous and crystalline domains are used to determine crystallinity in this technique.23 Several other methods, such as dilatometry,24,25 and differential scanning calorimetry (DSC),26−29 are commonly used for studying the crystallinity of polymer materials. Vibrational spectroscopy has also been used to estimate percent crystallinity (PC) of polymers (e.g., polyethylene,30,31 polystyrene,32,33 polylactide,34 polyethylene terephthalate,35 polypropylene,36 etc.). A two-state phase-transition model (crystalline and amorphous/molten) is generally assumed, and the intensity ratios of characteristic bands were converted to percent crystallinity values by applying different calibration methods. However, agreement observed between the values estimated with different techniques is not always satisfactory.32 Generally, polymer chains existing in crystalline and amorphous domains exhibit unique conformational characteristics.15,37 Therefore, the frequency and bandwidth of the corresponding vibrational modes in Raman spectrum are different. Integral intensities of these specific bands can be directly used to estimate the percent crystallinity. However, the scattering cross-sections of these bands are expectedly different and are not easy to estimate. Hence, there could be errors associated with treating intensities as the absolute measure of concentrations. Furthermore, separating individual components from a composite Raman spectrum, consisting of more than one spectral component, is not straightforward, as there will be considerable overlap between bands. To perform such analysis, we have recently introduced a new methodology, viz., multivariate curve resolution (MCR) by alternating leastsquares (ALS),17,38 to separate individual spectral components such that a combination of these components constitutes a Raman spectrum at different temperatures. To perform MCRALS analysis, it is favorable to know the number of possible spectral components in the Raman spectrum at each temperature. Singular value decomposition (SVD) analysis can be performed prior to MCR-ALS to determine the number of spectral components present in the Raman spectrum.17,39 In our previous publication, we have used this methodology to study side-chain crystallization of alkylated dextran derivatives and estimated its PC accurately.17 The advantage of our technique is that we can estimate the PC from the intensity of amorphous spectral component alone, thereby avoiding the need for scattering cross-sections of Raman bands. In the present paper, we have employed our methodology to estimate percent crystallinity of polyethylene (PE). In our earlier study on side-chain crystallization of dextran derivatives, there were only two phases to consider: amorphous and crystalline.17 The situation can be complicated in the case of long chain polymeric systems, such as PE. PE exists in four different polymorphic states, viz., triclinic,40 monoclinic,41−43 orthorhombic,44 and hexagonal.45 The orthorhombic form is thermodynamically stable at normal conditions of temperature and pressure. Monoclinic crystal of PE forms under high stress42 or when the molten polymer is slowly cooled after thermal annealing at high temperatures for long duration.43 Hexagonal form exists under high pressure conditions.45 In hexagonal form, PE chains are conformationally disordered (not all-trans) but chain packing in the lattice is preserved.46

Interestingly, the metastable hexagonal form is also reported to appear at normal conditions in a constrained PE gel−film during melting.46 It is also hypothesized that upon cooling from melt, PE crystallizes into a hexagonal lattice first and then changes into the orthorhombic form.45−47 There could be other changes in crystal structure possible prior to actual melting, causing distortion of the lattice, such as appearance of rotator phases,48,49 as indicated by previous studies.50 These molecular changes are observable with Raman spectroscopy. Here we examine the modifications in the PE crystal lattice during melting using the Raman-MCR-ALS methodology. We find that even subtle changes in lattice parameters can be identified with this methodology. Despite the changes in crystal structure during melting, our methodology can estimate PC without compromising accuracy.

