AI-Optimized Quantitative RINEPT (AIOQ-RINEPT) 1D ¹³C NMR for Rapid Polyolefin Microstructure Analysis

Abstract

Polyolefins, which are vital materials in a wide range of industries, demand accurate and rapid microstructural analysis to enhance and optimize their performance characteristics. Triad sequence distributions are widely used to evaluate critical parameters, including comonomer content, monomer number-average sequence length, and the blockiness Koenig B value. While conventional algebraic methods for determining these values often lack accuracy, this study presents a more precise approach based on matrix operations. Traditional quantitative ¹³C NMR has long served as the primary technique for analyzing polyolefin microstructures. However, its low sensitivity and lengthy acquisition time limit high-throughput analysis and hinder the practical determination of certain microstructural details. To overcome these limitations, we propose a synergistic approach that combines chromium­(III) acetylacetonate (Cr­(acac)₃), a relaxation agent, with an artificial intelligence (AI)-optimized quantitative RINEPT (AIOQ-RINEPT) pulse sequence. Using a customized simulated annealing algorithm, a machine learning technique commonly used in AI model training, we optimized the variable delays τ₂ in the RINEPT sequence while keeping the delay τ₁ fixed. This optimization leads to uniform sensitivity enhancement across CH, CH₂, and CH₃ signals. The AIOQ-RINEPT technique, incorporating triply compensated 180° pulses (G5), ensures a broad excitation bandwidth. This method achieved a 7.5-fold increase in sensitivity, equivalent to a 56.3-fold reduction in acquisition time compared to conventional inverse-gated ¹³C NMR. When combined with cryoprobe technology, a 41.3-fold improvement in sensitivity could be realized, resulting in a 1,706-fold decrease in acquisition time, making high-throughput analysis feasible. Experimental validation using a poly­(ethylene-co-1-butene) (EB) copolymer with a sufficiently high weight-average molecular weight (M _w = 120,700 kg/mol) demonstrated accurate quantification of triad sequence distributions, comonomer content, and blockiness parameters. Two additional EB samples with lower weight-average molecular weights (M _w = 86,000 and 58,000 kg/mol) were also employed to further validate the method. The method also effectively resolved signal overlap issues commonly encountered in samples with a high comonomer content. Moreover, the approach is broadly applicable to a wide range of polyolefins. This advancement enables rapid, automated ¹³C NMR analysis of virgin and recycled polyolefins, allowing high-throughput characterization and sensitive detection of low-abundance features like long-chain branching (LCB). Additionally, the technique is suitable for analyzing low molecular weight saturated hydrocarbons, including Fischer–Tropsch products, such as waxes, lubricating oils, and jet fuel.

Introduction

Polyolefins, primarily composed of polyethylene (PE) and polypropylene (PP), represent one of the most widely used classes of polymers globally with a market value of approximately 160 billion USD. These materials are typically derived from natural gas, coal, or petroleum feedstocks. Notably, the large-scale production of coal-based PE and PP was established in China starting in 2012. Key types of polyethylene include high-density polyethylene (HDPE), low-density polyethylene (LDPE), linear low-density polyethylene (LLDPE), polyolefin elastomers (POEs), and PE and PE/PP block copolymers. The main polypropylene variants consist of isotactic polypropylene (iPP), syndiotactic polypropylene (sPP), atactic polypropylene (aPP), impact copolymers (ICP), and ethylene-propylene rubber (EPR), as well as PP and PP/EPR block copolymers.

PE and PP are widely utilized across numerous industries, including packaging, batteries, agriculture, electronics, healthcare, construction, chemicals, textiles, automotive, and military applications. Their performance is strongly influenced by their microstructures, which govern key morphological features such as crystallinity, crystallite size, and the presence of tie chains connecting adjacent crystallites. These structural characteristics, in turn, determine critical physical properties such as toughness, rheological behavior, creep resistance, interfacial adhesion in multilayer films, and failure mechanisms. Despite being composed exclusively of carbon and hydrogen atoms, PE and PP can exhibit a diverse range of microstructures due to variations in the arrangement of these atoms. Even minor changes in the microstructure can result in substantial differences in material properties, allowing for improved or customized performance suited to particular applications.

One-dimensional (1D) ¹³C NMR has long served as the primary analytical technique for investigating the microstructures of PE and PP. − However, the technique suffers from inherently low sensitivity due to several fundamental properties of the ¹³C nucleus: its low natural abundance (1.1%), its relatively small gyromagnetic ratio (γ)-which defines the ratio of angular momentum to magnetic dipole moment, and its long spin–lattice relaxation time (T ₁). These factors collectively result in extended acquisition time, limiting the efficiency and applicability of conventional ¹³C NMR in polyolefin characterization.

