Temperatures of rotating clusters

The effect of the spatial anisotropy in the distribution of components of particle momenta of the rotating Ar₃ cluster is studied at a given total energy and different values of the total angular momentum. The Schwarzschild formula applied to describe this distribution gives three parameters which can serve as a measure of the internal temperatures of the cluster. A new definition of the energy of the overall non-rigid rotation based on the Schwarzschild distribution is proposed.     

Statistical evaporation of rotating clusters. III. Molecular clusters

Unimolecular evaporation of weakly bound clusters made of rigid molecules is considered from the points of view of statistical theories and molecular dynamics simulations. We explicitly work out expressions for the kinetic energy released and product angular momentum distributions within the sphere+sphere and sphere+linear rigid body assumptions of phase space theory (PST). Various approximations are investigated, including the shape of the interaction potential between the two fragments and the anharmonicity of the vibrational density of states. The comparison between phase space theory and simulation for nitrogen and methane clusters shows a quantitative agreement, thereby suggesting that PST is accurate in predicting statistical observables in a wide range of systems under various physical conditions.     

Superfluid effects in rotating helium clusters

We study the response of Bose⁴He clusters to an external field corresponding to a rotation with frequency ω. An explicit form for the normal (nonsuperfluid) fraction of the system as a function of the temperatureT and of the mass numberN of the cluster is obtained under the assumption that only surface modes are thermally excited. The critical behaviour of⁴He clusters at high rotational frequencies is also investigated.     

Fractal structure of three-dimensional Witten—Sander clusters

Five large (25 000 particle) three-dimensional Witten—Sander clusters have been generated, and geometric relationships characterizing this structure have been examined. The quantities measured include the dependence of the radius of gyration. (r²)^{$\text{1}\text{2}$}, and (r⁴)^{$\text{1}\text{4}$} on cluster size N, the mass M(r) contained within a distance r from the center mass, the dependence of the areas of projections of the clusters onto a plane of cluster size N, the density—density correlation function and the distribution of particles (occupied lattice sites) in cubes of side λ as a function of λ. Although uncertainties are quite large, our results are consistent with the concept hat the geometric scaling properties of three-dimensional Witten—Sander clusters can be described in terms of a single effective dimensionality D with a value of = 2.45. Additional results are also presented for two-dimensional Witten—Sander clusters which indicate a single effective dimensionality with a value of = 5/3.     

Effective magnetization of rotating free ferromagnetic metal clusters

The deflection of free magnetic metal clusters in a Stern-Gerlach magnetic field is studied. In particular we investigate magnetic resonance effects resulting from lattice anisotropy and cluster rotation. In analogy to small suspended particles in an oscillating magnetic field the anisotropy field fixed to the rotating atomic lattice of the cluster acts on the cluster magnetization like an rf field in NMR experiments. In our calculation we have used the Bloch equations and assumed different anisotropy field symmetries (uniaxial, cubic). A minimum in the magnetization as a function of the Stern-Gerlach field and also of the cluster size, as observed recently, is obtained under certain conditions. However, such a resonance behavior occurs only if the distribution of the rotation frequency _rot is relatively narrow, while a broad distribution of _rot yields an almost superparamagnetic behavior. In addition, the strength of the anisotropy field and the relaxation time are important variables which determine the magnetic behavior of the clusters.     

Nanoscopic structure and function of polymer‐protected metal clusters

Colloidal dispersion of polymer‐protected metal clusters were prepared by heat treatment of macromolecule‐metal complexes, composed of water‐soluble polymer and noble metal ions. The mixtures of two kinds of noble metal ions can provide polymer‐protected bimetallic nanoclusters with a core/shell structure by the same procedure. In contrast, bimetallic clusters with the inverted core/shell structure are difficult to be prepared by the similar procedure. A sacrificial hydrogen strategy has been successfully proposed for the preparation of the inverted ones. When copper or nickel ions were used as one of the elements to prepare bimetallic clusters, rather random alloy structured nanoparticles were produced. The catalytic activity of these bimetallic clusters is, in general, higher than that of the corresponding monometallic ones.     

Statistical evaporation of rotating clusters. IV. Alignment effects in the dissociation of nonspherical clusters

Unimolecular evaporation in rotating, nonspherical atomic clusters is investigated using phase space theory in its orbiting transition state version. The distributions of the total kinetic energy release epsilon(tr) and the rotational angular momentum J(r) are calculated for oblate top and prolate top main products with an arbitrary degree of deformation. The orientation of the angular momentum of the product cluster with respect to the cluster symmetry axis has also been obtained. This statistical approach is tested in the case of the small eight-atom Lennard-Jones cluster, for which comparison with extensive molecular dynamics simulations is presented. The role of the cluster shape has been systematically studied for larger, model clusters in the harmonic approximation for the vibrational densities of states. We find that the type of deformation (prolate versus oblate) plays little role on the distributions and averages of epsilon(tr) and J(r) except at low initial angular momentum. However, alignment effects between the product angular momentum and the symmetry axis are found to be significant, and maximum at some degree of oblateness. The effects of deformation on the rotational cooling and heating effects are also illustrated.     

