Speedy, Robust and Quantitative Analysis of Polyolefins Using

Article pubs.acs.org/Macromolecules

Speedy, Robust and Quantitative Analysis of Polyolefins Using Sensitivity-Enhanced 13C NMR Spectroscopy Jianbo Hou,* Yiyong He, and Xiaohua Qiu Corporate R&D, The Dow Chemical Company, 1897 Building, Midland, Michigan 48667, United States ABSTRACT: We report a novel NMR methodology that enables quantitative analysis of polyolefin materials in a fast and robust manner. The method is named quantitative adiabatic refocused insensitive nuclei enhanced by polarization transfer (QA-RINEPT). With the aid of adiabatic pulses, QA-RINEPT enables rigorous and controllable polarization transfer via combining the advantage of polarization transfer with the concept of response factor calibration that is widely used in chromatography to yield predictable 13C NMR spectra. The spectra obtained remain highly sensitive without compromising the quantitative nature. The effectiveness and robustness of QA-RINEPT have been demonstrated using a model compound on three NMR instruments equipped with different consoles and probes. QA-RINEPT further demonstrates its remarkable capability with polyolefin materials by saving up to 50−60× experimental time. The 13C NMR spectra obtained have been analyzed and compared with the standard quantitative single-pulse method by two individual analysts. Analytical results regarding composition and monomer sequence distribution show excellent agreement between different methods and analysts. due to its “nonquantitative” nature. What further exacerbates the situation is perhaps the lack of information from quaternary carbon using such a methodology. Indeed, RINEPT cannot be generically applied to systems, which require information on nonprotonated carbons, e.g., carboxylic and quaternary carbons. On the other hand, though polarization transfer may not generate an innately quantitative 13C NMR spectrum, a 13C spectrum with controllable, i.e., predictable, signal enhancement can be achieved, owing to the well-established theoretical framework of NMR spectroscopy. In other words, the relative enhancement among each functional group can be calculated theoretically and measured experimentally, and the factors that determine the enhancement are known and can be controlled. The scenario becomes even more favored for most polyolefin materials, where quaternary carbons are not present5,7 and variation of JCH coupling constant among aliphatic groups is negligible (124−125 Hz). In analogy to the calibration protocol of chromatography, a specific response factor can be determined for each type of NMR peak (CH, CH2, or CH3) so sensitive and quantitative 13C NMR spectra will become possible. Henderson developed the Q-DEPT method by cycling the flip angle of read pulse and polarization transfer delay time to achieve uniform 13C signal enhancement across a broad range of J coupling constants.9 Jiang et al. later extended the Q-DEPT method to include more comprehensive spin systems and further proposed Q-POMMIE as an alternative method to generate quantitative 13C spectra.10 However, our experimental results suggest that speedy and quantitative 13C spectra merely obtained by conventional DEPT or other polarization based

1. INTRODUCTION Polyolefins, with annual production over billions of pounds, represent one of the most important class of thermoplastics that finds a variety of applications in packaging, roofing, medical goods, and fabrics, etc. Regardless of their simplicity using hydrocarbons as the fundamental building blocks, many novel properties of polyolefin materials are tailored by the versatile combination and arrangement of aliphatic groups that form unique microstructures and compositions.1−4 Effective and robust analysis regarding the microstructure and composition of polyolefin therefore represents an indispensable step not only in product manufacturing but also in development of new materials. The reliability of the above analysis critically relies on obtaining high quality quantitative spectra by 13C NMR, which has been widely used for compositional and structural characterization owing to its unparalleled spectra resolution.5−7 However, the poor sensitivity of 13C NMR in nature presents a grand challenge to obtain sensitive spectra for effective analysis and even prohibits its application as a routine measurement. A typical concentration of a polyolefin solution ranges from 0.05 to 0.1 g/mL, which is limited by the sample viscosity. For polyolefin analysis, a typical experiment takes overnight to yield an acceptable quantitative 13C NMR spectrum using a conventional 400 MHz instrument.5 The advent of cryogenic probe technology has fundamentally changed the circumstance by boosting the NMR sensitivity to enable a dramatic reduction of the experimental time. The trade-off, as a consequence, is the cost of an NMR cryoprobe, which typically reaches an order of magnitude higher than its conventional counterpart. Herein, we adopt a different strategy to address the issue of low sensitivity encountered with 13C NMR. Our approach rests on the basis of refocused insensitive nuclei enhanced by polarization transfer (RINEPT).8 At a first glance, such a concept may seem unacceptable to many NMR practitioners © XXXX American Chemical Society

