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Progress in Catalyst Systems， Synthesis Strategies， and Characterization Methods of Disentangled Ultrahigh Molecular Weight Polyethylene

Pingde Ning , Zhi Luo , Qian Li , Huayi Li , Youliang Hu

Progress in Chemistry ›› 2026, Vol. 38 ›› Issue (9) : 1610 -1624.

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Progress in Chemistry ›› 2026, Vol. 38 ›› Issue (9) : 1610-1624 DOI: 10.7536/PC20260201
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Progress in Catalyst Systems， Synthesis Strategies， and Characterization Methods of Disentangled Ultrahigh Molecular Weight Polyethylene
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Abstract

Disentangled ultrahigh molecular weight polyethylene（Dis-UHMWPE）has garnered significant attention due to its capacity to undergo solvent-free solid-state processing and its suitability for producing tapes and films with exceptional mechanical properties. In this review， catalyst systems for Dis-UHMWPE synthesis are categorized into two types based on polymerization temperature and design strategy： one suitable for low-temperature polymerization and the other for high-temperature polymerization. The intrinsic molecular chain disentanglement mechanisms within each system are elaborated separately. Furthermore， a systematic review of characterization methods for UHMWPE entanglement was conducted， including melt rheology， solid-state nuclear magnetic resonance analysis， thermal annealing analysis， and solid-state processing tensile testing. It is noteworthy that contemporary characterization methodologies continue to be the subject of deliberation， predominantly regarding the timescale for disentangled metastable states to recover the entangled equilibrium state upon entering the melt. We eschew subjective evaluation of the methods and viewpoints discussed， instead focusing on a systematic review and analysis of the characterization methods and their points of contention. The objective of this review is to provide a theoretical foundation for the optimization and standardization of characterization methods for disentangled states. It is proposed that solid-state processing and achieving ultra-drawability represent the most critical and indispensable characterization methods for Dis-UHMWPE.

Contents

1 Introduction

2 Catalyst systems for Dis-UHMWPE synthesis

2.1 Low temperature polymerization system

2.2 High temperature polymerization system

3 Characterization of the disentangled state in UHMWPE

3.1 Melt rheology

3.2 Solid-state NMR

3.3 Thermal annealing analysis

3.4 Solid-state processing tensile test

4 Conclusion and outlook

Graphical abstract

Keywords

disentangled ultrahigh molecular weight polyethylene / catalyst design strategy / characterization of disentangled state / melt rheology / solid-state NMR analysis / thermal annealing analysis / solvent-free solid-state processing

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Pingde Ning, Zhi Luo, Qian Li, Huayi Li, Youliang Hu. Progress in Catalyst Systems， Synthesis Strategies， and Characterization Methods of Disentangled Ultrahigh Molecular Weight Polyethylene. Progress in Chemistry, 2026, 38(9): 1610-1624 DOI:10.7536/PC20260201

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1 Introduction

Ultra-high molecular weight polyethylene (UHMWPE) is defined by the American Society for Testing and Materials standard (ASTM D4020-18) as having a viscosity-average molecular weight (Mv) greater than 3.0×106 g/mol linear long-chain polyethylene. In the industrial sector, polyethylene with a molecular weight exceeding 1.0×106 g/mol is typically classified within the UHMWPE category. The ultra-long molecular chains endow this polymer material with many unique and excellent properties: chemical inertness, high impact resistance, wear resistance, self-lubrication, and good biocompatibility, etc.[1]. These superior properties make UHMWPE the preferred polymer material for applications in harsh environments, such as UHMWPE high-strength fibers being extensively used to manufacture bulletproof vests, bulletproof armor, cut-resistant gloves, fishing nets, mooring ropes, and offshore wind turbine mooring lines, etc.[2-3]; UHMWPE pipes can be used for ore transportation[4]; high-purity UHMWPE can be manufactured into medical prostheses for internal use such as hip joints, knee joints, and heart valves[5]; UHMWPE porous films are widely used in lithium battery separators, etc.[6](Figure 1a). Fiber products and separator materials constitute the two most important segments of the UHMWPE downstream consumer market. In recent years, demand for fiber products has maintained steady growth (Figure 1b), while separator materials, driven by the rapid development of the new energy battery industry, have achieved explosive growth (Figure 1c). Overall, the downstream market demand for high-end UHMWPE products is robust, with broad development prospects. However, with the continuous expansion of UHMWPE production capacity and the gradual decline in average market prices, competition in the low-end product market will become increasingly fierce, and profit margins may continue to narrow. Therefore, promoting the development of UHMWPE products toward the high-end has become an inevitable trend for the future development of this industry.
The ultra-long molecular chains of UHMWPE are a "double-edged sword," endowing the material with excellent properties while simultaneously drastically increasing its processing difficulty[7]. When UHMWPE enters the molten state, its molecular chains rapidly become heavily entangled. After reaching entanglement equilibrium, the average molecular weight between entanglement points (Me) is approximately 1200 g/mol[8]. Based on this calculation, at least 800 entanglement points exist on a single UHMWPE molecular chain. These entanglement networks greatly hinder the movement and relaxation of the molecular chains. Consequently, its melt viscosity reaches as high as 108 Pa·s, making traditional melt processing methods (such as extrusion and injection molding) difficult to achieve efficient processing of UHMWPE. Industrially, gel spinning is primarily employed to spin UHMWPE, producing high-strength, high-modulus UHMWPE fibers[9-10]. The core of this process lies in using a large amount of solvent as a plasticizer (decalin for dry spinning and paraffin oil for wet spinning) to weaken secondary bonds between molecular chains, opening the entanglement network during high-temperature dissolution, and fixing this low-entanglement state within the gel precursor fiber through cooling and extraction. During quenching, the disentangled molecular chains coil and fold on crystal growth surfaces, forming a folded-chain crystal structure; this structural feature is precisely the key that enables gel precursor fibers to achieve high strength through high-draw-ratio stretching[11].
However, the gel spinning process extensively uses solvents and must be paired with expensive solvent recovery and treatment systems, significantly increasing the processing cost of UHMWPE fibers. Furthermore, solvents used in this process, such as decalin, acetone, and dichloromethane, possess biological toxicity, making the spinning process neither green nor environmentally friendly. In response to these process and environmental issues, academia and industry urgently need to find an economical and environmentally friendly processing method to efficiently process UHMWPE and prepare high-performance products. In recent years, researchers have focused on selecting suitable catalytic systems and polymerization processes to directly polymerize ultra-high molecular weight polyethylene in a low-entanglement state (Dis-UHMWPE)[12]. Below its melting point (<140 °C) and above theαcrelaxation temperature[13](>90 °C) within a wide processing temperature range, Dis-UHMWPE can achieve solid-state super-drawing without solvents, thereby producing fibers and films with high strength (3.8 GPa) and high modulus (165 GPa)[14]. Based on Dis-UHMWPE, solvent-free solid-state processing technology enables the economical and environmentally friendly processing and preparation of high-performance UHMWPE products, thus becoming a processing route with more sustainable development prospects.
Currently, commercialized UHMWPE raw materials (Com-UHMWPE) mainly rely on the traditional Ziegler-Natta catalytic system (Z-N catalytic system, MgCl2-supported TiCl4), achieving industrial production via slurry polymerization at relatively high polymerization temperatures (60~90 ℃)[15-16]. The Z-N catalytic system is a heterogeneous system; its active sites are densely and randomly distributed on the support, causing significant overlapping of neighboring growing polyethylene molecular chains during polymerization, thereby forming a highly entangled chain topology. Furthermore, under high-temperature polymerization conditions, the crystallization rate of polyethylene chains is far lower than the growth rate. The growing single molecular chains cannot avoid inter-chain entanglement by forming ordered lamellae through adjacent folding, which further exacerbates the degree of molecular chain entanglement. Therefore, Com-UHMWPE raw materials prepared via high-temperature polymerization using the Z-N catalytic system exhibit a high density of molecular chain entanglements, making it difficult to achieve the aforementioned solvent-free solid-state processing route.[17]. Screening suitable catalytic systems and optimizing polymerization conditions are key prerequisites for preparing low-entanglement ultra-high molecular weight polyethylene.
This paper first systematically reviews catalytic systems suitable for preparing Dis-UHMWPE and classifies them into two categories based on polymerization temperature and catalyst design strategies: one suitable for low-temperature polymerization (<30 °C) and the other for high-temperature polymerization (>30 °C). The boundary of this classification is based on the relative relationship between the crystallization rate of molecular chains and the chain growth rate during the polymerization process.[18]: Under low-temperature conditions, the crystallization rate of nascent molecular chains is higher than the chain growth rate, whereas the opposite is true under high-temperature conditions. Common methods for characterizing Dis-UHMWPE are summarized, and some controversial points in current characterization methods are discussed.

