Stress relaxation of polybutadiene at large deformation. Measurements of stress and birefringence in shear and elongation

The rheological behavior of an uncrosslinked polybutadiene on sudden application of finite strain was examined. The shear stress σ, two components of birefringence, and the extinction angle were measured in shear (magnitude of shear γ ≤ 3.5) and tensile stress and the birefringence were measured in uniaxial elongation (elongation ratio λ ≤ 3.8). Measurements were performed at 30°C with a tensile tester equipped with appropriate sample holders. The stress-optical coefficient was 3.01 × 10^?9Pa^?1. The first and second normal-stress differences v₁ and v₂ were separately evaluated with the use of stress-optical law. The Lodge—Meissner relation v₁ = γσ held good. The ratio v₂/v₁ was independent of time and varied from about ?0.3 to ?0.2 with increasing γ in the range of measurements. Each of the stress components was factored into a function of strain and one of time, and the latter was common to all the stress components. Simple formulas were proposed to represent stress components in step deformations.     

Entanglement networks of 1,2-polybutadiene crosslinked in states of strain. VII. Stress-birefringence relations

Crosslinks are introduced by γ irradiation into 1,2-polybutadiene while strained in uniaxial extension near T_g with stretch ratio λ₀, thereby trapping a proportion of the entanglements originally present. The stress at any subsequent strain λ is accurately given by the sum σ_N + σ_x, where σ_N is the stress contributed by a trapped entanglement network with λ = 1 as reference and a Mooney–Rivlin stress-strain relation, and σ_x is that contributed by a crosslink network with λ = λ₀ as reference and neo-Hookean stress-strain relation. The birefringence is accurately given as δn = ?_Nσ_N + ?_xσ_x, where the ?'s are the respective stress-optical coefficients. From measurements at λ = λ₀ where σ_x = 0, ?_N can be determined separately. For polymer with 88% 1,2 microstructure, ?_N and ?_x are nearly equal and independent of irradiation dose, though strongly dependent on temperature. For polymer with (95–96)% 1,2, ?_N and ?_x are different (even opposite in sign) and dependent on dose. This behavior is associated with a side reaction of cyclization by the γ irradiation, which is inhibited by the 1,4 moiety in the polymer with lesser 1,2 content. It is responsible for residual birefringence in the state of ease (λ = λ_s) where σ_N = –σ_x and the stress is zero.     

1,2‐Bis­(methylsulfanyl)‐1,2‐dicarba‐closo‐dodecaborane(12)

In the title compound, 1,2‐(SCH₃)₂‐1,2‐closo‐C₂B₁₀H₁₀ or C₄H₁₆B₁₀S₂, the methylsulfanyl groups are bonded to the C atoms of the 1,2‐dicarba‐closo‐dodecaborane cage. The C_cage—C_cage distance is 1.8033 (18) Å and the S—C_cage—C_cage—S torsion angle is 1.07 (13)°. The C_cage—C_cage distance is compared with those in other 1,2‐dicarba‐closo‐dodecaborane derivatives.     

Synthesis and characterization of three dinuclear copper(I) complexes of 1,2‐bis(diphenylphosphino)‐1,2‐dicarba‐closo‐dodecaborane

Three dinuclear copper(I) complexes, [Cu₂(µ‐Cl)₂(1,2‐(PPh₂)₂‐1,2‐C₂B₁₀H₁₀)₂]·2CH₂Cl₂ ( 1 ), [Cu₂(µ‐Br)₂(1,2‐(PPh₂)₂‐1,2‐C₂B₁₀H₁₀)₂]·2THF ( 2 ) and {Cu₂(µ‐I)₂[1,2‐(PPh₂)₂‐1,2‐C₂B₁₀H₁₀]₂} ( 3 ) have been synthesized by the reactions of CuX (X = Cl, Br and I) with the closo ligand 1,2‐(PPh₂)₂‐1,2‐C₂B₁₀H₁₀. All these complexes were characterized by elemental analysis, FT‐IR, ¹H and ¹³C NMR spectroscopy and X‐ray structure determination. Single crystal X‐ray structure determinations show that every complex contained di‐µ‐X‐bridged structure involving a crossed parallelogram plane formed by two Cu atoms and two X atoms (X = Cl, Br, I). The geometry at the Cu atom was a distorted tetrahedron, in which two positions were occupied by two P atoms of the PPh₂ groups connected to the two C atoms of carborane (Cc), and the other two resulted from two X atoms which bridged the other Cu atom at the same time. To the best of our knowledge, this is the first example of copper(I) complexes with 1,2‐diphenylphosphino‐1,2‐dicarba‐closo‐dodecaborane as ligand characterized by X‐ray diffraction. The catalytic property of the complex 3 for the amination of iodobenzene with aniline was also investigated. Copyright © 2005 John Wiley & Sons, Ltd.     

