二甲苯在ZSM-5分子筛中的吸附与扩散

本文在298K-493K温度范围内,测定了二甲苯在ZSM-5分子筛中的吸附等温线和扩散系数。间二甲苯在HZSM-5分子筛中的吸附是需要较高活化能而为扩散控制的物理吸附,只有在较高温度下(>393K),才能进入分子筛的敛孔,其扩散系数比对二甲苯小三个数量级。对、间二甲苯在HZSM-5分子筛中的吸附量随温度升高而渐趋接近。但HZSM-5经镁改性后,间二甲苯吸附量大幅度下降,而对二甲苯吸附量变化不大,说明孔道结构因素对提高烷基苯转化的对位选择性起着相当重要的作用。增大分子筛的晶粒尺寸,二甲苯的扩散系数变化不大,表明大晶粒ZSM-5之所以能提高对位选择性,原因在于扩散路线的增长导致扩散较慢的间二甲苯异构化为扩散较快的对二甲苯。     

Magnetization of the Ising model on the generalized checkerboard lattice

We consider the Ising model on the generalized checkerboard lattice. Using a recent result by Baxter and Choy, we derive exact expressions for the magnetization of nodal spins at two values of the magnetic field,H=0 andH=i1/2kT. Our results are given in terms of Boltzmann weights of a unit cell of the checkerboard lattice without specifying its cell structures.     

Quasi-geodesic segments and Gromov hyperbolic spaces

It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equialent for geodesic metric spaces.Supported as a Feodor Lynen Fellow of the Alexander von Humboldt foundation.     

Relative perturbation bounds for the unitary polar factor

LetB be anm×n (m≥n) complex (or real) matrix. It is known that there is a uniquepolar decomposition B=QH, whereQ*Q=I, then×n identity matrix, andH is positive definite, providedB has full column rank. Existing perturbation bounds suggest that in the worst case, for complex matrices the change inQ be proportional to the reciprocal ofB's least singular value, or the reciprocal of the sum ofB's least and second least singular values if matrices are real. However, there are situations where this unitary polar factor is much more accurately determined by the data than the existing perturbation bounds would indicate. In this paper the following question is addressed: how much mayQ change ifB is perturbed to $\tilde B = D_1^* BD_2 $ , whereD ₁ andD ₂ are nonsingular and close to the identity matrices of suitable dimensions? It is shown that for a such kind of perturbation, the change inQ is bounded only by the distances fromD ₁ andD ₂ to identity matrices and thus is independent ofB's singular values. Such perturbation is restrictive, but not unrealistic. We show how a frequently used scaling technique yields such a perturbation and thus scaling may result in better-conditioned polar decompositions.     

On smallest covers of finite projective spaces

A t-cover of a finite projective space ℙ is a set of t-dimensional subspaces covering all points of ℙ. Beutelspacher [1] constructed examples of t-covers and proved that his examples are of minimal cardinality. We shall show that all examples of minimal cardinality “look like” the examples of Beutelspacher.     

Nonstandard analysis of ordered sets

We introduce a nonstandard approach to the study of ordered setsX based on a classification of the elements of the ordered set *X into three types, upward, downward, and lateral, which may be thought of dynamically as arising from the possibilities of upward, downward, and lateral motion withinX. Initial applications include the characterization thatX has no infinite diverse subset iff *X has no lateral elements, a result subsequently exploited in work on the interval topology and order-compatibility, where we give a nonstandard proof of Naito's result that ifX has no infinite diverse subset, it has a unique order-compatible topology. We also describe how the completion of a nonempty linearly ordered setX may be obtained as a quotient of *X.     