To improve the sensitivity of ¹³C NMR, a highly effective approach is the use of a 10 mm high-temperature cryogenically cooled NMR probe (cryoprobe), which can enhance the sensitivity by approximately 5.5-fold. , This improvement translates to an ∼30-fold reduction in acquisition time (5.5² ≈ 30), − significantly accelerating data collection. However, the widespread adoption of this technique is limited by its high cost and low global availability; only a few dozen 10 mm cryoprobes are currently in use, restricting access in most NMR laboratories. Although much less effective than a cryoprobe, chromium­(III) acetylacetonate (Cr­(acac)₃) can serve as a practical alternative by acting as a relaxation agent that effectively reduces T ₁, enabling shorter NMR acquisition time without the need for advanced hardware. −

Distortionless Enhancement by Polarization Transfer (DEPT) and Refocused Insensitive Nuclei Enhanced by Polarization Transfer (RINEPT) are established NMR techniques used to enhance spectral sensitivity. , Henderson introduced a quantitative DEPT (Q-DEPT) method based on two-dimensional quantitative heteronuclear single quantum coherence (Q-HSQC) spectroscopy. , This approach involves cycling selected polarization transfer delays and read pulse angles, offering a theoretical sensitivity improvement of approximately 2.3-fold, although no experimental validation of this enhancement was provided. Jiang et al. noted that Henderson’s method was effective primarily for CH signals and proposed an improved variant known as Q-DEPT⁺. Additionally, they developed the Quantitative Phase Oscillations to Maximize Editing (Q-POMMIE) method to achieve uniform sensitivity enhancement across CH, CH₂, and CH₃ signals. Using these approaches, they reported a 1.6-fold increase in sensitivity. Furthermore, the authors evaluated the influence of spin–spin relaxation time (T ₂) and concluded that experimental reliability remains largely consistent, provided the T ₂ values of the signals involved are of the same order of magnitude.

Quantitative 1D ¹³C NMR spectroscopy using refocused constant-time INEPT (Q-INEPT-CT) for uniform sensitivity enhancement across CH, CH₂, and CH₃ signals was first introduced by Mäkelä et al., who demonstrated an approximately 1.8-fold improvement in sensitivity. Unlike DEPT, which depends on modulating radio frequency (RF) pulse lengths, Q-INEPT-CT enhances the sensitivity by adjusting the delay times within the INEPT pulse sequence. This approach significantly reduces the sensitivity to RF inhomogeneity, offering greater experimental robustness. Manu and Kumar later investigated Q-INEPT-CT as well, confirming a comparable 1.8-fold uniform improvement in sensitivity.

Duan et al. employed RINEPT to selectively enhance the sensitivity of CH₃ signals for the analysis of tacticity in PP. Zhou et al. applied the same technique to improve the detection of CH₂ signals in LDPE, integrating RINEPT with conventional quantitative 1D ¹³C NMR to accurately quantify long-chain branching (LCB). Hou et al. introduced an adiabatic RINEPT approachreferred to as the “good point” methodthat provided uniform sensitivity enhancement for both CH₂ and CH₃ signals; then, they applied a correction factor to the CH signal integrals, equalizing sensitivity enhancement among CH, CH₂, and CH₃ groups. This enabled the determination of comonomer content in poly­(ethylene-1-octene) (EO) copolymers with octene concentrations ranging from 8.8 to 12.7 mol %.

However, the method proposed by Hou et al. requires calibration across three distinct groups of CH signalsEOE (EXE), EOO (EXX), and OOO (XXX)where EXE, EXX, and XXX represent triads and X denotes the comonomer. For some polyolefins, such as EO with higher octene content, overlapping CH and CH₂ signals prevent the calibration. Another example is poly­(ethylene-1-butene) (EB) with butene comonomer content exceeding 12 mol %, where the CH_EBE signal overlaps with the αα_BBBE CH₂ signal, while the CH_BBB signal overlaps with the αγ_BBEBB and αγ_BBEBE CH₂ signals. Additionally, experimentally determining the optimal “good point” for the adiabatic RINEPT sequence is not only laborious and time-intensive but also limits the practical applicability of this method for routine analysis.

Very recently, an automated ultrafast ¹³C NMR analysis of polyolefin materials was reported. However, this ultrafast approach requires high-throughput generation of ¹³C NMR data to close the analytical loop-particularly challenging when dealing with the small sample quantities typically produced in parallel pressure reactor experiments during R&D. Therefore, a quantitative high-speed 1D ¹³C NMR method based on the RINEPT technique is urgently needed to simultaneously enhance the ¹³C NMR signals of CH, CH₂, and CH₃ groups in polyolefins. Such a method would greatly facilitate microstructural analyses, including the determination of comonomer content, triad sequence distribution, monomer number-average sequence length, and blockiness (Koenig B value). − In this work, we introduce a fast and accurate polyolefin characterization technique that integrates a relaxation agent, Cr³⁺, with an AI-optimized quantitative RINEPT (AIOQ-RINEPT) 1D ¹³C NMR approach. The method was validated using a sufficiently high weight-average molecular weight (M _w = 120,700 kg/mol) poly­(ethylene-1-butene) (EB) sample containing 0.025 M Cr³⁺, achieving a 7.5-fold simultaneous sensitivity enhancement across CH, CH₂, and CH₃ signals. Two additional EB samples with lower weight-average molecular weights (M _w = 86,000 and 58,000 kg/mol) were also employed to further validate the method. This improvement translates to a 56.3-fold reduction (7.5²) in NMR acquisition time compared to a conventional inverse-gated ¹³C NMR experiment conducted under the same conditions with Cr³⁺. When implemented on an NMR spectrometer equipped with a cryoprobe of the same field strength, the method could yield a 41.3-fold (7.5 × 5.5) overall sensitivity gain, leading to a 1,706-fold reduction (41.3²) in total acquisition time. This advancement dramatically accelerates both routine and in-depth microstructural analyses of virgin and recycled polyolefins, while enabling the detection and precise characterization of low-abundance structural features, such as LCBthat were previously difficult to analyze. It also enables high-throughput, AI-driven automated ¹³C NMR analysis, significantly enhancing the speed and accuracy of polymer characterization. Beyond polyolefins, the technique is also applicable to the analysis of low molecular weight saturated hydrocarbons, including foam blowing agents, aerosol propellants, refrigerants, soybean oil attractants, adhesives, paints, cleaning agents, and fuel additives such as antiknock agents, as well as Fischer–Tropsch products like waxes, lubricating oils, and jet fuel. This broad applicability extends the utility of the method beyond polymer science to diverse industrial and chemical domains.

