A Hydrogen Bonded Supramolecular Framework Birefringent Crystal

Birefringent crystals could modulate the polarization of light and are widely used as polarizers, waveplates, optical isolators, etc. To date, commercial birefringent crystals have been exclusively limited to purely inorganic compounds such as α-BaB₂O₄ with birefringence of about 0.12. Herein, we report a new hydrogen bonded supramolecular framework, namely, Cd(H₂C₆N₇O₃)₂⋅8 H₂O, which exhibits exceptionally large birefringence up to about 0.60. To the best of our knowledge, the birefringence of Cd(H₂C₆N₇O₃)₂⋅8 H₂O is significantly larger than those of all commercial birefringent crystals and is the largest among hydrogen bonded supramolecular framework crystals. First-principles calculations and structural analyses reveal that the exceptional birefringence is mainly ascribed to strong covalent interactions within (H₂C₆N₇O₃)⁻ organic ligands and the perfect coplanarity between them. Given the rich structural diversity and tunability, hydrogen bonded supramolecular frameworks would offer unprecedented opportunities beyond the traditional purely inorganic oxides for birefringent crystals.     

A High-Performance Nonlinear Optical Crystal with a Building Block Containing Expanded π-Delocalization

Common nonlinear optical (NLO) crystals consist of traditional functional building blocks with inherent optical limitation. Herein, inspired by traditional (B₃O₆)³⁻ inorganic building block, we theoretically identified a new type of organic functional building blocks and then successfully synthesized the first cyamelurate NLO crystal, Ba(H₂C₆N₇O₃)₂ ⋅ 8 H₂O. To our surprise, the constituent (H₂C₆N₇O₃)⁻ building block is not in structurally optimal arrangement, but Ba(H₂C₆N₇O₃)₂ ⋅ 8 H₂O exhibits excellent optical properties including wide band gap of 4.10 eV, very large birefringence of 0.24@550 nm, and exceptionally strong second-harmonic generation (SHG) response of about 12×KH₂PO₄. Both the SHG response and birefringence are much larger than those of commercial NLO crystal β-BaB₂O₄ with optimally aligned (B₃O₆)³⁻ building block. Theoretical calculations suggest that the expanded π-conjugation delocalization within (H₂C₆N₇O₃)⁻ vs (B₃O₆)³⁻ should be responsible to the enhanced performance. This work implies that there is still much room to develop new NLO crystals with excellent functional building blocks that may be longly neglected.     

The first salt of an isolated penta­chloro­plumbate(II) trianion

The title compound, tris(cyclo­hexane‐1,2‐diamine‐κ²N,N′)cobalt penta­chloro­plum­bate sesquihydrate, [Co(C₆H₁₄N₂)₃][PbCl₅]·1.5H₂O, crystallizes in the monoclinic space group C2/c, with a tricationic cobalt complex, a penta­chloro­plumbate trianion, one water mol­ecule in a general position and a second water mol­ecule on a crystallographic twofold axis. The compound is the first example of an isolated [PbCl₅]³⁻ moiety; the Pb atom is coordinated in a square‐pyramidal fashion, with four longer bonds to Cl atoms in the basal plane and a shorter distance to the apex. The ionic constituents and the solvent mol­ecules form a three‐dimensional network of hydrogen bonds.     

Graphitic C3N4 Decorated with CoP Co‐catalyst: Enhanced and Stable Photocatalytic H2 Evolution Activity from Water under Visible‐light Irradiation

In this work, graphitic C₃N₄ decorated with a CoP co‐catalyst (g‐C₃N₄/CoP) is reported for photocatalytic H₂ evolution reaction based on two‐step hydrothermal and phosphidation method. The structure of g‐C₃N₄/CoP is well confirmed by XRD, FTIR, TEM, XPS, and UV/Vis diffuse reflection spectra techniques. When the weight percentage of CoP loading is 3.4 wt % (g‐C₃N₄/CoP‐3.4 %), the highest H₂ evolution amount of 8.4×10² μmol g⁻¹ is obtained, which is 1.1×10³ times than that over pure g‐C₃N₄. This value also is comparable with that of g‐C₃N₄ loaded by the same amount of Pt. In cycling experiments, g‐C₃N₄/CoP‐3.4 % shows a stable photocatalytic activity. In addition, g‐C₃N₄/CoP‐3.4 % is an efficient photocatalyst for H₂ evolution under irradiation with natural solar light. Based on comparative photoluminescence emission spectra, photoelectrochemical I –t curves, EIS Nyquist plots, and polarization curves between g‐C₃N₄/CoP‐3.4 % and pure g‐C₃N₄, it is concluded that the presence of the CoP co‐catalyst accelerates the separation and transfer of photogenerated electrons of g‐C₃N₄, thus resulting in improved photocatalytic activity in the H₂ evolution reaction.     