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EXPERIMENTAL SECTION Materials. Linear polyethylene PE7k (Mn ∼ 7700 g/mol; PDI 4.5) was purchased from Sigma-Aldrich, Inc., and PE52k (Mn ∼ 52000 g/mol; PDI 2.9) was purchased from Polysciences, Inc. Both samples are used as received without further purification. Raman Spectroscopy. A confocal Raman microspectrometer with the following components was used for the measurements. The second harmonic (532 nm) of a cw Nd:YVO4 laser (Verdi-V5, Coherent) was used as the excitation laser light. Using a high-resolution wavelength meter (WS-7, HighFinesse), the output wavelength was continuously monitored and maintained at 18 789.902 cm−1 with an accuracy of 60 MHz. The beam was directed to a beamexpander (expansion factor ∼5) and then into an inverted microscope (iX71, Olympus). The laser was focused into the sample with a long working-distance objective (20×, NA 0.45). A pinhole with a 75 μm diameter was used in the collection path to achieve confocal configuration. Three volume Bragg gratings (VBG) were used as the Rayleigh scattering rejection filters (BragGrate notch filters, OptiGrate). The elimination bandwidth was as narrow as 10 cm−1. The scattered light was introduced into a spectrometer (f = 50 cm, f/6.5; SP-2558, Princeton Instruments) and detected with a liquid nitrogencooled CCD detector (Spec 10:400B, Princeton Instruments). The sample was heated (10 °C/min) on a heating−cooling stage (Instec, MK2000-48VDC-5A-S, Boulder, CO). We have given a pretreatment to the polymer sample by completely melting it and then cooling it to 30 °C at the rate of 10 °C/min. The sample temperature was then increased (10 °C/min) from 30 °C stepwise at an increment of 2 °C (but for PE52k, the interval was 5 °C until 120 °C; after that, the interval was 2 °C). At each temperature, the sample was equilibrated for 2 min prior to recording the Raman spectrum. The laser power at the sample was 1−2 mW. Spectra were recorded with 5 s exposure and 20 accumulations. Variable temperature measurements were continued until no further change in relative intensities was observed with a change in temperature (e.g., until 108 °C for PE7k and 138 °C for PE52k). Multivariate Curve Resolution by Alternating LeastSquares. Multivariate curve resolution (MCR) by alternating least-squares (ALS)51−53 is a well documented multivariate statistical method for identifying spectral components which are otherwise not quantitatively separable in the original data matrix. In this method, an original data matrix (A) can be decomposed into spectral components (W) and their concentration profiles (H) as given below. 3044

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Figure 1. Variable temperature Raman spectra: PE7k (a) and PE52k (b). Only a few selected spectra are shown for clarity.

A = WH + E

(1)

intensity should be converted to the corresponding PC value by using external standards. Our methodology eliminates the need for cross-sections because we have estimated PC (eq 2) from one spectral component (amorphous) alone. Thus, it requires no external standard to convert spectral intensity ratios to corresponding PC values. Wide-Angle X-ray Scattering (WAXS) and Differential Scanning Calorimetry (DSC). A Bruker APEX DUO single crystal X-ray diffractometer with a microfocus air-cooled sealed Cu tube source, 50 W (50 kV, 1 mA; Kα radiation 0.1542 nm), was used to collect wide-angle X-ray diffraction data. The diffraction patterns were recorded with an APEX II CCD camera kept approximately 60 mm from sample position. The exposure time was 10 s for PE7k and 1 s for PE52k. A Cryostream heater from Oxford Cryosystems was used to control the temperature of the sample. The temperature was externally monitored using a thermocouple and found to be accurate within ±0.5 °C. The data were recorded with an interval of 2 °C/min until 108 °C for PE7k. The temperature interval was 5 °C/min for PE52k until 120 °C and then 1 °C/ min until 138 °C. The PE samples were extruded into thick fibers (∼0.5 mm diameter) for the measurements.

E is the residual. In the present case, A (m × n matrix) consists of n spectra at different temperatures with m data points. If the original data consists of p spectral components, A is decomposed to m × p matrix W, whose columns represent pure component spectra, and p × n matrix H, whose rows represent the intensity (or concentration) profiles of the corresponding individual spectral components. The residual will be minimum if p is chosen accurately. MCR-ALS calculation is performed by minimizing the error E iteratively such that the Frobenius norm ∥A − WH∥2 is the minimum. We apply non-negativity constraints (W ≥ 0 and H ≥ 0), during the minimization procedure, to obtain physically meaningful solutions.38,51 These constraints arise from the fact that neither the Raman spectra nor the concentration profiles can have negative values. In our methodology, we employ singular value decomposition (SVD) to get a reasonable estimate of the number of components (p) prior to MCR-ALS. In SVD, original m × n matrix (e.g., A) is decomposed into UΣVT (U is m × m, Σ is m × n, and VT is n × n), where Σ represents the singular value matrix (diagonal matrix). The SVD components with significant spectral signatures and singular values will give an estimate of number of spectral components (p) in the data matrix (A). A software program written in the laboratory was used to perform MCR-ALS.17,38 We have estimated PC from the results of MCR analysis using eq 1. The error in the value of PC was estimated in the following way. The MCR residual curves (E) were integrated after converting the ordinate values to their absolute magnitudes. The integrated values are then multiplied by weighting factors (for each temperature) that represent the fractional contribution of molten-spectral intensity to the overall intensity of Raman spectrum (Imolten /(Imolten + Icrystalline)). The error was then calculated by incorporating this weighted integrated residual intensity into eq 2. (Tf is 108 °C for PE7k and 138 °C for PE52k).