NMR Experiments

A relatively high molecular weight EB was selected for this study to investigate the effects of T ₂ relaxation during the application of the AIOQ-RINEPT pulse sequence. A melt index (MI) of 0.41 g/10 min was measured with ASTM D1238 procedure B, and a weight-average molecular weight (M _w) of 120,700 kg/mol was measured with ASTM D6474-19 (procedures are detailed in Supporting Information). Two additional EB samples with lower weight-average molecular weights (M _w = 86,000 and 58,000 kg/mol) were also employed. Cr­(acac)₃ was sourced from Sigma-Aldrich and used without further purification; a concentration of 0.025 M Cr­(acac)₃ was used. Tetrachloroethane-d₂ (TCE-d ₂, 99.9% D) was purchased from Cambridge Isotope Laboratories. NMR experiments were conducted at 120 °C with a 400 MHz Bruker Avance III NMR spectrometer equipped with a 10 mm BBO probe. For ¹³C NMR, the bi-Waltz65-256pl ¹H decoupling method was employed, , with the ¹H NMR decoupling offset and the ¹³C transmitter offset at 1.2 and 25.3 ppm, respectively. The chemical shift of the EEE triad was referenced to 30.0 ppm. Using the inversion recovery method, the T ₁ relaxation times for ¹H and ¹³C were measured as 0.19 and 1.23 s, respectively, for the CH₃ group in EB with 0.025 M Cr­(acac)₃. Seven times the measured ¹³C and ¹H T ₁ values were used as recovery delays (D ₁ + AQ) in conventional inverse-gated ¹³C NMR (D ₁ = 7.0 s, AQ = 1.6 s) and RINEPT (D ₁ = 0.6 s, AQ = 0.8 s) pulse sequences, respectively. , This reduction in recovery delay from 8.6 to 1.4 s yields a time-saving factor of 6.14, corresponding to a 2.48-fold hypothetical sensitivity enhancement. Detailed experimental parameters are provided in the section Results and Discussion and the Supporting Information.

AI-Optimized Searching for τ₂ Using Simulated Annealing

RINEPT can enhance the sensitivity of CH, CH₂, and CH₃ signals. The enhancement factors E are described in eqs 1S–3S, and they depend on pulse delays of τ₁ and τ₂. A 3D visualization for the first time is presented in Figure . Clearly, the dependence is complicated.

1.

Dependence of E on τ₁ and τ₂ in eqs 1S–3S.

In eqs 1S–3S, J is the one-bond heteronuclear scalar J coupling constant between ¹H and ¹³C, where γ_H and γ_C are gyromagnetic ratios for proton and carbon, respectively. The J coupling constant is approximately 125 Hz for polyolefins. First, eqs 1S–3S were used for Monte Carlo simulations to obtain sets of τ₂ pulse delays that maximize the sensitivity enhancement factors E _CH, E _CH2, and E _CH3 values while keeping them as close to each other as possible (details are described in Supporting Information). The Monte Carlo method relies solely on random search strategies, which may be inadequate for locating the global optimum in the extensive search space encountered in this study. To address this limitation, we employed a customized simulated annealing algorithm, a type of machine learning algorithm with adaptive and learning behaviors, to find near-optimal solutions to complex problems by mimicking the annealing process in metallurgy. Simulated annealing is widely used in AI applications, such as solving combinatorial optimization problems, tuning hyperparameters while training artificial neural networks, and robotic path planning. It aims to identify the global optimum in a high-dimensional space by iteratively refining the current optimal solution through adaptive adjustments. To address the specific challenges of this study, we modified the default simulated annealing algorithm, aiming to achieve a balance between maximizing the values of enhancement factors and minimizing their variance (see details below). By systematically optimizing the search trajectory, this customized simulated annealing algorithm increases the likelihood of convergence to the global optimum, improving the chances of discovering more optimal τ₂ delay sets.

