Kinetics insights into size effects of carbon nanotubes'growth and their supported platinum catalysts for 4,6-dinitroresorcinol hydrogenation

Size effects are a well-documented phenomenon in heterogeneous catalysis,typically attributed to alterations in geometric and electronic properties.In this study,we investigate the influence of catalyst size in the preparation of carbon nanotube(CNT)and the hydrogenation of 4,6-dinitroresorcinol(DNR)using Fe_(2)O_(3)and Pt catalysts,respectively.Various Fe_(2)O_(3)/Al_(2)O_(3)catalysts were synthesized for CNT growth through catalytic chemical vapor deposition.Our findings reveal a significant influence of Fe_(2)O_(3)nanoparticle size on the structure and yield of CNT.Specifically,CNT produced with Fe_(2)O_(3)/Al_(2)O_(3)containing 28%(mass)Fe loading exhibits abundant surface defects,an increased area for metal-particle immobilization,and a high carbon yield.This makes it a promising candidate for DNR hydrogenation.Utilizing this catalyst support,we further investigate the size effects of Pt nanoparticles on DNR hydrogenation.Larger Pt catalysts demonstrate a preference for 4,6-diaminoresorcinol generation at(100)sites,whereas smaller Pt catalysts are more susceptible to electronic properties.The kinetics insights obtained from this study have the potential to pave the way for the development of more efficient catalysts for both CNT synthesis and DNR hydrogenation.

Size effects on the tensile strength and fracture toughness of granitic rock in different tests

This study investigates the tensile failure mechanisms in granitic rock samples at different scales by means of different types of tests.To do that,we have selected a granitic rock type and obtained samples of different sizes with the diameter ranging from 30 mm to 84 mm.The samples have been subjected to direct tensile strength(DTS)tests,indirect Brazilian tensile strength(BTS)tests and to two fracture toughness testing approaches.Whereas DTS and fracture toughness were found to consistently grow with sample size,this trend was not clearly identified for BTS,where after an initial grow,a plateau of results was observed.This is a rather complete database of tensile related properties of a single rock type.Even if similar databases are rare,the obtained trends are generally consistent with previous scatter and partial experimental programs.However,different observations apply to different types of rocks and experimental approaches.The differences in variability and mean values of the measured parameters at different scales are critically analysed based on the heterogeneity,granular structure and fracture mechanics approaches.Some potential relations between parameters are revised and an indication is given on potential sample sizes for obtaining reliable results.Extending this database with different types of rocks is thought to be convenient to advance towards a better understanding of the tensile strength of rock materials.

Multi-dimensional size effects and representative elements for nonpersistent fractured rock masses: A perspective of geometric parameter distribution

This study takes a fractured rock mass in the Datengxia Hydropower Station,China as an example to analyze the size effects and determine the representative elementary sizes.A novel method considering geometric parameter distributions is proposed in this work.The proposed method can quickly and simply determine the size effects and representative elementary sizes.Specifically,geometric parameter distributions,including fracture frequency,size and orientation,are generated on the basis of the Bernoulli trial and Monte Carlo simulation.The distributions are assessed using the coefficient of variation(CV),and the acceptable variations for CV(5%,10%and 20%)are used to determine representative elementary sizes.Generally,the representative element of rock masses is the representative elementary volume(REV).The present study extends the representative element to other dimensions,i.e.representative elementary length(REL)and representative elementary area(REA)for one and two dimensions,respectively.REL and REA are useful in studying the size effects of one-(1D)and twodimensional(2D)characteristics of rock masses.The relationships among multi-dimensional representative elementary sizes are established.The representative elementary sizes reduce with the increase in the dimensions,and REA and REV can be deduced by REL.Therefore,the proposed method can quickly and simply determine REL and further estimate REA and REV,which considerably improves the efficiency of rock mass analysis.

Size effects on the mixed modes and defect modes for a nano-scale phononic crystal slab

The size-dependent band structure of an Si phononic crystal(PnC)slab with an air hole is studied by utilizing the non-classic wave equations of the nonlocal strain gradient theory(NSGT).The three-dimensional(3D)non-classic wave equations for the anisotropic material are derived according to the differential form of the NSGT.Based on the the general form of partial differential equation modules in COMSOL,a method is proposed to solve the non-classic wave equations.The bands of the in-plane modes and mixed modes are identified.The in-plane size effect and thickness effect on the band structure of the PnC slab are compared.It is found that the thickness effect only acts on the mixed modes.The relative width of the band gap is widened by the thickness effect.The effects of the geometric parameters on the thickness effect of the mixed modes are further studied,and a defect is introduced to the PnC supercell to reveal the influence of the size effects with stiffness-softening and stiffness-hardening on the defect modes.This study paves the way for studying and designing PnC slabs at nano-scale.

