The cage effect in systems of hard spheres
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The cage effect is generally invoked when discussing the delay in the decay of time correlation functions of dense fluids. In an attempt to examine the role of caging more closely, we consider the spread of the displacement distributions of Brownian particles. These distributions are necessarily biased by the presence of neighbouring particles. Accommodation of this bias by those neighbours conserves the displacement distribution locally and presents a collective mechanism for exploring configuration space that is more efficient than the intrinsic Brownian motion. Caging of some particles incurs, through the impost of global conservation of the displacement distribution, a delayed, non-local collective process. This non-locality compromises the efficiency with which configuration space is explored. Both collective mechanisms incur delay or stretching of time correlation functions, in particular the particle number and flux densities. This paper identifies and distinguishes these mechanisms in existing data from experiments and computer simulations on systems of particles with hard sphere interactions.Keywords:
Cage effect
Particle (ecology)
Cage
The experimental data on investigations of the cage effect in polymers are examined for the decomposition of 2,2′-azoisobutyronitrile and lauroyl peroxide. The kinetic schemes taking into account only translational motion of radicals are shown not to describe the cage effects in polymers. The experimental dependence of the cage effect on molecular mobility in polymers may be explained on the basis of schemes taking into account both the rotational and translational motions of particles. The study of cage effects in oriented polymeric films proves an important role of the form of the cage. In polymers the molecular mobility influences the rate of slow reactions. This is explained for the scope of the model of a rigid cage where orientation of the particles depends on the form of the cage.
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Matrix (chemical analysis)
Peroxide
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Classical trajectories of a system of I2 plus 22 inert gas atoms confined to a spherical volume reproduce the cage effect as measured experimentally. Analysis of the trajectories shows that the primary cage effect can be subdivided into three categories but there is no clear borderline between one of these (delayed primary) and the secondary cage effect.
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Inert gas
Inert
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The cage recombination efficiency of the [(η 5 -C 5 H 4 Me)(CO) 3 W ·, ·W(CO) 3 (η 5 -C 5 H 4 Me)] radical cage pair in hydrocarbon solvent systems is higher than that of the analogous, but less massive, [(η 5 -C 5 H 4 Me)(CO) 3 Mo ·, ·Mo(CO) 3 (η 5 -C 5 H 4 Me )] cage pair; the difference is shown to be attributable not to differences in the radical masses but to differences in the metal–metal bond energies or in the spin–orbit coupling.
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Xenon trapped in the alpha cages of zeolite NaA exhibits distinct NMR signals for clusters Xe1, Xe2, Xe3,..., up to Xe8. Using multisite magnetization transfer experiments, we have measured the rate constants kmn for the elementary processes that are involved in the cage-to-cage transfer of Xe atoms in the zeolite NaA, that is, for a single Xe atom leaving a cage containing Xen to appear in a neighboring cage containing Xem−1, thereby forming Xem. In a random walk simulation, these rate constants reproduce over a hundred magnetization decay/recovery curves that we have measured in four samples of Xe in zeolite NaA at room temperature, in selective inversion, and complementary experiments for all the significantly populated clusters. The simulations also lead to the correct experimental equilibrium distributions, that is, the fractions of the alpha cages containing Xe1,Xe2,...,Xe8.
