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Axially moving structures are applied extensively in many engineering equipments. In this paper, the parametric stability of an axially accelerating viscoelastic Timoshenko beam is analytically and numerically investigated. On account of the axial tension fluctuation, the relationship between the time dependent tension and the axial speed is introduced emphatically. The axial tension of the system is assumed as a harmonic variation over a constant initial tension. On the basis of the generalized Hamilton principle, a novel coupled dynamic model with the linear partial-differential equations and the corresponding boundary conditions are established. The material time derivative is employed to reveal the viscoelastic characteristic by the Kelvin-Voigt energy dissipation mechanism. The method of multiple scale is applied to analyze the governing equations. The instability boundaries of the moving beam are obtained according to the solvability condition and the Routh-Hurwitz criterion. The display expression of the instability boundary is given. The effects of some system parameters on the resonance instability region of the first two harmonic parameters are displayed. The stability of The Timoshenko Beam is first compared by two different methods. The dependence of the stability on the truncation order of Galerkin method is highlighted.

s In this article, dynamic stabilities of axially accelerating viscoelastic beams with interdependent speed and tension is investigated. The effect of the interdependent speed and tension is highlighted. However, time dependent speeds and time dependent tensions are independent of each other in previous studies. The dynamic equilibrium approach is used to obtain the governing equation of the axially accelerating viscoelastic beam with internal and principal parametric resonance. Another highlight is that the simply supported boundary conditions are given in precise forms, that are, inhomogeneous forms. The nonhomogeneous terms are closely related to Kelvin–Voigt viscoelastic constitutive relation. The method of directly multiple scales with a first-order uniform expansion is employed. By using the technique of the modified solvability conditions, the complex variable modulation equations are deduced in detail. By some numerical examples, the influences of viscosity, internal resonance, axial tension perturbation amplitude, axial speed perturbation amplitude, and old and current models on the stability boundaries are given. In addition, the approximate analytical results are compared with the numerical integration results by applying the differential quadrature method.

In this paper, a new nonlinear model of an axially accelerating viscoelastic beam is established. The effects of a speed-dependent tension (a time-dependent tension due to perturbation of the speed) and a tension-dependent speed (a time-dependent speed due to perturbation of the tension) are highlighted. However, there was one common characteristic in previous studies about parametric vibration of axially moving beams with time-dependent tensions and time-dependent speeds: Axial tension and axial speed are independent of each other. Another highlight is that the inhomogeneous boundary conditions arising from Kelvin viscoelastic constitutive relation are taken into account. The technique of the modified solvability conditions is employed to resolve the existing solvability conditions failure because of the inhomogeneous boundary conditions. The influences of material’s viscoelastic coefficients, axial speed fluctuation amplitude, axial tension fluctuation amplitude, and dependent and independent models on the steady-state vibration responses are demonstrated by some numerical examples. Furthermore, the approximate analytical results are verified by using the differential quadrature method.

Nonlinear transverse vibrations of in-plane accelerating viscoelastic plates are analytically and numerically investigated in the presence of principal parametric and 3:1 internal resonance. Due to the axial acceleration, the plate tension varies in the transporting direction. For a range of mean velocity, the natural frequency of the second mode is almost equal to three times that of the first mode, and that leads to a possible 3:1 internal resonance. The governing equation and the corresponding boundary conditions are derived from the generalized Hamilton principle. The method of multiple scales is applied to reveal that the steady-state responses have two types: trivial and nontrivial (two-mode) solutions. The stabilities of the steady-state responses are determined via the Routh–Hurwitz criterion. The analytical investigations demonstrate the effects of viscous damping coefficient, the viscoelastic coefficient, and the moving speed fluctuation amplitude on the stability of zero solutions and the amplitude of the nontrivial solutions. A differential quadrature scheme is developed to solve numerically the governing equation under the given boundary conditions. The numerical results agree well with the approximate analytical results.