The customized simulated annealing approach starts by randomly selecting a set of τ₂ delays within the range of 0 to 4 ms while keeping τ₁ fixed. The total enhancement factors and their variations among the CH, CH₂, and CH₃ groups are then calculated and assessed. If the new delay set yields a higher total enhancement factor or reduces variation, it is retained as the current optimal set. The optimization criteria are dynamically adjusted based on the state of the current optimal set. Specifically, if the total enhancement factor is below 3 or the variance is below 0.01, the algorithm prioritizes increasing the total enhancement factor in subsequent iterations. Conversely, when the total enhancement factor reaches 3 or higher and the variance is 0.01 or greater, the algorithm shifts its focus to minimizing variance in the next iteration. If the newly selected delay set does not improve the total enhancement factor or reduce variance, the algorithm may still probabilistically accept it as the current optimal set. This acceptance probability is determined by the initial temperature, the cooling rate (parameters simulating the annealing process), and the current iteration count. In early iterations, the higher probability of accepting nonimproving delay sets promotes broader exploration of the search space, helping to reduce the likelihood of converging to a local optimum.

Additional adaptive strategies were implemented based on the characteristics of the current optimal set. If the current optimal set has a total enhancement factor greater than 3 and a variance below 0.05, then the next iteration involves retaining half of the delay values from the current set and replacing the other half for comparison. When the total enhancement factor exceeds 3.1 and the variance is below 0.01, only one delay value is randomly replaced in the subsequent iteration. In all other scenarios, a completely new delay set is selected for evaluation.

In this optimization process, the initial temperature was set to 100, and the cooling rate was established at 0.995. The search was conducted over 100,000,000 iterations to determine the final optimized τ₂ delay sets. Utilizing this algorithm, optimized τ₂ delay sets were identified for 4, 8, 16, and 32 values.

Results and Discussion

Comonomer content, triad sequence distribution, monomer number-average sequence length, and the blockiness Koenig B value are four key polyolefin microstructure parameters obtained from 1D ¹³C NMR. − Figure presents a 1D ¹³C NMR spectrum of the EB polyolefin, along with the integration range from A to G and peak assignments [note: the integral range A (37–40 ppm) from ref is inaccurate, as it includes the CH signal at 37.2 ppm from EBB and BBE, leading to overestimation of the butene content]. The ¹³C NMR spectrum was acquired by using the conventional inverse-gated method (Bruker “zgig” pulse sequence) with a total acquisition time of 8 h and 40 min.

2.

¹³C NMR spectrum of the EB polyolefin acquired with a “zgig” pulse sequence at 120 °C. The integration A–G ranges were set based on Randall’s report, except range A (integral range A (37–40 ppm) from Randall’s report is inaccurate, as it includes the CH signal at 37.2 ppm from EBB and BBE, leading to an overestimation of the butene content; correct integral range A (38.7–40.4 ppm) is used, as shown in this figure). The assignment nomenclature is shown in Figure S1.

The triad sequence distribution can be calculated from eqs 4S–9S; it should be noted that there was a typo in eq 9S in Randall’s paper, where it should be BBB = 2I_A – I_C instead of BBB = 2I_A – 2I_C, where I _X represents the integral of range X (X being any range from A to G), such as I _A, which is the integral of range A in Figure . The comonomer content of E and B can be calculated using eqs 10S and 11S, respectively. The butene molar ratio B mol % is then easily derived from these calculations. Table S1 summarizes the triad sequence distributions and B mol % for the EB sample (shown in the ¹³C NMR in Figure ) along with data from 4 additional replicate NMR experiments.

This approach has two issues:

• The calculation method discussed above is based on simple algebra, which is not very accurate. A matrix method would yield more accurate results.

• Acquiring a single ¹³C NMR spectrum using the conventional inverse-gated “zgig” method in the presence of 0.025 M Cr³⁺ (with the recovery delay determined by ¹³C T ₁) took 8 h and 40 min. Conducting five experiments required a total of 40 h and 20 min. Therefore, methods that can enhance sensitivity and reduce acquisition time are urgently needed.

The matrix calculation method was briefly outlined for EP in a U.S. patent without details. Here, we provide a detailed explanation of how to establish a matrix calculation method using EB analysis as an example. The same approach can be easily extended to EP, EH, and EO polyolefins. A matrix method is defined by the equation s = f × M, where “s” is a spectrum row vector, “f” is a mole fraction composition vector, and “M” is an assignment matrix. An example of the matrix method to calculate triad sequence distribution and butene molar ratio (B, mol %) in an EB polyolefin is shown in Table .