Synthesis,characterization and luminescence of the tetranuclear gold cluster: [Au4{7,8-(PPh2)2-7,8-C2B9H10}2(PPh3)2]

A tetranuclear gold cluster has been synthesized by the reaction of [Au(PPh₃)NO₃] with the closo carborane diphosphine 1,2-(PPh₂)₂-1,2-C₂B₁₀H₁₀ in THF, and characterized by elemental analysis, FT-IR, ¹H and ¹³C?NMR spectroscopy and X-ray structure determination. The cluster crystallizes in the triclinic Pī, a?=?15.118(8)?Å, b?=?16.057(9)?Å, c?=?24.284(13)?Å, α?=?80.822(9)°, β?=?79.624(8)°, γ?=?81.938(8)°, Z?=?2, R ₁?=?0.0626, wR ₂?=?0.1894. A single crystal structure determination showed that four gold atoms form a tetrahedral framework. Among these four gold atoms, two were chelated by two nido carborane diphosphine [7,8-(PPh₂)₂-7,8-C₂B₉H₁₀]^? anions coming from the degradation of the initial closo ligand 1,2-(PPh₂)₂-1,2-C₂B₁₀H₁₀, while the other two were ligated to two PPh₃ groups. The luminescence of this cluster was also investigated in dichloromethane solution at room temperature.     

Synthesis and properties of bis(biphenyl)chromium(<Emphasis Type="SmallCaps">i</Emphasis>) 1,4-di(2-cyanoisopropyl)-1,4-dihydrofulleride and 1-(2-cyanoisopropyl)-1,2-dihydrofullerene

Radical-ion salts bis(biphenyl)chromium(i) 1,4-di(2-cyanoisopropyl)-1,4-dihydrofulleride [(Ph₂)₂Cr]^+·[1,4-(CMe₂CN)₂C₆₀]^−· and bis(biphenyl)chromium(i) 1-(2-cyanoisopropyl)-1,2-dihydrofulleride [(Ph₂)₂Cr]^+·[1,2-(CMe₂CN)(H)C₆₀]^−·, the salt bis(biphenyl)chromium(i) (2-cyanoisopropyl)fulleride [(Ph₂)₂Cr]^+·[(CMe₂CN)C₆₀]⁻, and neutral 1-(2-cyanoisopropyl)-1,2-dihydrofullerene 1,2-(CMe₂CN)(H)C₆₀ have been synthesized for the first time. The compounds [(Ph₂)₂Cr]^+·[1,4-(CMe₂CN)₂C₆₀]^−· and [(Ph₂)₂Cr]^+·[1,2-(CMe₂CN)(H)C₆₀]^−· decompose in THF to form [(Ph₂)₂Cr]^+·[(CMe₂CN)C₆₀]⁻, whose protonation affords 1,2-(CMe₂CN)(H)C₆₀. 1,4-Di(2-cyanoisopropyl)-1,4-dihydrofullerene 1,4-(CMe₂CN)₂C₆₀ and 1,2-(CMe₂CN)(H)C₆₀ are stable in vacuo up to 513 K. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1935–1939, September, 2008.     