In this paper, instability boundaries of axially accelerating plates with internal resonance are investigated for the first time. The relation between the acceleration and the longitudinally varying tensions are introduced. The governing equation and the corresponding boundary conditions are derived from the generalized Hamilton principle. The effects of internal resonances and the nonhomogeneous boundary conditions on the instability boundaries are highlighted. By the method of multiple scales, the modified solvability conditions in principal parametric and internal resonances are established. The Routh-Hurwitz criterion is introduced to determine the instability boundaries. The effects of the viscoelastic coefficient and the viscous damping coefficient on the instability boundaries are examined. Abnormal instability boundaries are detected when the internal resonance is introduced. The phenomenon of local zigzag and V-shape boundaries are explained from the viewpoint of modal interactions. The numerical calculations of the differential quadrature schemes about the first four complex frequencies, the first four complex modes, and the stability boundaries are used to confirm the results of the analytical method.

In this paper, the instability boundaries of an axially moving viscoelastic beam due to parametric resonance are revisited for the internal resonance case. The relation between the time-dependent tension and the time-dependent axial speed is constructed, which provides a new model in the study of axially moving material with pulsation parameters. The instability boundaries caused by the combination of parametric and internal resonances are studied using the method of multiple time scales. Some strange instability boundaries are detected when the internal resonance is considered. The phenomenon of local zigzag boundary contour is explained from the viewpoint of modal interactions.

Complex modes and traveling waves in axially moving Timoshenko beams are studied. Due to the axially moving velocity, complex modes emerge instead of real value modes. Correspondingly, traveling waves are present for the axially moving material while standing waves dominate in the traditional static structures. The analytical results obtained in this study are verified with a numerical differential quadrature method.

s Irregular instability boundaries of axially accelerating beams with 1:3 internal resonance are analytically and numerically investigated in this paper. The distributed parameter is due to the small simple harmonic axial speed. The viscoelastic characteristic of the beam is described by the Kelvin–Voigt model in which the material time derivative is used. A linear partial-differential equation with the variable coefficient and the relevant boundary conditions governing the transverse motion is presented. The effects of the nonhomogeneous boundaries are highlighted. By the method of multiple scales, the solvability conditions in summation and principal parametric resonances are established by some different manipulations in the process of the classical multiple scales method. The Routh–Hurwitz criterion is used to determine the instability boundaries. The effects of viscoelastic coefficient and the viscous damping coefficient are examined on the instability boundaries. Irregular instability boundaries appeared when the 1:3 internal resonance is introduced. It is shown that the numerical calculations by the differential quadrature scheme can verify the approximate analytical results.

In this paper, the idea of an axially moving time-dependent beam model is briefly introduced. The nonlinear response of an axially moving beam is investigated. The effects of a time and spatial dependent tension depending on the external forces at the boundary and a tension dependent speed are highlighted, which gives a new model to study the parametric vibration of axially moving structures. This paper focuses on simultaneous resonant cases that are the principal parametric resonance of first mode and internal resonance of the first two modes. In general, the method of multiple scales can study nonlinear vibration of axially moving structures with homogeneous boundary conditions. Taking Kelvin viscoelastic constitutive relation into account, the inhomogeneous boundary conditions make the solvability conditions fail, which is also one of the highlights of this paper. In order to resolve this problem, the technique of the modified solvability conditions is employed. The influence of some parameters, such as material’s viscoelastic coefficients, viscous damping coefficients, and the axial tension fluctuation amplitudes, on the steady-state vibration responses is demonstrated by some numerical examples. Furthermore, the approximate analytical results are verified by using the differential quadrature method (DQM).

s In this paper, the dynamic stability of axially transporting viscoelastic beams with two-frequency parametric excitation and 1:3 internal resonance is investigated for the first time. The governing equation and corresponding inhomogeneous boundary conditions are developed by the Newton's second law. The viscoelastic characteristic of the transporting Euler-Bernoulli beam obeys the Kelvin-Voigt model. The axial tension is considered to vary longitudinally. Direct method of multiple scales is employed to obtain the solvability conditions in principal parametric resonances. The stability boundary conditions are obtained by the Routh-Hurwitz criterion. Numerical examples are shown to illustrate the effects of relevant parameters on the stability boundaries. Unusual and interesting phenomena of stability boundaries occur in two-frequency parametric excitation and 1:3 internal resonance. The accuracies of the approximate analytical results are verified by comparing with the numerical results, which obtained by a differential quadrature method.