Intervals in lattices of quasiorders

We investigate the structure of intervals in the lattice of all closed quasiorders on a compact or discrete space. As a first step, we show that if the intervalI has no infinite chains then the underlying space may be assumed to be finite, and in particular,I must be finite, too. We compute several upper bounds for its size in terms of its heighth, which in turn can be computed easily by means of the least and the greatest element ofI. The cover degreec of the interval (i.e. the maximal number of atoms in a subinterval) is less than 4h. Moreover, ifc4(n–1) thenI contains a Boolean subinterval of size 2 ⁿ , and ifI is geometric then it is already a finite Boolean lattice. While every finite distributive lattice is isomorphic to some interval of quasiorders, we show that a nondistributive finite interval of quasiorders is neither a vertical sum nor a horizontal sum of two lattices, with exception of the pentagon. Many further lattices are excluded from the class of intervals of quasiorders by the fact that no join-irreducible element of such an interval can have two incomparable join-irreducible complements. Up to isomorphism, we determine all quasiorder intervals with less than 9 elements and all quasiorder intervals with two complementary atoms or coatoms.     

Pdn(n=1-7)团簇及其与甲烷相互作用的密度泛函理论研究

用密度泛函理论(DFT)的B3LYP方法, 对Pdn(n=1-7)团簇的几何结构、振动频率及其与甲烷分子间的相互作用进行了理论研究. 结果表明, 随着Pd原子数增多, 团簇结构对团簇大小的依赖性减弱, 结构参数向金属晶体趋近. 在Pdn(n=1-7)团簇上, 甲烷的表面吸附作用较弱. Pd2CH4中, 甲烷受到两个Pd原子的活化作用, 活化程度增强, 吸附能增大. 在PdnCH4 (n=1, 3-7)体系中, 甲烷的吸附能随着团簇模型的增大而减小, 趋近于其在金属晶面上的吸附能.     

BrO-H2O 及 HOBr-H2O复合物偶合方式的理论研究

在6-311++G(d,p)水平上采用四种方法讨论了两种BrO-H₂O和三种HOBr-H₂O复合物的构型性质。在两种BrO-H₂O复合物中，结合能为11.37–13.92 J/mol的复合物2 （电子态为²A′）最稳定，该复合物是通过BrO中的Br原子和水中的O原子结合的。三种HOBr-H₂O复合物中，复合物3和4的结合能约为16.30–21.32 J/mol，三种复合物的稳定顺序为：复合物3 ≈ 复合物4 > 复合物5。     

Iridium-imine and -amine complexes relevant to the (S)-metolachlor process: structures, exchange kinetics, and C-H activation by Iri causing racemization

Iridium complexes of DMA-imine [2,6-dimethylphenyl-1'-methyl-2'-methoxyethylimine, 1 a) and (R)-DMA-amine [(1'R)-2,6-dimethylphenyl-1'-methyl-2'-methoxyethylamine, 2 a] that are relevant to the catalytic imine hydrogenation step of the Syngenta (S)-Metolachlor process were synthesized: metathetical exchange of [Ir2Cl2(cod)2] (cod=1,5-cyclooctadiene) with [Ag(1 a)2]BF4 and [Ag((R)-2 a)2]BF4 afforded [Ir(cod)(kappa2- -1 a)]BF4 (11) and [Ir(cod)(kappa2-(R)-2 a)]BF4 ((R)-19)), respectively. These complexes were then used in stopped-flow experiments to study the displacement of amine 2 a from complex 19 by imine 1 a to form the imine complex 11, thus modeling the product/substrate exchange step in the catalytic cycle. The data suggest a two-step associative mechanism characterized by k1=(2.6+/-0.3) x 10(2) M(-1) s(-1) and k2=(4.3+/-0.6) x 10(-2) s(-1) with the respective activation energies EA1=(7.5+/-0.6) kJ mol(-1) and EA2=(37+/-3) kJ mol(-1). Furthermore, complex 11 reacted with H2O to afford the hydrolysis product [Ir(cod)(eta(6-)-2,6-dimethylaniline)]BF4 (12), and with I2 to liberate quantitatively the DMA-iminium salt 14. On the other hand, the chiral amine complex (R)-19 formed the optically inactive eta6-bound compound [Ir(cod)(eta6-rac-2 a)]BF4 (rac-18) upon dissolution in THF at room temperature, presumably via intramolecular C-H activation. This racemization was found to be a two-step event with k'1=9.0 x 10(-4) s(-1) and k2=2.89 x 10(-5) s(-1), featuring an optically active intermediate prior to sp3 C-H activation. Compounds 11, 12, rac-18, and (R)-19 were structurally characterized by single-crystal X-ray analyses.