Microscopic calculation of the energetics of charged states in amorphous polyethylene

Polarization energies are calculated for a single excess charge on a polyethylene chain in amorphous polyethylene using (i) local segment and nonlocal distributed molecular polarizabilities, (ii) material structures simulated by both general-purpose and specialist Monte Carlo software, and (iii) uniform and Gaussian distributions of charge with different extents of charge delocalization. Local and distributed response lead to results that are essentially the same except that they correspond to different mean polarizabilities. With increasing delocalization of the charge along the chain, the polarization energies shift to higher values and the width of their distribution decreases, the differences being more pronounced for the uniform distribution. The polarization energies for charges delocalized over 10-20 methylene units form a distribution some 14 eV wide centered around 1 eV, narrowing significantly for more homogeneous polymer melts. The calculations are relevant to trapping of charge in polyethylene. They also yield the microscopic variation in the potential along the polymer chain caused by the polarization energy difference, and so may provide useful inputs to theories of electronic conduction in polymer materials.     

Breakdown of the anisotropic lorentz approximation in p-terphenyl

Polarizability changes for tetracene and pentacene in a p-terphenyl host crystal calculated from Stark measurements using the anisotropic Lorentz local field disagree with physical intuition. A local field taking better account of the anisotropic p-terphenyl structure gives acceptable polarizability changes.     

The thermal expansion of axial metals

The thermal expansion of axial metals is surveyed with particular reference to recent very low temperature data for zinc, cadmium, magnesium, β-tin, indium, bismuth and antimony. For a given solid, the independent thermal expansion coefficients α_⊥ and α_‖ are conveniently compared at low temperatures by plotting α_⊥/T ³ and α_‖/T ³ against T. The plots show clearly how contraction in one principal symmetry direction ensues from rapid expansion in the other direction. The Grüneisen functions γ_⊥ and γ_‖ are discussed for each solid using data from lattice-dynamical models and neutron-diffraction measurements. They show how features of the individual thermal expansions arise from a combination of vibrational, elastic and electronic effects. For these solids and for zirconium, titanium, yttrium and thallium the larger of γ_⊥ and γ_‖ at high temperatures is that referring to strains in the direction of the stronger forces (judged from the axial ratio). At lower temperatures the inequality reverses, except for tin, implying that the highest normal-mode frequencies depend most strongly on strain in the direction of the stronger forces. More experimental studies of thermal expansion at the lowest temperatures are desirable, as well as more second and third-order elastic constant data. Theoretical work is needed on realistic lattice models applicable to non-cubic metals.     

Energy of charged states in the acetanilide crystal: trapping of charge-transfer states at vacancies as a possible mechanism for optical damage

Calculations for the acetanilide crystal yield the effective polarizability (16.6 A(3)), local electric field tensor, effective dipole moment (5.41 D), and dipole-dipole energy (-12.8 kJ/mol). Fourier-transform techniques are used to calculate the polarization energy P for a single charge in the perfect crystal (-1.16 eV); the charge-dipole energy W(D) is zero if the crystal carries no bulk dipole moment. Polarization energies for charge-transfer (CT) pairs combine with the Coulomb energy E(C) to give the screened Coulomb energy E(scr); screening is nearly isotropic, with E(scr) approximately E(C)/2.7. For CT pairs W(D) reduces to a term deltaW(D) arising from the interaction of the charge on each ion with the change in dipole moment on the other ion relative to the neutral molecule. The dipole moments calculated by density-functional theory methods with the B3LYP functional at the 6-311++G(**) level are 3.62 D for the neutral molecule, changing to 7.13 D and 4.38 D for the anion and cation, relative to the center of mass. Because of the large change in the anion, deltaW(D) reaches -0.9 eV and modifies the sequence of CT energies markedly from that of E(scr), giving the lowest two CT pairs at -1.98 eV and -1.41 eV. The changes in P and W(D) near a vacancy are calculated; W(D) changes for the individual charges because the vacancy removes a dipole moment and modifies the crystal dielectric response, but deltaW(D) and E(C) do not change. A vacancy yields a positive change DeltaP that scatters a charge or CT pair, but the change DeltaW(D) can be negative and large enough to outweigh DeltaP, yielding traps with depths that can exceed 150 meV for single charges and for CT pairs. Divacancies yield traps with depths nearly equal to the sum of those produced by the separate vacancies and so they can exceed 300 meV. These results are consistent with a mechanism of optical damage in which vacancies trap optically generated CT pairs that recombine and release energy; this can disrupt the lattice around the vacancy, thereby favoring trapping and recombination of CT pairs generated by subsequent photon absorption, leading to further lattice disruption. Revisions to previous calculations on trapping of CT pairs in anthracene are reported.     