PC WAXS = 100{(I(110) + I(200))/(I(110) + I(200) + Iamorphous)}

Differential scanning calorimetry (DSC) experiments were carried out with TA Instruments Q20 with refrigerated cooling system RCS90. About 1 mg of sample was used in each measurement. The heating rate was 10 °C/min. The ΔH for 100% crystalline PE was taken as 293 J/g.54

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PCDSC = 100 × ΔHsemicrystalline/ΔHfully crystalline

(4)

RESULTS AND DISCUSSION The Raman spectra of polyethylene samples are shown in Figure 1. Spectra were recorded at regular intervals from 30 °C to a temperature above melting point after which no spectral changes were observed. As expected, the spectral features observed are similar to those of alkyl chains.17,30,55,56 The bands at 1128, 1296, and 1418 cm−1 are characteristic of all-trans CH2CH2 chains in the crystalline domains. Upon melting, the intensities of these crystalline bands reduce and those of the 1081 and 1305 cm−1 bands increase. The new bands are the spectral signatures of the molten PE chains (spectrally identical

PC(at 30 °C) = 100{[Imolten(at Tf > Tmp) − Imolten(at 30 °C)]/Imolten(at Tf > Tmp)}

(3)

(2)

Tf is the temperature above which no spectral changes are observed. To estimate the crystalline and the amorphous contents from the Raman spectrum of PE, the corresponding scattering cross-sections should be known. Otherwise, in general, the ratio of crystalline to amorphous Raman spectral 3045

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Figure 2. Change in composition of amorphous content (H values) at different temperatures obtained from MCR analysis (red) and the corresponding percent crystallinity calculated with eg.2 (blue) for PE7k (a) and PE52k (b). Vertical lines in the respective traces indicate the error bars associated with PC.

Table 1. Molecular Weight of PE (MW in g/mol), Polydispersity Index (PDI), Melting Point (mp), the Distance between (200) Planes (d(200)), and the Percent Crystallinity Estimated for PE7k and PE52k % crystallinity (PC)a PE sample

MW (PDI)

mp (°C)

temperature

d(200) (Å)

Raman

DSC

WAXS

PE7k

7700 (4.5)

92

17.3

46.3

52000 (2.9)

132

3.75 3.81 3.70 3.83

52.4

PE52k

30 °C 92 °C 30 °C 132 °C

81.3

72.9

76.3

PC values at 30 °C. Error in the estimation is calculated for WAXS and Raman from residuals in the band fitting and MCR analysis, respectively. See Figure 5. a

to the Raman spectrum of amorphous PE).17,30,55,56 Earlier investigators have conducted several quantum mechanical calculations, to understand the nature of spectral intensities of the above-mentioned all-trans Raman bands. A general consensus is that a long −CH2CH2− chain consisting of at-least five consecutive trans conformers gives intensity to 1296 and 1128 cm−1 Raman bands. Any −CH2CH2− chain configuration consisting of two (or less) consecutive trans sequence gives intensity to the broad amorphous bands at 1081 and 1305 cm−1.57,58 Variable temperature Raman spectra of two different PE samples, viz., PE7k (Figure 1a) and PE52k (Figure 1b), show similar spectral features. Raman spectra of the completely molten PE52k (at 138 °C) and PE7k (at 104 °C) are identical. This spectrum represents pure molten component consisting of −CH2CH2− chains with different trans−gauche sequences probably with a maximum of two consecutive trans sequences. At 30 °C, the Raman spectrum of PE52k and PE7k exhibits different relative intensity patterns (Figure 1a,b), which can be attributed to the differences in the relative contributions of crystalline and amorphous components.17,30,50 In other words, the relative intensity contribution of the molten spectral component (see signature at 1081 cm−1) appears higher for PE7k at room temperature than for PE52k, indicating a lower PC for PE7k. For the quantitative estimation of PC, the contributions of molten and crystalline spectral contributions should be separated from each other. The MCR-ALS method can be applied to separate them quantitatively. The MCR-ALS method decomposes the composite Raman spectra (A) of PE at different temperatures to their pure spectral components (W) and corresponding concentrations (intensities; H). The PC can be estimated from these concentrations using eq 2. Generally a two-state phase transition model is assumed for representing polymer melting (crystal → molten). If this is true, then SVD analysis of variable temperature Raman spectral data should indicate only two major components: crystalline and