1. An Example of the Matrix Method for Calculating Triad Sequence Distribution and B mol % in an EB Polyolefin .

Matrix method s = f × M
		A	B	C	D	E	F	G	Sum
	Chemical shift from (ppm)	39.0	37.2	33.9	29.3	26.4	24.1	10.8
	Chemical shift to (ppm)	40.5	37.8	35.4	31.5	28.0	25.2	12.0
	Integral (s vector)	12.65	1.30	24.53	100.00	33.35	2.93	13.29	188.1
	Normalized s vector	0.067	0.007	0.130	0.532	0.177	0.016	0.071	1.0
	f × M	0.155	0.018	0.310	1.239	0.411	0.031	0.164	2.3
	Normalized f × M	0.067	0.008	0.133	0.532	0.176	0.013	0.071	1.0
	(Normalized s vector – Normalized f × M)2	3.9 × 10–7	9.5 × 10–7	6.6 × 10–6	5.2 × 10–8	8.9 × 10–7	4.5 × 10–6	7.7 × 10–9	1.3 × 10–5
Triad	f vector	M
EEE	0.558	0	0	0	2	0	0	0
EEB	0.123	0	0	0	1	1	0	0
EBE	0.145	1	0	1	0	1	0	1
BBE	0.009	1	1	0	0	1	0	1
BEE	0.123	0	0	1	0	1	0	0
EBB	0.009	0	1	1	0	1	0	1
BEB	0.031	0	0	1	0	0	1	0
BBB	0.001	1	0	1	0	1	0	1

^aB mol % = 100 × (EBE + BBE + EBB + BBB).

The components of the “s” spectrum row vector are the integrals of the seven regions (A to G) shown in Figure . In the “f” mole fraction composition vector, three necessary relationships exist in the EB: BEE = EEB, EBB = BBE, and BEB + EEB = EBE + EBB. Additionally, the sum of the eight triads must equal one. These relationships reduce the eight triads in the “f” mole fraction composition vector to four independent variables. Other constraints are that all triad values should be greater than 0 and less than 1. The assignment matrix M represents the contribution of the carbon atoms in the center monomer unit of each triad to each integral region. Since the “s” row vector contains seven integrals and the “f” mole fraction composition vector consists of four independent variables, the system is overdetermined. This setup helps correct inconsistencies in integrals that may arise from regions of low signal-to-noise (S/N). Microsoft Excel’s solver can be used to minimize the sum of (normalized s vector – normalized f × M)² (shown in bold in Table ) to determine the eight triads and the butene molar ratio (B mol %). The matrix method results are presented in Table . Comparing Table S1 and Table , the values of standard deviation (SD) of all the triads and B mol % are smaller in Table , and no negative triads are observed. This indicates that the matrix method is superior to the algebra method. ,

2. EB Triad Sequence Distributions and B mol % Calculated from the Matrix Method .

Experiment	EEE	BEE-ES	BEB	SE	EBB-BEE	BBB	B mol %
Run 1	0.558	0.246	0.031	0.145	0.018	0.001	16.4
Run 2	0.559	0.246	0.032	0.146	0.018	0.000	16.4
Run 3	0.559	0.241	0.034	0.145	0.018	0.002	16.5
Run 4	0.559	0.243	0.034	0.147	0.018	0.000	16.4
Run 5	0.561	0.246	0.031	0.145	0.017	0.000	16.2
Average	0.559	0.244	0.032	0.146	0.018	0.001	16.4
SD	0.001	0.002	0.002	0.001	0.000	0.001	0.1

^{a 13}C NMR was run with the conventional inverse-gated “zgig” pulse sequence at 120 °C.

Regarding the sensitivity issue, RINEPT can enhance the sensitivity of CH, CH₂, and CH₃ signals (Figure ). The enhancement factor E is defined in eqs 1S–3S, and it depends on pulse delays τ₁ and τ₂ shown in Figure .

3.

NMR pulse sequences. Top: Bruker RINEPT “ineptrd”. Bottom: RINEPT “ineptrdG5” (note that “ineptrd” and “ineptrdG5” use ¹³C 180° hard pulses and triply compensated 180° pulse G5, respectively). Red arrows represent cycling, with τ₂ numbers derived from AI-simulated annealing in this study.

If τ₁ is set to 1/(2J) (for saturated CH, CH₂, and CH₃ groups in polyolefins, J is 125 Hz), eqs 1S–3S can be simplified to the following equations:

$$E_{\mathrm{CH}}=\frac{{\gamma }_{\mathrm{H}}}{{\gamma }_{\mathrm{C}}}\sin (\pi J{\tau }_2)$$

$$E_{\mathrm{C}{\mathrm{H}}_2}=\frac{{\gamma }_{\mathrm{H}}}{{\gamma }_{\mathrm{C}}}\sin (2\pi J{\tau }_2)$$

$$E_{\mathrm{C}{\mathrm{H}}_3}=\frac{3{\gamma }_{\mathrm{H}}}{4{\gamma }_{\mathrm{C}}}[\sin (\pi J{\tau }_2)+\sin (3\pi J{\tau }_2)]$$

Now, the enhancement factor E only depends on τ₂ in the RINEPT pulse sequences.

A visualization of E’s dependence on τ₂ (with τ₁ held constant) can be seen in Figure . Clearly, the enhancement factor E values are not uniform for CH, CH₂, and CH₃ at any given τ₂, complicating the quantitative analyses of the four key polyolefin microstructures discussed earlier. Hou et al. proposed using the crossing point of CH₂ and CH₃ (the “good point”, indicated as a red dot in Figure S2) in an adiabatic version of RINEPT [Bruker “ineptrdsp (Crp60comp.4)” pulse sequence] to achieve equal sensitivity enhancement for both CH₂ and CH₃ signals. They then multiplied the CH signal integrals by a correction factor to normalize the enhancement across CH, CH₂, and CH₃, facilitating the calculation of comonomer content in EO copolymers with octene molar percentages ranging from 8.8% to 12.7%.

