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Graphene origami (G-ori) can possess unique mechanical properties and achieve some distinctive functionalization by engineering their configurations. However, it remains a tremendous challenge to modulate its formation and properties at the micro- and nano-scales. Herein, we systemically present the formation of G-ori activated by creased marks via molecular dynamics (MD) simulations. The pre-existing creased mark in graphene is created in a controlled way by transforming sp2 to sp3 bonds at the crease. Our results show that the presence of interlayer sp3 bonds at the crease can direct crack growth and hence pave a new way to tailor graphene sheets into specified pieces. The crease also guides the folding process of graphene into various geometric configurations. Sophisticated G-ori can be constructed by designing rational crease distribution on the graphene surface. Checking against the folding process of paper origami shows that the crease-induced targeted folding can be achieved at both nano- and macro-scales in exactly the same way. Our findings provide a simple and feasible method to construct graphene-based nano-devices by designing rational morphological configurations of G-ori.

Carbon anchored titanium carbonitride for supercapacitor electrode material was prepared by a direct semi-solid-sate carbonitridation method. The prepared sample is highly conductive and mesoporous (250 m2 g−1), enabling fast electron transfer and ion transport. As a result, a high capacitance of 360 F g−1 at 0.5 A g−1, and an impressive capacitance retention ratio 100Ag-1/1 A g−1 of 53%, as well as long cyclic capability (>10,000 cycles) can be obtained in 1 M H2SO4. The thick electrode also presents a high area capacitance up to 1.77 F cm−2. A flexible H2SO4/PVA symmetric supercapacitor was fabricated to demonstrate its practicality. Remarkably, the supercapacitor presents high-rate performance (up to 25 kW kg−1) and long cyclic performance (>10,000 cycles), illustrating its potential application in flexible integrated energy storage devices. This work provides a novel insight into designing and preparing carbonitride based materials for high performance supercapacitor.

The interface between ZnO and SrTiO3 (STO) provides a paradigm for combining perovskite oxides and wurtzite-structure semiconductors. However, the heteroepitaxial and energy band structures of the polar-to-polar STO/ZnO(000 1 ¯ ) interfaces has rarely been studied. In this study, it is shown that the STO films prepared on the ZnO(000 1 ¯ ) substrate by pulsed laser deposition possess [0 1 1]STO and [1 1 1]STO azimuth orientations, which exhibit three- and two-fold rotation domains respectively, as demonstrated by X-ray diffraction and transmission electron microscopy. The band structures of the STO(0 1 1)/ZnO ( 000 1 ¯ ) and STO(1 1 1)/ZnO ( 000 1 ¯ ) interfaces are bending downward as shown in the I-V characteristic spectra and first principle calculations. These results are different from the single orientation ZnO films grown on STO-(0 1 1) and -(1 1 1) substrate, as reported in previous literatures, showing the heteroepitaxial asymmetry between STO/ZnO and ZnO/STO interfaces. This work presents an approach towards the physical modeling of combinations between perovskite oxides and wurtzite-structure semiconductors.

The SrTiO3(STO)/ZnO heterointerface, which is widely used in the fabrication of novel optoelectronic devices, is a classical system combining functional perovskite oxides and wurtzite-structure semiconductor materials. The electronic structure of the heterointerface often plays a significant role in controlling the functions of novel devices. In this study, the electronic structure was explored using in situ photoemission spectroscopy and X-ray absorption spectroscopy. X-ray diffraction results showed the coexistence of (1 1 1)STO and (0 1 1)STO orientations for the STO film deposited on the ZnO-(000 1 - ) substrate via pulsed laser deposition. High-resolution transmission electron microscopic results revealed two types of polar interfaces: [11 2 - ][10 1 - ](1 1 1)STO//[1 2 - 10][10 1 - 0](000 1 - )ZnO and [1 1 1][2 1 - 1 - ](0 1 1)STO//[10 2 - 1 ][10 1 - 0](000 1 - )ZnO. In situ photoemission spectroscopic results revealed downward band bending and the transformation of the valence states of Ti from 4+ to 3+, with extra electrons transferring to the hybridization states between O 2p and Ti t2g orbitals at the polar-to-polar STO/ZnO interface. We propose that the polar discontinuity drives the electron transfer to the STO/ZnO interface during the growth process. This study provides insight into the electronic structure of the STO/(000 1 - )ZnO heterointerface.

