Influence of barium titanate nanofiller on PEO/PVdF-HFP blend-based polymer electrolyte membrane for Li-battery applications

Organic-inorganic hybrid membranes based on poly(ethylene oxide) (PEO) 6.25 wt%/poly(vinylidene fluoride hexa fluoro propylene) [P(VdF-HFP)] 18.75 wt% were prepared by using various concentration of nanosized barium titanate (BaTiO₃) filler. Structural characterizations were made by X-ray diffraction and Fourier transform infrared spectroscopy, which indicate the inclusion of BaTiO₃ in to the polymer matrix. Addition of filler creates an effective route of polymer-filler interface and promotes the ionic conductivity of the membranes. From the ionic conductivity results, 6 wt% of BaTiO₃-incorporated composite polymer electrolyte (CPE) showed the highest ionic conductivity (6 × 10^?3 Scm^?1 at room temperature). It is found that the filler content above 6 wt% rendered the membranes less conducting. Morphological images reveal that the ceramic filler was embedded over the membrane. Thermogravimetric and differential thermal analysis (TG-DTA) of the CPE sample with 6 wt% of the BaTiO₃ shows high thermal stability. Electrochemical performance of the composite polymer electrolyte was studied in LiFePO₄/CPE/Li coin cell. Charge-discharge cycle has been performed for the film exhibiting higher conductivity. These properties of the nanocomposite electrolyte are suitable for Li-batteries.     

Electrical and Structural Properties of Poly (Methyl Methacrylate) Doped Potassium Iodide (KI) Solid Polymer Electrolyte

A high-conducting salt-doped polymer electrolyte layer has been created here for use in photocell technologies. The solution casting method is used to produce ion conducting film where poly (methyl methacrylate) (PMMA) is used as the host polymer and potassium iodide (KI) as the dopant. The conductivity and amorphic increases of the polymer electrolytes with the addition of salt concentrations helps in the enhancement of the charge transfer properties. Using electrochemical impedance spectroscopy (EIS), ionic conductivity is evaluated where maximum conductivity is 3.99 × 10⁻⁶ S cm^-1 at 20 wt% KI concentration. Polarized optical microscopy (POM) shows the reduction in crystallinity by salt doping, while Fourier transforms infrared spectroscopy (FTIR) shows the complexation as well as composite nature of the film. Ionic transference number (t_ion) measurement shows the predominantly ionic nature of this polymer electrolyte.     

PEO-LITFSI-SiO2-SN System Promotes the Application of Polymer Electrolytes in All-Solid-State Lithium-ion Batteries

All-solid-state polymer lithium-ion batteries are ideal choice for the next generation of rechargeable lithium-ion batteries due to their high energy, safety and flexibility. Among all polymer electrolytes, PEO-based polymer electrolytes have attracted extensive attention because they can dissolve various lithium salts. However, the ionic conductivity of pure PEO-based polymer electrolytes is limited due to high crystallinity and poor segment motion. An inorganic filler SiO₂ nanospheres and a plasticizer Succinonitrile (SN) are introduced into the PEO matrix to improve the crystallization of PEO, promote the formation of amorphous region, and thus improve the movement of PEO chain segment. Herein, a PEO₁₈−LiTFSI−5 %SiO₂−5 %SN composite solid polymer electrolyte (CSPE) was prepared by solution-casting. The high ionic conductivity of the electrolyte was demonstrated at 60 °C up to 3.3×10⁻⁴ S cm⁻¹. Meanwhile, the electrochemical performance of LiFePO₄/CSPE/Li all-solid-state battery was tested, with discharge capacity of 157.5 mAh g⁻¹ at 0.5 C, and capacity retention rate of 99 % after 100 cycles at 60 °C. This system provides a feasible strategy for the development of efficient all-solid-state lithium-ion batteries.     