Hydrogen‐bonded sheet structures in neutral,anionic and hydrated 6‐amino‐2‐(morpholin‐4‐yl)‐5‐nitrosopyrimidines

In each of 6‐amino‐3‐methyl‐2‐(morpholin‐4‐yl)‐5‐nitrosopyrimidin‐4(3H)‐one, C₉H₁₃N₅O₃, (I), morpholin‐4‐ium 4‐amino‐2‐(morpholin‐4‐yl)‐5‐nitroso‐6‐oxo‐1,6‐dihydropyrimidin‐1‐ide, C₄H₁₀NO⁺·C₈H₁₀N₅O₃⁻, (II), and 6‐amino‐2‐(morpholin‐4‐yl)‐5‐nitrosopyrimidin‐4(3H)‐one hemihydrate, C₈H₁₁N₅O₃·0.5H₂O, (III), the bond distances within the pyrimidine components are consistent with significant electronic polarization, which is most marked in (II) and least marked in (I). Despite the high level of substitution, the pyrimidine rings are all effectively planar, and in each of the pyrimidine components, there are intramolecular N—H...O hydrogen bonds. In each compound, the organic components are linked by multiple N—H...O hydrogen bonds to form sheets of widely differing construction, and in compound (III) adjacent sheets are linked by the water molecules, so forming a three‐dimensional hydrogen‐bonded framework. This study also contains the first direct geometric comparison between the electronic polarization in a neutral aminonitrosopyrimidine and that in its ring‐deprotonated conjugate anion in a metal‐free environment.     

A flexible functional module to regulate ultraviolet optical nonlinearity for achieving a balance between a second-harmonic generation response and birefringence

Rigid planar π-conjugated groups are adopted for designing ultraviolet (UV) nonlinear optical (NLO) materials extensively. However, for these UV NLO crystals, the realization of a strong second harmonic generation (SHG) response is commonly accompanied by undesired overlarge birefringence. Herein, we propose a new functional gene, the flexible π-conjugated (C₃H₂O₄)²⁻ group, for designing a UV NLO crystal with a balance between the SHG response and birefringence. Furthermore, the combination of low-coordinated and high-coordinated alkali cations with the flexible (C₃H₂O₄)²⁻ group results in finding a new mixed alkali malonate, KLi(C₃H₂O₄)·H₂O (KLMW). As expected, KLMW exhibits a strong SHG efficiency (3 × KDP) and moderate birefringence (0.103 @ 1064 nm). In addition, it has a short UV cut-off edge of 231 nm and can be conveniently grown from solution. More importantly, it realized fourth harmonic generation with type-I phase-matching. Therefore, these excellent properties make KLMW a potential practical UV NLO material.

The flexible (C₃H₂O₄)²⁻ groups were employed to design a new mixed alkali malonate KLi(C₃H₂O₄)·H₂O as an potential UV NLO crystal achieving the balance between strong SHG efficiency and moderate birefringence.     

Seven-coordinate complexes of molybdenum(II) and tungsten(II) containing pyrazole as a ligand