Aqueous electrolytes are promising for high performance electrochemical supercapacitors. However, their present narrow electrochemical window, high-cost or toxicity , set limits for wide application. Here, we demonstrate the viability of employing the PEO-strengthened 3 m LiTFSI aqueous electrolytes, which are high-conductive and eco-friendly, for high voltage supercapacitors application. Furthermore, symmetric supercapacitor with 3 m LiTFSI/30 g L−1 PEO is assembled. High operating-voltage of 2.4 V with excellent performance (125 F g−1 at 0.5 A g−1, and 67.3% capacitance retention of 50Ag-1/1 Ag-1) and longevity (>10,000 cycles) are achieved. Therefore, this work provides an effective and promising way to prepare green and high potential window electrolyte for high-voltage operating energy storage devices.

How to effectively manipulate the mechanical properties of atomically thin materials, is critical and can enable many new types of devices for various applications, such as sensing, actuation, energy harvesting, and so on. Here, we propose and demonstrate a new way to regulate the polarity of phosphorene’s mechanical properties by controlling the level of oxidation. Phosphorene and its low-level oxides are treated with ab initio methods in order to evaluate the influence of oxidation on the anisotropic mechanical properties of phosphorene. Our results show that the mechanical properties of phosphorene are anisotropic. For the stable configuration, the anisotropy is gradually reduced with the increase of the oxygen coverage. We have fitted the formulas of Young’s (shear) modulus and Poisson’s ratio of phosphorene oxide. We also investigated the mechanical properties of metastable configurations. The diagonal configuration increases the anisotropy. The horizontal configuration is very unstable and has no shear moduli. Our results demonstrate that the mechanical properties of phosphorene can be regulated by oxidation, which is useful in design of phosphorene-based mechanical and optoelectronic devices. Our general model for calculating the elastic modulus along arbitrary direction can be applied in any 2D materials.

ZnO films with carrier concentration as low as 5.0 × 10 13 cm −3 have been prepared via a lithium and nitrogen codoping method, and ultraviolet photodetectors have been fabricated from the films. The photodetectors can be used to detect weak signals with power density as low as 20 nw/cm 2 , and the detectivity and noise equivalent power of the photodetector can reach 3.60 × 10 15 cmHz 1/2 /W and 6.67 × 10 −18 W −1 , respectively, both of which are amongst the best values ever reported for ZnO based photodetectors. The high-performance of the photodetector can be attributed to the relatively low carrier concentration of the ZnO:(Li,N) films.

Based on first-principles methods and Boltzmann transport theory, we investigated the biaxial strain effects on electronic and thermoelectric properties of three group-III nitrides (BN, AlN and GaN) 2D honeycomb mono-layered nanosheets. The direct-indirect band gap transitions occurred for BN and GaN nanosheets when the strain was applied. In addition, the band gaps decreased with increase of tensile strain; and we uncovered the mechanism behind by the total and projected density-of-state (PDOS) analyses. At the same time, we presented the contour plots of their electrical transport properties as a function of both temperature and carrier concentration at strain-free states. Power-factors of BN, AlN and GaN nanosheets were also calculated. We found only peak power factors of p-type GaN and n-type BN showed a strong dependence on biaxial strain. Such differences of the strain-dependent thermoelectric performance among BN, AlN and GaN may be due to the competition between covalency and ionicity in these 2D structures. Our results provide a new avenue to optimize thermoelectric properties of 2D nanosheets by strain engineering.

NbO2/porous carbon matrix composite material for supercapacitor application is prepared by a facile sugar blowing method. Owing to the unique porous and intergrowth structure, this material possesses effective electron-ion-conductive-network. Thus, it delivers an impressive capacitance of 261 Fg−1 (686 F cm-3) at 1 A g−1 and 175 Fg−1 (460 F cm−3) at 50 A g−1 in 1 M H2SO4. With a wide potential window of 1.8 V in 1 M Li2SO4, it achieves 184 Fg−1 (484 F cm−3) at 1 A g−1 and 130 Fg−1 (342 F cm−3) at 50 A g−1, respectively. Remarkably, a symmetric two-electrode-cell with this material using 1 M Li2SO4 retains its operating voltage of 1.8 V, delivering 18.2 Wh kg−1 (47.9 Wh l−1) at 810 W kg−1 (2130.3 W l−1), and 10.5 Wh kg−1 (27.6 Wh l−1) at 81000 W kg−1 (213030 W l−1), as well as excellent cyclic capability (>10000 cycles). These interesting performance reveals the significant prospect of this material to be utilized in supercapacitors and other electrochemical devices.