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The bis-bidentate bridging ligand L {α,α'-bis[3-(2-pyridyl)pyrazol-1-yl]-1,4-dimethylbenzene}, which contains two chelating pyrazolyl-pyridine units connected to a 1,4-phenylene spacer via flexible methylene units, reacts with transition metal dications to form a range of polyhedral coordination cages based on a 2M:3 L ratio in which a metal ion occupies each vertex of a polyhedron, a bridging ligand lies along every edge, and all metal ions are octahedrally coordinated. Whereas the Ni(II) complex [Ni(8)L(12)](BF(4))(12)(SiF(6))(2) is an octanuclear cubic cage of a type we have seen before, the Cu(II), Zn(II), and Cd(II) complexes form new structural types. [Cu(6)L(9)](BF(4))(12) is an unusual example of a trigonal prismatic cage, and both Zn(II) and Cd(II) form unprecedented hexadecanuclear cages [M(16)L(24)]X(32)(X = ClO(4) or BF(4)) whose core is a skewed tetracapped truncated tetrahedron. Both Cu(6)L(9) and M(16)L(24) cages are based on a cyclic helical M(3)L(3) subunit that can be considered as a triangular "panel", with the cages being constructed by interconnection of these (homochiral) panels with additional bridging ligands in different ways. Whereas [Cu(6)L(9)](BF(4))(12) is stable in solution (by electrospray mass spectrometry, ES-MS) and is rapidly formed by combination of Cu(BF(4))(2) and L in the correct proportions in solution, the hexadecanuclear cage [Cd(16)L(24)](BF(4))(32) formed on crystallization slowly rearranges in solution over a period of several weeks to the trigonal prism [Cd(6)L(9)](BF(4))(12), which was unequivocally identified on the basis of its (1)H NMR spectrum. Similarly, combination of Cd(BF(4))(2) and L in a 2:3 ratio generates a mixture whose main component is the trigonal prism [Cd(6)L(9)](BF(4))(12). Thus the hexanuclear trigonal prism is the thermodynamic product arising from combination of Cd(II) and L in a 2:3 ratio in solution, and arises from both assembly of metal and ligand (minutes) and rearrangement of the Cd(16) cage (weeks); the large cage [Cd(16)L(24)](BF(4))(32) is present as a minor component of a mixture of species in solution but crystallizes preferentially.
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In order to study the performance of the rotating-cage spraying atomizer of biological pesticide.Firstly,the atomizing principle of cage,and the optimal range of the droplet diameter were proposed theoretically.Secondly,the experiment of normal temperature water and biological pesticide white muscardine fungi was performed along with the change of the mesh number,cage diameter,flow rate,motor rotational speed and the spraying pressure,the achieved atomization effect was analyzed.The results showed that the diameter of the droplet was about 100 μm and the activity of biological pesticide was up to 75 %.The farther collected location was,the bigger droplet diameter was and the lower activity was.The diameter of droplet increased firstly and then decreased with the increase of the rotating velocity,mesh number and the cage diameter,but there was no impact on the activity.The larger pressure was,the lower activity was.
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This study measured and compared the combination efficiencies (FcP) of geminate radical cage pairs to nongeminate (collisional) radical cage pairs (Fc'). For the [Cp'(CO)3Mo·, ·Mo(CO)3Cp'] radical cage pair, Fc' was found to be smaller than FcP in solutions having the same viscosity. It is proposed that the difference in FcP and Fc' arises because the radicals in the collisional cage pair are less likely to have the correct orbital orientation for radical-radical combination to occur, whereas photochemically generated geminate cage pairs are more likely to have the correct orbital orientation. As predicted, FcP and Fc' both increase when the microviscosity of a solution increases.
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John Cage
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We show that a [3 + 6] trigonal prismatic imine (a) cage can rearrange stoichiometrically and structurally to form a [6 + 12] cage (b) with a truncated tetrahedral shape. Molecular simulations rationalize why this rearrangement was only observed for the prismatic [3 + 6] cage TCC1 but not for the analogous [3 + 6] cages, TCC2 and TCC3. Solvent was found to be a dominant factor in driving this rearrangement.
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Tetrahedron
Imine
Stoichiometry
Trigonal crystal system
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The use of time-lapse and normal speed photography as a tool in evaluating the effect of cage size on physical activity in the beagle dog was examined. Normal speed motion pictures also served to demonstrate the degree of physical activity possible within specific sized cages, and the effect of changes in external activity on the dogs' activity within the cage. Viewing of these films showed that specific activity measurements can be made, providing a feasible scientific method for evaluating cage activity in a wide range of cage sizes. Physiological data collected over the course of this experiment from dogs housed in 2 different sized cages failed to show a cause-and-effect relationship.
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Beagle
Cage effect
John Cage
Degree (music)
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