2 Preparation of the polymerization catalytic system for Dis-UHMWPE

2.1 Low-temperature polymerization catalytic system

This catalytic system achieves the preparation of Dis-UHMWPE under conditions of low temperature and low catalyst concentration, where low-temperature polymerization often plays a decisive role. At low temperatures, the crystallization rate of molecular chains exceeds their growth rate; nascent polyethylene chains can rapidly undergo intra-chain crystallization to form folded-chain crystals immediately upon growth, thereby effectively preventing inter-chain entanglement during the polymerization process. Low catalyst concentration ensures that active centers are far apart from each other during polymerization, allowing nascent polyethylene chains to form folded-chain crystals in isolation, further avoiding inter-chain entanglement.[14]. Low catalyst concentration also enables the reaction heat generated during the polymerization process to be rapidly removed via heat exchange, reducing the mobility of the growing polyethylene chains.
In 1987, Smith et al.[19]deposited and loaded VCl3onto glass slides to prepare UHMWPE under the activation of triisobutylaluminum. The authors studied the solid-state processability of nascent UHMWPE raw materials at different polymerization temperatures, proposing that each catalytic system has a specific "optimal" polymerization temperature, at which the obtained UHMWPE raw material exhibits the best solid-state processability. Two years later, Rotzinger et al.[20]used SiO2-supported VCl3heterogeneous catalysts and vanadium acetylacetonate homogeneous catalysts (Figure 2a) to successfully prepare Dis-UHMWPE under low-temperature (-20 °C, -40 °C) and low catalyst concentration (20 μmol V/100 mL toluene) conditions. Lower polymerization temperatures are more favorable for improving the solid-state draw ratio of Dis-UHMWPE; the product obtained at -40 °C achieved a draw ratio greater than 40 times, and the resulting fibers exhibited excellent modulus (>100 GPa) and strength (>3 GPa). Smith believed that the low-temperature and low-catalyst-concentration polymerization conditions significantly reduced the reaction activity and production efficiency of vanadium catalysts, thus this polymerization method failed to achieve industrialization.
In 2001, Fujita et al.[21-22]prepared a fluorine-substituted phenoxy-imine titanium catalyst (Figure 2b, FI-type catalyst), which exhibited characteristics of living polymerization in ethylene polymerization, yielding polymers with a narrow molecular weight distribution (Mw/Mn=1.05~1.19) and high catalytic activity (TOF > 20000/min/atm, 1 atm = 101325 Pa). In 2005, Rastogi et al.[14,23,24]used this FI catalyst, activated by methylaluminoxane (MAO), to successfully prepare Dis-UHMWPE under conditions of low temperature (10 ℃), low catalyst concentration (1.2 μmol Ti/100 mL toluene), and a polymerization time of 1 h (Mw=2.8×106 g/mol, Mw/Mn=3.0). By comparing the tensile mechanical properties of Com-UHMWPE with their self-made Dis-UHMWPE, Rastogi et al.[19]found that, at the same draw ratio, the tapes of Dis-UHMWPE after stretch orientation exhibited higher modulus and strength. Unlike Com-UHMWPE, Dis-UHMWPE could achieve solid-state super-drawing without using solvents, with draw ratios up to 300 times. After solid-state super-drawing at 139 ℃, the resulting fibers had a modulus and strength of 165 GPa and 3.8 GPa, respectively, comparable to the performance of fibers prepared by gel spinning (modulus about 135 GPa, strength about 3.5 GPa). In addition, Dis-UHMWPE could also achieve solid-state biaxial stretching under solvent-free conditions. Pandey et al.[17]used this catalytic system to further study the distribution of entanglement density along the polymer chains; the entanglement density was highest in the terminal regions of the polymer chains and gradually decreased closer to the active center, indicating a non-uniform distribution of entanglement density along the polymer chains. This suggests that entanglements of polyethylene chains often occur during the initial stages of polymerization (Figure 2e).
In 2014, Romano et al.[25]used a monocyclopentadienyl chromium catalyst[26](Figure 2c). After activation with MAO modified by 2,6-di-tert-butyl-4-methylphenol, Dis-UHMWPE was successfully prepared under low temperature (10 °C) and low catalyst concentration (0.9 μmol Cr/100 mL toluene) conditions. Since the low-entanglement samples did not reach a true entanglement equilibrium within the limited time frame of the rheological tests, Romano did not precisely characterize the molecular weight and molecular weight distribution of the samples. The obtained Dis-UHMWPE exhibited excellent mechanical properties after solid-state drawing, with a modulus as high as 207 GPa and a tensile strength as high as 3.6 GPa. In 2018, Spronck et al.[27]used a phenylimido vanadium(V) catalyst (Figure 2d). After activation with MAO, Dis-UHMWPE was prepared under low temperature (10 °C) and low catalyst concentration conditions (4 μmol Cr/100 mL toluene). In this study, the authors did not characterize the molecular weight of the polymer or demonstrate the solid-state processing performance of the resulting material.
In 2026, Ning et al.[28]developed a series of β-diketone titanium catalysts (Figure 2f), which enable the direct production of bimodal polyethylene (PE wax/UHMWPE) through one-step catalyst synthesis and polymerization. The content of polyethylene wax can be effectively regulated by polymerization conditions (such as temperature and catalyst structure). Under low-temperature polymerization conditions (0 °C), the β-diketone titanium catalysts exhibit optimal catalytic activity. The bimodal polymer prepared at 0 °C has a polyethylene wax mass fraction of less than 5%, and its UHMWPE component is in a low-entanglement state, enabling solvent-free solid-state processing. After solid-state hot stretching at 120 °C, the draw ratio exceeds 75 times (up to 300 times). The modulus of the strips after 75-fold drawing orientation is >56 GPa, and the tensile strength is >800 MPa.