Synthesis and characterization of electrospun PVdF-HFP/silane-functionalized ZrO2 hybrid nanofiber electrolyte with enhanced optical and electrochemical properties

A facile method to produce a hybrid of organic-inorganic nanofiber electrolyte via electrospinning is hereby presented. The incorporation of functionalized zirconium oxide (ZrO₂) nanoparticles into poly(vinylidene fluoride-co-hexafluoropropylene) (PVdF-HFP) and complexed with lithium trifluoromethanesulfonate (LiCF₃SO₃) provided an enhanced optical transmissivity and ionic conductivity. The dependence of the nanofiber's morphology, optical and electrochemical properties on the various ZrO₂ loading was studied. Results show that while nanofiller content was increased, the diameter of the nanofibers was reduced. The improved bulk ionic conductivity of the nanofiber electrolyte was at 1.96 × 10⁻⁵ S cm⁻¹. Owing to the enhanced dispersibility of the 3-(trimethoxysilyl)propyl methacrylate (MPS) functionalized ZrO₂, the optical transmissivity of the nanofiber electrolyte was improved significantly. This new nanofiber composite electrolyte membrane with further development has the potential to be next generation electrolyte for energy efficient windows like electrochromic devices.     

Enhancing the molecular cooperativity of polyvinyl butyral using liquid additives

The specific role of acetonitrile and methoxypropionitrile, as accelerators of the relaxation dynamics of polyvinyl butyral (PVB), was investigated in polymer/additive mixtures with a saturation liquid content. The aim was to improve the ionic mobility of PVB‐based solid electrolytes to be used in solid dye‐sensitized solar cells. Mechanical and dielectric relaxation measurements between 120 K and 380 K revealed that the α‐relaxation observed above 330 K in dry‐PVB is shifted quite below room temperature in PVB/additives. Both the additives cause a growing intermolecular cooperativity, the sub‐glass β‐relaxation exhibiting a strength enhanced by a factor 3 and a frequency factor which increases from 10¹⁵ s⁻¹ to 10²¹ s⁻¹. This discloses an activation entropy as high as 165.7 J/K mol in comparison to 40.8 J/K mol in dry‐PVB. It is suggested the existence of cooperative transitions, mainly driven by bridges formed through additive molecules, which influence both short‐ and long‐scale segmental motions and also favor the ion dynamics in PVB/additive/electrolyte systems. The room temperature ionic conductivity σ_rt exhibits large changes from 6.4*10⁻¹⁴ S/m in dry PVB, through 1.5*10⁻⁸ S/m in PVB/LiI, to 2.45*10⁻⁵ S/m in PVB/MPN/LiI. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 340–346     

A lithium secondary battery using a thin film of polymer electrolyte as a separator

Ion-conductive polymer which shows an ionic conductivity (σ_i) of 1.4 × 10^?4S/cm at 25°C when mixed with LiClO₄ (molar ratio in Li/OE = 0.05) was used as a separator of electrodes in a lithium secondary battery. The effect of high ionic conductivity on the performance of the battery was studied. The polymer structure was and the cathode was comprised of poly(1,3,4-thiadiazole disulfide), graphite powder and the polymer electrolyte. The cell [(?)Li/polymer electrolyte/graphite–poly(disulfide) (+)] had an open circuit voltage (V_oc) of 3.25 V, a plateau voltage of 2.75 V, a discharge density (i_d) of 0.05 mA/cm² with the cathode utilization of 63%, and achieved over several tens of cycles at 25°C.     

Ionic conductivity and interfacial stability of Li6PS5Cl–Li6.5La3Zr1.5Ta0.5O12 composite electrolyte

Solid electrolytes which possess excellent lithium-ion conductivity and chemical compatibility with electrode materials are necessary for the commercialization of all-solid-state lithium batteries. However, a single solid electrolyte meeting above requirements is difficult. Consequently, the composite electrolytes have attracted more attention. In this paper, Li₆PS₅Cl–xLi_6.5La₃Zr_1.5Ta_0.5O₁₂ (LLZTO) (x = 0, 2.5 wt%, 5 wt%, 10 wt%) composite electrolytes are prepared by a simple planetary grinding process. It has been found that adding an appropriate amount of LLZTO can increase the lithium-ion conductivity. At 30 °C, the lithium-ion conductivity increases from 2.6 × 10⁻⁴ S/cm (Li₆PS₅Cl) to 5.4 × 10⁻⁴ S/cm (Li₆PS₅Cl-5 wt% LLZTO). Besides, the addition of LLZTO to the Li₆PS₅Cl can influence the growth rate of the SEI. It has been shown that the SEI growth rate obeys a parabolic rate law, and the growth rates of Li₆PS₅Cl, Li₆PS₅Cl-2.5 wt% LLZTO, Li₆PS₅Cl-5 wt% LLZTO, and Li₆PS₅Cl-10 wt% LLZTO are 8.62, 3.53, 3.33, and 3.38 Ω/h^1/2 at 60 °C, respectively. In lithium plating and stripping experiment, the voltage of symmetrical Li/Li₆PS₅Cl/Li cell suddenly drops to 0 V after cycling 39 h at 0.103 mA/cm² (0.097 mAh/cm²). On the contrary, the Li/Li₆PS₅Cl–xLLZTO (x = 2.5 wt%, 5 wt%, 10 wt%)/Li symmetrical cell exhibits a stable voltage profile over 100 h at the same test conditions. The corresponding interfacial impedance of Li/Li₆PS₅Cl–xLLZTO (x = 2.5 wt%, 5 wt%, 10 wt%) remains stable after 10, 30, and 50 charge/discharge cycles.

