Dynamic Coupling at Low Reynolds Number

Collective and emergent behaviors of active colloids provide useful insights into the statistical physics of out‐of‐equilibrium systems. Colloidal suspensions containing microscopic active swimmers have been intensively studied to understand the principles of energy transfer at low Reynolds number conditions. Studies on active enzymes and Ångström‐sized organometallic catalysts have demonstrated that energy can even be transferred by molecules to their surroundings, thereby influencing the overall dynamics of the systems substantially. By monitoring the diffusion of non‐reacting tracers in active solutions, it has been shown that the nature of energy transfer in systems containing different swimmers is surprisingly similar—irrespective of their size, modes of energy transduction, and propulsion strategies. This Review discusses research results obtained so far in this direction, highlighting the common features observed in the dynamic coupling of swimmers with their surroundings.     

A Correlation of the Drag Force Coefficient on a Sphere with Interface Slip at Low and Intermediate Reynolds Numbers

The hydrodynamics of a sphere with interface slip has been numerically investigated for flows of Reynolds number ranging 0 < Re ≤ 75. A simple correlation of the drag force coefficient in the present of interface slip has been derived based on our numerical simulations. The correlation takes the slip coefficient and Reynolds number as two input parameters. By comparing results found in the literature, we believe that the present correlation is more accurate; it provides a source for future experiment study and for numerical simulations of large multi-particle system where the interface slip is important.     

Dynamics of Rear Stagnant Cap Formation at Low Reynolds Numbers

The rising of a gas bubble in a surfactant solution is considered within the framework of the rear stagnant cap (r.s.c.) model at low Reynolds number. The adsorption is supposed to be the slowest process in the system. The bubble velocity is predicted to depend on time due to the nonstationary process of surface stagnant zone formation. Various types of bubble behavior are discussed. It is shown which information on the characteristics of adsorption one can extract from the time dependency of the bubble velocity. Copyright 2000 Academic Press.     

Low Reynolds Number Interactions between Colloidal Particles near the Entrance to a Cylindrical Pore

The interaction between stable colloidal particles arriving at a pore entrance was studied using a numerical method for the case where the particle size is smaller than but of the same order as the pore size. The numerical method was adapted from a front-tracking technique developed for studying incompressible, multifluid flow by S. O. Unverdi and G. Tryggvason (J. Comp. Phys. 100, 25, 1992). The method is based on the finite difference solution of Navier-Stokes equation on a stationary, structured, Cartesian grid and the explicit representation of the particle-liquid interface using an unstructured grid that moves through the stationary grid. The simulations are in two dimensions, considering both deformable and nondeformable particles, and include interparticle colloidal interactions. The interparticle and particle-pore hydrodynamic interactions, which are very difficult to determine using existing analytical and semi-numerical, semi-analytical techniques in microhydrodynamics, are naturally accounted for in our numerical method and need not be explicity determined. Two- and three-particle motion toward a pore has been considered in our simulations. The simulations demonstrate how the competition between hydrodynamic forces and colloidal forces acting on particles dictate their flow behavior near the pore entrance. The predicted dependence of the particle flow behavior on the flow velocity and the ratio of pore size to particle size are qualitatively consistent with the experimental observations of V. Ramachandran and H. S. Fogler (J. Fluid Mech. 385, 129, 1999). Copyright 2000 Academic Press.     

Synthesis of Nickel Powders: From Spheres to Monodispersed Clusters

Well dispersed nickel powders with uniform size were synthesized using hydrazine hydrate as reducing reagent, with no surfactant introduced. The morphology of the products could be controlled from smooth spheres to flowerlike clusters by simply choosing solvent and adjusting the molar ratio of NaOH/Ni or N₂H₄/Ni. A two-step reduction process was proposed for the formation mechanism based on the experimental results. The crystal phase of the as-prepared sample was characterized by XRD. The morphology and microstructure were inspected with FESEM. The magnetic properties were recorded using VSM. The novel flowerlike clusters exhibit unique magnetic properties.     