Using first-principles calculations, we have investigated the electronic structures, mechanical properties and carriers mobilities of π-conjugated X(X = Ni, Pd, Pt) bis(dithiolene) nanosheets (XDts). Firstly, Gaussian-Perdue–Burke–Ernzerhof (Gau-PBE) functional band structures of XDts have been calculated. XDts are narrow band gap semiconductors, and the band gaps are 0.392 eV (NiDt), 0.082 eV (PdDt), 0.336 eV (PtDt), respectively. Secondly, we present a method to calculate the elastic modulus of 2D material in arbitrary direction. Using this method, we predict that the elastic moduli of XDts are isotropic, and the Young’s moduli of those nanosheets are 87 GPa (NiDt), 78.2 GPa (PdDt), and 86.5 GPa (PtDt), respectively, which are much softer than graphene due to their large porosity. Thirdly, we have calculated the mobilities of XDts by deformation potential method. The electron mobilities of XDts are higher than 2.0 × 103 cm2 V−1 s−1. In particular, the electron mobility of PdDt reaches 14.86 × 103 cm2 V−1 s−1. Our results show that XDts have a wide range of potential applications in nano devices.

Kirigami structure, from the macro- to the nanoscale, exhibits distinct and tunable properties from original 2-dimensional sheet by tailoring. In present work, the extreme reduction of the thermal conductivity by tailoring sizes in graphene nanoribbon kirigami (GNR-k) is demonstrated using nonequilibrium molecular dynamics simulations. The results show that the thermal conductivity of GNR-k (around 5.1 Wm-1K-1) is about two orders of magnitude lower than that of the pristine graphene nanoribbon (GNR) (around 151.6 Wm-1K-1), while the minimum value is expected to be approaching zero in extreme case from our theoretical model. To explore the origin of the reduction of the thermal conductivity, the micro-heat flux on each atoms of GNR-k has been further studied. The results attribute the reduction of the thermal conductivity to three main sources as: the elongation of real heat flux path, the overestimation of real heat flux area and the phonon scattering at the vacancy of the edge. Moreover, the strain engineering effect on the thermal conductivity of GNR-k and a thermal robustness property has been investigated. Our results provide physical insights into the origins of the ultralow and robust thermal conductivity of GNR-k, which also suggests that the GNR-k can be used for nanaoscale heat management and thermoelectric application., Comment: 15 pages, 10 figures

Effect of temperature on monocrystalline and multicrystalline silicon solar cells processed from chemical (EG-Si) and metallurgical (SoG M -Si) routes was investigated in the range of 280–350 K. The temperature coefficients of important parameters related with the cell property were discussed. Experimental results indicate that the T -coefficient of conversion efficiency ( η ) of multicrystalline EG-Si cell processed from chemical is only 68% that of the monocrystalline EG-Si cell. Furthermore, the η of both types of SoG M -Si cells decrease much less than that of the EG-Si cells with the increase in temperature. Additionally, the recombination fraction, the minority carrier lifetime, the carrier mobility decrease and the band-gap shrinkage were also investigated to reveal the intrinsic temperature dependence mechanism. In order to confirm the results, we used numerical simulation software AMPS-1D (analysis of microelectronic and photonic structure in one dimension program) to simulate the temperature dependence of solar cell performances. The results of numerical simulation were basically consistent with the experimental results.

Specialized Research Fund for the Doctoral Program of Higher Education [20120121110021]; Natural Science Foundation of China [U1232110]; Natural Science Foundation of Fujian Province of China [2013J01026]; Fundamental Research Funds for Central Universities [2013121012]; Institute for Complex Adaptive Matter, University of California, Davis, CA [ICAM-UCD13-08291]

A dense and vertically aligned single-walled carbon nanotube (SWCNT) array was assembled between a chip and a substrate by a fluidic assembly method. The SWCNT bridged the interface as a thermal interface material (TIM). The minimum interfacial thermal resistance was measured close to 4.5 mm 2 K/W by the laser flash method. This value was lower than that of commercial thermal grease. Filling up the remaining space of the SWCNT array with a highly penetrative glue (LOCTITE ® 4699™, Henkel Co. Korea) was found to produce a significant increase in shear strength from 450 kPa to 3 MPa, as well as an approximate 10% decrease in thermal diffusivity. The material's higher thermal performance is expected to allow a chip to make a good connection to a heat sink in microelectronics packaging, thus acting as a substitute for conventional thermal adhesives.