Received: January 25, 2017 Revised: March 3, 2017

A

DOI: 10.1021/acs.macromol.7b00193 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules methods are not reliable and lack of generic reproducibility. This happens because one of the key experimental challenges, i.e., inhomogeneity of B1 magnetic field, was not captured in those studies, and it is indeed the very key hurdle that prevents generic application of these methods for quantitative analysis. The presence of B1 field inhomogeneity leads to anomalous polarization transfer and phase behaviors in the obtained spectrum, which also exhibit a dependence across various instruments. The practicality of using DEPT-based experiments for rigorous quantitative analysis is further limited by the difficulty to rigorously and precisely control the flip angle of read pulse across the spectrum width. One of the most effective solutions to address the issue of B1 field inhomogeneity is to implement adiabatic pulses. Though the concept and application of adiabatic pulses have prevailed in the field of magnetic resonance imaging,11 its value has yet been widely recognized by general NMR users, thereby limiting its broad applications. Merkle et al. first recognized the issue of B1 field inhomogeneity with RINEPT and employed adiabatic pulses to mitigate the situation.12 Kupče and Freeman later employed matched pairs of adiabatic pulses to further extend the effective bandwidth accessible to RINEPT.13 Thibaudeau et al. employed polarization transfer with adiabatic pulses for sitespecific isotopic measurement.14 Herein, we report the first successful launch of an effective and robust NMR methodology using polarization transfer with adiabatic pulses for quantitative analysis of polyolefin materials. The method is named quantitative adiabatic refocused insensitive nuclei enhanced by polarization transfer (QA-RINEPT), which enables controllable (predictable) 1H−13C polarization transfer without compromising other experimental aspects (e.g., resolution) so that quantitative and sensitive 13C NMR spectra can be obtained. For the ease of illustration, the rest of this paper will be organized as follows: First, we will briefly discuss the theory and key experimental aspects related to polarization transfer based experiments. Second, we will use a model compound to compare experimental results with theoretical prediction to comprehensively evaluate QA-RINEPT on different NMR instruments, the result of which provides a solid basis for controllable polarization transfer using such a technique. Third, the quality of representative quantitative 13C NMR spectra obtained by different methods and instruments is compared to further demonstrate the superior novelty of QA-RINEPT in quantitative analysis. Finally, successful application of QARINEPT on polymeric materials will be presented. In all cases studied, the gain of sensitivity by QA-RINEPT is comparable to or even better than that offered by the cryogenic probe.

Scheme 1. Pulse Sequences of (a) DEPT, (b) RINEPT Using Hard 180 Pulses, and (c) QA-RINEPTa

a

Narrow and wide solid (green) boxes represent hard 90 and 180 pulses, respectively. The patterned boxes represent adiabatic 180 inversion and refocusing pulses. τ, τ1, and τ2 are time intervals that modulate the level of polarization transfer.

focus is to establish it as a generic and robust protocol for quantitative analysis. Let S and I be the respective spin operator of X nuclei (13C in this case) and 1H, which are initially in the Sz and Iz state, and they evolve as the pulse sequence progresses. The first part of the sequence (901H-τ1-1801H,13C-τ1901H,13C) generates in-phase Sx and antiphase magnetization IzSx (i.e., NMR signal), which are then converted into antiphase IzSy and in-phase Sy signal, respectively, by the second 180 refocusing pulse (-τ2-1801H,13C-τ2). In the presence of proton decoupling, the antiphase components (IzSy) cancel out each other, leaving only the in-phase part Sy detected. By converting IzSx into Sy, the polarization of Iz (1H signal) is automatically transferred to Sy; thereby, the sensitivity of X nucleus signals is enhanced. In the absence of pulse imperfection and spin relaxation, the signal enhancement factor ACHn associated with RINEPT or DEPT for different aliphatic carbons, i.e., CHn groups (n = 1, 2, 3), can be expressed by the following equations:8,9