2.2 High-temperature polymerization catalytic system

Although low-temperature polymerization facilitates the disentanglement of polyethylene molecular chains, it generally reduces the catalytic activity of most polyethylene catalytic systems. Furthermore, maintaining reactor operation at low temperatures in industrial production tends to increase energy consumption. Therefore, developing catalytic systems suitable for high-temperature polymerization to prepare Dis-UHMWPE holds broader prospects for industrial application. During high-temperature polymerization, the growth rate of polyethylene chains exceeds their crystallization rate, which easily induces chain entanglement. Consequently, catalytic systems applicable to high-temperature polymerization require specific design strategies to mitigate or eliminate the entanglement of growing chains.

2.2.1 Catalytic active center isolation strategy

In 2013, Osichow et al.[29]used a water-soluble phenoxy-imine nickel catalyst (Figure 3a) to prepare ultra-high molecular weight polyethylene nanocrystals with ideal configuration via microemulsion polymerization (Mw=2.8×106 g/mol, Mw/Mn=3.0). This polymerization system uses water as the solvent, with small amounts of polyethylene glycol and sodium dodecyl sulfate surfactant added. During polymerization, the catalyst precursor is self-activated by ethylene; its water-soluble ligand detaches, converting the catalyst into an oil-soluble form that enters surfactant micelles as single molecules. Due to the low catalyst concentration, the surfactant micelles achieve compartmentalization and isolation of active sites. The dispersed active centers catalyze ethylene polymerization within the micelles, forming nanoscale polyethylene particles. Their molecular chains are highly ordered, with almost no branching and no entanglement. The team considers this a "perfect" ordered nano-polyethylene crystal (Figure 3c). In recent years, using the strategy of compartmentalizing catalytic active centers via microemulsion polymerization, this team has developed a series of hydrophilic and lipophilic salicylaldimine nickel and phenyl-phosphine nickel catalysts[30-33](Figure 3b), achieving the preparation of Dis-UHMWPE at higher polymerization temperatures (30~60 °C) (Mn>2.0×106 g/mol, Mw/Mn=1.02~1.34). This series of catalytic systems also exhibits characteristics of living polymerization. Unlike hydrophilic catalyst precursors, lipophilic catalysts require dissolution in a small amount of water-insoluble solvent (such as toluene or benzene) prior to polymerization. They are then added to the aqueous solution containing surfactant via ultrasonic dispersion, ensuring uniform distribution of the catalyst within the microemulsion and achieving mutual isolation of the catalytic active centers.
In 2016, Li et al.[34]utilized oligomeric silsesquioxane (POSS)-modified SiO2to support FI catalysts, implementing an active center isolation strategy to prepare Dis-UHMWPE at a polymerization temperature of 30 °C (Mw=2×106 g/mol, PDI=2.4), with a catalytic activity (based on Ti) of 7.8×105 g/(mol·h). This study used POSS containing only two —OH groups to modify SiO2treated with MAO. After the —OH groups bonded with the aluminum atoms of MAO, the POSS modified on the SiO2surface acted as inert groups, isolating subsequently loaded FI catalyst molecules, thereby achieving mutual isolation of growing polyethylene chains (Figure 4a). Subsequently, the team continued to employ this strategy, using POSS-modified Z-N catalysts to polymerize Dis-UHMWPE at 60 °C[35-37]. This work first mixed POSS with MgCl2in tetrahydrofuran to form nano-aggregates, then adsorbed the prepared nano-aggregates (POSS/MgCl2) onto SiO2, followed by activation with triethylaluminum and reaction with TiCl4, successfully preparing POSS-modified Z-N catalysts (Figure 4b). Density functional theory calculations indicated that Mg atoms in MgCl2coordinate simultaneously with two hydroxyl O atoms of POSS, while Ti atoms in TiCl4 coordinate with Cl atoms in MgCl2, forming a POSS/MgCl2/TiCl4 adduct. This adduct exhibits low polymerization activity and thus can serve as an inert barrier to separate adjacent active sites. During catalyst preparation, most TiCl4 directly coordinates and binds with O atoms on the SiO2surface, acting as active sites for ethylene polymerization. Under the separation by inert groups (POSS/MgCl2/TiCl4), the distance between adjacent active centers exceeds the critical length for polymer chain crystallization (8.5~19.3 nm)[38], thus molecular chains are less prone to entanglement, enabling the catalytic system to prepare Dis-UHMWPE under high-temperature conditions (60 °C). Recently, the team further developed strategies assisted by nitrogen microbubbles[39] or fluorosiloxane microdroplets[40] to assist ethylene polymerization, achieving mutual isolation of catalytic centers and preparing Dis-UHMWPE at high temperatures of 75~90 °C.