Size effects on plastic deformation behavior in micro radial compression of pure copper

Micro radial compression tests were carried out on cylindrical specimens of pure copper polycrystals with different grain sizes. Experimental results indicated that phenomena of decreasing forming force, increasing scatter of forming force and more irregular surface topography occurred with the increase of grain size. A modified surface model based on dislocations pile-up in surface layer grains, and a flow stress scattering formulation based on standard deviation and grain size distribution were proposed to analyze size effects on forming force in micro compression. The inhomogeneous deformation of surface layer grains was discussed by the main deformation manner of rotation. A good agreement with the experimental results was achieved.

Size effects on flow stress of C3602 in cylinder compression with different lubricants

Micro parts are more difficult to be formed than macro parts because of size effects. The size effects on the flow stress of copper alloy C3602 with different lubricants were studied. Specimens were heat treated at 350℃ for 1 h and 700℃ for 3 h in nitrogen atmosphere, respectively. The initial diameters of the specimens were varied from 5 to 1 mm with a height-to-diameter ratio h0/D0 = 1.5. Cylinder compression was carried out in the lubrication condition with talc powder, without lubricant, with petroleum jelly, and with vegetable oil. The experiment was carried out at room temperature on a universal testing machine INSTRON 5569 with a strain rate of ε = 0.0025 A. The results show that with the same lubricant, the yield strength decreases with a decrease in specimen size for the specimens annealed at 350℃ for 1 b; however, it increases with a decrease in specimen size for the specimens annealed at 700℃ for 3 h. The yield strength decreases with an increase in grain size. The influences of lubricants on yield strength become larger with miniaturization of the specimens.

Size effects in lithium ion batteries

Size-related properties of novel lithium battery materials, arising from kinetics, thermodynamics, and newly discov- ered lithium storage mechanisms, are reviewed. Complementary experimental and computational investigations of the use of the size effects to modify electrodes and electrolytes for lithium ion batteries are enumerated and discussed together. Size differences in the materials in lithium ion batteries lead to a variety of exciting phenomena. Smaller-particle materials with highly connective interfaces and reduced diffusion paths exhibit higher rate performance than the corresponding bulk materials. The thermodynamics is also changed by the higher surface energy of smaller particles, affecting, for example, secondary surface reactions, lattice parameter, voltage, and the phase transformation mechanism. Newly discovered lithium storage mechanisms that result in superior storage capacity are also briefly highlighted.

Flow stress and tribology size effects in scaled down cylinder compression

Microforming is an effective method to manufacture small metal parts.However,macro forming can not be transferred to microforming directly because of size effects.Flow stress and tribology size effects were studied.Scaled down copper T2 cylinder compression was carried out with the lubrication of castor oil and without lubrication.The results show that the flow stress decreases with decreasing the initial specimen diameter in both lubrication conditions,and the flow stress decreases by 30 MPa with the initial specimen diameter decreasing from 8 mm to 1 mm.The friction factor increases obviously with decreasing the initial specimen diameter in the case of lubricating with castor oil,and the friction factor increases by 0.11 with the initial specimen diameter decreasing from 8 mm to 1 mm.However,the tribology size effect is not found in the case without lubrication.The reasons of the flow stress and tribology size effects were also discussed.

Micro-plasticity Constitutive Model Taking Account of Size Effects for Pure Aluminum by Microindentation

The macro-plasticity power function constitutive model （MPFCM）, the modified macro- plasticity power function constitutive model （MMPFCM） and the micro-plasticity constitutive model （MCM） taking the material intrinsic length were established to characterize the microindentation size effects of pure aluminum, respectively. The experimental results indicated MPFCM only determined precisely in the great indentation load. While a modified one named MMPFCM was subsequently established taking account of the parameters variation with the increase of indentation depth. The conventional dimensional analysis method was employed to determine the strength coefficient K and the strain hardening exponent n of this modified model. And then MCM taking account of size effects was proposed based on the Taylor dislocation model. The first- order steepest gradient descent method was adopted to obtain the material intrinsic length for the geometrically necessary dislocations. The parameters of MCM were identified by using the UMAT subroutine of ABAQUS software. The average absolute relative error of MCM is relatively lower than that of the macro-one. Although the precision of the modified one is also high, the applied scope is limited, only for the microindentation material. In addition, the intrinsic length 5.09 bun of pure aluminum is also obtained based on the strain gradient theory.