Diversification of ortho‐Fused Cycloocta‐2,5‐dien‐1‐one Cores and Eight‐ to Six‐Ring Conversion by σ Bond C−C Cleavage

Sequential treatment of 2‐C₆H₄Br(CHO) with LiC≡CR¹ (R¹=SiMe₃, tBu), nBuLi, CuBr?SMe₂ and HC≡CCHClR² [R²=Ph, 4‐CF₃Ph, 3‐CNPh, 4‐(MeO₂C)Ph] at ?50 °C leads to formation of an intermediate carbanion (Z)‐1,2‐C₆H₄{C_A(=O)C≡C_BR¹}{CH=CH(CH^?)R²} ( 4 ). Low temperatures (?50 °C) favour attack at C_B leading to kinetic formation of 6,8‐bicycles containing non‐classical C‐carbanion enolates ( 5 ). Higher temperatures (?10 °C to ambient) and electron‐deficient R² favour retro σ‐bond C?C cleavage regenerating 4 , which subsequently closes on C_A providing 6,6‐bicyclic alkoxides ( 6 ). Computational modelling (CBS‐QB3) indicated that both pathways are viable and of similar energies. Reaction of 6 with H⁺ gave 1,2‐dihydronaphthalen‐1‐ols, or under dehydrating conditions, 2‐aryl‐1‐alkynylnaphthlenes. Enolates 5 react in situ with: H₂O, D₂O, I₂, allylbromide, S₂Me₂, CO₂ and lead to the expected C ‐E derivatives (E=H, D, I, allyl, SMe, CO₂H) in 49–64 % yield directly from intermediate 5 . The parents (E=H; R¹=SiMe₃, tBu; R²=Ph) are versatile starting materials for NaBH₄ and Grignard C=O additions, desilylation (when R¹=SiMe) and oxime formation. The latter allows formation of 6,9‐bicyclics via Beckmann rearrangement. The 6,8‐ring iodides are suitable Suzuki precursors for Pd‐catalysed C?C coupling (81–87 %), whereas the carboxylic acids readily form amides under T3P® conditions (71–95 %).     

cis‐[1,2‐Bis(diisopropylphosphino‐κP)‐1,2‐dicarba‐closo‐dodecaborane]dichloroplatinum(II) dichloromethane hemisolvate

The asymmetric unit of the title complex, [PtCl₂(C₁₄H₃₈B₁₀P₂)]·0.5CH₂Cl₂ or cis‐[PtCl₂{1,2‐(PⁱPr₂)₂‐1,2‐C₂B₁₀H₁₀}]·0.5CH₂Cl₂, contains one disordered solvent mol­ecule and two mol­ecules of the complex, in which each Pt^II atom displays slightly distorted square‐planar coordination geometry. The P atoms connected to the cage C atoms are coordinated to the Pt^II atom. The Pt—P distances vary slightly [2.215 (3) and 2.235 (4) Å] and the Pt—Cl distances are equal [2.348 (3) and 2.353 (5) Å].     

The SO2(3B1) photosensitized isomerization of cis- and trans-1,2-dichloroethylene

The photolysis of SO₂ at 3712 Å in the presence of the 1,2-dichloroethylenes has been investigated at 22deg;C. The data are consistent with the SO₂(³B₁) photosensitized isomerization of the 1,2-dichloroethylene isomer. A kinetic treatment of the initial quantum yield data was consistent with the formation of a polarized charge-transfer intermediate whenever SO₂(³B₁) molecules and one of the 1,2-dichloroethylene isomers collide which ultimately decays unimolecularly to the cis-isomer with a probability of 0.70 ± 0.26 and to the trans-isomer with a 0.37 ± 0.16 probability. Quenching rate constants for removal of SO₂(³B₁) molecules by cis- and trans-1,2-dichloroethylene have been estimated from quantum yield data and from laser excited phosphorescence lifetimes using an excitation wavelength of 3130 Å. Estimates of the quenching rate constant (units of 1./mole ± sec) are for the cis-isomer, (1.63 ± 0.71) × 10¹⁰, quantum yield data, and (2.44 ± 0.11) × 10¹⁰, lifetime data; and for the trans-isomer,(2.59 ± 0.09)×10¹⁰, lifetime data, and (2.35 ±0.89) × 10¹⁰, quantum yield data. An experimentally determined photostationary composition,[cis-C₂Cl₂H₂]/[trans-C₂Cl₂H₂] = 1.8 - 0.1, was in good agreement with a value of 2.00 - 1.15 which was predicted from rate constants derived in this study.     