molten/amorphous.17 We have performed SVD analysis on the variable temperature Raman data set of PE52k and PE7k. The results of SVD analysis (Supporting Information S1) indicate the presence of two major components with relatively large singular values. However, contrary to the expectation, a continuous change in singular values of the remaining components is also seen. The singular values corresponding to these components are relatively small, but the corresponding spectral components have significant spectral features (not just noise), especially the third component in each case (Supporting Information S1). A direct interpretation of SVD results is not possible because the spectral features have negative signatures. However, SVD results indicate the need for more than two components to accurately interpret the changes in polyethylene during melting. Considering the signal-to-noise in the SVD components, we have decided to consider at-least three spectral components (this was also supported by the negligible residual in MCR-ALS; see Figure S2). One of the three components should necessarily be the molten component, and the remaining two spectral components are from crystalline PE. Hence, SVD analysis indicates a change in the orthorhombic crystal structure of PE during heating. To separate Raman spectral components in the composite Raman spectrum at each temperature, we have performed MCR-ALS analysis of the variable temperature Raman spectral data set by assuming three spectral components (p = 3; see Experimental Section). The Raman spectrum of completely molten PE is considered as a pure spectral component (spectra at the final temperature in each case; see Figure 1), because there is no change in the spectrum after this temperature. Hence, this spectral profile was used as a known spectral component for solving the eq 1. The results of the MCR-ALS analysis are given in the Supporting Information S2. Because there is only one amorphous component, PC of the polymers (PE7k and PE52k) can be determined from the concentration profile of the corresponding amorphous component. According 3046

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Figure 3. Results of MCR reconstruction analysis for PE7k (a, b) and PE52k (c, d). The composite Raman spectrum obtained at 30 °C (A30), MCR molten ((WmoltenHmolten)30) spectrum and MCR crystalline spectrum ((Wcrystalline_totalHcrystalline_total)30) for PE7k (a) and PE52k (c). The MCR crystalline spectra at different temperatures for PE7k (b) and PE52k (d). An expanded plot indicating the shift in position of the Raman at 1418 cm−1 during heating for PE7k and PE52k are provided as an inset in the corresponding figures (b and d).

PC on devices nondestructively and could help optimizing conditions for better device performance. The Raman-MCR-ALS method can provide PC as a function of temperature (Figure 2). There is a marked difference between the PC temperature curves for the two PE samples. PE52k has a sharp reduction in PC close to the melting point while PE7k has a gradual change over a broader temperature range. We believe this behavior again reflects the difference in the molecular weight distribution (PDI) between the samples. A continuous reduction in crystallinity over the temperature range shows a higher inhomogeneity in lamellar crystal size for PE7k compared to PE52k.59 The change in total crystalline content in the PE samples as a function of temperature agrees well with the change in percent crystallinity estimated (Supporting Information S2). Two different crystal components suggested by SVD analysis indicate a change in the crystal structure of PE during heating. Monoclinic and orthorhombic forms of PE are reported to exist under normal pressure conditions. Monoclinic to orthorhombic transformation can take place during heating.43 Studies have also suggested the transformation of orthorhombic PE to metastable hexagonal crystal form at temperatures close to its melting point.46 Increase in the dichroic ratio of the infrared band at 1466 cm−1 was suggested as the indicator for orthorhombic to hexagonal phase transition.46 X-ray diffraction measurements also indicated the appearance of the (100) reflection of hexagonal form. It is important to understand the changes that occur in PE lamellar crystal form during heating. By assuming a simplest model possible (p = 3), we have solved the MCR-ALS equation. We found that both crystalline spectral components are mostly identical except for the change in position of Raman bands at 1128 and 1418 cm−1 (Supporting Information S2). Because the Raman band at 1418 cm−1 is

