•The sodium atoms transfer their 3s electrons to aluminum and exist as +1 cations.•The molecular orbitals accord with the types predicted by the jellium model.•Al5Na5 and Al6Na2 show enhanced stabilities as the 20 valence electrons form closed electronic shells.•Aln moieties in the AlNa binary clusters form Zintl anions.•AlNa clusters can be used as building blocks to form cluster-assembled Zintl-phase materials.The low-energy structures of Al5Nam (m = 1–5) and Al6Nam (m = 0–4) are searched by using the genetic algorithm combined with MOPAC package. The stabilities and the electronic structures are studied by density functional theory models and by first principle perturbation theory at MP4 level. The results show that the Na atoms are located at the outside of the clusters. Analysis on the density of states and the charge distribution indicate the sodium atoms transfer their 3s electrons to aluminum and exist as +1 cations. The molecular orbitals agree with the types predicted by the jellium model, and Al5Na5 and Al6Na2 show enhanced stabilities as the 20 valence electrons form closed electronic shells. However, the valence orbitals don’t encompass the Na+ cores. The electron localization function clearly demonstrates that the valence electrons reside at the outside of the Al3+ cores, and the Na+ cores are exposed at the outside of the valence electrons. All the results confirm that Aln moieties in the AlNa binary clusters form Zintl anions and the Na+ cations are ionically bonded to them. It suggests AlNa clusters can be used as building blocks to form cluster-assembled Zintl-phase materials.Download high-res image (294KB)Download full-size image

•The fractional dielectric relaxation models are established using cap-resistors.•Cole–Cole equation is a special case of the generalized fractional Maxwell model.•The cap-resistor corresponds to the complex impedance used in the classical models.•Only the fractional models can represent outspread wings in the Cole–Cole plots.•Relaxation processes of liquid crystal cells embedded with Pd are fitted perfectly.The polarization of dielectric materials in electric field lags behind the external field and the relaxation losses energy. In this paper, the relaxation characteristics of the fractional models established by using a fractional differential operator (cap-resistor) are analyzed. It is found that the cap-resistor just corresponds to the complex impedance used by Cole brothers to represent the dissipation in the dielectrics, and Cole–Cole equation is a special case of the generalized fractional Maxwell model. The fractional models are used to simulate the dielectric relaxation of liquid crystal cells embedded with Pd nanoparticles. The Cole–Cole plot of the relaxation data shows outspread wings in the low frequency range, and the fractional models can represent the relaxation behavior very well.

•Low-energy isomers of B12Al12N24 are determined.•Adsorption of H2 on different sites of B24N24, Al24N24 and B12Al12N24 are compared.•van der Waals interactions are corrected for H2 adsorption.•Interaction mechanisms between H2 and the clusters are clarified.The adsorption of H2 on B24N24, Al24N24 and B12Al12N24 clusters is studied by density functional theory calculations. Typical candidate isomers of B24N24, Al24N24 and B12Al12N24 are optimized and the lowest-energy structures are determined. H2 adsorption on the three lowest-energy structures is investigated. The results show that H2 is adsorbed on B/Al atoms in the side-on manner and on N atoms in the end-on manner. The adsorption of H2 on Al sites is much stronger than the adsorption on B sites, and the mixing of B and Al as in B12Al12N24 enhances the adsorption of H2 obviously. After considering van der Waals interactions, the adsorption energies on Al, B and N are about −0.11 to −0.18, −0.05 and −0.04 to −0.06 eV, respectively. Interaction mechanisms between H2 and the clusters are clarified by analyzing the electronic structures of the adsorption complexes.

•An electric field can promote the adsorption of H2 on (MgO)9.•Under an electric field, the mass density of hydrogen storage of (MgO)9 is 9.1 wt%.•The mechanism of the electric field effect is discussed.•Subjecting the (MgO)9 to an electric field is a potential hydrogen storage method.(MgO)9(MgO)9 with a rocksalt structure, a magic number cluster of (MgO)n(MgO)n, exhibits high stability. In this study, the hydrogen storage properties of (MgO)9(MgO)9 under an external electric field are explored by DFT calculation. The results reveal that H2H2 can be adsorbed on single Mg/O atoms. Because the (MgO)9(MgO)9 and H2H2 are effectively polarized by the external electric field, the adsorption strength of H2H2 at certain adsorption sites is substantially enhanced. The adsorption energies of H2H2 on three-coordinated Mg/O atoms increase from −0.071/−0.056 eV in the absence of an electric field to −0.186/−0.237  eV under a field intensity of 0.025 a.u. Under the field, (MgO)9(MgO)9 can adsorb a maximum of 18 H2H2 molecules, and the corresponding mass density of hydrogen storage reaches 9.1 wt%. Our results suggest that subjecting the (MgO)9(MgO)9 to an external electric field is a potential hydrogen storage method. In this paper, the interaction mechanism between H2H2 and (MgO)9(MgO)9 under the external electric field is also investigated through an electronic structure analysis.