2.2.2 Nanocarrier Strategy

Anchoring the catalyst on a nanosized support can also achieve separation of active sites. This is because the number of active sites that can be loaded on nanosized support particles is limited, thereby greatly reducing the probability of overlap in polymer chain growth during the polymerization process.[41-42](Figure 5). Meanwhile, the nanosized support can also effectively act as a heterogeneous nucleating agent, further lowering the crystallization nucleation barrier for growing polyethylene chains. This nanoscale supported catalytic system enables the preparation of Dis-UHMWPE under high-temperature polymerization conditions. During the polymerization process, the polymer can replicate the morphology of the catalyst support, and no polymer sticking or reactor fouling issues occur, which is beneficial for achieving continuous industrial production.
In 2012, Ronca et al.[42]used nano-TiO2 (<25 nm) and single-walled carbon nanotubes to support FI catalysts, preparing Dis-UHMWPE under polymerization conditions at 25 °C. The catalytic activity (based on Ti) was 6.8×105 g/(mol·h·bar) (1 bar = 100 kPa). The samples achieved solid-state super-drawing within a wide temperature window (125~145 °C), with a draw ratio as high as 200 times. The drawn tapes exhibited excellent mechanical properties after orientation, with a tensile strength of 3.8 GPa and a tensile modulus of 170 GPa. In 2018, Gote et al.[43]prepared MgCl2/Ti(OEt)4 supported catalysts with sizes of 109~206 nm via a one-pot method. The catalyst was activated sequentially with Et2AlCl and MMAO-12. At an Al:Ti ratio of 600, the catalytic system exhibited single-active-center characteristics, enabling the preparation of Dis-UHMWPE at 60 °C. The catalytic activity (based on Ti) was 6.7×105 g/(mol·h·atm). In 2021, Chammingkwan et al.[44]prepared a core-shell structured MgO/MgCl2/TiCl4 catalyst with a size of approximately 80 nm, which could prepare Dis-UHMWPE (Mv=5.6×106 g/mol) at 70 °C. In 2023, Gote et al.[41]in situ prepared a MgClx/EtnAly(2-ethyl-1-hexoxide)z complex with dual functions of activation and support in the polymerization reactor. Transmission electron microscopy indicated that the complex size was less than 25 nm, enabling the support and activation of FI catalysts. At 40 °C, this catalytic system could prepare Dis-UHMWPE with a catalytic activity (based on Ti) of approximately 1.6×106 g/(mol·h). The Dis-UHMWPE prepared by this method yielded fibers via solid-state processing with a tensile strength of 4 GPa and a tensile modulus of 200 GPa, exhibiting mechanical properties superior to those of the Dis-UHMWPE raw material obtained using FI catalysts via low-temperature (10 °C) homogeneous polymerization described earlier.

2.2.3 "Self-fixing" load strategy

In 1998, Alt[45]introduced alkenyl and alkynyl substituents onto dichlorozirconocene molecules for catalyzing ethylene polymerization. He discovered that complexes containing these substituents act as comonomer units, inserting into the growing polyethylene chains, thereby anchoring catalyst molecules onto the polymer chains. During this process, the catalytic system transitions from homogeneous to heterogeneous, achieving "self-immobilization" of the catalytic system. In 2004, Zhang et al.[46]introduced allyloxy functional groups into the benzene ring attached to the imine nitrogen of FI catalysts, and also observed the "self-immobilization" phenomenon of the catalytic system during ethylene polymerization (Figure 6b). In 2007, Ivancheva et al.[47]found that MAO-activated FI catalysts bearing allyloxy groups could catalyze the living polymerization of ethylene to prepare UHMWPE within a temperature range of 20–80 °C. In 2012, Ozerin et al.[48-49]used this catalytic system to prepare Dis-UHMWPE at 40–60 °C; this raw material enables solvent-free solid-state processing. The resulting fibers exhibited excellent mechanical properties, with a storage modulus as high as 187 GPa and a tensile strength up to 3.87 GPa. In 2020, Oleynik et al.[50]adopted a similar strategy by introducing diallylamino groups into the benzene ring attached to the imine nitrogen of FI catalysts (Figure 6c), finding that this catalytic system also exhibits the "self-immobilization" phenomenon during ethylene polymerization and can produce Dis-UHMWPE at 40 °C.
Oleynik et al.[50]explained the intrinsic mechanism by which this class of "self-immobilized" catalytic systems can prepare Dis-UHMWPE under high-temperature conditions. During the polymerization process, the catalyst molecules, i.e., the active centers, first "self-immobilize" on the growing polyethylene chains or polyethylene crystals, transforming the polymerization system from homogeneous to heterogeneous, and continuing to initiate chain growth. Each active center corresponds to a small polyethylene carrier particle; these particles loaded with active centers act as heterogeneous nuclei, thereby reducing the nucleation barrier for crystallization (Figure 6d). Therefore, nascent polyethylene chains can crystallize rapidly even at higher temperatures, effectively avoiding entanglement between molecular chains. Catalytic systems possessing "self-immobilization" characteristics can effectively solve the problems of wall sticking and fouling of polymers in the reactor and can regulate the morphology of polyethylene particles.

2.2.4 Utilizing the interaction between catalytic active sites and polymer chains

In 2023, Zhang et al.[51]prepared Dis-UHMWPE using a dinuclear synergistic rare earth metal scandium complex. The team synthesized a methylene-bridged difluorenyl dinuclear scandium catalyst[52](Figure 7a), which exhibited high activity in ethylene polymerization (calculated based on Sc) of 6.6×106 g/(mol·h). The prepared polyethylene had a molecular weight Mn>2.8×106 g/mol. The catalyst could prepare Dis-UHMWPE under a wide temperature range (25~120 ℃) and ethylene pressure (2~13 bar, 1 bar=100 kPa). After solid-state processing, the resulting Dis-UHMWPE tapes exhibited a tensile strength and modulus of 149.2 MPa and 1.5 GPa, respectively. The authors used density functional theory calculations to explain the polymerization mechanism of the catalytic system for preparing Dis-UHMWPE under high-temperature conditions. In the initial stage of polymerization, an interaction exists between the H atom on the β-carbon of the polyethylene chain and the metal center, known as the "agostic effect" (Figure 7b, β-agostic interaction). This interaction enables the polymer chains to arrange in an orderly manner during the growth stage. When the size of the ordered chain segments grows to a certain extent, they can spontaneously aggregate to form crystal nuclei even at high temperatures, reducing the nucleation barrier and initiating chain crystallization, thereby effectively reducing the degree of chain entanglement (Figure 7b).
In 2026, Wu et al.[53]synthesized a monocyclopentadienyl half-sandwich fluorinated phenoxy-imine titanium catalyst (Figure 7c). During polymerization, the planar configuration of the two bulky ligands in the catalyst structure, along with the β-agostic interaction between the fluorine atom and the growing chain, synergistically restricted chain transfer reactions and the growth direction of the polyethylene chains. This ensured regular chain growth and rapid crystallization during polymerization, thereby imparting low entanglement characteristics to the product. Using this catalyst at 40 °C, ultra-high molecular weight (>7×106 g/mol), narrow distribution (Mw/Mn<1.3), and high linearity Dis-UHMWPE were prepared.