     

Synthesis and properties of all solid polymer electrolytes based on poly(vinyl acetate‐co‐acetyl ethylene oxide acrylate)

Poly(acetyl ethylene oxide acrylate‐co‐vinyl acetate) (P(AEOA‐VAc)) was synthesized and used as a host for lithium perchlorate to prepare an all solid polymer electrolyte. Introduction of carbonyl groups into the copolymer increased ionic conductivity. All solid polymer electrolytes based on P(AEOA‐VAc) at 14.3 wt% VAc with 12wt% LiClO₄ showed conductivity as high as 1.2 × 10^?4 S cm^?1 at room temperature. The temperature dependence of the ionic conductivity followed the VTF behavior, indicating that the ion transport was related to segmental movement of the polymer. FTIR was used to investigate the effect of the carbonyl group on ionic conductivity. The interaction between the lithium salt and carbonyl groups accelerated the dissociation of the lithium salt and thus resulted in a maximum ionic conductivity at a salt concentration higher than pure PAEO‐salts system. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of NiO nanofiller concentration on the properties of PEO-NiO-LiClO4 composite polymer electrolyte

Composite polymer electrolyte films comprising polyethylene oxide (PEO) as the polymer host, LiClO₄ as the dopant, and NiO nanoparticle as the inorganic filler was prepared by solution casting technique. NiO inorganic filler was synthesized via sol-gel method. The effect of NiO filler on the ionic conductivity, structure, and morphology of PEO-LiClO₄-based composite polymer electrolyte was investigated by AC impedance spectroscopy, X-ray diffraction, and scanning electron microscopy, respectively. It was observed that the conductivity of the electrolyte increases with NiO concentration. The highest room temperature conductivity of the electrolyte was 7.4?×?10^?4 S cm^?1 at 10 wt.% NiO. The observation on structure shows the highest conductivity appears in amorphous phase. This result has been supported by surface morphology analysis showing that the NiO filler are well distributed in the samples. As a conclusion, the addition of NiO nanofiller improves the conductivity of PEO-LiClO₄ composite polymer electrolyte.     

Effect of nanoscale CeO<Subscript>2</Subscript> on PVDF-HFP-based nanocomposite porous polymer electrolytes for Li-ion batteries

New poly (vinylidenefluoride-co-hexafluoro propylene) (PVDF-HFP)/CeO₂-based microcomposite porous polymer membranes (MCPPM) and nanocomposite porous polymer membranes (NCPPM) were prepared by phase inversion technique using N-methyl 2-pyrrolidone (NMP) as a solvent and deionized water as a nonsolvent. Phase inversion occurred on the MCPPM/NCPPM when it is treated by deionized water (nonsolvent). Microcomposite porous polymer electrolytes (MCPPE) and nanocomposite porous polymer electrolytes (NCPPE) were obtained from their composite porous polymer membranes when immersed in 1.0 M LiClO₄ in a mixture of ethylene carbonate/dimethyl carbonate (EC/DMC) (v/v = 1:1) electrolyte solution. The structure and porous morphology of both composite porous polymer membranes was examined by scanning electron microscope (SEM) analysis. Thermal behavior of both MCPPM/NCPPM was investigated from DSC analysis. Optimized filler (8 wt% CeO₂) added to the NCPPM increases the porosity (72%) than MCPPM (59%). The results showed that the NCPPE has high electrolyte solution uptake (150%) and maximum ionic conductivity value of 2.47 × 10⁻³ S cm⁻¹ at room temperature. The NCPPE (8 wt% CeO₂) between the lithium metal electrodes were found to have low interfacial resistance (760 Ω cm²) and wide electrochemical stability up to 4.7 V (vs Li/Li⁺) investigated by impedance spectra and linear sweep voltammetry (LSV), respectively. A prototype battery, which consists of NCPPE between the graphite anode and LiCoO₂ cathode, proves good cycling performance at a discharge rate of C/2 for Li-ion polymer batteries.     