to our hypothesis, when the polymer is completely molten (e.g., at Tf = 138 °C for PE52k), its Raman spectrum represents a single component and its intensity represents total concentration of the polymer. MCR-ALS analysis estimates the composition of this molten component in all the Raman spectra (having three components) in the variable temperature data set by solving eq 1. The difference in the intensity of the molten component at Tf and at any lower temperature will then be the concentration of polymer that went into crystalline state.17 Therefore, using eq 2, we can then estimate PC accurately. The results are shown in the Figure 2. The estimated values of PC were compared with values obtained from DSC and WAXS. Raman, DSC, and WAXS analysis gave comparable values of PC for PE52k, but DSC values were considerably lower for PE7k (Table 1). This is a consequence of broad molecular weight distribution in PE7k (PDI 4.5) compared to PE52k (PDI 2.9). The presence of low molecular weight fractions in PE7k increases the structural inhomogeneity59 of the lamellar crystallites (lamellar thickness; Thomson−Gibbs Correlation60). Thinner lamellar crystallites melt at relatively lower temperatures.59 This causes a reduction in heat released during solid to melt phase-transition at the melting point. Consequently, the PC calculated (eq 4) gives a lower value. PE52k (PDI = 2.9) has lower PDI and hence the DSC melting (and crystallization) peak gives an accurate value of crystallinity. Further, percent crystallinity (PC) of PE having a molecular weight 52 000 g/mol estimated with dilatometric technique is reported (∼85%), and the value is closely in agreement with the Raman estimated value.25 PC is an important property that regulates the efficiency of polymeric devices. The PC value estimated for a bulk polymer could be different from the PC of the processed thin-film (used in devices), and it may also have spatial variations. Our method will allow direct estimation of 3047

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Figure 4. Comparison of WAXS spectra at two different temperatures (a and b): (a) at 30 °C (blue) and 92 °C (red) for PE7k, (b) at 30 °C (blue) and 130 °C (red) for PE52k. Lattice expansion is evident from the change in positions of crystalline (110) and (200) reflections. Broad peak at the lower scattering angle is due to amorphous PE. The position of the Raman band at 1418 cm−1 and the spacing between (200) planes versus temperature for PE7k (c) and PE52k (d).

specific to the orthorhombic form,46 the changes we observe are due to changes in the orthorhombic lattice rather than its polymorphic transformation. Together with the continuous changes in singular values in SVD analysis, we can interpret the MCR-ALS results as the continuous modification of the orthorhombic lattice of PE during heating. Under this situation, it is more meaningful to reconstruct the total crystalline spectrum from the MCR-ALS spectral components. Assuming ‘p’ spectral components,

bending) appearing due to correlation splitting in the orthorhombic form of PE, where two chains occupy a unitcell.46,55 This band has been demonstrated to be absent in the hexagonal form.46 Interestingly, this band is present in all the MCR reconstructed crystalline spectra (Figure 3b and 3d). Therefore, we believe that there is no polymorphic transformation to a hexagonal form in the present case. On the other hand, a change in molecular arrangement within the PE crystal is evident from the observed peak shift. The position of the peak 1418 cm−1 moves to higher frequency and that of 1128 cm−1 shifts to lower frequency (Figure 4c and 4d; Supporting Information S3). Within the PE crystal, adjacent PE chains interact with each other, which affects the normal mode of vibration (e.g., correlation splitting).55 A change in interchain interactions should affect the frequency of the vibrational mode. Hence, a possible explanation for the observed changes is lattice expansion. The lattice expansion changes interchain distance, and hence the Raman spectrum at room temperature will be different from the Raman spectrum at a temperature close to melting. Thus, Raman analysis indicates a continuous change in the spacing between the neighboring PE chains in the orthorhombic lattice. We find no evidence for the polymorphic transformation in PE during melting. We have conducted variable temperature wide-angle X-ray scattering (WAXS) measurements to confirm the lattice expansion hypothesis. The WAXS spectra at 30 and 92 °C (mp 92 °C) for PE7k are shown in Figure 4a. Similarly, the spectra recorded at 30 and 130 °C (mp = 132 °C) for PE52k are shown in Figure 4b. Both WAXS spectra are suggestive of an orthorhombic crystal lattice. However, the difference in peak position of (110) and (200) reflections at two different temperatures indicates lattice expansion. The distance between (200) planes (d(200)) estimated from the WAXS peaks are tabulated in Table 1. The results from WAXS analysis support the MCR-ALS results. Further, the change in peak position of

A = W1H1 + W2H2 + ..... + WpHp + E

Because in the present case we reliably approximate p = 3 with one molten and two crystalline spectral components, A = WmoltenHmolten + Wcrystalline1Hcrystalline1 + Wcrystalline2 Hcrystalline2 + E A = WmoltenHmolten + Wcrystalline_totalHcrystalline_total + E