3 Characterization of Entanglement Degree of UHMWPE

The nascent structure with low entanglement is a thermodynamic metastable state. When this structure enters the molten state, folded-chain crystals are destroyed, and driven by entropy, molecular chains transition from order to disorder, leading to entanglement. This process is extremely rapid.[54], existing technical means cannot accurately determine the time at which entanglement occurs.[55]. Currently, there are two different viewpoints regarding the timescale for the recovery from a low-entanglement state to an entangled equilibrium state: one view holds that the recovery process is slow, potentially lasting several hours or even days, involving a non-equilibrium low-entanglement melt state, known as the "melt memory" effect; the other view argues that entanglement equilibrium is reached instantaneously, referred to as the "chain explosion" effect. Therefore, some methods currently used to characterize the low-entanglement state remain controversial. The focus of this chapter is to review these characterization methods and comprehensively introduce the controversies associated with them.

3.1 Melt Rheology

De Gennes[56], Doi, Edwards, et al.[57]jointly established the "tube model," which considers the constraining effects of chain entanglements, describes the rheological properties of entangled polymer chains, and provides a theoretical research foundation for the entanglement behavior of polymer melts. The "tube model" states that the average molecular weight between entanglement points (Me) is inversely proportional to the entanglement density; using this model, one can estimate the plateau modulus of a polymer melt in an entangled equilibrium state,G0N, as calculated by Equation (1). For long linear UHMWPE, the plateau modulusG0Nis typically 2 MPa[8,58].
G0N=gN ρRT/Me
in the formula:gNis a dimensionless correction factor related to the theoretical model, taking a value of 1 or 4/5;ρis the polymer melt density; for UHMWPE, it is 0.86 g/cm3;Ris the gas constant;Tis the thermodynamic temperature;Meis the average molecular weight between entanglement points.
In 2005, Rastogi et al.[24,59]tracked the entanglement behavior of Dis-UHMWPE after entering the melt via oscillatory shear time sweep using a rheometer. The specific experimental protocol was as follows: Dis-UHMWPE was compression-molded at 50 °C (below the melting point) and 200 bar for 1 h to prepare circular discs with a diameter of 8 mm and a thickness of 1 mm for rheological testing. In the rheometer, the test disc was rapidly heated to 180 °C at a rate of 30 °C/min, held isothermally for 200 s, and then subjected to an oscillatory shear time sweep at a fixed frequency of 10 rad/s with an applied strain of 0.5% to track the storage modulus (G') changes.
The experimental results are asshown in Figure 8a. Dis-UHMWPE exhibits a low initial storage modulus (G't=0). As the scanning time extends, the storage modulus (G') increases slowly, eventually reaching the plateau modulus (G0N) characteristic of the entanglement equilibrium state. In contrast, the entangled Com-UHMWPE raw material behaves oppositely; after entering the molten state, its storage modulus (G') shows no significant growth process, meaning the initial storage modulus is close to the plateau modulus (G't=0≈G0N) manifested at entanglement equilibrium. Rastogi et al.[24,59]proposed that the transition from a low-entanglement state to an entanglement equilibrium state is a dynamic process primarily controlled by "chain reptation." The time required to reach entanglement equilibrium is related to the polymer's molecular weight, following a scaling relationship of 3.0 (τ∼M3). This characterization method by Rastogi et al.[24,59]has been recognized and adopted by most researchers[14,60], which involves determining whether a sample is in a low-entanglement state by measuring the variation of its storage modulus in the molten state.
The timescale issue for Dis-UHMWPE melts to reach entanglement equilibrium is still under debate. Among them, many researchers believe that the establishment of entanglement equilibrium is completed instantaneously, because after briefly annealing Dis-UHMWPE above its melting point, the material almost instantly loses its ultra-drawability[11,62]. Based on this viewpoint, in 2024, Litvinov et al.[61]redesigned the melt rheology testing protocol to determine whether the non-equilibrium low-entanglement melt described by Rastogi exists, that is, whether there is a slow establishment process of the plateau modulus. Litvinov used a partitioned plate fixture, which differs from the conventional parallel plate fixture used by Rastogi and can effectively avoid the influence of edge effects on modulus growth. Using this special fixture structure, Litvinov executed the same time-scan procedure as Rastogi. The experimental results (Figure 8b) indicate that for both Dis-UHMWPE and Com-UHMWPE samples, no growth process of the polymer melt modulus, i.e., the establishment process of the plateau modulus, could be observed. The initial storage moduli of both are close to the plateau modulus exhibited at entanglement equilibrium (G't=0≈G0N). Therefore, Litvinov believes that entanglement equilibrium should be established instantaneously once UHMWPE enters the molten state, regardless of the polymer's molecular weight. The plateau modulus establishment process observed by Rastogi may stem from systematic errors in the experimental protocol, caused mainly by the following factors.
1) Wall slip. Since a certain axial stress (4 N) was applied during the time sweep process, wall slip may occur between the sample and the conventional parallel plate fixture, affecting the gap variation between the fixtures during the test, and consequently influencing the modulus variation.
2) Insufficient thermal equilibrium time. Due to the long relaxation time of UHMWPE molecular chains, it exhibits rubber-like elastomeric behavior in the molten state, causing its volume to expand as temperature rises. When measurements are taken before the sample reaches thermal equilibrium, this volume expansion also affects changes in the gap value, thereby influencing modulus variations.
3) Edge effects. Due to the application of a certain axial stress (4 N) during the time sweep process, the gap value between the fixtures inevitably decreases during prolonged testing. Under axial compression, part of the rubbery-state UHMWPE melt creeps radially, causing an increase in radial diameter. Since the rheometer assumes that the diameter of the tested disk remains unchanged, the actual excess edge portion results in an increase in modulus, leading to edge effects.
4) Preparation of rheological test discs. Since the Dis-UHMWPE test discs are prepared by compression molding below the melting point, the resulting test discs may contain bubbles and voids, which can also affect the modulus changes during time sweep tests.
In 2026, Ning et al.[28]The study indicates that using conventional parallel plate fixtures and executing the same time-sweep procedure as Rastogi, the gap value between the fixtures indeed decreased during the test (a 5% reduction from the original height within 3 hours). The rheological test discs were standardized to a diameter of 8 mm and a thickness of 1 mm. The trend of gap variation was similar for both entangled and low-entangled samples; however, there were significant differences in the growth of the storage modulus: within 3 hours, the storage modulus of low-entangled samples increased rapidly, whereas for entangled samples, the initial modulus upon entering the molten state was close to the plateau modulus.G0Nincreased slowly. Therefore, the contribution of edge effects caused by the reduced gap value to the modulus growth is secondary. The rapid modulus growth in low-entangled samples may be attributed to the transition from heterogeneous entanglements to homogeneous entanglements.