Iodinated ortho‐Carboranes as Versatile Building Blocks to Design Intermolecular Interactions in Crystal Lattices

The crystal structures of numerous iodinated ortho‐carboranes have been studied, which has revealed the diversity of intermolecular interactions that these substances can adopt in the solid state. The nature—mostly as it relates to hydrogen and/or halogen bonds—and relative strength of such interactions can be adjusted by selectively introducing substituents onto the cluster, thus enabling the rational design of crystal lattices. In this work we present the newly determined crystal structures of the following iodinated ortho‐carboranes: 9‐I‐1,2‐closo‐C₂B₁₀H₁₁, 4,5,7,8,9,10,11,12‐I₈‐1,2‐closo‐C₂B₁₀H₄, 3,4,5,6,7,8,9,10,11,12‐I₁₀‐1,2‐closo‐C₂B₁₀H₂, 1‐Me‐8,9,10,12‐I₄‐1,2‐closo‐C₂B₁₀H₇, 1,2‐Me₂‐8,9,10,12‐I₄‐1,2‐closo‐C₂B₁₀H₆, and 1,2‐Ph₂‐8,9,10,12‐I₄‐1,2‐closo‐C₂B₁₀H₆. Their 3D supramolecular organization has been thoroughly investigated and compared to similar previously published crystal structures. Such a systematic survey has allowed us to draw some general trends. C_c? H???I? B hydrogen bonds (C_c= cluster carbon atoms) appear to be significant in the growth of the crystal lattices of these compounds, given the acidity of hydrogen atoms bonded to C_c, and the polarization of B? I bonds. These hydrogen bonds can be disrupted by selectively blocking the positions next to C_c, that is, B(3) and B(6), with bulky substituents that prevent iodine atoms from approaching as hydrogen acceptors. Halogen bonds of the type B? I???I? B are frequently observed in most cases, thus suggesting that these interactions could be attractive in boron clusters. In addition, different substituents can be grafted onto the ortho‐carborane surface, thereby providing further possibilities for homomeric or heteromeric molecular assembly.     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

Y16I19C8B4 – ein Yttriumboridcarbidhalogenid mit B2C4-Einheiten

Y₁₆I₁₉C₈B₄ – a Yttrium Boride Carbide Halide Containing B₂C₄ Units The new compound Y₁₆I₁₉C₈B₄ was prepared from Y, YI₃, C and B at 1050–1150 °C. The structure of a twinned crystal was determined by means of X-ray diffraction (space group P 1¯, a = 12.311(2) Å, b = 13.996(3) Å, c = 19.695(3) Å, α = 74.96(2)°, β = 89.51(2)°, γ = 67.03(2)°, Z = 2). Y₁₆I₁₉C₈B₄ is a semiconductor and contains nearly planar B₂C₄ units which are located in cages built up by 12 yttrium atoms. Assuming (B₂C₄)^12–, these units can be regarded as isoelectronic with B₂F₄. The yttrium cages are connected via faces to form rods, which are surrounded by iodine atoms. Bridging iodine atoms connect the rods so that layers are formed. The characteristic twinning observed can be understood from the geometry of the crystal structure.     

Syntheses of Halogenated Polyhedral Phosphaboranes: Crystal Structure of conjuncto‐3,3′‐(closo‐1,2‐P2B4Br3)2

Co‐pyrolysis of B₂Br₄ with PBr₃ at 480 °C gave, in addition to the main product closo‐1,2‐P₂B₄Br₄, conjuncto‐3,3′‐(1,2‐P₂B₄Br₃)₂ ( 1 ) and the twelve‐vertex closo‐1,7‐P₂B₁₀Br₁₀ ( 2 ), both in low yields. X‐ray structure determination for 1 [triclinic, space‐group P1 with a = 7.220(2) Å, b = 7.232(2) Å, c = 8.5839(15) Å, α = 97.213(15)°, β = 96.81(2)°, γ = 94.07(2)° and Z = 1] confirmed that 1 adopts a structure consisting of two symmetrically boron–boron linked distorted octahedra with the bridging boron atoms in the 3,3′‐positions and the phosphorus atoms in the 1,2‐positions. The intercluster 2e/2c B–B bond length is 1.61(3) Å. The shortest boron–boron bond within the cluster framework is 1.68(2) Å located between the boron atoms antipodal to the phosphorus atoms. The icosahedral phosphaborane 2 was characterized by ¹¹B‐¹¹B COSY NMR spectroscopy showing cross peaks indicative for the isomer with the phosphorus atoms in 1,7‐positions. Both the X‐ray data of 1 and the NMR spectroscopic data of 1 and 2 give further evidence for the influence of an antipodal effect of heteroatoms to cross‐cage boron atoms and, vice versa, of an additional shielding of the phosphorus atoms caused by B‐Hal substitution at the boron positions trans to phosphorus.     