Sedimentation Velocity and Potential in Concentrated Suspensions of Charged Spheres with Arbitrary Double-Layer Thickness

The sedimentation in a homogeneous suspension of charged spherical particles with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model. Overlap of the double layers of adjacent particles is allowed, and the polarization effect in the double layer surrounding each particle is considered. The electrokinetic equations that govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. An analytical expression for the settling velocity of the charged sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged spheres is also derived by using the requirement of zero net electric current. Our results demonstrate that the effects of overlapping double layers are quite significant, even for the case of thin double layers. Copyright 2000 Academic Press.     

Long-Range Electrostatic Interaction between a Charged Wall and Two Similarly Charged Colloidal Spheres at Low Surface Potentials

The long-range electrostatic interaction between a pair of similarly charged colloidal spheres and a charged planar wall at low surface potentials is theoretically investigated. The linear Poisson-Boltzmann equation (PBE) and the point charge approximation of the charged sphere are used. The electrical potential distribution in the electrolyte solution is found from the PBE at the constant surface potentials using the image charge method. The electrostatic forces acting on the spheres are then calculated. The results show that the repulsive interaction between a pair of similarly charged colloidal spheres clearly decreases when a charged wall appears nearby, but it is impossible for an attractive force to emerge at the scaled surface potentials less than 1. There is, however, an attractive force between the charged wall and the similarly charged colloidal spheres, when the surface potential zetap on the wall is sufficiently higher than the surface potential zetas on the spheres to make zetap > zetasexp(kappah) (h is the distance from the wall to the sphere center). In this case, there are negative surface charges on the spheres at positive surface potential zetas. It is these negative charges that produce the above attraction. Copyright 1999 Academic Press.     

The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

The electrophoresis in a monodisperse suspension of dielectric spheres with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations, which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell, are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of the colloidal sphere in closed form correct to O(zeta) are obtained. Based on the solution of the electrokinetic equations in a cell, a closed-form formula for the electric conductivity of the suspension up to O(zeta(2)) is derived from the average electric current density. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made for both the electrophoretic mobility and the electric conductivity. Copyright 2001 Academic Press.     

Phosphorescence at Low Temperature by External Heavy-Atom Effect in Zinc(II) Clusters

Luminescent Zn^II clusters [Zn₄L₄(μ₃-OMe)₂X₂] (X=SCN ( 1 ), Cl ( 2 ), Br ( 3 )) and [Zn₇L₆(μ₃-OMe)₂(μ₃-OH)₄]Y₂ (Y=I⁻ ( 4 ), ClO₄⁻ ( 5 )), HL=methyl-3-methoxysalicylate, exhibiting blue fluorescence at room temperature (λ_max=416≈429 nm, Φ_em=0.09–0.36) have been synthesised and investigated in detail. In one case the external heavy-atom effect (EHE) arising the presence of iodide counter anions yielded phosphorescence with a long emission lifetime (λ_max=520 nm, τ=95.3 ms) at 77 K. Single-crystal X-ray structural analysis and time-dependent density-functional theory (TD-DFT) calculations revealed that their emission origin was attributed to the fluorescence from the singlet ligand-centred (¹LC) excited state, and the phosphorescence observed in 4 was caused by the EHE of counter anions having strong CH−I interactions.     

Sedimentation of spheres at small Reynolds number

The effect of fluid inertia on the settling of spheres in a viscous incompressible fluid is studied in the limit of small Reynolds number. The kinetic energy of flow depends on the positions of the spheres, and gives rise to forces on the spheres. In the dilute limit it suffices to study the corresponding pair interaction. The interaction is calculated from the Stokes flow for two spheres settling between plane walls in the point particle limit. The dissipative interaction between a pair of spheres is calculated from the Proudman-Pearson [I. Proudman and J. R. A. Pearson, J. Fluid Mech. 2, 237 (1957)] solution of the Navier-Stokes equations for flow about a sphere in unbounded geometry. The combination of kinetic and dissipative interaction gives rise to a repulsive force of range of the order of the sphere diameter divided by the Reynolds number.     

B24N24团簇的结构与稳定性

采用密度泛函理论,在B3LYP/6-31G^*水平下,对B₂₄N₂₄笼状团簇的12种异构体进行了优化,并对它们的几何构型、化学键性质、振动光谱和稳定性进行了探讨.研究表明:具有S₈对称的含有2个八元环、8个四元环和16个六元环的结构h是B₂₄N₂₄笼状团簇最稳定的异构体,只存在B-N键,而无N-N和B-B键.含有五元环结构的稳定性最低.B-B和N-N键对的数目越多,结构的稳定性越低.12种异构体的稳定性顺序为h＞a＞b＞I＞g＞l＞c＞k＞j＞d＞e＞f.     