Summary Equimolar quantities of [MI₂(CO)₃(NCMe)₂] (M = Mo or W) and C₃H₄N² (pyrazole) react in CH₂C1₂ at room temperature to give the iodo-bridged dimers [M(μ-I) (CO)₃(C₃H₄N²)]₂ (1) and (2). Two equivalents of C₃H₄N² react with [MI₂(CO)₃(NCMe)₂] (M = Mo or W) to give the bis(pyrazole) complexes [MI₂(CO)₃(C₃H₄N²)₂] (3) and (4) in good yield. Three and four equivalents of pyrazole react with [MoI₂(CO)₃(NCMe)₂] to give the cationic complexes [MoI(CO)₃(C₃H₄N²)₃]I (5) and [MoI(CO)₂(C₃H₄N²)₄]I (6), respectively. The mixed ligand complexes [MI₂(CO)₃(C₃H₄N²)L] (M = Mo or W; L = PPh₃, AsPh₃ or SbPh₃) (7)-(12) are prepared by reacting equimolar amounts of [MI₂(CO)₃(NCMe)₂] and L in CH₂C1₂ at room temperature, followed by an in situ reaction with one equivalent of C₃H₄N². The MoSnCl₃ complex [MoCl(SnCl₃)(CO)₃(C₃H₄N²)₂] (13) is prepared in an analogous manner using acetone as the solvent, whilst the mixed ligand compound [MoCl(SnQ₃)(CO) ₃(C₃H₄N²)(PPh₃)] (14) was prepared by treating the dimeric complex [Mo(μ-Cl)(SnCl₃)(CO)₃(PPh₃)]₂ with two equivalents of C₃H₄N². All the new complexes were characterised by elemental analysis (carbon, hydrogen and nitrogen), i.r. and ¹H n.m.r. spectroscopy.     

NC12H8(NH)2[Gd(N3C12H8)4] und [Gd(N3C12H8)3(N3C12H9)]·PhCN: Ein Beitrag zur Reaktivität und Kristallchemie homoleptischer Selten‐Erd‐Pyridylbenzimidazolate

NC₁₂H₈(NH)₂[Gd(N₃C₁₂H₈)₄] and [Gd(N₃C₁₂H₈)₃(N₃C₁₂H₉)]·PhCN: A Contribution to the Reactivity and Crystal Chemistry of Homoleptic Pyridylbenzimidazolates of the Rare Earth Elements Transparent colourless crystals of the compound NC₁₂H₈(NH)₂[Gd(N₃C₁₂H₈)₄] were obtained by solvent‐free reaction of gadolinium metal with molten 2‐(2‐Pyridyl)‐benzimidazole. Transparent yellow crystals of the compound [Gd(N₃C₁₂H₈)₃(N₃C₁₂H₉)]·PhCN were obtained by further reacting NC₁₂H₈(NH)₂[Gd(N₃C₁₂H₈)₄] with benzonitrile thermally. Both compounds exhibit homoleptic pure nitrogen coordinations of gadolinium, the PhCN ligand is not coordinating. Whilst NC₁₂H₈(NH)₂[Gd(N₃C₁₂H₈)₄] is salt like and consists of (NC₁₂H₈(NH)₂)⁺ and [Gd(N₃C₁₂H₈)₄]^— ions, [Gd(N₃C₁₂H₈)₃(N₃C₁₂H₉)]·PhCN has a molecular structure of uncharged [Gd(N₃C₁₂H₈)₃(N₃C₁₂H₉)] units.     

Bis(1‐methyl­guanidinium) tetra­chloro­cuprate(II) and 4‐(2‐pyrimidin‐1‐io)­piperazinium tetra­chloro­cuprate(II)

The crystal structures of the title compounds, (C₂N₃H₈)₂[CuCl₄], (I), and (C₈H₁₄N₄)[CuCl₄], (II), have been studied by X‐ray diffraction. The structures consist of discrete [CuCl₄]^2? anions with two monoprotonated (C₂N₃H₈)⁺ cations for (I) and a diprotonated (C₈N₄H₁₄)²⁺ cation for (II). The [CuCl₄]^2? anions of both compounds have flattened tetrahedral geometries. There are several N—H?Cl weak bonds that join the [CuCl₄]^2? anions and the organic cations helping retain the pseudo‐tetrahedral geometries of the anions.     

Low-temperature Heat Capacities and Thermodynamic Properties of the Solid State Complexes(C2H10N2)MCl4(s)(M=Cu and Cd)