Electrochemical capacitors deliver high power and have long operational lives; however, their energy densities are limited. Compared to carbon-based electrical double-layer capacitors, pseudocapacitors with an aqueous electrolyte are predicated to provide both high gravimetric and volumetric capacitance while being cost-effective and eco-friendly. However, their narrow operational potential windows limit the practical delivery of energy. In this study, we synthesized novel NbCxN1-x nanoparticles encapsulated in a uniform carbon layer. This pseudocapacitive material exhibits a high volumetric capacitance, a wide potential window stability (∼345 F cm−3, 2.1 V, in 1 M of Li2SO4), and a long cycling life (>10 000 cycles). Moreover, the symmetric cells (2.2 V, in 1 M of Li2SO4) exhibit high energy density as well as excellent cyclability and rate performances. These findings provide new opportunities for the design of aqueous energy storage devices having a wide applied potential difference and excellent performance.

N/P co-doped porous carbon is prepared from biomass (silkworm cocoon) and natural product (phytic acid) by an eco-friendly self-activation approach. Owing to the rational pore structure, and abundant pseudocapacitive active sites of heteroatom doping, the prepared Cheese-brick-like porous carbon presents outstanding performances. The optimized S2 sample delivers both high gravimetric capacitance and volumetric capacitance of 317 F g−1 (482 F cm−3) at 1 A g−1, and an impressive capacitance of 159 F g−1 (242 F cm−3) at a high current density of 50 A g−1 in 1 M H2SO4. Also, the thick electrode (10 mg cm−2) can deliver a high areal capacitance up to 2.44 F cm−2 at 10 mA cm−2 and 1.29 F cm−2 at 500 mA cm−2. Additionally, the porous carbon based flexible symmetric supercapacitor (1.4 V) can deliver a remarkable 19.6 Wh kg−1 (29.8 Wh l−1) at 350 W kg−1, and 9.6 Wh kg−1 (14.6 Wh l−1) at 17500 W kg−1, respectively, as well as outstanding cyclic longevity (~98% capacitance retention after 10000 cycles). These attractive performances enable a wonderful potential of our porous carbon applied in supercapacitors for wearable electronics and other energy storage devices.

NSFC [61072014, 51103164]; National Program on Key Basic Research Project (973 Program); Ministry of Science and Technology of China; Chinese Academy of Sciences; Minjiang Scholar Distinguished Professorship Program through Xiamen University of China; Specialized Research Fund for the Doctoral Program of Higher Education [2009012112002, 20100121120026]

Specialized Research Fund for the Doctoral Program of Higher Education [20090121120028, 20100121120026]; National Science Foundation of China [U1232110]

Specialized Research Fund for the Doctoral Program of Higher Education [20090121120028]; Natural Science Foundation of Fujian Province, China [2009J01015]; Xiamen University

National Nature Science Foundation of China [10702056, 10774124]; Xiamen University of China; Natural Science Foundation of Fujian Province, China [2009J01015]; Xiamen University

Using molecular dynamics simulations with the quantum corrected Sutton–Chen type many-body potential, we have investigated the mechanical responses of Au nanowires along the [1 0 0], [1 1 0], and [1 1 1] crystallographic orientations under compression and tension. The main focus of this work is the orientation-dependent effects on the mechanical properties. The common neighbor analysis method is used to investigate the structural evolution and deformation mechanism of Au nanowires. The simulation results show that the Young’s modulus is strongly dependent on nanowire’s orientation. Under tension, all the oriented nanowires yield via the activities of Shockley partial dislocations, and their plastic deformation is accommodated by partial dislocation activities without twining. Under compression, the [1 0 0] nanowire presents the same yield mechanism together with the deformation twins occurring in its plastic deformation, however, for the [1 1 0] and [1 1 1] nanowires, the buckling instability preferentially occurs, followed by full dislocation activities to carry the plastic deformation without partial dislocations involved. The deformation behaviors indicate that the predication of the Schmidt factor based on bulk single crystal is valid for Au nanowires under compression but not under tension. Our study also shows that the [1 1 0] Au nanowire exhibits a better ductibility, while the [1 1 1] Au nanowire possesses excellent overall mechanical properties.