Parametric resonance is one of the key topics in studying the dynamics of structures. In this paper, dynamic analysis of rotating beams with varying rotational speed in the presence of principal parametric resonance is investigated. The equations of motion are based on the von Karman strain–displacement relationship. The beam is made of isotropic material with rectangular cross section. The flapping and axial motions are considered along the thickness and length of the beam, respectively. The Galerkin discretization approach is implemented to determine the natural frequencies. The method of multiple scales is applied directly to the ordered equations of motion for the dynamic stability analysis. The method of multiple scales delivers a closed form relation for the stability region boundary in terms of the adimensional rotational speed, axial mode frequency and damping ratio coefficient. The differential quadrature method is employed to validate the multiple scales results. A comprehensive study is accomplished to find the effects of damping ratio coefficient and mode number on the critical parametric excitation amplitude and the parametric excitation frequency. Damping ratio coefficient, mode number and parametric excitation amplitude influences on the stability region boundaries are also examined.

In this paper, the vibration characteristics of axially moving plates with viscous damping are analyzed. A partial differential linear equation of motion with four simply supported edges is presented. The effects of two different viscous damping models are highlighted, while both of them have been introduced in previous studies. The investigation into the two different viscous damping models is interesting in itself. It is noteworthy that which model is closer to the fact, for which there are no systematic techniques of investigation to deal with this problem. In order to give a reference for possible verification in experiment, the difference of the two different viscous damping models in theory was proposed. The complex frequencies and its corresponding complex modes are studied by the complex mode approach. As other parameters are fixed, the effect of some parameters, such as viscous damping coefficients, axial speeds, aspect ratios, stiffness ratios, and support stiffness parameters, on the frequencies and critical speeds are examined. The complex modes illustrated in the 3-demensional figures are neither symmetric nor anti-symmetric to the midpoint of the plate owing to the plate motion. The differential quadrature scheme is used to verify the modes for the first time. The numerical calculations confirm the analytical results.

In this paper, parametric and 3:1 internal resonance of axially moving viscoelastic beams on elastic foundation are analytically and numerically investigated. The beam is restricted by viscous damping force. The beam’s material obeys the Kelvin model in which the material time derivative is used. The governing equations of coupled planar vibration and the associated boundary conditions are derived from the generalized Hamilton principle. The effects of the nonhomogeneous boundary conditions due to the viscoelasticity are highlighted, while the boundary conditions are assumed to be homogeneous in previous studies. In small but finite stretching problems, the equation is simplified into a governing equation of transverse nonlinear vibration. It is a nonlinear integro-partial differential equation with time-dependent and space-dependent coefficients. The dependence of the tension on the finite axial support rigidity is also modeled. The method of multiple scales is directly applied to establish the solvability conditions. The nonlinear steady-state oscillating response along with the stability and bifurcation of the beam is investigated. A detailed study is carried out to determine the influence of the viscoelastic coefficient and the viscous damping coefficient on dynamic behavior of the system. The numerical calculations by the differential quadrature scheme confirm the approximate analytical results.

One important issue in the investigation of axially moving systems is the viscoelastic constitutive relation. In the present paper, the effects of viscosity on the natural frequency of transverse vibration of an axially moving viscoelastic beam are studied. The viscoelastic material of the moving Euler-Bernoulli beam obeys the Kelvin model. For the first time, the qualitative difference between the natural frequencies with the material time derivative and the partial time derivative in the constitutive relation is investigated. The method of multiple scales with three terms is directly applied to obtain the approximate analytical solutions of the natural frequency. An interesting phenomenon is found in this study. Specifically, for an axially moving viscoelastic beam constituted by the material time derivative, the natural frequencies of transverse vibration may increase with the axial speed. Furthermore, the validity of the analytical results is examined by comparing with two numerical approaches, the differential quadrature methods (DQM) via separating variables and DQM combined with the fast Fourier transforms. There is qualitative difference between the results based on the constitutive relations with the material time derivative and the partial time derivative. Therefore, the results of this work provide an possible approach to determine which kind of the constitutive relation should be adopted to describe the viscoelastic property of axially moving materials.