Collective excitations and quantum size effects on the surfaces of Pb(111)films:An experimental study

Pb(111)film is a special system that exhibits strong quantum size effects in many electronic properties.The collective excitations,i.e.,plasmons,in Pb(111)films are also expected to show signatures of the quantum size effect.Here,using high-resolution electron energy loss spectroscopy,we measured the plasmons on the surface of Pb(111)films with different film thicknesses and analyzed the plasmon dispersions.One surface plasmon branch exhibits prominent damping in the small momentum range,which can be attributed to the interaction between the top and bottom interfaces of the Pb(111)films.With the film thickness increasing,the critical momentum characterizing the damping in Pb(111)films decays not only much slower in Pb(111)films than in other metal films,and even in films with the thickness up to 40 monolayers the damping still exists.The slow decay of the surface plasmon damping,manifesting the strong quantum size effect in Pb(111)films,might be related to the strong nesting of the Fermi surface along the(111)direction.

Size Effects of the Critical Temperature in Ferroelectric Thin Films

The size effects of the critical behaviors for the systems of interacting spins are discussed extensively inliterature.In this paper,the finite-size dependence of the critical temperature and susceptibility of the ferroelectric thinfilm are investigated numerically based on the four-state Potts model with the nearest-neighbor interactions between thedipole moments.The four orientations of the domains exist in the ferroelectric film and the movement of the domainwalls determines the polarization switching process besides the boundary conditions of the film.The critical exponentsare obtained and our investigations show that the boundary conditions play the important roles for the ferroelectricproperties of the thin films and the critical behavior of the thin films strongly depends on the feature of the surface.

Simulation of size effects by a phase field model for fracture

In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time inte- gration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture mod- els are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investi- gates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to exnerimental data.

Size Effects for the Adsorption of Alkali Metal Atoms on the Si(001) Surface

The adsorptions of a series of alkali metal （AM） atoms, Li, Na, K, Rb and Cs, on a Si（001）-2 × 2 surface at 0.25 monolayer coverage have been investigated systematically by means of density functional theory calculations. The effects of the size of AM atoms on the Si（001） surface are focused in the present work by examining the most stable adsorption site, diffusion path, band structure, charge transfer, and the change of work function for different adsorbates. Our results suggest that, when the interactions among AM atoms are neglectable, these AM atoms can be divided into three classes. For Li and Na atoms, they show unique site preferences, and correspond to the strongest and weakest AM-Si interactions, respectively. In particular, the band structure calculation indicates that the nature of Li-Si interaction differs significantly from others. For the adsorptions of other AM atoms with larger size （namely, K, Rb and Cs）, the similarities in the atomic and electronic structures are observed, implying that the atom size has little influence on the adsorption behavior for these large AM atoms on the Si（001） surface.

First-Principles Calculations of the Quantum Size Effects on the Stability and Reactivity of Ultrathin Ru (0001) Films

We carry out first-principles calculations of Ru（0001） films up to 30 monolayers （MLs） to study the quantum size effect （Q, SE） of Ru films for two cases： the freestanding Ru films and Ru films on Pt（111） substrates. Our studies show that the properties of these films （surface energy, work-function, charge density decay length in a vacuum and chemical reactivity） exhibit pronounced oscillatory behavior as a function of the film thickness, with an oscillation period of about four MLs for both cases due to the relationship of the match between the Fermi wave vector and the film thickness. Due to the localization of d-electron of Ru films, these quantum oscillations almost disappear when the thickness of the film is more than -20 ML for the free standing Ru films, while for the Ru films on Pt substrates the oscillations disappear quickly when the thickness of the film is beyond -13 ML. Our results reveal that the stability and reactivity of the Ru films could be tailored through Q, SE and the Ru bilayer grown on Pt substrates observed in the experiment is also related to the effect.

Size effects on deformation behavior of C5210 phosphor bronze thin sheet

To investigate the effects of thickness and grain size on mechanical and deformation properties of C5210 phosphor bronze thin sheets, samples with different grain sizes were obtained through annealing heat treatment at different temperatures; and then tensile tests of samples with different thicknesses and grain sizes were conducted at room temperature. The results show that yield strength increases with decreasing thickness from 800 to 50 μm, but work hardening exponent and total elongation decrease, and a modified model was proposed to describe the relation between yield strength and thickness; yield strength decreases as the grain size increases, but work hardening exponent shows an increasing trend, total elongation increases to a peak and then decreases. Fracture morphology of tensile specimens was observed by SEM, which indicates that all tensile specimens are ductile fracture. The dimple intensity increases as the specimen thickness increases but reduces with the specimen grain size increasing.