2. THEORY The original work on polarization transfer via chemical bond dates back to the pioneer work on INEPT by Morris and Freeman.15 Ernst et al. later established RINEPT by adding the refocusing pulses to the INEPT sequence.8 In the following years, Doddrell and co-workers developed the methodology of distortionless enhancement by polarization transfer (DEPT),16 which overcame the peak distortion in coupled 13C NMR spectra acquired by INEPT. For illustration, Scheme 1 compares the pulse sequences of (a) DEPT, (b) RINEPT using hard 180 pulses, and (c) QA-RINEPT. The product operator formalism is well suited to describe the evolution of NMR magnetization during each pulse sequence, and detailed information can be found elsewhere.17−19 For simplicity, we briefly describe the mechanism of RINEPT since our main

⎛γ ⎞ ARINEPT,CHn(t ) = n⎜⎜ 1H ⎟⎟ sin(πJCH t ) cosn − 1(πJCH t ) ⎝ γ13C ⎠ B

(1)


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Macromolecules

Figure 1. Theoretical signal enhancement of aliphatic CHn groups by polarization transfer techniques: DEPT vs RINEPT. Signal enhancement factor ACHn is modulated by the flip angle of read pulse θ in DEPT and refocusing time t in RINEPT. One of the good points chosen is located at θ = 48° and t = 2.15 ms, and the theoretical enhancement factor reaches ∼4.0 for both CH2 and CH3 groups and ∼3.0 for the CH group.

⎛γ ⎞ ADEPT,CHn(θ ) = n⎜⎜ 1H ⎟⎟ sin(θ ) cosn − 1(θ ) ⎝ γ13C ⎠

be generically reproduced on different instruments and/or applied to other systems. Consequently, neither DEPT nor RINEPT using hard 180 pulses represents a reliable method to yield quantitative 13C NMR spectra that can be generally utilized by an NMR user. One of the most effective solutions to address the above issue is to replace the hard 180 pulses with adiabatic 180 pulses due to its very low sensitivity to B1 field inhomogeneity.20 In general, adiabatic pulse is a type of phase (i.e. frequency) and amplitude modulated sweeping pulse that scans through a broad range of spectrum width within a finite time (∼2 ms) so that uniform rotation of magnetization (NMR signal) can be generated regardless of the chemical shift. The underlying principle stands on the fact that by slowly sweeping the frequency across the spectrum, the adiabatic condition can be achieved, meaning that the rate of change in Beff field orientation is much slower than the characteristic Rabi frequency γBeff (rotation frame).20,21 Under such a condition, all the magnetization will follow the “reorientation” of Beff field during the sweeping pulse; thereby, uniform rotation can be fulfilled for all resonances in the spectrum. As a result, rigorous control of polarization transfer can be achieved across a broad range of spectrum width to yield quantitative 13C NMR spectra.

(2)

Here, γ1H and γ13C represent the gyromagnetic ratios of 1H and 13 C nuclei, respectively. n is the number of protons per CHn group. JCH is the one bond coupling constant, θ is the flip angle of read pulse, and t = 2τ2 is the total refocusing time. The above equation rests on the premise that τ = 1/(2JCH) and τ1 = 1/ (4JCH), which remains valid for the current discussion unless otherwise specified. In the absence of JCH variation, DEPT and RINEPT have identical format of polarization transfer function where ACHn varies with either θ or t with a specific periodicity, depending on the number of attached protons, i.e., n value. Figure 1 illustrates the above statement by comparing the theoretical curves of signal enhancement for different CHn groups as a function of θ (DEPT) and t (RINEPT). Since polyolefin is essentially an assembly of covalently connected CHn groups, it is tempting to optimize and control the polarization transfer for quantitation. Consequently, the first nonzero crossing point of CH3 and CH2 curves located at θ = 48° and t = 2.15 ms (dashed line) can be chosen as the “good point” (the point that is good for quantitative analysis) for quantitative analysis because (1) the average of ACHn reaches its maximum, (2) only ACH needs to be corrected by a response factor of ∼0.76 since ACH2 = ACH3, and (3) t ∼ 2.15 ms is relatively short that minimizes the signal loss and bias in quantitation caused by spin relaxation. Ideally, both DEPT and RINEPT are capable of generating quantitative 13C NMR spectra via calibrating the response factor at the “good point”. One can also purposely vary experimental parameters, e.g., θ and τ, and repeat the experiment in a constructive way to generate uniform enhancement across a broad range of J coupling constants.10 In practice, quantitative 13C NMR spectra necessitate rigorous control of polarization transfer, which, in general, presents a challenge to X nuclei (e.g., 13C, 19F, and 29Si) on high field NMR instruments since uniform rotation (inversion or refocusing) of spin magnetization by hard 180 pulses is very difficult as limited by the homogeneity of B1 field over a broad spectrum width. The situation may also depend on the instrument and experimental parameters, e.g., NMR probe, coil geometry, and carrier frequency. Though it might be possible to meticulously adjust the experimental parameters to minimize the effect of B1 inhomogeneity under some circumstances, the success is quite probe limited and cannot