The tetrachlorocuprate(II) ethylenediammonium and tetrachlorocadmate(II) ethylenediammonium were synthesized. Chemical analysis, elemental analysis, and X‐ray crystallography were applied to characterize the compositions and crystal structures of the two complexes. The lattice potential energies and the radiuses of the anions of two complexes were calculated to be U_POT[(C₂H₁₀N₂)CuCl₄]=1810.19 kJ·mol^?1, U_POT[(C₂H₁₀N₂)CdCl₄]=1784.39 kJ·mol^?1, r[(CuCl₄)^2?]=0.308 nm, and r[(CdCl₄)^2?]=0.321 nm from the data of the crystal structure, respectively. Low‐temperature heat capacities of the two complexes were measured by a precision automatic adiabatic calorimeter with the small sample over the temperature range from 78 to 400 K, respectively. Two polynomial equations of heat capacities against the temperatures were fitted by least square method: C_p,_m[(C₂H₁₀N₂)CuCl₄, s] =213.553+118.578X?5.816X²+4.392X³+0.276X⁴ and C_p,_m[(C₂H₁₀N₂)CdCl₄, s] =190.927+98.501X?7.931X²+0.657X³+3.834X⁴, in which X= (T?239)/161. Based on the fitted polynomial equations, the smoothed heat capacities and thermodynamic functions of the two complexes relative to the standard reference temperature 298.15 K were calculated at intervals of 5 K.     

Two lanthanum(III) complexes containing η2‐pyrazolate and η2‐1,2,4‐triazolate ligands: intramolecular C—H...N/O interactions and coordination geometries

The lanthanum(III) complexes tris(3,5‐diphenylpyrazolato‐κ²N,N′)tris(tetrahydrofuran‐κO)lanthanum(III) tetrahydrofuran monosolvate, [La(C₁₅H₁₁N₂)₃(C₄H₈O)₃]·C₄H₈O, (I), and tris(3,5‐diphenyl‐1,2,4‐triazolato‐κ²N¹,N²)tris(tetrahydrofuran‐κO)lanthanum(III), [La(C₁₄H₁₀N₃)₃(C₄H₈O)₃], (II), both contain La^III atoms coordinated by three heterocyclic ligands and three tetrahydrofuran ligands, but their coordination geometries differ. Complex (I) has a mer‐distorted octahedral geometry, while complex (II) has a fac‐distorted configuration. The difference in the coordination geometries and the existence of asymmetric La—N bonding in the two complexes is associated with intramolecular C—H...N/O interactions between the ligands.     

Reaktionen von Organometallverbindungen. VI1. Bildung von Trichloroplumbaten(II) beim Zerfall von Dimethylbleidichlorid in Pyridin und Homologen

Reactions of organometal compounds. VI. Formation of Trichloroplumbates(II) by decomposition of dimethyl lead dichloride in pyridine and its homologues (CH₃)₂PbCl₂ disproportionates in pyridine, 2-methylpyridine and quinoline solution to give (CH₃)₂PbCl and – as a result of the decomposition of the second disproportionation product CH₃PbCl₃ in the presence of the bases – the trichloroplumbates(II) of the N-methylated bases: [C₅H₅N · CH₃][PbCl₃], [C₆G₇N · CH₃][PbCl₃] and [C₉H₇N · CH₃] · [PbCl₃]. N-methylpyridinium-trichloroplumbate(II) crystallizes orthorhombic, space group Pna2₁ or Pnma.     

Pt2II and Pt2III dimers containing a Pt2(2,2′‐bipyridine)2(μ‐N,N‐dimethyl­guanidinato)2 unit

The syntheses and crystal structures of the title Pt₂^II and Pt₂^III dimers doubly bridged with N,N‐dimethyl­guanidinate ligands, namely bis­(μ‐N,N‐dimethyl­guanidinato)bis­[(2,2′‐bipyridine)platinum(II)](Pt—Pt) bis­(hexa­fluoro­phosphate) acetonitrile disolvate, [Pt₂^II(C₃H₈N₃)₂(C₁₀H₈N₂)₂](PF₆)₂·2CH₃CN, (I), and guanidinium bis­(μ‐N,N‐dimethyl­guanidinato)bis­[(2,2′‐bipyridine)sulfatoplatinum(III)](Pt—Pt) bis­(hexa­fluoro­phosphate) nitrate hexa­hydrate, (C₃H₁₀N₃)[Pt^III₂(C₃H₈N₃)₂(SO₄)₂(C₁₀H₈N₂)₂]NO₃·6H₂O, (II), are reported. The oxidation of the Pt₂^II dimer into the Pt₂^III dimer results in a marked shortening of the Pt—Pt distance from 2.8512 (6) to 2.5656 (4) Å. The change is mainly compensated for by the change in the dihedral angle between the two Pt coordination planes upon oxidation, from 21.9 (2) to 16.9 (3)°. We attribute the relatively strong one‐dimensional stack of dimers achieved in the Pt₂^II compound in part to the strong Pt^II⋯C(bpy) associations (bpy is 2,2′‐bipyridine) in the crystal structure [Pt⋯C = 3.416 (10) and 3.361 (12) Å].     