National Nature Science Foundation of China [10702056, 10774124]; Program for New Century Excellent Talents in Fujian Province University, China (NCETFJ); Xiamen University of China; Natural Science Foundation of Fujian Province, China [2009JO1015]

The energetic and structural evolution of a squared gold nanowire under heating process is investigated via molecular dynamics with many-body potential. The simulations reveal that the nanowire undergoes distinct energetic and structural developments during the following four heating processes: low temperature, melting, breaking and high temperature. The cross-section of nanowire is found to change from a square to a circle shape with rising temperature at first. A neck is then found to be initiated above the overall melting point, followed by the formation of a two- to five-atom-thick chain structure before the breaking of neck. The nanowire transforms to a spherical cluster after the final breaking.

We present a general physical picture for the one-dimensional nanomagnetism of elements with only s- or sp- valence electrons based on the atomic orbital interactions, first-principles calculations and Stoner criterion combined. It is shown that s- and sp- electron atoms, such as Na, Mg, Al, and Si, can exhibit magnetism in the geometry of linear chains. The s- electron elements show magnetism when the bonds are compressed, and, in contrast, the sp -elements exhibit magnetism when the bonds are elongated. The underlying mechanism has been understood by a general physical picture, that is, the exchanges among electronic states of multiple subbands around the Fermi level.

The structures and electronic properties of binary alloys C 3 N 4 and C 3 P 4 were examined closely using first principles method based on the density functional theory and the local density approximation. Our calculations revealed that electronegativity plays a dominant role in determining the electronic properties of these compounds. Different crystal structures are preferred by the nitride and phosphide because of the different bonding preferences of nitrogen and phosphorus. The relative stability of these two phases changes gradually with composition in the ternary alloy C 3 N 4− n P n , but the electronic properties change drastically in the presence of phosphorus. Other group IV phosphides and nitrides show similar properties and trends, except some deviations by Sn 3 N 4 and Sn 3 P 4 .

We performed first-principles calculation on several possible polymorphs of C 3 P 4 to investigate the structural and electronic properties of hypothetical carbon phosphide solids. Our calculations predict that C 3 P 4 is metallic within LDA. Unlike C 3 N 4 , the calculations also predict that pseudocubic-C 3 P 4 is the most energetically favored structure at zero pressure. Being also the densest structure at zero pressure, it is perhaps only possible to synthesize pseudocubic-C 3 P 4 .

Surface oxidation studies on pre-deuterated (1 0 0)-oriented single crystal diamond have been performed by oxidizing the diamond surfaces macroscopically using an oxygen atomic beam source as well as microscopically using local anodic oxidation by atomic force microscope (AFM). Oxygen-deuterium exchange on diamond (1 0 0) was investigated by X-ray photoelectron spectroscopy, elastic recoil detection and time-of-flight SIMS. Exchange of pre-adsorbed D by atomic O is thermally activated, with almost complete exchange of surface D by atomic O at 300 °C. At higher oxidation temperatures, oxidation states which are chemically shifted from the C 1s bulk peak by 3.2 eV was observed together with a disordering of the diamond surface. Micron-scale, localized oxygenation of the diamond surface at room temperature could be achieved with a biased AFM tip where we confirmed that the modified areas show a lower secondary electron yield and higher oxygen content. In addition, the electronic structure of the oxygenated diamond surface (on-top (OT) and bridging model) has been investigated by calculating the layered-resolved partial density of states using first principles plane wave ab initio pseudopotential method within the local density functional theory. For the oxygen OT model, sharp features due to occupied surface states in the valence band and unoccupied surface states in the gap exist. The increase in emission intensity near the valence band edge for oxygenated diamond (1 0 0) was verified by ultraviolet photoelectron spectroscopy study.