This work explores the steady-state periodic transverse responses with their stabilities of axially accelerating viscoelastic strings. Longitudinally varying tension due to the axial acceleration is recognized in the modeling, while the tension was approximatively assumed to be longitudinally uniform in previous investigations. Exact internal resonances are highlighted in the analysis, while the resonances have been neglected in all available works. A governing equation of transverse nonlinear vibration is derived from the generalized Hamilton principle and the Kelvin viscoelastic model on the assumption that the string deformation is not infinitesimal, but still small. The axial speed is supposed to be a small simple harmonic fluctuation about the constant mean axial speed. The method of multiple scales is applied to solve the governing equation in the parametric resonances when the axial speed fluctuation frequency approaches the first three natural frequencies of the linear generating system based on 1–3 term truncations. The amplitude, the existence conditions, and the stability are determined, and the effects of the viscosity, the mean axial speed, the axial speed fluctuation amplitude, and the axial support rigidity on the amplitude and the existence are examined via the numerical examples. It is found that the 1-term, the 2-term, and the 3-term truncations yield the qualitatively same and the quantitatively close results in the case that there exist the exact internal resonances among the first three frequencies.

Stability of axially accelerating viscoelastic Timoshenko beams is treated. The effects of longitudinally varying tensions due to the axial acceleration are focused in this paper, while the tension was approximatively assumed to be longitudinally uniform in previous works. The dependence of the tension on the finite axial support rigidity is also modeled. The governing equations and the accurate boundary conditions for coupled planar motion of the Timoshenko beam are established based on the generalized Hamilton principle and the Kelvin viscoelastic constitutive relation. The boundary conditions were approximate in previous studies. The method of multiple scales is employed to investigate stability in parametric vibration. The stability boundaries are derived from the solvability conditions and the Routh–Hurwitz criterion for principal and summation parametric resonances. Some numerical examples are presented to demonstrate the effects of the tension variation, the viscosity, the mean axial speed, the shear deformation coefficient, the rotary inertia coefficient, the stiffness parameter, and the pulley support parameter on the stability boundaries.

In this paper, stability in parametric resonance of axially moving viscoelastic plates subjected to plane stresses is investigated. The plate material obeys the Kelvin–Voigt model in which the material time derivative is used. The generalized Hamilton principle is employed to obtain the governing equation. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The governing equation can be regarded as a continuous gyroscopic system with small periodically parametric excitations and a damping term. The method of multiple scales is applied to the governing equation to establish the solvability conditions in principal and summation parametric resonances. The natural frequencies and modes of linear generating equation are numerically calculated based on the given boundary conditions. The necessary and sufficient condition of the stability is derived from the Routh–Hurwitz criterion. Some numerical examples are presented to demonstrate the effects of related parameters on the frequencies and the stability boundaries. The differential quadrature scheme is developed to solve numerically the linear generating system and the primitive equation model. The numerical calculations confirm the analytical results.

This paper analytically and numerically investigates the nonlinear vibration in parametric and internal resonances of in-plane accelerating viscoelastic plates subjected to plane stresses. An approximate nonlinear plate theory was developed under the Kirchoff assumptions. The in-plane translating speed is characterized as a simple harmonic variation about the constant mean axial speed. The governing equation with the associated boundary conditions is derived from the generalized Hamilton principle and the Kelvin constitutive relation. The method of multiple scales is applied to establish the solvability conditions in principal parametric and internal resonances. The steady-state responses are predicted in three possible patterns: trivial, single-mode, and two-mode solutions. The stabilities of the steady-state responses are determined based on the Routh-Hurwitz criterion. The effects of the mean in-plane translating speed, the in-plane translating speed fluctuation amplitude, the viscosity coefficient, and the nonlinear coefficient on the steady-state responses are examined. The differential quadrature schemes are developed for the two-dimensional full plate model and the one-dimensional reduced plate model to solve the nonlinear governing equations numerically. The numerical calculations confirm the approximate analytical results regarding the trivial and single-mode solutions of the steady-state responses.

Nonlinear forced vibrations of in-plane translating viscoelastic plates subjected to plane stresses are analytically and numerically investigated on the steady-state responses in external and internal resonances. A nonlinear partial-differential equation with the associated boundary conditions governing the transverse motion is derived from the generalized Hamilton principle and the Kelvin relation. The method of multiple scales is directly applied to establish the solvability conditions in the primary resonance and the 3:1 internal resonance. The steady-state responses are predicted in two patterns: single-mode and two-mode solutions. The Routh–Hurvitz criterion is used to determine the stabilities of the steady-state responses. The effects of the in-plane translating speed, the viscosity coefficient, and the excitation amplitude on the steady-state responses are examined. The differential quadrature scheme is developed to solve the nonlinear governing equations numerically. The numerical calculations confirm the approximate analytical results regarding the single-mode solutions of the steady-state responses.