Two ZnII mononuclear coordination compounds with pyridinedicarboxylate and auxiliary N‐(pyridin‐4‐ylmethylidene)hydroxylamine ligands

Two new mononuclear coordination compounds, bis{4‐[(hydroxyimino)methyl]pyridinium} diaquabis(pyridine‐2,5‐dicarboxylato‐κ²N,O²)zincate(II), (C₆H₇N₂O)₂[Zn(C₇H₃NO₄)₂(H₂O)₂], (1), and (pyridine‐2,6‐dicarboxylato‐κ³O²,N,O⁶)bis[N‐(pyridin‐4‐ylmethylidene‐κN)hydroxylamine]zinc(II), [Zn(C₇H₃NO₄)(C₆H₆N₂O)₂], (2), have been synthesized and characterized by single‐crystal X‐ray diffractometry. The centrosymmetric Zn^II cation in (1) is octahedrally coordinated by two chelating pyridine‐2,5‐dicarboxylate ligands and by two water molecules in a distorted octahedral geometry. In (2), the Zn^II cation is coordinated by a tridentate pyridine‐2,6‐dicarboxylate dianion and by two N‐(pyridin‐4‐ylmethylidene)hydroxylamine molecules in a distorted C₂‐symmetric trigonal bipyramidal coordination geometry.     

Synthesis,Reactivity and Crystal Structures of the Palladium(II) Complexes with the Pyrimidine Containing Ligand: Crystal Structures of [Pd(PPh3)(η1‐C4H3N2)(η2‐S2CNC4H8)] and [Pd(PPh3)(η1‐C4H3N2)(η2‐Tp)]

Treatment of Pd(PPh₃)₄ with 5‐bromo‐pyrimidine [C₄H₃N₂Br] in dichloromethane at ambient temperature cause the oxidative addition reaction to produce the palladium complex [Pd(PPh₃)₂(η¹‐C₄H₃N₂)(Br)], 1 , by substituting two triphenylphosphine ligands. In acetonitrile solution of 1 in refluxing temperature for 1 day, it do not undergo displacement of the triphenylphosphine ligand to form the dipalladium complex [Pd(PPh₃)Br]₂{μ,η²‐(η¹‐C₄H₃N₂)}₂, or bromide ligand to form chelating pyrimidine complex [Pd(PPh₃)₂(η²‐C₄H₃N₂)]Br. Complex 1 reacted with bidentate ligand, NH₄S₂CNC₄H₈, and tridentate ligand, KTp {Tp = tris(pyrazoyl‐1‐yl)borate}, to obtain the η²‐dithiocarbamate η¹‐pyrimidine complex [Pd(PPh₃)(η¹‐C₄H₃N₂)(η²‐S₂CNC₄H₈)], 4 and η²‐Tp η¹‐pyrimidine complex [Pd(PPh₃)(η¹‐C₄H₃N₂)(η²‐Tp)], 5 , respectively. Complexes 4 and 5 are characterized by X‐ray diffraction analyses.     

Phosphan-, Phosphit- und Phosphido-Komplexe des Vanadiums(V)

Phosphane, Phosphite, Phosphido, Complexes of Vanadium(V) Complex formation of tert-butylimidovanadium(V)trichloride ( 1 ) with phosphanes und phosphites has been studied. Syntheses of phosphidovanadium(V) compounds ^tC₄H₉N?VCp(NH^tC₄H₉)[P(SiMe₃)₂] and ^tC₄H₉N?VCp(NⁱProp₂)(PR₂) (R?SiMe₃, Ph) are described starting from the corresponding chlorovanadium(V) complexes. The reaction of 1 with silver hexafluorophosphate yields a bis(fluoro)phosphidovanadium(IV complex [(μ-PF₂)₂V₂Cl₂)(N^tC₄H₉)₂]; as primary intermediate product of the unknown redox reaction a cationic vanadium(V) complex [^tC₄H₉N?VCl₂ · PPh₃]⁺PF₆^? has been isolated. 1 reacts with an excess of diisopropylamine forming ^tC₄H₉N?V(NⁱProp₂)Cl₂ ( 16 ); in addition the following diisopropylamido-tert-butylimidovanadium(V) compounds ^tC₄H₉N?VCp(NⁱProp₂)Cl ( 3 ) and ^tC₄H₉N?V(NⁱProp₂)X₂ (X?CH₂CMe₃, O^tC₄H₉, CH₃COO) has been prepared. All compounds obtained are characterized by ¹H, ⁵¹V, ³¹P NMR spectroscopy. The X-ray diffraction analysis of 16 and 3 indicate a planar coordination sphere of the amido nitrogen atom.     