A model for thermal spin relaxation in rotating ferromagnetic clusters

A model for thermal spin relaxation in isolated ferromagnetic clusters is proposed and investigated theoretically by means of nonequilibrium thermodynamics. It is shown that thermal agitation mediates relaxation of the spin towards the total angular momentum vector of the cluster so that the clusters are magnetically polarized in the direction of their rotational axis. A relaxation mechanism via thermal moment of inertia fluctuations is proposed. The results are discussed for a Fe₁₂₅-cluster.     

Poly[di‐μ3‐chloro‐μ2‐trans‐1,2‐di‐4‐pyridylethyl­ene‐dicopper(I)]: a two‐dimensional organic–inorganic hybrid constructed from linear CuCl clusters and bridging ligands

The structure of the title compound, [Cu₂Cl₂(C₁₂H₁₀N₂)]_n, contains infinite CuCl staircase‐like chains, which lie about inversion centres. The trans‐1,2‐di‐4‐pyrid­ylethyl­ene mol­ecules also lie about inversion centres and connect the CuCl chains through Cu—N coordination bonds into a two‐dimensional organic–inorganic hybrid network. The planar sheets are stacked along the c axis and associated through weak C—H⋯Cl inter­actions. The results show a reliable structural motif with controllable separation of the CuCl chains by variation of the length of the ligand.     

A kinetic model of carbon clusters growth

A kinetic model of carbon cluster growth is suggested, including the processes of polycyclic clusters formation and their isomerization to fullerenes, discovered recently in experiments. The model is based on Smoluchowski equations, describing the rates of clusters formation in various possible reactions. The simulation results are in agreement with the experimental observations.     

3a‐Phenyl‐2,3,3a,4‐tetrahydro‐1H‐benzo[d]pyrrolo[1,2‐a]imidazol‐1‐one,a potential plant‐growth regulator

Molecules of the title compound, C₁₆H₁₄N₂O, a potential plant‐growth regulator, are linked into chains by intermolecular C=O...H—N hydrogen bonds. These chains are weakly interconnected by π–π stacking interactions to form a three‐dimensional framework. A comparison of the geometric parameters of the title molecule and several related benzimidazoles and pyrrolidones is presented.<!?tpb=22pt>     

A three‐dimensional hybrid framework based on novel [Co4Mo4] bimetallic oxide clusters with 3,5‐bis(3‐pyridyl)‐1,2,4‐triazole ligands

In the title organic–inorganic hybrid complex, poly[[[μ‐3,5‐bis(3‐pyridyl)‐1,2,4‐triazole]tri‐μ₃‐oxido‐tetra‐μ₂‐oxido‐oxidodicobalt(II)dimolybdenum(VI)] monohydrate], {[Co₂Mo₂O₈(C₁₂H₉N₅)]·H₂O}_n, the asymmetric unit is composed of two Co^II centers, two [Mo^VIO₄] tetrahedral units, one neutral 3,5‐bis(3‐pyridyl)‐1,2,4‐triazole (BPT) ligand and one solvent water molecule. The cobalt centers both exhibit octahedral [CoO₅N] coordination environments. Four Co^II and four Mo^VI centers are linked by μ₂‐oxide and/or μ₃‐oxide bridges to give an unprecedented bimetallic octanuclear [Co₄Mo₄O₂₂N₄] cluster, which can be regarded as the first example of a metal‐substituted octamolybdate and exhibits a structure different from those of the eight octamolybdate isomers reported to date. The bimetallic oxide clusters are linked to each other through corner‐sharing to give two‐dimensional inorganic layers, which are further bridged by trans‐BPT ligands to generate a three‐dimensional organic–inorganic hybrid architecture with six‐connected distorted α‐Po topology.     

Cross‐linking of poly(methyl methacrylate) by oxozirconate and oxotitanate clusters

Radical polymerization of methyl methacrylate with 0.5‐2 mol% of the (meth)acrylate‐substituted oxozirconium and oxotitanium clusters Zr₆(OH)₄O₄(OMc)₁₂ (OMc = methacrylate), Zr₄O₂(OMc)₁₂, Ti₆O₄(OEt)₈(OMc)₈ and Ti₄O₂(OPrⁱ)₆(OAcr)₆ (OAcr = acrylate) results in an efficient cross‐linking of the organic polymers. The obtained inorganic‐organic hybrid polymers exhibit a higher thermal stability due to inhibited depolymerization reactions. Contrary to undoped poly(methyl methacrylate), the cluster cross‐linked polymers are insoluble but swell in organic solvents. The solvent uptake upon swelling decreases with an increasing amount of polymerized cluster. The impedance spectra of PMMA doped with various proportions of Zr₄O₂(OMc)₁₂ show that the capacitance of the polymers decreases with an increasing proportion of the cluster. The polymer doped with 2 mol% of Zr₄O₂(OMc)₁₂ shows an increase in conductivity to 0.9·10⁻⁷ S·cm⁻¹ at 74°C.     