However, this normalization is not feasible for certain polyolefins, such as EO copolymers with higher octene content. The same issue arises in EB copolymers with B comonomer content exceeding 12 mol %, where CH and CH₂ signals overlap, as demonstrated by Sahoo et al. (the CH_EBE signal overlaps with the αα_BBBE CH₂ signal; the CH_BBB signal overlaps with αγ_BBEBB and αγ_BBEBE CH₂ signals). Additionally, experimentally determining the optimal “good point” of the adiabatic version of RINEPT “ineptrdsp (Crp60comp.4)” is both labor-intensive and time-consuming, limiting the practicality for routine analyses.

Therefore, we developed the AIOQ-RINEPT technique to achieve the same enhancement for all CH, CH₂, and CH₃ ¹³C NMR signals in polyolefins. To accomplish this, a series of computer-aided Monte Carlo simulations were first conducted to identify an optimal set of τ₂ values in the RINEPT “ineptrd” and “ineptrdG5” pulse sequences (Figure ). Simulations were performed for sets of 8, 16, 32, 64, and 128 τ₂. The results, listed in Table S2, show that 32 τ₂ values provide the highest sensitivity enhancement. The 32 τ₂ values (detailed in the Supporting Information) were applied in subsequent experiments using the RINEPT “ineptrd-vd” and “ineptrdG5-vd” pulse sequences (Figure , where the modified Bruker pulse sequence codes are shown in the Supporting Information).

The average results from five NMR experiments using the AIOQ-RINEPT method, which incorporates Monte Carlo-optimized 32 τ₂ values, are presented in Table S3. For comparison, Table S3 also includes the average results from the five NMR experiments using the conventional “zgig” method. The polymer blockiness Koenig B factor, the ethylene average sequence length (L _E), and the butene average sequence length (L _B) in Table S3 were calculated from the triad results using eqs 12S–14S. , For reference, the Koenig B factors for a fully block, random, and alternating copolymer are 0, 1, and 2, respectively.

Table S3 shows that the two RINEPT pulse sequences “ineptrd-32vd” and “ineptrdG5-32vd” achieved similar S/N in just 12 min as the S/N from the conventional “zgig” pulse sequence with 8 and 40 min of data acquisition. This indicates a sensitivity increase of approximately 6.6-fold for both RINEPT pulse sequences. The improvement can be attributed to the combined effects of the relaxation agent Cr³⁺ and the polarization transfer in RINEPT. It is important to note that the signal sensitivity of the experiment using the “zgig” pulse sequence heavily relies on ¹³C T ₁ relaxation, whereas RINEPT utilizes ¹H T ₁ relaxation to allow magnetization to relax back to the Z-axis. Since ¹H T ₁ is significantly shorter than ¹³C T ₁, this alone accounts for a 2.48-fold increase in S/N (see Experimental section). Additionally, the RINEPT with a Monte Carlo-optimized set of 32 τ₂ values further increased S/N by 2.78-fold (Table S2). The theoretical synergistic effect (2.48 × 2.78 = 6.9-fold) is consistent with our experimental result of 6.6-fold sensitivity enhancement.

The comonomer content of B (16.2 mol %) obtained with the “ineptrd-32vd” pulse sequence was slightly lower than the 16.4 mol % measured with the conventional “zgig” method. This discrepancy may be due to the excitation bandwidth of the two 180° hard pulses of the ¹³C channel being slightly narrower than the required bandwidth for EB (which has a chemical shift range of 29 ppm or 2,918 Hz on a 400 MHz NMR spectrometer). In the “ineptrdG5-32vd” pulse sequence, the two 180° hard pulses of the ¹³C channel were replaced with triply compensated 180° pulses (G5), which can correct off-resonance effects, RF inhomogeneity/miscalibrations, and J modulation. , The length of the “ineptrdG5-32vd” pulse sequence is nearly the same as “ineptrd-32vd”, but its excitation bandwidth for ¹³C on a 600 MHz NMR spectrometer is 120 ppm (∼18,000 Hz) based on our previous study. As shown in Table S3, B mol % obtained using the “ineptrdG5-32vd” pulse sequence matched that of the conventional “zgig” method, while reducing NMR acquisition time by a factor of 43, thanks to the 6.6-fold S/N enhancement.

It should be emphasized that the Monte Carlo method inherently involves a degree of randomness. As such, the optimized τ₂ values obtained may not represent the global optimum, regardless of the number of τ₂ values used. To address this, we employed the machine learning approach of simulated annealing mentioned earlier to further enhance the S/N. Sets with 4, 8, 16, and 32 τ₂ values were explored. The outcomes are listed in Table S4.