X-Ray and X-ray Photoelectron Spectroscopy Studies of the Electronic Structure of Borane Derivatives

This paper reviews the results of electronic structure studies of a number of typical members of borane series by X-ray and X-ray photoelectron spectroscopy using quantum chemical calculations. Fragment analysis of the molecular orbital structure is given. The nature of chemical interaction in boron cluster compounds is studied on models: simple molecules NH₃, BH₃, and BF₃ and their adducts NH₃BH₃ and NH₃BF₃. The electronic structure of B₁₀H₁₂L₂ type compounds with Lewis bases L = NH₃, (CH₃)₂S, (C₆H₅)₃P is analyzed. The complexes are considered in terms of the concept of donor–acceptor interactions between the fragments. The donor–acceptor bond has contributions from both occupied and vacant acceptor orbitals. X-ray photoelectron data on the charged states of atoms in the compounds are overviewed. Electron distribution in complex compounds with transition metals [(1,2-B₉C₂H₁₁)₂M]^–, M = Fe^III, Co^III, Ni^III, and Ni^IV and chain type polycobaltocarborane anions {[(3)-1,2-B₉C₂H₁₁]₂Co _n [(3,6)-1,2-B₈C₂H₁₀]_n-1} ^n– , n = 2-7, is considered.     

A CAS study on S‐loss and O‐loss dissociation mechanisms of the SO2+ ion in the C,D, and E states

In the present work, we mainly study dissociation of the C ²B₁, D²A₁, and E²B₂ states of the SO₂⁺ ion using the complete active‐space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods. We first performed CASPT2 potential energy curve (PEC) calculations for S‐ and O‐loss dissociation from the X, A, B, C, D, and E primarily ionization states and many quartet states. For studying S‐loss predissociation of the C, D, and E states by the quartet states to the first, second, and third S‐loss dissociation limits, the CASSCF minimum energy crossing point (MECP) calculations for the doublet/quartet state pairs were performed, and then the CASPT2 energies and CASSCF spin‐orbit couplings were calculated at the MECPs. Our calculations predict eight S‐loss predissociation processes (via MECPs and transition states) for the C, D, and E states and the energetics for these processes are reported. This study indicates that the C and D states can adiabatically dissociate to the first O‐loss dissociation limit. Our calculations (PEC and MECP) predict a predissociation process for the E state to the first O‐loss limit. Our calculations also predict that the E²B₂ state could dissociate to the first S‐ and O‐loss limits via the A²B₂ ← E²B₂ transition. On the basis of the 13 predicted processes, we discussed the S‐ and O‐loss dissociation mechanisms of the C, D, and E states proposed in the previous experimental studies. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Koordinationseigenschaften von Carbaboranylchlorophosphanen: Synthese und Molekülstruktur von cis-rac-Molybdäntetracarbonyl{1,2-bis(chlorophenylphosphino)-1,2-dicarba-closo-dodecaboran(12)}

Coordination Properties of Carbaboranylchlorophosphines: Synthesis and Molecular Structure of cis-rac -Molybdenumtetracarbonyl{1,2-bis(chlorophenylphosphino)-1,2-dicarba-closo-dodecaborane(12)} Rac-1,2-bis(chlorophenylphosphino)-1,2-dicarba-closo-dodecaborane(12) ( 1 ) reacts with [Mo(CO)₄(NBD)] (NBD = norbornadiene) after several hours at 50–55 °C to yield cis-rac-[Mo(CO)₄{1,2-(PPhCl)₂C₂B₁₀H₁₀}] ( 2 ). 2 was characterised spectroscopically (¹H, ¹³C, ¹¹B and ³¹P NMR) and by crystal structure determination.     