Synthesis of well‐defined aromatic polyesters by chain‐growth polycondensation under suppression of transesterification

For the synthesis of aromatic polyesters with defined molecular weights and narrow molecular weight distributions (MWDs), we investigated the chain‐growth polycondensation of active amide derivatives of 4‐hydroxybenzoic acid, 1a and 1b , having an octyl or 4,7‐dioxaoctyl side chain, respectively. To suppress the transesterification of the polymer backbone with the monomer, the polymerization of 1 was carried out in tetrahydrofuran (THF) at −30 °C in the presence of initiator 2 and Et₃SiH/CsF/18‐crown‐6, which generated a hydride ion as a base in situ. The number‐average molecular weight (M_n) of poly 1a was controlled, and narrow MWDs were maintained, until the [ 1a ]₀/[ 2 ]₀ feed ratio was 14.3 (M_n ≤ 3500), whereas that of poly 1b was controlled until the feed ratio was 30 (M_n ≤ 7250). The difference stemmed from the higher solubility of poly 1b in THF. This chain‐growth polycondensation was applied to the synthesis of a diblock copolyester of 1a and 1b of a defined architecture. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4109–4117, 2005     

O‐Benzyl‐N‐tert‐butoxy­carbonyl‐N‐methyl‐l‐tyrosine

The crystal structure of the title compound, alternatively called 3‐[4‐(benzyl­oxy)­phenyl]‐2‐(N‐tert‐butoxy­car­bonyl‐N‐methyl­amino)­propi­onic acid, C₂₂H₂₇NO₅, has been studied in order to ex­amine the role of N‐methyl­ation as a determinant of peptide conformation. The conformation of the tert‐butoxy­carbonyl group is trans–trans. The side chain has a folded conformation and the two phenyl rings are effectively perpendicular to one another. The carboxyl­ate hydroxyl group and the urethane carbonyl group form a strong intermolecular O—H?O hydrogen bond.     

Enantioselective Synthesis of Ethyl 4,5,7,8,9‐Penta‐O‐acetyl‐2,6‐anhydro‐ 3‐deoxy‐D‐erythro‐L‐gluca‐nononate: a 2‐Monodeoxygenated Derivative of `2‐Keto‐3‐deoxy‐D‐glycero‐D‐galacto‐nononic Acid'

A study aimed at developing an enantioselective synthesis of the title compound 23 , a 2‐monodeoxy analogue of the naturally occurring (+)‐2‐keto‐3‐deoxy‐D ‐glycero‐D ‐galacto‐2‐nononic acid (KDN), is reported. From D ‐mannose as starting material, the chiral 1,3‐diene 10 , activated by a silyloxy substituent at C(2), was prepared in six steps (Scheme 1). However, the intermediates were often contaminated with varying amounts of by‐products arising from overoxidation during cleavage with periodic acid. An alternative route starting from the inexpensive and readily available D ‐isoascorbic acid ( 12 ), though a little longer than the first, satisfactorily circumvented the purification problem and led to the desired dienes 17 in good yields (scheme 2). The [Co^II(S,S)‐(+)‐salen]‐catalyzed hetero‐Diels‐Alder reactions of the aforementioned dienes with ethyl glyoxylate proceeded smoothly at room temperature, giving the dihydropyrano adducts 18 in moderate yields (Scheme 3). Dihydroxylation of 18a followed by reduction of the keto function gave the desired 4,5‐trans dihydroxy moiety of the KDN framework (Scheme 4, see 21 ). The spectroscopic data of the penta‐O‐acetylated 2‐deoxy‐KDN ethyl ester 23 were consistent with those reported for the corresponding methyl ester derived from natural KDN.     

Kinetic study of copper(I)‐catalyzed click chemistry step‐growth polymerization

Oligomers and polymers containing triazole units were synthesized by the copper(I)‐catalyzed 1,3‐dipolar cycloaddition step‐growth polymerization of four difunctional azides and alkynes. In a first part, monofunctional benzyl azide was used as a chain terminator for the polyaddition of 1,6‐diazidohexane and α,ω‐bis(O‐propargyl)diethylene glycol, leading to polytriazole oligomers of controlled average degree of polymerization (DP_n = 3–20), to perform kinetic studies on low‐viscosity compounds. The monitoring of the step‐growth click polymerization by ¹H NMR at 25, 45, and 60 °C allowed the determination of the activation energy of this click chemistry promoted polyaddition process, that is, E_a = 45 ± 5 kJ/mol. The influence of the catalyst content (0.1–5 mol % of Cu(PPh₃)₃Br according to azide or alkyne functionalities) was also examined for polymerization kinetics performed at 60 °C. In a second part, four high molar mass polytriazoles were synthesized from stoichiometric combinations of diazide and dialkyne monomers above with p‐xylylene diazide and α,ω‐bis(O‐propargyl)bisphenol A. The resulting polymers were characterized by DSC, TGA, SEC, and ¹H NMR. Solubility and thermal properties of the resulting polytriazoles were discussed based on the monomers chemical structure and thermal analyses. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5506–5517, 2008