•B12C6N6 is an electron deficient fullerene.•H2 adsorption and dissociation on the low energy isomers is studied.•Molecular adsorption is weak physical adsorption.•H2 can be dissociated easily with an energy barrier of 0.35 eV.B12C6N6 is an electron deficient fullerene. This paper investigates hydrogen adsorption and dissociation on two lowest energy isomers of this cluster. The results show that the adsorption of H2 molecule on the cage surface is weak physical adsorption; the adsorption energies are about 0.03 eV. The stable dissociation products are determined and the dissociation processes are traced. Molecular orbital compositions show that strong orbital interaction between the hydrogen and the cluster occurs in the process of dissociation and H2 molecule can be easily dissociated on B12C6N6. We present four dissociation paths. The lowest energy barrier is only 0.35 eV, which means the dissociation can take place at moderate temperatures.

•All the isomers of B12C6N6 are optimized and the low energy structures are decided.•C and N atoms in this cage are inclined to segregate and form B2C2 and B2N2 squares.•B–N bonds are identical in B12CxN12−x (x=0,6) and the B–C bonds possess stronger covalent character.•The natural charge on N is about −1.17 in both B12N12 and B12C6N6 and the charge on C ranges from −0.60 to −0.72.•The energy gaps of C24, B12N12 and B12C6N6 are 2.52, 6.84 and 3.22 eV, respectively.An electron deficient fullerene B12C6N6 is studied by using ab initio calculations. The structure is generated by replacing N with C in the B12N12 cage to ensure only B–C and B–N bonds are formed. All the possible isomers are optimized and the low energy structures are determined. C and N atoms in the low energy isomers are inclined to segregate and form B2C2 and B2N2 squares. Natural bond analysis shows that the atomic orbitals of B, C and N in this cage hybrid approximately in sp2.3 and then form B–C and B–N bonds. The 2p orbitals perpendicular to the cage surface are partially occupied and the molecular orbitals formed by these orbitals are highly delocalized. The natural charge on N is about −1.17 in both B12N12 and B12C6N6, and the charge on C is −0.72 to −0.60. The molecular orbital compositions show that the B–N bonds are the same in B12N12 and B12C6N6, and the B–C bonds possess stronger covalent character. The HOMO of B12C6N6 is formed by 2p of B and C, and the LUMO is formed by 2p of C. The energy gap of C24, B12N12 and B12C6N6 is 2.52, 6.84 and 3.22 eV, respectively.The low energy isomers of B12C6N6 are optimized using density functional method. The electronic structure and bonding character in this electron deficient cage are investigated.

Generalized fractional Maxwell model is applied to simulate the creep and the relaxation behavior of PEEK and PPS measured at different aging stages and different temperatures. Genetic algorithm and the conjugated gradient method are combined to optimize the model parameters. The results show that the fractional Maxwell model can describe both the creep and relaxation data very well when the model parameters are fitted properly. The momentary creep compliance and the relaxation modulus change with the time at an increasing rate; the fractional orders of the two fractional elements building up the model correspond to the creep or relaxation exponents at the initial glassy stage and the terminal fluid state. The relaxation time τ of the model, which corresponds to the characteristic time of α transition of the sample, shifts towards longer time with increasing the aging time and lowering the aging temperature. In the time domain scaled by the relaxation time τ, all the creep or relaxation curves measured at different aging times and temperatures superpose automatically, which means the time–aging time superposition and the time–temperature superposition present themselves. The shift rates and the temperature shift factors can be then obtained from the model parameters. Good simulation for the creep and relaxation behavior and optimum superposition of the experimental data achieved by the fractional model may offer reliable predictions for the long-term stress-strain response.Graphical abstract