Table S4 shows that the enhancement factors are very similar across all tested sets of τ₂ values, and all are higher than the best results obtained using Monte Carlo simulation (Table S2). The minimum number of scans for “ineptrd-vd” and “ineptrdG5-vd” pulse sequences is 4 due to the phase cycle. Therefore, the τ₂ sets with 4 values (3.7969, 2.218, 1.9532, 1.9244 ms) and 8 values (3.8998, 2.0943, 2.0936, 2.2531, 1.9272, 2.0618, 1.7521, 3.6853 ms) from the simulated annealing along with the set of 32 τ₂ values from Monte Carlo simulation (shown in the Supporting Information) are compared experimentally. Table presents the comparison of the NMR results for the 4, 8, and 32 τ₂ sets, with the numbers representing averaged results from five NMR experiment runs.

3. Comparison of the NMR Results from 4 to 8 τ₂ Value Sets (Simulated Annealing) and 32 τ₂ Value Sets (Monte Carlo Simulation) .

NMR method		EEE	BEE + EEB	BEB	EBE	EBB + BBE	BBB	B mol %	Koenig B	L E	L B	NMR time	S/N
ineptrd- 32vd	Average	0.561	0.248	0.029	0.145	0.016	0.000	16.1	1.1	5.5	1.1	5 min	1379
	SD	0.001	0.002	0.001	0.001	0.002	0.000	0.1	0.0	0.0	0.0
ineptrdG5-32vd	Average	0.555	0.250	0.031	0.147	0.017	0.000	16.4	1.1	5.4	1.1	5 min	1340
	SD	0.001	0.001	0.001	0.001	0.002	0.000	0.1	0.0	0.0	0.0
ineptrd-8vd	Average	0.561	0.248	0.029	0.145	0.017	0.000	16.2	1.1	5.5	1.1	5 min	1560
	SD	0.002	0.002	0.002	0.001	0.002	0.000	0.2	0.0	0.1	0.0
ineptrdG5-8vd	Average	0.557	0.246	0.032	0.147	0.017	0.000	16.4	1.1	5.4	1.1	5 min	1575
	SD	0.001	0.001	0.001	0.001	0.001	0.000	0.0	0.0	0.0	0.0
ineptrd- 4vd	Average	0.562	0.243	0.032	0.146	0.016	0.001	16.2	1.1	5.4	1.1	5 min	1531
	SD	0.002	0.004	0.002	0.001	0.001	0.001	0.0	0.0	0.0	0.0
ineptrdG5-4vd	Average	0.559	0.244	0.033	0.147	0.017	0.000	16.3	1.1	5.4	1.1	5 min	1538
	SD	0.001	0.002	0.001	0.001	0.001	0.000	0.0	0.0	0.0	0.0

^aThe numbers are averaged results from five NMR experimental runs .

The same trend was observed for the B mol % values. The “ineptrd-vd” pulse sequence provided slightly lower values (16.1 to 16.2 B mol %) compared to the conventional “zgig” pulse sequence (16.4 B mol %). In contrast, the “ineptrdG5-vd” pulse sequence provided the same B mol % value (16.3 to 16.4 B mol %) equivalent to those from the “zgig” pulse sequence. This discrepancy is likely due to the narrower excitation bandwidth of the “ineptrd-vd” pulse sequence and the broader excitation bandwidth of the “ineptrdG5-vd” pulse sequence. ,

In Table , the sensitivity enhancements using the 4 and 8 τ₂ values (from the machine learning approach of simulated annealing) were higher than those using 32 τ₂ values (from the Monte Carlo simulation), consistent with the predictions from Tables S2 and S4. Based on the results in Tables S3 and , the combined Cr³⁺ and RINEPT sensitivity enhancement with either 4 or 8 τ₂ values is approximately 7.5-fold, translating to a 56.3-fold reduction in NMR acquisition time compared to conventional inverse-gated ¹³C NMR with 0.025 M Cr³⁺. The theoretical synergistic effect [2.48 × 3.12 (Table S4) = 7.7-fold] is consistent with our experimental result of a 7.5-fold sensitivity enhancement. If implemented on an NMR spectrometer with a cryoprobe of the same field strength, the sensitivity could be increased by approximately 41.3-fold (7.5 × 5.5), corresponding to a potential 1,706-fold (41.3²) reduction in acquisition time. This enhancement will not only accelerate routine analyses of polyolefins but also improve the detection of low level polyolefin microstructures, such as LCB.