At a particular temperature T, (A)T = (WmoltenHmolten)T + (Wcrystalline_totalHcrystalline_total)T + ET

The results of MCR reconstruction analysis are given in the Figure 3. The composite Raman spectrum obtained at 30 °C, the MCR-ALS reconstructed crystalline spectrum, and the corresponding molten spectrum are separately shown (Figure 3a and 3c). The reconstructed crystalline MCR spectra at different temperatures are shown in Figure 3b and 3d. The intensity of this spectral component is proportional to the crystalline content in the polymer at different temperatures. As explained previously, a continuous peak shift is evident at 1128 and 1418 cm−1 (inset in Figure 3b and 3d). The Raman band at 1418 cm−1 has been assigned as an interchain mode (CH2 3048

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Figure 5. Comparison of percent crystallinity estimated from Raman (blue) and WAXS (red) for PE7k (a) and PE52k (b).

1418 cm−1 band corresponds well with the change in lattice spacing between (200) planes estimated from the WAXS spectra (Figure 4). The change in the position of 1128 cm−1 peak is shown in the Supporting Information S3 and it follows a similar trend. It is also possible to calculate the percent crystallinity from the WAXS data. The intensity of crystalline reflections (110) and (200) gives the measure of concentration of crystalline contribution. The intensity of the broad peak (amorphous halo) under crystalline reflections gives the concentration of amorphous content. From these integrated intensities we have calculated the PC values for each PE sample at different temperatures. The estimated PC vs temperature profile for PE7k and PE52k are shown in Figure 5. Corresponding PC values estimated with Raman-MCR-ALS are also given for comparison. A reasonable agreement is observed between these two values. Raman technique gives a slightly higher value for PC compared to WAXS. Such discrepancies between the PC values estimated with different techniques have been shown to exit.17,32 The differences arise from the accuracy of separation of crystalline and amorphous contents. It has been shown that the quantitative separation of diffuse scattering poses a challenge to estimating PC accurately with WAXS, and it may be the cause for the differences observed here.23 We believe that the separation of amorphous and crystalline content is quantitative in Raman spectroscopy by employing MCR-ALS, and hence it represents the accurate value of PC.

distribution in the PE7k sample is the cause for the observed deviation. Our study indicates that, in the case of polymer samples with broader distribution, DSC gives inaccurate results. Raman spectroscopy with our MCR-ALS method gives accurate results in either case despite differences in the molecular weight and PDI. Further, the determination of percent crystallinity by Raman spectroscopy is very promising because it allows direct estimation of PC on fabricated devices in a space-resolved manner.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.6b04750. SVD analysis results, additional results from MCR-ALS analysis, and variation in 1128 cm−1 peak position with lattice expansion (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 03-5712121 ext. 56504. ORCID

Ashok Zachariah Samuel: 0000-0002-6901-6348 Chien-Lung Wang: 0000-0002-5977-2836

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Notes

The authors declare no competing financial interest.

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CONCLUSION Raman spectroscopy in conjunction with MCR-ALS is well suited for the detailed characterization of melting of polymers. Small changes caused by lattice expansion could be detected accurately with Raman spectroscopy. Interchain interaction between PE chains in the orthorhombic crystal changes with lattice expansion, and that causes shift in the frequency of Raman bands at 1128 and 1418 cm−1 by about 3 to 4 cm−1. Lattice expansion conjecture arrived at from Raman-MCR-ALS analysis was confirmed with wide-angle X-ray scattering studies. In the present study, the changes in peak position are smaller compared to its bandwidth, allowing the MCR-ALS analysis with three spectral components accurately (crystalline components 2 and 3 with initial final peak positions; see Supporting Information S2). When the shifts in peak positions are larger, several other components will become necessary. The main aim of the present Raman-MCR-ALS study is to determine PC of polyethylene. The PC values for PE52k estimated with WAXS, DSC, and Raman are in good agreement. However, the PC values for PE7k estimated with DSC differed considerably from those estimated with Raman and WAXS. We believe that the broad molecular weight

ACKNOWLEDGMENTS The authors acknowledge the support from the Ministry of Science and Technology of Taiwan (MOST105-2113-M-009002 and MOST105-2745-M-009-001-ASP) and the Ministry of Education of Taiwan (“Aim for the Top University Plan” of National Chiao Tung University).

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