3. EXPERIMENTAL SECTION 2-Ethylhexyl acrylate (2-EHA) was obtained from Aldrich and used as a model compound to prepare two separate solutions containing 5 and

Table 1. Instrumental Information and 90° Pulse Duration for Respective 1H and 13C Channels instrument

console

A. 400 MHz

nanobay

B. 400 MHz

microbay

C. 400 MHz

microbay

probe conventional 5 mm conventional 10 mm cryoprobe 10 mm

90° pulse of 1 H (μs)

90° pulse of 13 C (μs)

15.0

9.25

26.0

14.0

16.5

11.4

20 wt % of 2-EHA in deuterated 1,1,2,2-tetrachloroethane-d2 (TCEd2). Each solution also contained 1 mM chromium(III) acetylacetonate as the relaxation agent, which enables all resonances to quickly reach equilibrium for fast experimental repetition using multiple scans to save experimental time without significantly sacrificing the spectra resolution. 0.6 mL of the 20 wt % solution was transferred into a 5 mm NMR tube. 2.5 mL of the 5 wt % solution was transferred into a 10 mm NMR tube. These two solutions were used as the standard to C


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Figure 2. QA-RINEPT of aliphatic groups of 2-EHA on two NMR instruments: experimental vs theory. Experimental data of signal enhancement for different CHn groups are plotted as a function of refocusing time, t. The data associated with each CHn group show excellent fitting using eq 3 and consistently yields the same fitting parameters to demonstrate the robustness of the method. At the good point (designated by the arrow), the enhancement factor ACHn = 2.5, 3.3, and 3.3 for CH, CH2, and CH3, respectively. The error bar associated with the relative ratio among different ACHn (e.g., ACH/ACH2) is 2−3%.

Table 2. Fitting Parameters C0,n and τ0,n Based on Eq 3 instrument

C0,CH

C0,CH2

C0,CH3

τ0,CH (ms)

τ0,CH2 (ms)

τ0,CH3 (ms)

C0,Ave

τ0,Ave

B C

0.83 0.82

0.83 0.81

0.87 0.86

0.65 0.71

0.68 0.73

0.66 0.70

0.84 0.83

0.66 0.71

Figure 3. 13C NMR spectra of 2-EHA (aliphatic region) by single pulse and QA-RINEPT methods. Aliphatic carbon peaks of 2-EHA are labeled by numbers. Both of the single pulse and QA-RINEPT methods recorded the same number of scans. The spectral noise has been adjusted to the same level for direct comparison of sensitivity. for 13C. For DEPT, τ = 1/(2JCH) = 4 ms and θ = 48°. For RINEPT, τ1 = 1/(4JCH) = 2 ms and t = 2.15 ms. For QA-RINEPT experiment, the adiabatic 180 pulses consisted of 2 ms composite chirp pulses that covers a bandwidth of 60 kHz (Crp60comp.4). τ1 is fixed at 2 ms, and τ2 varied from 0.75 to 3.6 ms.

evaluate the quality of quantitative 13C spectra obtained by different instruments and methods. Polyolefin samples were prepared using manufacture grade ethylene−octene copolymer (EO). Typically, 0.2 g of sample was added into a 10 mm NMR tube containing 2.5 mL of TCE-d2 with 8 mM relaxation agent. The sample was heated to 110 °C and constantly inverted back and forth until the sample flowed homogeneously. 13C NMR experiments employed single pulse and polarization transfer methods on three different Bruker instruments, and detailed instrumental information is listed in Table 1. Typically, 8−2048 scans were recorded with two dummy scans to yield adequate signal-to-noise ratio (SNR). An acquisition time of 1.5 s was used, and the relaxation delay (d1) was set to at least 5× the longitudinal relaxation time T1 for 1H and 13C, depending on the experiment and sample. The carrier frequency was set at 1.2 ppm for 1H and 90 ppm