3.2 Solid-state NMR

3.2.1 1H Transverse Relaxation

For nascent UHMWPE powder, it is generally believed that the higher the crystallinity, the lower the entanglement density. This is because chain entanglements occur in the amorphous regions, while chains in the crystalline regions exhibit an ordered and regular arrangement. The primary mechanism affecting proton transverse relaxation (T2 relaxation) is dipole-dipole coupling between protons. The strength of this coupling interaction depends on two factors: 1) the spatial distance between protons; the greater the distance, the weaker the coupling; 2) the rate of molecular motion; the faster the motion, the more effectively the coupling is averaged out, resulting in a weaker apparent coupling. Since entangled networks and non-entangled regions correspond to different chain conformations, the entanglement state of UHMWPE chains can be characterized by comparing the T2relaxation decay process or by measuring the T2value [[63,64]]; a smaller T2value indicates a higher average entanglement density.
In 2005, Rastogi et al.[59]measured the T2relaxation processes of Dis-UHMWPE and Com-UHMWPE after entering the melt state. The experimental results showed that for Dis-UHMWPE, slow heating (0.2 °C/min) and fast heating (10 °C/min) to 150 °C resulted in melt states with different T2relaxation times (Figure 9b, right panel); the melt formed by slow heating had a longer T2relaxation time, while the melt formed by fast heating had a shorter T2relaxation time. For Com-UHMWPE, the above phenomenon was not observed; the T2relaxation time in the melt state was independent of the heating rate (Figure 9b, left panel). Based on these experimental results, Rastogi proposed that during slow heating, Dis-UHMWPE exhibits a heterogeneous melt structure, manifesting as a non-equilibrium low-entanglement melt state. This is because, during slow heating, molecular chains on the crystal surface detach and melt earlier; these melted chains entangle with neighboring chains (Figure 9a, A-A' and B-B'), thereby hindering the entanglement process of molecular chains melting within the crystal interior, leaving the internally melted chains in a low-entanglement state and forming a non-equilibrium low-entanglement melt (Figure 9a). The motion of molecular chains in the low-entanglement melt is not restricted, resulting in a longer T2relaxation time. During fast heating of Dis-UHMWPE, driven by a large entropy increase, molecular chains throughout the entire crystal melt simultaneously and become entangled; the entanglements are uniformly distributed along the chains, restricting chain motion, thus leading to a shorter T2relaxation time. By measuring the 1H NMR T2relaxation times of UHMWPE melts at different heating rates, the low-entanglement melt state can be identified.
Based on the viewpoint of the "chain explosion" effect, where entanglement equilibrium is established instantaneously, Litvinov et al. in 2024[61]redesigned the experimental protocol for measuring the1H NMR T2relaxation of Dis-UHMWPE melts. Compared to Rastogi's measurement of melt1H T2relaxation under high-field NMR, Litvinov chose to measure1H T2relaxation under low-field conditions, because low-field NMR equipment possesses more precise temperature control devices. Experimental results indicate that under two different heating rates, slow (0.1 °C/min) and fast (10 °C/min), Dis-UHMWPE melts exhibit similarT2relaxation decay processes (Figure 9cleft panel). Both Dis-UHMWPE and Com-UHMWPE possess identicalT2relaxation times (Figure 9cright panel), with no observation of a non-equilibrium low-entanglement melt state. Litvinov believes that Rastogi's experimental protocol contains systematic errors: on one hand, the lack of precise temperature control calibration for the testing NMR spectrometer and test samples causes the actual testing temperature to be lower than the set temperature, affecting the determination ofT2values; on the other hand, small amounts of ash impurities in Dis-UHMWPE (i.e., residues of catalysts or alkylaluminum co-catalysts) also affect the determination of T2values.

3.2.2 13C cross-polarization magic angle spinning

Solid-state NMR has been fully proven to characterize the subtle differences between the amorphous regions, crystalline regions, and their interfaces in semi-crystalline polymers. The position and width of signal peaks reflect molecular chain conformation information in different regions, because the statistical average of conformational motions and local interactions determines the peak shape and position in the spectrum.[65-66]. Yao et al.[67-69]used13C cross-polarization magic-angle spinning (13C-CP/MAS) technology to characterize the differences in molecular chain conformation in the amorphous regions of Dis-UHMWPE and Com-UHMWPE, in order to determine the entanglement state of UHMWPE.
Figure 10displays the 13C-CP/MAS spectra of four samples: Dis-UHMWPE, Com-UHMWPE, and both after heating-melting-cooling-crystallization (corresponding to MC-A and MC-B, respectively), comparing the differences between signal peaks at different test temperatures. The signal peak at 32.9 ppm (1 ppm = 1×10-6) with identical linewidth is attributed to the orthorhombic crystalline region of PE, where all molecular chains adopt an all-trans conformation. The most significant difference is observed at the signal peak around 31 ppm, which corresponds to the amorphous region of PE; here, the entanglement density of molecular chains differs, leading to different conformations (Figure 10a). For nascent Dis-UHMWPE, a broad amorphous region peak is present at 31.2 ppm (Δfwhh = 1.8 ppm). In contrast, for the entangled sample after melt crystallization, the peak at this position is much sharper (Δfwhh = 0.6 ppm). The broad amorphous region peak of Dis-UHMWPE indicates restricted local chain dynamics, which may originate from geometric constraints imposed by chain segment arrangement at the crystal-amorphous interface. This arrangement occurs during polymerization; under low-temperature polymerization conditions, growing polymer chains tend to fold adjacently to form crystals, thus adjacent re-entry structures are considered ubiquitous at the crystal-amorphous interface. Similar phenomena can be observed in UHMWPE samples crystallized from dilute solutions and are commonly found in reported Dis-UHMWPE samples[70]. Another signal distinguishing Dis-UHMWPE from Com-UHMWPE is a small signal peak appearing at 34.2 ppm, attributed to the monoclinic crystalline region, where all molecular chains adopt an all-trans conformation. The emergence of the monoclinic phase results from shear applied to the orthorhombic crystalline region during the sample loading process into the test rotor, reflecting to some extent the plastic deformation capability of the Dis-UHMWPE crystalline region[71]. As the test temperature increases, the signal peak gradually diminishes due to enhanced molecular chain mobility, which relaxes the internal stress generated in the sheared crystalline region (Figure 10b).