It is worth noting that the RINEPT pulse sequence is relatively longer than the conventional “zgig” pulse sequence, especially if the adiabatic version of RINEPT is used (the longest is ∼13 ms). Shorter RINEPT, such as our “ineptrdG5-vd” (the longest is ∼8 ms), is recommended to use to minimize T ₂ relaxation losses. Jiang et al. reported that the reliability of polarization transfer experiments remained unaffected as long as the T ₂ values were of the same order of magnitude. Hou et al. reported that the T ₂ values of the protons on saturated carbons of polyolefins were within the same order of magnitude (200–400 ms). With the 8 τ₂ values from simulated annealing: 3.8998, 2.0943, 2.0936, 2.2531, 1.9272, 2.0618, 1.7521, and 3.6853 ms, the average value is 2.4709 ms. For each τ₂ value, the change of signal intensity from the change of the τ₂ value and T ₂ relaxation is 1 – exp­[−|τ₂ – 2.4709|/T ₂]. The average change of signal intensity with the 8 τ₂ values is 0.33% if T ₂ = 200 ms. This change is not significant and can be neglected. To develop our AIOQ-RINEPT (ineptrdG5) method, a representative high molecular weight commercial product (MI 0.41 g/10 min and M _w 120,700 kg/mol) was purposely chosen. Comparing the eight triads and the B mol % numbers in Table (the results obtained from the conventional “zgig” pulse sequence, which is not affected by T ₂ relaxation and serves as a baseline for comparison) and Table (the results obtained from ineptrdG5-4vd and ineptrdG5-8vd) revealed that the numbers are almost the same. This serves as an ultimate assessment of the effect of T ₂ relaxation during our ineptrdG5-4vd and ineptrdG5-8vd pulse sequences. In other words, the method is valid if the MI of the polyolefin in question is higher than 0.41 g/10 min (or M _w is lower than 120,700 kg/mol). This testing approach was also used to validate the QA-RINEPT technique by Hou et al. for analyzing representative polyolefins (MI 0.5–5.0). As anticipated, our method performs particularly well for lower molecular weight samples. Table 5S presents a comparison of 20 NMR measurements on two EB samples with lower weight-average molecular weights (M _w = 86,000 and 58,000 kg/mol), obtained using the conventional zgig pulse sequence (each run lasting 8 h and 40 min) and our new method (each run taking only 12 min).

Conclusions

This study introduces a groundbreaking approach for rapid and accurate microstructural analysis of polyolefins by integrating AI-optimized quantitative RINEPT (AIOQ-RINEPT) ¹³C NMR with Cr­(acac)₃ as a relaxation agent. The method achieves a 7.5-fold sensitivity enhancement compared to conventional inverse-gated ¹³C NMR, translating to a 56.3-fold reduction in acquisition time. This enables high-throughput characterization of critical microstructural parameters, including triad sequence distributions, comonomer content, and blockiness (Koenig B value). When combined with cryoprobe technology, the sensitivity improvement could escalate to 41.3-fold, reducing experimental times by 1,706-fold and enabling unprecedented capabilities for trace structural analysis, such as detecting low-abundance long-chain branching (LCB). The AI-driven optimization of RINEPT pulse sequences, coupled with triply compensated 180° pulses (G5), ensures uniform sensitivity enhancement across CH, CH₂, and CH₃ signals over broad chemical shift ranges. The matrix-based computational method introduced here supersedes traditional algebraic approaches, offering superior accuracy and eliminating unphysical results (e.g., negative triad values). Experimental validation using a high molecular weight EB sample (M _w = 120,700 kg/mol), along with two lower molecular weight EB samples (M _w = 86,000 and 58,000 kg/mol), demonstrated robust reproducibility and alignment with baseline data from conventional NMR methods, confirming the reliability of our AIOQ-RINEPT method. Beyond polyolefins, this technique could enable efficient analyses of low molecular weight saturated hydrocarbons such as Fischer–Tropsch products, refrigerants, and fuel additives with transformative potential for industrial applications such as fast quality control, recycling, and polymer design. By addressing long-standing challenges in sensitivity, AIOQ-RINEPT establishes a new paradigm for AI-integrated NMR methodologies, paving the way for high-throughput, automated, high-precision microstructural characterization in both academic and industrial settings. This work not only advances polymer science but also highlights the power of AI-driven optimization in overcoming the fundamental limitations of traditional analytical techniques.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c07128

• Procedures of measuring MI and M _w; dependence of enhancement factors E on τ₁ and τ₂ (eqs 1S–3S); Monte Carlo simulation; the triad sequence distribution (eqs 4S–9S); the comonomer content of E and B (eqs 10S and 11S); Koenig B factor, the ethylene average sequence length (L _E), and the butene average sequence length (L _B) (eqs 12S–14S); nomenclature of peak assignments (Figure S1); EB triad sequence distributions and B mol % calculated from the algebra method, and ¹³C NMR was run with the conventional inverse-gated “zgig” method at 120 °C (Table 1S); dependence of enhancement factor of E on τ₂ in RINEPT pulse sequences (Figure 2S); the enhancement factors of CH, CH₂, and CH₃ carbon signals from Monte Carlo simulation (Table 2S); 32 τ₂ values in ms from Monte Carlo simulation; “ineptrd-vd” pulse sequence code; “ineptrd-vdG5” pulse sequence code; the average results of the EB polyolefin in TCE-d₂ containing 0.025 M Cr³⁺ from five NMR experiments using the AIOQ-RINEPT method (with Monte Carlo optimized 32 τ₂ values) and five NMR experiments using the conventional “zgig” method (Table 3S); the enhancement factors of CH, CH₂, and CH₃ carbon signals from annealing simulation (Table 4S); and a comparison of NMR results on two EB samples with lower weight-average molecular weights (M _w = 86,000 and 58,000 kg/mol), obtained using the conventional zgig pulse sequence (each run lasting 8 h and 40 min) and our new method (each run taking only 12 min) (Table 5S) (PDF)

#.

S.Y. and X.D. contributed equally to this work.

The authors declare no competing financial interest.