PARTICULATE SIZE EFFECTS IN THE PARTICLE-REINFORCED METAL-MATRIX COMPOSITES

The influences of I,article size on the mechanical properties of the particulate metal matrix composite;are obviously displayed in the experimental observations. However, the phenomenon can not be predicted directly using the conventional elastic-plastic theory. It is because that no length scale parameters are involved in the conventional theory. In the present research, using the strain gradient plasticity theory, a systematic research of the particle size effect in the particulate metal matrix composite is carried out. The roles of many composite factors, such as: the particle size, the Young's modulus of the particle, the particle aspect ratio and volume fraction, as well as the plastic strain hardening exponent of the matrix material, are studied in detail. In order to obtain a general understanding for the composite behavior, two kinds of particle shapes, ellipsoid and cylinder, are considered to check the strength dependence of the smooth or non-smooth particle surface. Finally, the prediction results will be applied to the several experiments about the ceramic particle-reinforced metal-matrix composites. The material length scale parameter is predicted.

MECHANICAL PROPERTIES AND SIZE EFFECTS OF SINGLE CRYSTAL SILICON

Six kinds of micro bridge-beam specimens with different sizes are fabricated using photolithography technology for bending test. Beam specimens with trapezoidal section could be representatives of those with rectangle and square section, which are usually applied in MEMS. Nano indentation method used in bending test can be applied to both elastic and plastic materials. Also, some mechanical properties parameters such as the modulus of elasticity, hardness and the bending strength are obtained. The average modulus of elasticity of SCS is 170.295 0±2.485 0 GPa, showing no size effects, but the bending strength ranges from 3.24 GPa to 10.15 GPa, displaying strong size effects, and the average hardness is 9.496 7±1.753 3 GPa,in which no obvious size effects are observed.

Pore size effects of nanoporous carbons with ultra-high surface area on high-pressure hydrogen storage

In this work, the morphologies and pore structures of a series of corncob-derived activated carbons and zeolite templated carbon with ultrahigh surface area were carefully investigated by SEM, HRTEM and N2-sorption characterization technologies. The high-pressure hydrogen uptake performance was analyzed using standard Pressure-Composition-Temperature apparatus in order to study the pore size effects on hydrogen uptake. These as-obtained porous carbons showed different characteristics of pore size distribution as well as specific surface area. The results indicate that the most effective pores for adsorbing hydrogen depended on the storage pressure. These ultramicropores （0.65-0.85 nm） could be the most effective pores on excess H2 uptake at 1 bar, however, micropores （0.85-2 nm） would play a more important role in excess H2 uptake at higher pressure at 77 K. At room temperature, pore size effects on H2 uptake capacity were very weak. Both specific surface area and total pore volume play more important roles than pore size for H2 uptake at room temperature, which was clearly different from that at 77 K. For applications in future, the corncob-derived activated carbons can be more available than zeolite templated carbons at 77 K. Element doping enhanced hydrogen uptake could be main research direction for improving H2 uptake capacity at room temperature.

Finite size effects on helical edge states in HgTe quantum wells with the spin orbit coupling due to bulk- and structure-inversion asymmetries

There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.

Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations

The Bauschinger and size effects in the thinfilm plasticity theory arising from the defect-energy of geometrically necessary dislocations （GNDs） are analytically investigated in this paper. Firstly, this defect-energy is deduced based on the elastic interactions of coupling dislocations （or pile-ups） moving on the closed neighboring slip plane. This energy is a quadratic function of the GNDs density, and includes an elastic interaction coefficient and an energetic length scale L. By incorporating it into the work- conjugate strain gradient plasticity theory of Gurtin, an energetic stress associated with this defect energy is obtained, which just plays the role of back stress in the kinematic hardening model. Then this back-stress hardening model is used to investigate the Bauschinger and size effects in the tension problem of single crystal Al films with passivation layers. The tension stress in the film shows a reverse dependence on the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L is determined, which is just several slip plane spacing, and accords well with our physical interpretation for the defect- energy. The Bauschinger effect after unloading is analyzed by combining this back-stress hardening model with a friction model. The effects of film thickness and pre-strain on the reversed plastic strain after unloading are quantified and qualitatively compared with experiment results.