Thermal decomposition of 1-butyne in shock waves

1-Butyne diluted with Ar was heated behind reflected shock waves over the temperature range of 1100–1600 K and the total density range of 1.36 × 10^?5?1.75 × 10^?5 mol/cm³. Reaction products were analyzed by gas-chromatography. The progress of the reaction was followed by IR laser kinetic absorption spectroscopy. The products were CH₄, C₂H₂, C₂H₄, C₂H₆, allene, propyne, C₄H₂, vinylacetyiene, 1,2- butadiene, 1,3-butadiene, and benzene. The present data were successfully modeled with a 80 reaction mechanism. 1-Butyne was found to isomerize to 1,2-butadiene. The initial decomposition was dominated by 1-butyne → C₃H₃ + CH₃ under these conditions. Rate constant expressions were derived for the decomposition to be k₇ = 3.0 × 10¹⁵ exp(?75800 cal/RT) s^?1 and for the isomerization to be k₄ = 2.5 × 10¹³ exp(?65000 cal/RT) s^?1. The activation energy 75.8 kcal/mol was cited from literature value and the activation energy 65 kcal/mol was assumed. These rate constant expressions are applicable under the present experimental conditions, 1100–1600 K and 1.23–2.30 atm. © 1995 John Wiley & Sons, Inc.     

A `tetrameric' 3,4‐di‐p‐tolyl‐1,2,5‐oxadiborole derivative

In the title compound, 1,1,6a,7,9a,10‐hexa­chloro‐2,3,5,6,8,9,11,12‐octa‐p‐tolyl‐1,6a,9a,12a‐tetraborata‐3a,4a,7,10‐tetrabora‐4a¹,6b,9b,12b‐tetraoxonia‐4‐oxatetra­cyclo­penta­[1,2‐a:2,1,5‐de:1,2‐g:1,2‐i]­naphthalene di­chloro­methane pentasolvate, C₆₄H₅₆B₈Cl₆O₅·5CH₂Cl₂, two condensed oxadiborole rings are attached to two further oxadiborole rings in a type of donor–acceptor bonding, thus forming a ten‐membered alternating (B—O)₅ naphthalene‐like arrangement as the central building block.     

Thermal isomerization and decomposition of 1,2-butadiene in shock waves

1,2-Butadiene diluted with Ar was heated behind reflected shock waves over the temperature and the total density range of 1100–1600 K and 1.36 × 10^?5 ? 1.75 × 10^?5 mol/cm³. The major products were 1,3-butadiene, 1-butyne, 2-butyne, vinylacetylene, diacetylene, allene, propyne, C₂H₆, C₂H₄, CH₄, and benzene, which were analyzed by gas chromatography. The UV kinetic absorption spectroscopy at 230 nm showed that 1,2-butadiene rapidly isomerizes to 1,3-butadiene from the initial stage of the reaction above 1200 K. In order to interpret the formation of 1,3-butadiene, 1-butyne, and 2-butyne, it was necessary to include the parallel isomerizations of 1,2-butadiene to these isomers. The present data were successfuly modeled with a 82 reaction mechanism. From the modeling, rate constant expressions were derived for the isomerization 1,2-butadiene = 1,3-butadiene to be k₃ = 2.5 × 10¹³ exp(?63 kcal/RT) s^?1 and for the decomposition 1,2-butadiene = C₃H₃ + CH₃ to be k₆ = 2.0 × 10¹⁵ exp(?75 kcal/RT) s^?1, where the activation energies, 63 kcal/mol and 75 kcal/mol, were assumed. These rate constants are only applicable under the present experimental conditions, 1100–1600 K and 1.23–2.30 atm. © 1995 John Wiley & Sons, Inc.     

Elastic moduli of ultradrawn polyethylene

The five independent elastic moduli C₁₁, C₁₂, C₁₃, C₃₃, and C₄₄ of oriented high-density polyethylene with draw ratio λ from 1 to 27 have been determined from ?60 to 100°C by an ultrasonic method at 10 MHz. At low temperature the sharp rise in the axial extensional modulus C₃₃ with increasing λ and the slight changes in the other moduli result from chain alignment and the increase in the number of intercrystalline bridges connecting the crystalline blocks. At high temperature (say, 100°C) the transverse extensional modulus C₁₁, as well as the axial (C₄₄) and transverse (C₆₆) shear moduli, also show substantial increases, reflecting the prominent reinforcing effect of stiff crystalline bridges in this temperature region where the amorphous matrix is rubbery. If the crystalline bridges are regarded as the fiber phase, the mechanical behavior can be understood in terms of the Halpin–Tsai equation for aligned short-fiber composites.