Volume Growth and the Topology of Manifolds with Nonnegative Ricci Curvature

Let M ⁿ be a complete, open Riemannian manifold with Ric≥0. In 1994, Grigori Perelman showed that there exists a constant δ _n >0, depending only on the dimension of the manifold, such that if the volume growth satisfies \(\alpha_{M}:=\lim_{r\rightarrow \infty}\frac{\operatorname{Vol}(B_{p}(r))}{\omega_{n}r^{n}}\geq 1-\delta_{n}\), then M ⁿ is contractible. Here we employ the techniques of Perelman to find specific lower bounds for the volume growth, α(k,n), depending only on k and n, which guarantee the individual k-homotopy group of M ⁿ is trivial.     

Supported bis(indenyl)– and bis(fluorenyl)–chromium catalysts for ethylene polymerization

Silica-supported bis(indenyl)– and bis(fluorenyl)–chromium catalysts show good activity in ethylene polymerization. For maximum productivity with the indenyl chromium catalyst, the silica must be dried, with higher dehydration temperatures giving a significant increase in polymerization activity. Less deactivation on thermal aging of the supported bis(indenyl)–chromium catalyst allows ethylene polymerization to proceed for many hours, which provides polyethylenes of low residual chromium content. In contrast to the behavior of supported chromocene catalysts, the indenyl–and fluorenyl–chromium catalysts require a higher hydrogen/ethylene ratio to achieve a specific polymer melt index. Nevertheless, highly saturated polyethylenes are produced with these new catalysts. This result indicates that chain transfer to hydrogen remains the major chain transfer reaction. Addition of cyclopentadiene to a supported indenyl–chromium catalyst provided a catalyst with a much higher transfer response to hydrogen. This result suggests that ligand exchange occurred, producing a supported chromocene catalyst. These overall results are consistent with an active-site model which comprises a supported divalent chromium center attached to an indenyl or fluorenyl ligand during the polymerization process. Polymerization is believed to occur by a coordinated anionic mechanism of the type previously discussed for a supported chromocene catalyst.     

Uptake of liquid alcohols by the flexible Fe(III) metal-organic framework MIL-53 observed by time-resolved in situ X-ray diffraction

A comprehensive, time‐resolved, energy‐dispersive X‐ray diffraction study of the uptake of liquid alcohols (methanol, ethanol, propan‐1‐ol and propan‐2‐ol) by the flexible metal‐organic framework solid MIL‐53(Fe)[H₂O] is reported. In the case of the primary alcohols, a fluorinated version of the MIL‐53(Fe) host (C2/c symmetry V ca. 1000 ų), in which a fraction of framework hydroxides are replaced by fluoride, shows uptake of alcohols to give initially a partially expanded phase (C2/c symmetry, V ca. 1200 ų) followed by an expanded form of the material (either Imcm or Pnam symmetry, V ca. 1600 ų). In the case of methanol–water mixtures, the EDXRD data show that the partially open intermediate phase undergoes volume expansion during its existence, before switching to a fully open structure if concentrated methanol is used; analogous behaviour is seen if the initial guest is propan‐2‐ol, which then is replaced by pyridine, where a continuous shift of Bragg peaks within C2/c symmetry is observed. In contrast to the partially fluorinated materials, the purely hydroxylated host materials show little tendency to stabilise partially open forms of MIL‐53(Fe) with primary alcohols and the kinetics of guest introduction are markedly slower without the framework fluorination: this is exemplified by the exchange of water by propan‐2‐ol, where a partially open C2/c phase is formed in a step‐wise manner. Our study defines the various possible pathways of liquid‐phase uptake of molecular guests by flexible solid MIL‐53(Fe).