The electronic structure of oxygenated diamond (100) surface is studied comparatively by experimental photoemission techniques and first principles calculations. Controlled oxygenation of the diamond (100) 2×1 surface at 300°C yields a smooth O:C (100) 1×1 surface with a distinctive emission state at ∼3 eV from the Fermi edge. Oxygenation of the hydrogenated surface at temperatures above 500°C, however, gives rise to extensive etching and roughening of the surface. The experimentally observed emission state at ∼3 eV following O adsorption is assigned to the O-induced surface state. When the oxygenated surface is annealed to 800°C to desorb chemisorbed O, the surface structure changes from 1×1 to 2×1 and another surface state emission at 2.5 eV associated with the clean surface reconstruction can be observed by UPS. This is attributed to the π-bond reconstruction of sub-surface carbon layers following the desorption of first layer CO from the surface. To understand the origin of the O-induced emission state, we calculated the density of states (DOS) of the oxygenated diamond using the first principles linear muffin-tin orbital (LMTO) method with atomic sphere approximation (ASA) based on density functional theory (DFT) and local density approximation (LDA).

The dependence of the photoluminescence (PL) from SiC nanocrystals embedded in a SiO 2 matrix on annealing is presented. Blue-green PL has been observed at room temperature from annealed SiC–SiO 2 composite films. The intensity of the single emission band at 460 nm (2.7 eV) shows a strong dependence on the annealing temperature. The combination of high-resolution transmission electron microscopy (HRTEM), Fourier transform infrared (FTIR) transmission spectra and PL results suggest that SiC nanocrystals have been incorporated into the SiO 2 matrix and O-deficient defects were formed. The origin of luminescence is attributed to the creation of defects in silicon oxide.

The ion-induced nitridation of GaAs(1 0 0) using 1.2 keV N 2 + ion beams has been investigated using in situ X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). Ga-rich surfaces produced by Ar + cleaning, promote initial nitridation and formation of GaN. The dependence of [N]/[Ga] and [As]/[Ga] atomic ratios on substrate temperature, nitridation time, and nitrided layer depth suggest that the process is self-limiting. The degree of nitridation increases with the temperature, but decreases again at higher temperatures (>450°C). Smooth nitrided layers are formed between room temperature and 450°C. For nitridation at T =600°C however, the aggregation of GaAs 1− x N x results in the roughening of the nitrided surfaces. Diffusion, sputtering, and decomposition effects in the nitridation process are considered, and the mechanisms of GaAs 1− x N x formation are discussed.

The electronic properties and bonding configuration at the interface between cubic (zinc blende) BN and 3C–SiC are studied using the first principle linear muffin-tin orbital (LMTO) method based on local-density-functional (LDA) theory. The (001) superlattice of BN( n )/SiC( n ) ( n =1–6) is used to study the interface. The calculated results show that the preferred bonding configuration is Si–N and C–B for the (001) BN/SiC interface. The formation energy of the interface is studied as a function of thickness of the superlattice. The origin of the bond formation as well as the electronic properties of the interface are also investigated.

The multilayer relaxations of Al(100) and Al(110) surface are studied using the plane wave ab initio pseudopotential method within the local density functional theory. Our calculations show that the surface relaxation of Al(100) is an ‘anomalous’ outward relaxation, which is in excellent agreement with experimental results, although several previous empirical and semi-empirical theoretical studies have predicted contractions that are contrary to the experiments. For the Al(110) surface, our calculations do show inward relaxation, which is consistent with LEED experiments and other theoretical calculations. The origin of ‘inward’ and ‘outward’ relaxation is discussed. The surface energy is also studied in this work.

In this paper, a new approximate formula to probability integral is deduced using theoretical analysis combining with computer numerical simulation. The absolute storage capacity of the Hopfield neural network is analyzed with this approximate formula and a more strict result is obtained.

The storage capacity of the three-dimensional rotation neural network model is discussed by using the signal-to-noise theory. Some results discussed in the Hopfield model, the complex phasor model and the Hamilton neural network are obtained. Compared to other multistate neural networks, a novel property of the model is that the storage capacity for a fixed neuronal state varies with the different combinations of numbers of rotation angles and axes. The maximum storage capacity can be obtained for a special combination of numbers of rotation angles and axes.

In this paper, the storage capacity of the Q-state complex phasor neural network is analysed with the signal-to-noise theory. The results indicate that the storage capacity of the model approaches that of the Hopfield model if the number Q is small; while the storage capacity is proportional to Q−2 if Q is large.