Effect of solvents on properties of polymer gel-electrolyte based on polyester diacrylate

New polymer gel electrolytes based on polyester diacrylates and LiClO₄ salt solutions in organic solvents are developed for lithium ion and lithium polymer batteries with a high ionic conductivity up to 2.7 × 10^?3 Ohm^?1cm^?1 at the room temperature. To choose the optimum liquid electrolyte composition, the dependence is studied of physico-chemical parameters of new gel electrolytes on the composition of the mixture of aprotic organic solvents: ethylene carbonate, propylene carbonate, and λ-butyrolacton. The bulk conductivity of gel electrolytes and exchange currents at the gel electrolyte/Li interface are studied using the electrochemical impedance method in symmetrical cells with two Li electrodes. The glass transition temperature and gel homogeneity are determined using the method of differential scanning calorimetry. It is found that the optimum mixture is that of propylene carbonate and λ-butyrolacton, in which a homogeneous polymer gel is formed in a wide temperature range of ?150 to +50°C.     

Ionic conductivity and thermal expansion of anion-deficient Sr11Mo4O23 perovskite

Transport properties of perovskite-type Sr₁₁Mo₄O₂₃ and composite Sr₁₁Mo₄O₂₃ - 1 wt% Al₂O₃ were studied at 400–1300 K in the oxygen partial pressure range from 0.21 down to 10⁻¹⁹ atm. The electromotive force and faradaic efficiency measurements, in combination with the energy-dispersive spectroscopy of the fractured electrochemical cells, unambiguously showed prevailing role of the oxygen ionic conductivity under oxidizing conditions. At temperatures above 600 K, protonic and cationic transport can be neglected. The oxygen ion transference numbers vary in the range of 0.95–1.00 at 973–1223 K. At temperatures lower than 550 K, the total conductivity of Sr₁₁Mo₄O₂₃ - 1 wt% Al₂O₃ composite measured by impedance spectroscopy tends to increase in wet atmospheres, thus indicating that hydration and protonic transport become significant. Reducing oxygen partial pressure below 10⁻¹⁰–10⁻⁹ atm leads to a significant increase in the n-type electronic conduction. The average thermal expansion coefficients in oxidizing atmospheres are (14.3–15.0) × 10⁻⁶ K⁻¹ at 340–740 K and (18.3–19.2) × 10⁻⁶ K⁻¹ at 870–1370 K.

     

LiTFSI as a plastic salt in the quasi-solid state polymer electrolyte for dye-sensitized solar cells

Ionic conductivity and the type of ions are important for the composite polymer electrolyte (CPE) of the dye-sensitized solar cells (DSSCs). Lithium bis(trifluoromethane sulphone)imide (LiTFSI for short) which is easy to dissociate, is added in the composite polymer electrolyte(CPE) as a plasticizer. The LiTFSI acts differently from the conventional LiClO₄. LiTFSI changes the conformation of the polymer chain and shows higher ionic conductivity than LiClO₄. That contributes to the improvement of the short current density of the DSSC. Furthermore, the DSSCs with LiTFSI modification show higher photovoltage than the LiClO₄. The anions of TFSI^? prohibit the interface recombination more effectively compared with the LiClO₄ as the electrochemical impedance spectroscopy indicated. With the LiTFSI modified electrolyte, the performances of the DSSCs under 1 Sun, AM1.5 are improved and reaches the highest of 4.82% at the LiTFSI:LiI = 0.116:1, much better than the original DSSC(3.6%) and the LiClO₄ modified CPE electrolyte DSSC(4.32%).     

