Mackay,Anti-Mackay,Double-Mackay,Pseudo-Mackay,and Related Icosahedral Shell Clusters

Mackay introduced two important crystallographic concepts in a short paper published 40 years ago. One is the icosahedral shell structure (iss) consisting of concentric icosahedra displaying fivefold rotational symmetry. The number of atoms contained within these icosahedral shells and subshells agrees well with the magic numbers in rare gas clusters, (C₆₀) _N molecules, and some metal clusters determined by mass spectroscopy or simulated on energy considerations. The cluster of 55 atoms within the second icosahedral shell occurs frequently and has been called Mackay icosahedron, or simply MI, which occurs not only in various clusters, but also in intermetallic compounds and quasicrystals. The second concept is the hierarchic icosahedral structures caused by the presence of a stacking fault in the fcc packing of the successive triangular faces in the iss. For instance, a fault occurs after the ABC layers resulting an ABCB packing. This is, in fact, a hierarchic icosahedral structure of a core icosahedron connected to 12 outer icosahedra by vertex sharing, or an icosahedron of icosahedra (double MI. Contrary to Mackay's iss, a faulted hierarchic icosahedral shell is, in fact, a twinlike face capping of the underlying triangles; it is, therefore, called an anti-Mackay cluster. The hierarchic icosahedral structure in an Al-Mn-Pd icosahedral quasicrystal has a core of body-centered cube rather than an icosahedron and, therefore, is called a pseudo-Mackay cluster. The hierarchic icosahedral structures have been studied separately in the past in the fields of clusters, nanoparticles, intermetallic compounds, and quasicrystals, but the underlying geometry should be the same. In the following a unified geometrical analysis is presented.     

化学气相沉积法制备氧化锡自组装纳米结构

采用化学气相沉积法在镀有5-10 nm厚金膜的SiO2衬底上, 通过控制生长条件, 实现了二氧化锡纳米结构的自组装生长, 成功制备出了莲花状和菊花状的二氧化锡自组装纳米结构. 利用扫描电子显微镜、X射线衍射等表征分析手段对样品的表面形貌、结构及成份进行表征和研究. 并在此基础上, 讨论了两种自组装纳米结构的生长机制.     

Kinetics of polyesterification: Adipic acid with ethylene glycol, 1,4-butanediol,and 1,6-hexanediol

Polyesterifications of adipic acid with ethylene glycol, 1,4-butanediol, and 1,6-hexanediol in the absence and presence of the foreign acid (p-toluene sulfonic acid) as catalyst were carried out under constant reaction temperatures of 140–180°C (rather than at constant oil-bath temperatures) and at ratios of diol to diacid of 0.9867–3.5880. The experimental data fit the rate equations proposed by Chen and Wu: d(RCOOR′)/dt = k_ae^αp(RCOOH)²(R′OH) – k_h(H₂O)(RCOOR′) and d(RCOOR′)/dt = k_ac(AH)e^αp(RCOOH)(RO′H) – k_h(H₂O)(RCOOR′) for self-catalyzed and acid-catalyzed reactions, respectively; the data did not fit the other equations appearing in the literature. Here p is the conversion of acid, and α is the constant related to dielectric constants. The reaction rate constants and activation energies for self-catalyzed and acid-catalyzed reactions are calculated. The activation energy is found to decrease with chain length of the alkyl group of the diol. This result is consistent with that observed by Brauman and Blair using ion cyclotron resonance spectroscopy for the variation of acidity of alcohols with chain length of the alkyl group.     

Synthesis of Iso-condensed Heteroaromatic Pyrroles and Their Application in the Preparation of Conducting Polymers

Iso-condensed heteroaromatic pyrroles 1 are 10 -electron aromatic compounds. They are of interest from both theoretical and synthetic points of view. They are the cyclic analogues of heteroaromatic ortho-quinodimethanes 2, and can react with dienophiles in a Diels-Alder reaction to give the synthetically useful cycloadducts 3. Many of them are also of potential pharmaceutical importance because they are isosteric with indoles. Iso-condensed heteroaromatic pyrroles 1 can be used also as the monomers for the synthesis of new conducting polymers 5 with special properties and characteristics. However, the methods for the efficient preparation of the iso-condensed heteroaromatic pyrroles are quite limited. Iso-condensed heteroaromatic pyrroles are generally unstable in acidic conditions and are easily oxidized by air. In our laboratories, we developed three methods for the preparation of this labile heterocyclic ring system under acidic, neutral, and basic conditions.1 Synthesis of the conjugated systems such as 6 for OLED applications will also be discussed.     

Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Dynamic modification of the capillary wall for electrophoretic separations of small ions

Separations of small ions were carried out under nonequilibrated conditions using capillaries treated with NaOH, HCl, or tris(hydroxymethyl)aminomethane (Tris) prior to analysis. For separations of benzoic acid isomers or acids and amines under weakly acidic conditions, capillaries flushed with 0.1 M NaOH and subsequently with running buffers prior to analysis were used. Separations of six benzoic acid isomers were accomplished in 4 min in 1 mM phosphate buffers, pH 4.01, containing 2.5 mM hydroxypropyl-beta-cyclodextrin. Without additives, the separation of biological amines and acids were also achieved in 10 min at pH 4.01. Capillaries treated with 0.1 M HCl prior to analysis were tested in separations of six phenols in 5 mM Tris solutions at pH 7.0. As a result of small electrophoretic mobilities of phenols against a small electroosmotic flow, resolution was optimized. We also found that reproducibility was improved using capillaries treated with HCl. The relative standard deviations of migration mobility of phenols were less than 1%, which were smaller than those obtained using capillaries treated with 0.1 M NaOH or Tris.     

Optimizing separation conditions for polycyclic aromatic hydrocarbons in micellar electrokinetic chromatography

We report the separation of polycyclic aromatic hydrocarbons (PAHs) using 0.1% poly(ethylene oxide) (PEO) in micellar electrokinetic chromatography (MEKC). In the presence of PEO, adsorption of PAHs on the capillary wall was reduced, leading to better resolution and reproducibility. Effects of tetrapentylammonium iodide (TPAI), dextran sulfate (DS), methanol, and sodium lauryl sulfate (SDS) on the separation of PAHs were elucidated. In terms of resolution and speed, DS, compared to TPAI, is a better additive for separation of PAHs. When using 0.1% PEO solution containing 45% methanol, 50 mM SDS, and 0.02% DS, separation of 10 PAHs containing 2 to 5 benzene rings was accomplished in less than 12 min at 15 kV in a commercial CE system. The method has also been tested for separating seven PAHs with high quantum yields when excited at 325 nm using a He-Cd laser. Unfortunately, separation of the seven PAHs was not achieved and sensitivity diminished under the same conditions. To optimize sensitivity, resolution and speed, a stepwise technique in MEKC has been proposed. The seven PAHs were resolved in 35 min at 15 kV when separation was performed in 0.1% PEO solution containing 35 mM SDS, 40% methanol and 0.02% DS for 2 min, and subsequently in 0.1% PEO solution containing 20 mM SDS, 50% methanol, and 0.02% DS.