A Rapid Microwave‐Assisted Thermolysis Route to Highly Crystalline Carbon Nitrides for Efficient Hydrogen Generation

Highly crystalline graphitic carbon nitride (g‐C₃N₄) with decreased structural imperfections benefits from the suppression of electron–hole recombination, which enhances its hydrogen generation activity. However, producing such g‐C₃N₄ materials by conventional heating in an electric furnace has proven challenging. Herein, we report on the synthesis of high‐quality g‐C₃N₄ with reduced structural defects by judiciously combining the implementation of melamine–cyanuric acid (MCA) supramolecular aggregates and microwave‐assisted thermolysis. The g‐C₃N₄ material produced after optimizing the microwave reaction time can effectively generate H₂ under visible‐light irradiation. The highest H₂ evolution rate achieved was 40.5 μmol h⁻¹, which is two times higher than that of a g‐C₃N₄ sample prepared by thermal polycondensation of the same supramolecular aggregates in an electric furnace. The microwave‐assisted thermolysis strategy is simple, rapid, and robust, thereby providing a promising route for the synthesis of high‐efficiency g‐C₃N₄ photocatalysts.     

Solar Hydrogen from an Aqueous,Noble‐Metal‐Free Hybrid System in a Continuous‐Flow Sampling Reaction System

We introduce the visible‐light photocatalytic H₂ evolution reaction as catalyzed by a cobaloxime/carbon nitride (C₃N₄) noble‐metal‐free hybrid photosystem by using a continuous‐flow sampling reaction system. The photocatalytic H₂ evolution rate is highly dependent on the structure of C₃N₄, in which porous C₃N₄ shows the best activity compared with bulk C₃N₄ (lamellar) and C₃N₄ nanosheets. When using porous C₃N₄, the system is neither affected by the solution pH, nor the C₃N₄ concentration, nor the structure of the cobaloxime complex.     

稀土配合物[Pr(C3H7NO2)2(C3H4N2)(H2O)](ClO4)3的标准生成焓及热分解动力学研究

合成了高氯酸镨和咪唑(C₃H₄N₂), DL-α-丙氨酸(C₃H₇NO₂)混配配合物晶体. 经傅立叶变换红外光谱、化学分析和元素分析确定其组成为[Pr(C₃H₇NO₂)₂(C₃H₄N₂)(H₂O)](ClO₄)₃. 使用具有恒温环境的溶解-反应量热计, 以2.0 mol•L^－1 HCl为量热溶剂, 在T＝(298.150±0.001) K时测定出化学反应PrCl₃•6H₂O(s)＋2C₃H₇NO₂(s)＋C₃H₄N₂(s)＋3NaClO₄(s)＝[Pr(C₃H₇NO₂)₂(C₃H₄N₂)(H₂O)](ClO₄)₃(s)＋3NaCl(s)＋5H₂O(1)的标准摩尔反应焓为Δ_rH_m^ө＝(39.26±0.11) kJ•mol^－1. 根据盖斯定律, 计算出配合物的标准摩尔生成焓为Δ_fH_m^ө{[Pr(C₃H₇NO₂)₂(C₃H₄N₂)(H₂O)](ClO₄)₃(s), 298.150 K}＝(－2424.2±3.3) kJ•mol^－1. 采用TG-DTG技术研究了配合物在流动高纯氮气(99.99%)气氛中的非等温热分解动力学, 运用微分法(Achar-Brindley-sharp和Kissinger法)和积分法(Satava-Sestak和Coats-Redfern法)对非等温动力学数据进行分析, 求得分解反应的表观活化能E＝108.9 kJ•mol^－1, 动力学方程式为dα/dt＝2(5.90×10⁸/3)(1－α)[－ln(1－α)]^－1exp(－108.9×10³/RT).