4. RESULTS AND DISCUSSION 4.1. Controllable Polarization Transfer by QA-RINEPT. Figure 2 shows the experimental data and fitting results of ACHn for different aliphatic CHn groups as a function of refocusing time t. The results obtained on two NMR instruments (B and C) are also compared. Each ACHn curve is fitted using the following equation based on eq 1: D


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Macromolecules

Figure 4. Comparison of quantitative 13C NMR spectra by three methods: DEPT, RINEPT and QA-RINEPT. The spectra were collected on three Bruker 400 MHz instruments equipped with 5 mm (A), 10 mm (B) and cryogenic probes (C). 48 degree read pulse and a refocusing time of 2.15 ms were chosen for DEPT and RINEPT respectively to generate quantitative 13C spectra with ICH=0.76ICH2=0.76ICH3. Different levels of phase anomalies resulted from the inhomogeneity of B1 field and its dependence on instruments. Defect−free quantitative 13C spectra were obtained consistently on all instruments using QA-RINEPT, which is designed to effectively eliminate the effect of B1 inhomogeneity.

⎛γ ⎞ A CHn(t ) = nC0, n⎜⎜ 1H ⎟⎟ sin(πJCH (t − τ0, n)) ⎝ γ13C ⎠ × cosn − 1(πJCH (t − τ0, n))

CH groups, respectively, at the good point (t = 2.92 ms) on both instruments. With these response factors, one can rigorously calibrate the obtained 13C NMR spectra for quantitative analysis. In particular, it is worth emphasizing that the ratio of ACH/ACH2 (or ACH3) = 0.76 ± 0.02 remains the same as its theoretical prediction, which strengthens the reliability of QA-RINEPT for quantitative analysis. 4.2. Spectra Quality by QA-RINEPT. Figure 3 exhibits the representative 13C NMR spectra of 2-EHA obtained by the single pulse and QA-RINEPT methods (t = 2.92 ms). Here, only the region of interest, i.e., aliphatic region, is shown for comparison. With the spectral noise being adjusted to the same level, one can directly compare the spectral sensitivity by each method. Using the response factor (ACH/ACH2 (or ACH3) = 0.76) derived from previous session, the spectra by QARINEPT also shows the quantitative characteristic as expected. Figure 4 further compares the quality of quantitative 13C NMR spectra of 2-EHA (aliphatic region) obtained on three 400 MHz NMR instruments (A, B, and C) using three different methods: DEPT, RINEPT, and QA-RINEPT. For DEPT and

(3)

Here, JCH = 125 Hz is used for all CHn groups. The fitting parameters are C0,n and τ0,n. C0,n is a correction factor accounting for the loss of polarization transfer due to any experimental imperfection. τ0,n is a time constant that characterizes the shift of ACHn along the time axis due to the relatively long duration of adiabatic pulses (2 ms). All the fitting results are listed in Table 2. In general, the polarization transfer theory (eq 3) well describes all the experimental data, which also consistently yields almost the same average value of C0,Ave and τ0,Ave for the two instruments, demonstrating the genericity and robustness of QA-RINEPT (the minor difference in τ0,Ave has a negligible effect). The key purpose of fitting ACHn curves in Figure 2 is to determine the mathematical formula of ACHn to find the location of good points. As designated by the arrow in Figure 2, ACHn reaches 3.30, 3.30, and 2.50 for CH3, CH2, and E


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Figure 5. Quantitative 13C NMR spectra of ethylene/octene (EO) copolymer using different methods. (a) 13C spectrum by QA-RINEPT in 20 mins of total data acquisition time and (b) 13C spectrum by the single pulse experiment using 14.25 hrs of data acquisition time. The peaks of CH groups are labeled, the integration of which should be corrected by the response factor for quantitative analysis. The noise level has been adjusted to the same in both spectra for direct comparison. The average peak intensity in (a) is still ∼20−30% higher than those in (b).