s Nonlinear parametric vibration is investigated for axially accelerating viscoelastic beams subject to parametric excitations resulting from longitudinally varying tensions and axial speed fluctuations. The effects of the longitudinally varying tension due to the axial acceleration are highlighted, while the tension was assumed to be longitudinally uniform in previous studies. The dependence of the tension on the finite axial support rigidity is also modeled. The governing equations of coupled planar vibration and the associated boundary conditions are derived from the generalized Hamilton principle and the viscoelastic constitutive relation. The equation is simplified into a governing equation of transverse nonlinear vibration in small but finite stretching problems. The governing equation of transverse vibration is a nonlinear integro-partial-differential equation with time-dependent and space-dependent coefficients. The method of multiple scales is employed to analyze the combination and the principal parametric resonances with the focus on steady-state responses. In the difference resonance, there is only trivial zero response which is always stable. In the summation and the principal resonances, the trivial responses may become unstable and bifurcate into nontrivial responses for certain excitation frequencies. Some numerical examples indicate that the longitudinal tension variation makes the instability frequency intervals of trivial responses small and the nontrivial response amplitudes large (small) in the summation (principal) resonance. It is also found that the nontrivial responses are not sensitive to the axial support rigidity. Numerical solutions are calculated via the differential quadrature to support results via the method of multiple scales.

In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilton principle. The method of multiple scales is applied to analyze the nonlinear partial differential equation. The natural frequencies and modes are investigated by performing the complex mode approach. The effect of natural frequencies with the stiffness and the axial speeds are numerically demonstrated. The solvability conditions are established for the cases of without and with 3:1 internal resonances. The relationships between the nonlinear frequencies and the initial amplitudes at different axial speeds and the nonlinear coefficients are showed for the case of without internal resonances. The effects of the related coefficients are demonstrated for the case of 3:1 internal resonances.

In this paper, nonlinear free transverse vibrations of in-plane moving plates subjected to plane stresses are investigated. The Hamilton principle is applied to derive the governing equation and the associated boundary conditions. The method of multiple scales is employed to analyze the nonlinear partial differential equation. The solvability conditions are established in the cases without internal resonance and with 3:1 or 1:1 internal resonances. Some numerical examples are presented to demonstrate the effects of in-plane moving speeds on the frequencies. The nonlinear frequencies of the in-plane moving plate without internal resonances are numerically calculated. The relationship between the nonlinear frequencies and the initial amplitudes is showed at different in-plane moving speeds and the nonlinear coefficients, respectively. It is feasible to investigate resonances without the modes not involved in the resonances. The effects of the related parameters are demonstrated for the case of 3:1 and 1:1 internal resonances, respectively. The differential quadrature scheme is developed to solve numerically the governing equation and confirm results via the method of multiple scales.

The crystal structure of tert-butoxycarbonyl-D, L-isoleucyl-glycyl methyl ester was determined by the X-ray method. The space group is P21 with a = 9.115(3), b= 12.075(4), c = 16.258(5) A, β = 89.84(3) and Z = 4. It was observed that in the peptides which contain IleGly fragment the carbonyl group of Gly residue has less tendency to form hydrogen bond than that of Ile residue. This tendency was supported by the atomic net charges calculated with the quantum mechanics program CNDO/2.

This paper investigates dynamic stability of an axially accelerating viscoelastic beam undergoing parametric resonance. The effects of shear deformation and rotary inertia are taken into account by the Timoshenko thick beam theory. The beam material obeys the Kelvin model in which the material time derivative is used. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The governing partial-differential equations are derived from Newton's second law, Euler's angular momentum principle, and the constitutive relation. The method of multiple scales is applied to the equations to establish the solvability conditions in summation and principal parametric resonances. The sufficient and necessary condition of the stability is derived from the Routh–Hurvitz criterion. Some numerical examples are presented to demonstrate the effects of related parameters on the stability boundaries.

This study investigates dynamic stability in transverse parametric vibrations of an axially accelerating tensioned beam of Timoshenko model on simple supports. The axial speed is assumed as a harmonic fluctuation about the constant mean speed. The Galerkin method is applied to discretize the governing equation into a finite set of ordinary differential equations. The method of averaging is applied to analyze the instability phenomena caused by subharmonic and combination resonance. Numerical examples demonstrate the effects of the mean axial speed, bending stiffness, rotary inertia and shear modulus on the instability boundaries.