Size-Dependent Dispersion of Rhodium Clusters into Isolated Single Atoms at Low Temperature and the Consequences for CO Oxidation Activity

Understanding the dynamic structural evolution of supported metal clusters under reaction conditions is crucial to develop structure reactivity relations. Here, we followed the structure of different size Rh clusters supported on Al₂O₃ using in situ/operando spectroscopy and ex situ aberration-corrected electron microscopy. We report a dynamic evolution of rhodium clusters into thermally stable isolated single atoms upon exposure to oxygen and during CO oxidation. Rh clusters partially disperse into single atoms at room temperature and the extent of dispersion increases as the Rh size decreases and as the reaction temperature increases. A strong correlation is found between the extent of dispersion and the CO oxidation kinetics. More importantly, dispersing Rh clusters into single atoms increases the activity at room temperature by more than two orders of magnitude due to the much lower activation energy on single atoms (40 vs. 130 kJ/mol). This work demonstrates that the structure and reactivity of small Rh clusters are very sensitive to the reaction environment.     

C24和B12N12团簇的结构与稳定性

本文采用量子化学密度泛函理论的B3LYP/6-31G*方法,对C24和B12N12团簇的12种异构体进行了优化,并对它们的几何构型、振动频率、核独立化学位移(NICS)和结合能进行了理论探讨, 比较了C24和B12N12团簇结构的稳定性。研究表明:C24团簇的最稳定几何构型为类石墨结构d,B12N12团簇的最稳定结构为4/6笼状结构g。C24异构体的稳定性大小顺序为d > b > f > c > a > e。B12N12团簇异构体稳定性大小顺序为a > f> c> d > e >b。     

Electronic Consequences of Ligand Substitution at Heterometal Centers in Polyoxovanadium Clusters: Controlling the Redox Properties through Heterometal Coordination Number

The rational control of the electrochemical properties of polyoxovanadate-alkoxide clusters is dependent on understanding the influence of various synthetic modifications on the overall redox processes of these systems. In this work, the electronic consequences of ligand substitution at the heteroion in a heterometal-functionalized cluster was examined. The redox properties of [V₅O₆(OCH₃)₁₂FeCl] ( 1-[V₅FeCl] ) and [V₅O₆(OCH₃)₁₂Fe]X ( 2-[V₅Fe]X ; X=ClO₄, OTf) were compared in order to assess the effects of changing the coordination environment around the iron center on the electrochemical properties of the cluster. Coordination of a chloride anion to iron leads to an anodic shift in redox events. Theoretical modelling of the electronic structure of these heterometal-functionalized clusters reveals that differences in the redox profiles of 1-[V₅FeCl] and 2-[V₅Fe]X arise from changes in the number of ligands surrounding the iron center (e.g., 6-coordinate vs. 5-coordinate). Specifically, binding of the chloride to the sixth coordination site appears to change the orbital interaction between the iron and the delocalized electronic structure of the mixed-valent polyoxovanadate core. Tuning the heterometal coordination environment can therefore be used to modulate the redox properties of the whole cluster.     

Ab Initio Study on the Stability of NgnBe2N2, NgnBe3N2 and NgBeSiN2 Clusters

The global minima of Be₂N₂, Be₃N₂ and BeSiN₂ clusters are identified using a modified stochastic kick methodology. The structure, stability and bonding nature of these clusters bound to noble gas (Ng) atoms are studied at the MP2/def2‐QZVPPD level of theory. Positive Be?Ng bond dissociation energy, which gradually increases down Group 18 from He to Rn, indicates the bound nature of Ng atoms. All of the Ng‐binding processes are exothermic in nature. The Xe and Rn binding to Be₂N₂ and Be₃N₂ clusters and Ar?Rn binding to BeSiN₂ are exergonic processes at room temperature; however, for the lighter Ng atoms, lower temperatures are needed. Natural population analysis, Wiberg bond index computations, electron density analysis, and energy decomposition analysis are performed to better understand the nature of Be?Ng bonds.     