Table 3. Composition of an EO Sample by Two Analysts Using 13C NMR Spectra Obtained by Different Methods mole fraction

weight fraction

analyst

NMR method

ethylene

octene

ethylene

octene

analyst 1

single pulse QA-RINEPT single pulse QA-RINEPT

0.872 0.872 0.875 0.871

0.128 0.128 0.125 0.129

0.631 0.631 0.636 0.628

0.369 0.369 0.364 0.372

analyst 2

Table 5. Composition of EO Samples with Melting Index (MI) Variations by Different Methods mole fraction (single pulse)

RINEPT, 48° flip angle of the read pulse and a refocusing time t = 2.15 ms were purposely applied, respectively, with the aim to yield 13C spectra with peak integration ICH = 0.76ICH2 = 0.76ICH3. Here, the integration range is about 70× broader than the half-width of each peak, and we consistently integrated the same range of chemical shift for a given peak to make a fair comparison among different methods. After taking the response factor (ICH = 0.76ICH2 = 0.76ICH3) into account, all peaks in the QA-RINEPT spectra yield the same integration within experimental uncertainty, demonstrating the quantitative and high quality features of the QA-RINEPT methodology. This is true for all 13C NMR spectra taken at the three instruments. In comparison, neither DEPT nor RINEPT is able to produce the expected quantitative spectra, and various levels of phase anomalies and quantitative error (up to 50%) exist in the spectra, depending on the instrument. One should note that phase anomalies become the worst for cryogenic probe but not quite evident for the 5 mm probe, which is consistent with the expectation that 5 mm probe usually has better B 1

mole fraction (QA-RINEPT)

sample ID

MI

ethylene

octene

ethylene

octene

EO-1 EO-2 EO-3

0.5 1 5

87.3 91.2 87.9

12.7 8.8 12.1

87.2 91.1 87.6

12.8 8.9 12.4

homogeneity. Nevertheless, even using the 5 mm probe (instrument A), quantitative error is still up to >20% with DEPT. Among all, only QA-RINEPT consistently and rigorously yields the high quality quantitative 13C spectra to further demonstrate the novelty of QA-RINEPT for quantitative analysis. 4.3. Quantitative Analysis of Polyolefin by QARINEPT. Upon validation of QA-RINEPT using the model compound, we further examine its applicability to polyolefin samples at elevated temperatures. Figure 5 compares the respective 13C NMR spectra of an ethylene−octene (EO) copolymer obtained by QA-RINEPT and single pulse experiments using the conventional probe (instrument B). As shown in the figure, the gain in sensitivity per unit time has been boosted up by ∼7−8× using QA-RINEPT as compared to the single pulse method. Such a gain in sensitivity is partially due to the fast repetition of the experiment since QA-RINEPT relies on the longitudinal relaxation T1 of 1H, which on average is 4− 7× shorter than that of 13C. More importantly, the transverse

Table 4. Monomer Sequence Distribution of an EO Sample by Two Analysts Using 13C NMR Spectra Obtained by Different Methods