3.2.3 13C Exchange Spectrum

Based on the measurementT1saturation recovery method for relaxation time[72], Yao et al.[68-69]observed the polarization transfer process from methylene units in the amorphous region to those in the crystalline region of UHMWPE by designing suitable pulse sequences and exchange time windows. This process is mainly influenced by the topological structure of molecular chains (entanglement density) in the amorphous region; therefore, by comparing the speed of transfer diffusion, the degree of chain entanglement can be characterized (Figure 11a).
The specific experimental results are asshown in Figure 11b[14], indicating that compared to Com-UHMWPE, Dis-UHMWPE exhibits faster polarization transfer from the amorphous region to the crystalline region. That is, as the exchange time increases (where the exchange time is far shorter than the crystalline region'sT1relaxation time), the intensity growth of the crystalline region signal peak (32.9 ppm) in Dis-UHMWPE is more significant. This is because the degree of chain entanglement in the amorphous region differs, resulting in different diffusion capabilities. From a thermodynamic perspective, compared to Com-UHMWPE, the molecular chain conformation in the amorphous region of Dis-UHMWPE differs less from that in the crystalline region. Consequently, the conformational entropy that molecular chains need to overcome for diffusion between the two phases is lower, leading to stronger chain diffusion capability.

3.3 Thermal Annealing Analysis

The topological structures of the molecular chains in Dis-UHMWPE and Com-UHMWPE differ significantly. Under specific annealing programs, nucleation barriers vary across regions with different chain topologies, resulting in distinct crystallization capabilities and thus different crystallization kinetics. Leveraging these differences, Rastogi et al.[59,70,73-75]developed two distinct DSC thermal annealing programs to characterize the degree of entanglement of UHMWPE molecular chains, hereinafter referred to as the low-temperature annealing program and the high-temperature annealing program, respectively.
However, based on the viewpoint of the "chain explosion" effect, Litvinov et al.[61]hold a different opinion; he believes that ash impurities in the nascent polymer also affect the local crystallization kinetics of the polymer melt. Therefore, the two annealing procedures designed by Rastogi cannot fully prove that the differences are caused by the topological structure of the molecular chains.

3.3.1 Low-temperature annealing program

The low-temperature annealing procedure is conducted at a temperature close to but below the polymer's melting point (Figure 12a, stage "b~c";Tais approximately 136 °C). At this annealing temperature, the melting process of primary low-entanglement folded-chain crystals is related to the topological structure (degree of entanglement) of the molecular chains in the amorphous region. During annealing, polyethylene molecular chains continuously detach from the crystal surface and enter the melt (Figure 12b). This detachment process is influenced by the topological structure of the surrounding amorphous molecular chains: the higher the degree of entanglement in the amorphous region, the slower the rate at which molecular chains detach from the crystal surface. The DSC curve of the final heating run (Figure 12a, stage "e~f") shows that for highly entangled commercial samples, even with continuously extended annealing time, the high-temperature peakAH(corresponding to the melting peak of primary low-entanglement folded-chain crystals) remains significantly present. However, for low-entanglement samples, the constraints imposed by the topological structure of the amorphous chains are smaller; as the annealing time extends, molecular chains continue to detach from the crystal surface and melt, causing the area of the high-temperature peakAHto gradually decrease. Meanwhile, the area of the low-temperature peakAL(corresponding to the melting peak of molecular chains that detached and melted, then crystallized during the cooling stage "c~d") gradually increases. Therefore, the relationship between theAL/(AL+AH) value and the annealing time can be measured to evaluate the degree of entanglement of UHMWPE molecular chains[59,75]. For Com-UHMWPE, theAL/(AL+AH) value is independent of the annealing time and remains at a low level (Figure 12c, Commercial). In contrast, for Dis-UHMWPE prepared via low-temperature polymerization using an FI catalyst, itsAL/(AL+AH) value continuously increases with extended annealing time, eventually approaching 100%, meaning the high-temperature peakAHtends to disappear (Figure 12c, Run 1~5).