Influence of Carbon Black on Conductivity and Structure of Polyethylene Oxide Based Polymer Electrolyte Film

The potential applications of carbon black are expected to grow as science and technology improve offering up new possibilities for innovation throughout disciplines included in the field of energy storage. The present work shows the influence of carbon black to improve the ionic conductivity of the polymer electrolyte. The synthesis of polyethylene oxide: ammonium iodide based polymer electrolyte incorporated with carbon black varying from 0.01 to 0.06 wt% with respect to PEO: NH4I system by solution casting method. Different characterizations like polarized optical microscopy (POM), impedance spectroscopy, and ionic transference number (t_ion) are studied in detail. The maximum ionic conductivity is achieved at 0.05 wt% carbon black shows 1.20 × 10⁻⁵ S cm⁻¹ at ambient temperature. In accordance with POM data, the amorphous region has increased whereas the crystalline region has shrunk which further indicated the increase in ionic conductivity . The value of (t_ion) is calculated to be 0.97 which shows the system is ionic in nature. PEO based polymer electrolyte doped carbon black can be used for the fabrication of energy storage devices.     

Nanocrystalline cellulose-reinforced composite mats for lithium-ion batteries: electrochemical and thermomechanical performance

Nanocrystalline cellulose (NCC)-reinforced poly(vinylidenefluoride-co-hexafluoropropylene) (PVdF-HFP) composite mats have been prepared by electrospinning method. Polymer electrolytes formed by activating the composite mats with 1 M lithium bis(trifluoromethanesulfonyl)imide/1-butyl-3-methypyrrolidinium bis(trifluoromethanesulfonyl)imide electrolyte solution. The addition of 2 wt% NCC in PVdF-HFP improved the electrolyte retention and storage modulus of the separator by 63 and 15 %, respectively. The developed electrolyte demonstrated high value of ionic conductivity viz. 4?×?10^?4?S?cm^?1 at 30 °C. Linear scan voltammetry revealed a wide electrochemical stability of the composite mat separator up to 5 V (vs. Li⁺/Li). Cyclic voltammetry of the polymer electrolyte with a graphite electrode in 2.5 to 0 V (vs. Li⁺/Li) potential range showed a reversible intercalation/de-intercalation of Li⁺ ions in the graphite. No peaks were observed related to the reduction of the electrolyte on the anode.     

P(VAc-MMA)为基体的聚合物电解质研究

以醋酸乙烯酯(VAc)和甲基丙烯酸甲酯(MMA)为单体, 采用半连续种子乳液聚合法制备了无规共聚物聚(醋酸乙烯酯-甲基丙烯酸甲酯)[P(VAc-MMA)], 并以此聚合物为基体制备了聚合物电解质. 用红外光谱(FTIR)、核磁共振氢谱(¹H NMR)、扫描电镜(SEM)、差热/热重分析(DSC/TG)、X射线衍射(XRD)、机械性能测试和电化学交流阻抗等方法对聚合物和聚合物电解质的性质进行了研究. 测试结果表明: VAc和MMA聚合生成P(VAc-MMA); 聚合物膜含有大量微孔结构, 利于离子传输; 聚合物电解质膜具有优良的热稳定性和机械强度; 25 ℃下, 最高的离子电导率达到了1.27× 10^－3 S•cm^－1; 离子电导率随着温度的升高而迅速增加, 电导率-温度曲线符合Arrhenius方程.     

Enhanced electrochemical properties of polyethylene oxide-based composite solid polymer electrolytes with porous inorganic–organic hybrid polyphosphazene nanotubes as fillers

Solid composite polymer electrolytes consisting of polyethylene oxide (PEO), LiClO₄, and porous inorganic–organic hybrid poly (cyclotriphosphazene-co-4, 4′-sulfonyldiphenol) (PZS) nanotubes were prepared using the solvent casting method. Differential scanning calorimetry and scanning electron microscopy were used to determine the characteristics of the composite polymer electrolytes. The ionic conductivity, lithium ion transference number, and electrochemical stability window can be enhanced after the addition of PZS nanotubes. The electrochemical impedance showed that the conductivity was improved significantly. Maximum ionic conductivity values of 1.5 × 10⁻⁵ S cm⁻¹ at ambient temperature and 7.8 × 10⁻⁴ S cm⁻¹ at 80 °C were obtained with 10 wt.% content of PZS nanotubes, and the lithium ion transference number was 0.35. The good electrochemical properties of the solid-state composite polymer electrolytes suggested that the porous inorganic–organic hybrid polyphosphazene nanotubes had a promising use as fillers in SPEs and the PEO₁₀–LiClO₄–PZS nanotube solid composite polymer electrolyte might be used as a candidate material for lithium polymer batteries.     