In this paper, parametric resonance of axially moving beams with time-dependent speed is analyzed, based on the Timoshenko model. The Hamilton principle is employed to obtain the governing equation, which is a nonlinear partial-differential equation due to the geometric nonlinearity caused by the finite stretch of the beam. The method of multiple scales is applied to predict the steady-state response. The expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by using the Lyapunov linearized stability theory. Some numerical examples are presented to demonstrate the effects of speed pulsation and the nonlinearity in the first two principal parametric resonances.

In this paper, natural frequencies, modes and critical speeds of axially moving beams on different supports are analyzed based on Timoshenko model. The governing differential equation of motion is derived from Newton’s second law. The expressions for various boundary conditions are established based on the balance of forces. The complex mode approach is performed. The transverse vibration modes and the natural frequencies are investigated for the beams on different supports. The effects of some parameters, such as axially moving speed, the moment of inertia, and the shear deformation, are examined, respectively, as other parameters are fixed. Some numerical examples are presented to demonstrate the comparisons of natural frequencies for four beam models, namely, Timoshenko model, Rayleigh model, Shear model and Euler–Bernoulli model. Finally, the critical speeds for different boundary conditions are determined and numerically investigated.

In this paper, the parametric stability of axially accelerating viscoelastic beams is revisited. The effects of the longitudinally varying tension due to the axial acceleration are highlighted, while the tension was approximately assumed to be longitudinally uniform in previous studies. The dependence of the tension on the finite support rigidity is also considered. The generalized Hamilton principle and the Kelvin viscoelastic constitutive relation are applied to establish the governing equations and the associated boundary conditions for coupled planar motion of the beam. The governing equations are linearized into the governing equation in the transverse direction and the expression of the longitudinally varying tension. The method of multiple scales is employed to analyze the parametric stability of transverse motion. The stability boundaries are derived from the solvability conditions and the Routh-Hurwitz criterion for principal and sum resonances. In terms of stability boundaries, the governing equations with or without the longitudinal variance of tension are compared and the effects of the finite support rigidity are also examined. Some numerical examples are presented to demonstrate the effects of the stiffness, the viscosity, and the mean axial speed on the stability boundaries. The differential quadrature scheme is developed to numerically solve the governing equation, and the computational results confirm the outcomes of the method of multiple scales. [DOI: 10.1115/1.4004672]

Publisher Summary The forms of active components present in heterogeneous catalysts are of importance to catalysis. A supported catalyst usually consists of an active component dispersed on a support with a highly specific surface. An active component dispersed on a support may end up in one of three forms: (1) it may retain its chemical identity as a separate crystalline or amorphous phase, (2) it may form a new stoichiometric compound with the support or additive, or (3) it may dissolve in the support to give a solid solution. This chapter provides a review of various aspects of the phenomenon of spontaneous monolayer dispersion, its nature, effects, and applications. Spontaneous monolayer dispersion of compounds on supports is a widespread phenomenon and displays many unique effects. The principles involved have applications not only to heterogeneous catalysis, but also to materials science and other related fields.

The crystal of the title compound, C 10 H 13 N 2 O + .Cl - , consists of 1-benzyl-3-oxo-1H + -pyrazolidinium cations and chloride anions. The five-membered ring of the cation has an approximate half-chair conformation. Atom N(1) is sp hybridized while atom N(2) is sp 2 hybridized. The C(3)-N(2) bond distance of 1.373 (4) A is a partial double bond. Both H atoms connected to N atoms are involved in hydrogen bonding of the N-H...Cl type

Publisher Summary The forms of active components present in heterogeneous catalysts are of importance to catalysis. A supported catalyst usually consists of an active component dispersed on a support with a highly specific surface. An active component dispersed on a support may end up in one of three forms: (1) it may retain its chemical identity as a separate crystalline or amorphous phase, (2) it may form a new stoichiometric compound with the support or additive, or (3) it may dissolve in the support to give a solid solution. This chapter provides a review of various aspects of the phenomenon of spontaneous monolayer dispersion, its nature, effects, and applications. Spontaneous monolayer dispersion of compounds on supports is a widespread phenomenon and displays many unique effects. The principles involved have applications not only to heterogeneous catalysis, but also to materials science and other related fields.