analyst 1 analyst 2

method

EEE

EEO + OEE

OEO

OOO

OOE + EOO

EOE

single pulse QA-RINEPT single pulse QA-RINEPT

0.673 0.665 0.675 0.663

0.187 0.194 0.184 0.194

0.012 0.014 0.015 0.013

0.003 0.000 0.001 0.002

0.037 0.033 0.034 0.033

0.088 0.094 0.09 0.095

F


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Macromolecules relaxation time T2 for 1H falls in the range of 200−400 ms for all peaks. Thus, even in the presence of a few milliseconds (∼6 ms) 1H relaxation weighting during the 2τ1 period (including the adiabatic pulse duration), the relative error among peak integrations is expected to be less than 2%. Such a statement is reaffirmed by the data analysis shown below in Tables 3 and 4, which summarize the composition and chain sequence distribution analyzed by two different analysts using the method established previously.22 Again, a correction factor of 0.76 is applied to the CH group for quantitative analysis. Table 5 further compares the compositional analysis of EO samples with different melting index, i.e., molecular weights, based on 13 C spectra acquired by different methods. Overall, the data acquired by single pulse and QA-RINEPT show excellent agreement and confirm the applicability, reliability, and efficiency of QA-RINEPT for analyzing polyolefin materials. 4.4. Limitations with QA-RINEPT and Its Prospective Applications. Despite the key advantage offered by QARINEPT in quantitative analysis, information on quaternary carbons is not accessible via the method. It is also worth mentioning that the reliability of QA-RINEPT depends on the shortest T2 value as well as its range among different peaks for a given system, although most liquid samples have a relatively long T2 value (>100 ms). As we discussed in the previous session, QA-RINEPT is well suited for polyolefins because even in the presence of a relatively high level of relaxation agent, T2 (both 1H and 13C) is adequately long and its range is not very broad. Thus, the relative quantification error among each peak due to unequal relaxation weighting is negligible. However, in the presence of relatively fast T2 relaxation (T2 ∼ 30−50 ms) due to a rigid backbone or a hard segment, the quantitative error by QA-RINEPT can reach 10−20% unless the range of T2 is very narrow. If T2 relaxation is very fast, e.g. T2 ≪ 10 ms, QA-RINEPT will not yield any 13C signal even if the carbon has an attached proton. Similarly, a high concentration of relaxation agent usually leads to fast T2 relaxation (broad line width) and causes large errors in quantitative analysis. This, however, is usually not a practical concern based on our experience since 2−3 mM of relaxation agent is often adequate to reduce T1 for practical purpose without causing significant line broadening. Furthermore, inhomogeneity is associated with both 1H and 13 C pulses, and the inhomogeneity of 13C 180°pulse is the major limiting factor that prohibits quantitative analysis using QA-RINEPT. Also, given the fact that the 1H spectra window covered by polyolefin is quite narrow (∼1 ppm), the inhomogeneity of 1H 180° pulse is not the success limiting factor. One can check if the inhomogeneity of 1H 180° pulse causes a major problem in quantitative analysis by changing the carrier frequency of the 1H pulse. If the range of the 1H chemical shift is broad and the homogeneity of the 1H 180°pulse is poor, implementation of 1H 180° adiabatic pulses is necessary. The inhomogeneity of 90°pulse may also become an issue with higher field instrument, e.g., 900 MHz NMR spectrometer. In such a case, the development of more sophisticated pulse sequence involving 90°adiabatic pulses is likely necessary. However, it is nontrivial to synchronize 90° adiabatic pulses with the QA-RINEPT sequence, and it would be interesting to explore such an idea in the future. When the above “defects” become a minor concern, the fitted ACHn results can be used as the master curves to predict and calibrate any given sample as long as JCH is known. Thus, the QA-RINEPT can potentially be extended to other appropriate systems, including polyols, polybutadiene, and

end-group analysis. Beyond the current scope on polymers, QA-RINEPT should allow organic chemists to quickly evaluate or screen the molecular structure of their synthesized compound, such as drug molecules to determine if further time-consuming quantitative 13C NMR using the single pulse method is needed.

5. CONCLUSION QA-RINEPT enables generation of sensitive and high quality 13 C NMR spectra for quantitative analysis. The methodology has been evaluated and validated both theoretically and experimentally using a 2-EHA as the model compound on three 400 MHz NMR instruments equipped with different consoles and probes. Different NMR instruments consistently yield the same ACHn curves, which form the basis for calibrating the 13C NMR spectra for subsequent quantitative analysis. Using the good point, all three instruments consistently yield the same quantitative 13C NMR spectra, which also agrees with theoretical prediction. The novelty and reliability of QARINEPT have been further demonstrated by applications to polyolefin materials with different molecular weight. The composition and chain sequence distribution of two polymer samples have been analyzed by two different analysts, from whom excellent agreement has been achieved. The difference in obtained polymer composition is less than 1% when comparing QA-RINEPT with the single pulse method. By far, our obtained sensitivity per unit time can be boosted up to ∼7−8× , i.e., saving 50−60× experimental time.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel +1-989-636-9711 (J.H.). ORCID

Jianbo Hou: 0000-0001-9714-6484 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Dr. David Redwine and Dr. Kebede Beshah for discussions and reading the manuscript. The authors thank Dr. David Redwine for suggesting the acronym of QARINEPT.

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REFERENCES

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Speedy, Robust and Quantitative Analysis of Polyolefins Using

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