Ultraviolet-Cured Semi-Interpenetrating Network Polymer Electrolytes for High-Performance Quasi-Solid-State Lithium Metal Batteries

Solid polymer electrolytes with relatively low ionic conductivity at room temperature and poor mechanical strength greatly restrict their practical applications. Herein, we design semi-interpenetrating network polymer (SNP) electrolyte composed of an ultraviolet-crosslinked polymer network (ethoxylated trimethylolpropane triacrylate), linear polymer chains (polyvinylidene fluoride-co-hexafluoropropylene) and lithium salt solution to satisfy the demand of high ionic conductivity, good mechanical flexibility, and electrochemical stability for lithium metal batteries. The semi-interpenetrating network has a pivotal effect in improving chain relaxation, facilitating the local segmental motion of polymer chains and reducing the polymer crystallinity. Thanks to these advantages, the SNP electrolyte shows a high ionic conductivity (1.12 mS cm⁻¹ at 30 °C), wide electrochemical stability window (4.6 V vs. Li⁺/Li), good bendability and shape versatility. The promoted ion transport combined with suppressed impedance growth during cycling contribute to good cell performance. The assembled quasi-solid-state lithium metal batteries (LiFePO₄/SNP/Li) exhibit good cycling stability and rate capability at room temperature.     

Studies on solid-state polymer composite electrolyte of nano-silica/hyperbranched poly(amine-ester)

A new solid-state polymer composite electrolyte based on hypergrafted nano-silica (SiO₂-g-HBPAE)/hyperbranched poly (amine-ester) (HBPAE) doped with lithium perchlorate (LiClO₄) was studied in this paper. The N,N-diethylol-3-amine-2-methyl methylpropionate monomer was firstly synthesized by methyl methacrylate (MMA) and diethanolamine through Michael addition reaction and then self-condensed on the surface of nano-silica pretreated by 3-aminopropyltriethoxysilane (APTES) and MMA. The synthetic procedure of the monomers and SiO₂-g-HBPAE/HBPAE was traced by fluorescence spectra. The size and grafting ratio of SiO₂-g-HBPAE were characterized by transmission electron microscopy, static light scattering and thermogravimetric analysis. Incorporating SiO₂-g-HBPAE to HBPAE could not only decrease the glass transition temperature of polymer according to the differential scanning calorimetry characterization, but also increase the elastic and viscosity modules indicated by rheological measurement results. Electrochemical properties of SiO₂-g-HBPAE/HBPAE/LiClO₄ were also investigated. The conductivity of SiO₂-g-HBPAE/HBPAE with 50 wt% LiClO₄ reached 1.4?×?10^?5 S/cm at 30 °C and 10^?3 S/cm at 100 °C. The lithium-ion transference number of synthesized hyperbranched electrolyte can be up to 0.55.     

EC modified PEO/PVDF-LLZO composite electrolytes for solid state lithium metal batteries

The polymer-ceramic composite electrolytes have great application potential for next-generation solid state lithium batteries, as they have the merits to eliminate the problem of liquid organic electrolytes and enhancing chemical/electrochemical stability. However, polymer-ceramic composite electrolytes show poor ionic conductivity, which greatly hinders their practical applications. In this work, the addition of plasticizer ethylene carbonate (EC) into polymer-ceramic composite electrolyte for lithium batteries effectively promotes the ionic conductivity. A high ionic conductivity can be attained by adding 40 wt% EC to the polyethylene oxide (PEO)/polyvinylidene fluoride (PVDF)-Li₇La₃Zr₂O₁₂ (LLZO) based polymer-ceramic composite electrolytes, which is 2.64 × 10⁻⁴ S cm⁻¹ (tested at room temperature). Furthermore, the cell assembled with lithium metal anode, this composite electrolyte, and LiFePO₄ cathode can work more than 80 cycles at room temperature (tested at 0.2 C). The battery delivers a high reversible specific capacity after 89 cycles, which is 119 mAh g⁻¹.