The maximum monolayer dispersion(the threshold)for WO_3 on γ-Al_2O_3 calcined at 500°,550°,600°,and 640℃ has been determined quantitatively by XRD(amount of crystalline phase)and XPS(intensity ratios I_(W4f)/I_(Al2s)).The results show that if the amount of WO_3 loaded is lower than the maximum monolayer dispersion,WO_3 will react with γ-Al_2O_3 to form surface com- pound due to mutual ionic interaction,and will be dispersed on γ-Al_2O_3 surface as monolayer then. In case the amount is higher than this value,the residual crystalline WO_3 will remain.The max- imum monolayer dispersion(threshold)is 0.21 g and 0.20 g WO_3/100 m~2 γ-Al_2O_3 by NRD and XPS respectively.It agrees with the value(0.189 g WO_3/100 m~2 or 4.90×10~(18) W atoms/m~2)cal- culated from the model on assumption that the WO_3 is dispersed as a closed-packed monolayer on γ-Al_2O_3 surface.Inasmuch as WO_3/γ-Al_2O_3 system is stable up to higher temperature,e.g.700℃, than MoO_3/γ-Al_2O_3 system,WO_3 seems unfavorable to form new buIk compound with γ-Al_2O_3 at that temperature.However,Al_2(MoO_4)_3 forms perceptibly in MoO_3/γ-Al_2O_3 system at 500℃. Besides,the size of residual crystalline WO_3 in WO_3/γ-Al_2O_3 is much smaller than that of MoO_3 in MoO_3/γ-Al_2O_3.It might be the reason that WO_3/γ-Al_2O_3 catalyst is superior to MoO_3/γ-Al_2O_3 in hydrodesulfurization(HDS)or hydrodenitrogenation(HDN)in some cases.

Active free radicals formed by the electrooxidation of substituted anilines RC_6H_4NH_3 (R=H, p-Br, p-Cl, p-I, p-Me, p-COOH, p-MeCO, p-NO_2, m-CO_2H, and m-Cl) are trapped by spin trap 2-methyl-2-nitroso propane (MNP). A multiple ESR signal of the solution containing electrolytic aniline and MNP is identified with the spin adduct of MNP and radical cation 1 by theore- tical simulation of observed spectrum. Furthermore, ESR spectra of para- or meta-substituted anilines give a reasonable explanation about spin adducts of MNP and the cation 2 or 3 by the same method.

The title compound has been synthesized by the reaction of α-dithionaphthoic acid with CuCl2 in pyridine or by recrystallizing Cu4(α-C10H7CSS2)4 ṁ 1/2CS2 in a mixture of pyridine and alcohol. The structure of the title compound is determined by a single-crystal X-ray diffraction analysis. The crystal belongs to triclinic space group with unit cell parameters: a=7.085(2)A, b= 8.672(3)A and c=13.598(5)A; a=92.40(3)°, β=102.59(4)° and γ=105.67(4)°; V=780.6A2; Z=1. The structure was refined to R=0.058 for 2390 reflections. The molecule of the title compound sits on a center of symmetry. The shorter Cu—Cu bond length (2.606A) shows considerable interaction between copper atoms. If the Cu—Cu interaction is ignored, the neighbouring S and N atoms are coordinated to copper atom in a configuration of distorted tetrahedron.

π-Cyclopentadienyl(dicarbonyl)(phenylcarbyne)rhenium-tetrabromoborate, [π-C5H5(CO)2-ReCC4H5]BBr4 (3), at low temperature reacts with (μ-phenylthio) (μ-thiolato)hexacarbonyldiiron anion, (μ-C6H5S) (μ-LiS)Fe2(CO)6 (2), to give π-cyclopentadienyl (dicarbonyl){phenyl[(μ-phenylthio)hexacarbonyldiiron (μ-thio)] carbene} rhenium, π-C5H5(CO)2ReC(C6H5)(μ-S)(μ-C6H5S)Fe2(CO)6 (4). The complex 4 was identified by elemental analyses, IR, 1H NMR and mass spectra, and finally confirmed by its single crystal X-ray structure determination. The results from spectroscopic experiments and X-ray diffraction were discussed.