3.3.2 High-temperature annealing program

The high-temperature annealing procedure is as follows: heat the polymer to above its melting point (e.g., 160 °C) and anneal for different durations, then cool to 128 °C for isothermal crystallization for 180 min, further cool to 50 °C, and finally reheat to above the polymer's melting point while recording the final heating curve. All heating and cooling rates are 10 °C/min (Figure 13a). For Com-UHMWPE, during the final heating process (Figure 13a, panels g~h), two melting peaks appear at 131.2 °C and 135.4 °C, respectively. As the annealing time extends, the high-temperature melting peak at 135.4 °C gradually disappears, leaving only the low-temperature melting peak at 131.2 °C (Figure 13d). Unlike Com-UHMWPE, Dis-UHMWPE exhibits a low-temperature peak at 134.2 °C and a prominent high-temperature peak at 141.7 °C during the final heating. The appearance of the 141.7 °C high-temperature peak is independent of the annealing time and persists (Figure 13c).
Zhao et al.[70], Yang et al.[73], and Liu et al.[74]believe that due to differences in the topological structure of nascent molecular chains, after Com-UHMWPE enters the molten state, the molecular chains form "woven entanglements" (Figure 13b), whereas after Dis-UHMWPE enters the molten state, the molecular chains form "nonwoven entanglements" (Figure 13b). The nucleation barriers for these two different molecular chain topological structures differ. The "nonwoven entanglements" formed by the Dis-UHMWPE melt have a higher nucleation density and a lower nucleation barrier; therefore, isothermal crystallization can occur even at higher temperatures (128 °C), corresponding to a melting endothermic peak near 141 °C. In contrast, the Com-UHMWPE melt has a higher nucleation barrier and requires lower temperatures and greater supercooling to undergo crystallization (Figure 13a, cooling to 50 °C during the "e~f" stage), corresponding to a melting endothermic peak at 135 °C. These "nonwoven entanglements" facilitated by Dis-UHMWPE are determined by initial polymerization conditions and are independent of any subsequent thermal treatment history.
Based on the perspective of "instantaneous recovery of melt entanglement equilibrium", in 2024, Wang et al.[9]conducted a detailed study on the melting enthalpy and crystallinity of Dis-UHMWPE during the final heating stage (g~h) of the aforementioned high-temperature annealing procedure. During the final heating process, Dis-UHMWPE exhibited similar melting enthalpy and crystallinity under different annealing times (3~720 min). This indicates that under different annealing times, the Dis-UHMWPE melt possesses similar molecular chain topological structures and entanglement states. Dis-UHMWPE reaches an entanglement equilibrium state the instant it enters the molten state, and the entanglement state of the molecular chains does not change with annealing time. Furthermore, Wang et al.[9]argued that the difference between the melting peaks at 141 ℃ and 135 ℃ is not caused by the "woven" and "non-woven" chain topological structures in the molten state mentioned by Rastogi, but rather results from differences in the thickness of the growing lamellae under different crystallization temperatures and degrees of supercooling, thereby leading to the difference in melting peaks.[76]. Specifically, during isothermal crystallization at 128 ℃, a lower degree of supercooling leads to the formation of thicker lamellae, corresponding to the higher melting peak at 141 ℃.

3.4 Solid-state processing tensile test

The most essential characteristic of Dis-UHMWPE is its ability to achieve solvent-free solid-state super-drawing within the processing temperature range above the αcrelaxation temperature and below the polymer melting point (90~140 ℃)[11,13]. Its draw ratio is greater than 7, with a maximum approaching 400 times. This is because Dis-UHMWPE belongs to the "crystal-mobile" type of polymer, where regularly arranged molecular chains exhibit high intracrystalline mobility. During stretching, active molecular chains are easily pulled out from lamellae, thereby driving the formation of extended-chain crystals and achieving the super-drawing process. The stretching process of semi-crystalline polymers typically undergoes four microstructural evolution stages[9]: 1) Elastic and plastic deformation of spherulites (pre-yield stage); 2) Fragmentation and orientation of crystallites (yield and strain softening stage); 3) Plastic flow of crystallites induced by polymer chain extension (fibrillation process); 4) Entanglement-controlled strain hardening. The super-drawing capability of Dis-UHMWPE mainly stems from the prolonged fibrillation process (Figure 14, stage Ⅲ), which is primarily attributed to the regularly arranged structure of the molecular chains.
An important practical application of Dis-UHMWPE is its ability to achieve solvent-free ultra-drawing, yielding high-performance tapes or films. Therefore, the most critical and widely uncontested characterization method for Dis-UHMWPE is the solvent-free solid-state drawing technique.Table 1summarizes the solvent-free solid-state ultra-drawing data of Dis-UHMWPE prepared by the polymerization catalytic systems described in this paper, as well as the mechanical properties of the corresponding drawn tapes. For the solvent-free solid-state drawing of Dis-UHMWPE, there is a synergistic effect between the polymer's molecular weight and molecular weight distribution[77-79]. A higher molecular weight is a necessary condition for the drawn tapes to ultimately achieve exceptional strength, while a broader molecular weight distribution helps increase the draw ratio but will reduce the mechanical properties of the tapes to some extent. This is because low-molecular-weight components acting as plasticizers cannot effectively form a stress transfer network, thereby failing to enhance mechanical strength.

4 Conclusion and Outlook

Low-entanglement ultra-high molecular weight polyethylene (Dis-UHMWPE) has attracted widespread attention due to its ability to enable green, economical, and efficient solvent-free solid-state processing for preparing tapes and films with excellent mechanical properties. Since related research began in 1978, this field has undergone nearly half a century of development, during which various catalytic systems for preparing Dis-UHMWPE have emerged successively. Essentially, catalytic systems used for preparing Dis-UHMWPE achieve disentanglement of molecular chains primarily by regulating the spacing distance between catalytic active centers and the crystallization rate of growing polyethylene chains. The molecular chain disentanglement strategies of all catalytic systems discussed in this article can be attributed to the regulation of these two key factors. Whether using homogeneous or heterogeneous catalysts, Dis-UHMWPE can be obtained under conditions where the spacing between active centers is appropriate and the chain crystallization rate exceeds the growth rate.
The transition of molecular chains from a low-entanglement state to an entanglement equilibrium state induces changes in rheology, NMR relaxation times, and crystallization kinetics. Therefore, these methods can be used to characterize the entanglement density of UHMWPE molecular chains, thereby distinguishing UHMWPE samples with different entanglement states. However, due to differing understandings and characterizations of the time scale required for low-entanglement states to reach entanglement equilibrium after entering the melt, the aforementioned characterization methods have yielded contradictory viewpoints and results. Consequently, these characterization methods require further refinement; relying on a single method alone cannot fully confirm the low-entanglement state of UHMWPE. Nevertheless, solvent-free solid-state processing and the ultimate achievement of ultra-drawing represent the most critical features and decisive characterization means for Dis-UHMWPE. This approach is undisputed and holds practical application prospects. Therefore, regardless of the catalytic system used or whether low-temperature or high-temperature polymerization processes are employed to prepare UHMWPE, as long as solvent-free solid-state ultra-drawing can be achieved to obtain high-strength materials, it can be regarded as Dis-UHMWPE.
Currently, low-cost, industrially scalable preparation methods for Dis-UHMWPE still require further development, and solid-state solvent-free ultra-multiple stretching processes and equipment also need advancement. These two technologies must develop synergistically to rapidly form a complete technical chain, thereby enabling the low-cost production of high-performance UHMWPE materials and ultimately achieving industrial-scale manufacturing.

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Funding

National Natural Science Foundation of China(U23A20127)

National Natural Science Foundation of China(U24B20191)

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