Strain Energies in Homoatomic Nitrogen Clusters N(4), N(6), and N(8)

Strain energies and resonance energies can be obtained as the energy changes for appropriate homodesmotic reactions using ab initio calculated total energies as the energies of the reactants and products involved. Homodesmotic reactions conserve bond types and preserve valence environments at all atoms, requirements that favor the cancellation of basis set and electron correlation errors in the ab initio energies. In this paper we calculate strain energies and resonance energies for N(4), N(6), and N(8) clusters in a number of chemically significant but, for nitrogen, hypothetical structural forms. The nitrogen cluster strain energies are generally of the same order of magnitude as those of isostructural hydrocarbon clusters, and individual differences can be explained by using the ring strain additivity rule and recognizing the effect of the presence of lone pairs of electrons on nitrogen clusters but not on the hydrocarbons. Resonance energies of the nitrogen clusters are much smaller than those of the comparable aromatic hydrocarbons. The differences can be rationalized by considering the relative strengths of CC and NN single and double bonds. Strain and resonance energies of nitrogen clusters are compared with those previously reported for homoatomic clusters of phosphorus and arsenic. Trends through the series are remarkably similar, but strain energies for clusters from lower periods are progressively smaller. Strain and resonance have been important organizing concepts in organic chemistry for many years. Estimates of corresponding parameters for inorganic analogs are only now becoming available.     

Heteroallene Capture and Exchange at Functionalised Heptaphosphane Clusters

Despite being known for decades the chemical reactivity of homoatomic seven-atom phosphorus clusters towards small molecules remains largely unexplored. Here, we report that neutral tris(silyl) functionalised heptaphosphane (P₇(SiR₃)₃) cages are capable of heteroallene capture between the P−Si bonds of the cluster. A range of isocyanates and an isothiocyanate were investigated. In the case of isocyanates, silyl bonding at oxygen or nitrogen is regioselectively directed by the functional group on the isocyanate and substituents on the silyl moiety. Above all, we find that captured isothiocyanate molecules can be exchanged for isocyanate molecules, indicative of small molecule catch and release. Small molecule catch and release at these Zintl-derived clusters reveals their potential application as chemical storage materials or as reusable probes.     

Drawing of annular liquid jets at low Reynolds numbers

Asymptotic methods based on the slenderness ratio are used to obtain the leading-order equations that govern the fluid dynamics of axisymmetric, isothermal, Newtonian, annular liquid jets such as those employed in the manufacture of textile fibres, annular membranes, composite fibres and optical fibres, at low Reynolds numbers. It is shown that the leading-order equations are one-dimensional, and analytical solutions are obtained for steady flows at zero Reynolds numbers, zero gravitational pull, and inertialess jets. A linear stability analysis of the viscous flow regime indicates that the stability of annular jets is governed by the same eigenvalue equation as that for the spinning of round fibres. Numerical studies of the time-dependent equations subject to axial velocity perturbations at the nozzle exit and/or the take-up point indicate that the annular jet dynamics evolves from periodic to chaotic motions as the extension or draw ratio is increased. The power spectrum of the annular jet's radius at the take-up point broadens and the phase diagrams exhibit holes at large draw ratios. The number of holes increases as the draw ratio is increased, thus indicating the presence of strange attractors and chaotic motions.     

低价双核Mo—S—CO簇合物的质谱研究

本文报道了二个低价钼簇合物的快原子轰击(FAB)和电子轰击(EI)质谱:(Et_4N)_2[Mo_2(CO)_8(μ-SPh)_2]的FAB和FAB—NI谱及Mo_2(CO)_8(μ-SPh)_2的FAB和EI谱。分别获得它们的完整的配位阳离子和阴离子峰。这类簇合物的大致裂断解途径可能是首先脱CO、然后脱C_6H_5—,在EI—MS谱中观察到双金属离子裂解为单金属碎片离子的反应。文中探讨了质谱条件下标题簇合物的氧化还原反应。研究结果同时表明,Mo价态明显影响碎片离子峰的相对丰度和Mo对配位体CO、—SPh、—S的络合能力。另外,还报道了Mo_2(CO)_6(μ-SPh)_2(CH_3CN)_2的FAB—MS和EIMS谱。