Systems of oblate molecules. Monte Carlo study

Monte Carlo (MC) simulations were performed for systems of hard oblate spherocylinders with breadth-to-height ratios φ = 0.5–3.5 and packing fractions y = 0.25–0.45 and for Kihara oblate molecule systems of φ = 1 at reduced temperatures T* = 0.75 and 1.0 and y = 0.05–0.45. The compression factors and the dependence of the average correlation functions on the shortest surface-to-surface distance were determined for the case of hard oblate spherocylinders and the compression factors, residual internal energies and average correlation functions for the case of the generalized Kihara molecule systems. In addition, values of the third virial coefficient of the hard oblate spherocylinders were evaluated in the range of φ = 1–3. Results of the MC simulations for the hard oblate spherocylinders compare well with the available data in the literature and theoretical values; thermodynamic functions of the Kihara molecule systems were determined from the second-order perturbation theory. They agree well with our MC values at lower densities and higher reduced temperatures.     

An equation of state for hard convex body chains

The thermodynamic perturbation theory of hard sphere chains is generalized to derive an equation of state for hard convex body chains. The hard convex body chain equation of state contains two parameters that are related directly and rigorously to the geometry of the hard convex body. The compressibility factors and second virial coefficients of chains composed of prolate spherocylinders, oblate spherocylinders and doublecones are calculated and compared with hard sphere chain calculations. The comparison indicates that the nature of the hard convex body has a profound influence on the properties of the chain.     

Hard body fluids again: Virial coefficients and equations of state

The table of the virial coefficientsB ₂ throughB ₄ of all hard body fluid models considered so far has been completed by calculating the missing coefficients. Applicability of these coefficients to predicting the thermodynamic behaviour of dense hard body fluids is assessed and certain discrepancies in the data for oblate spherocylinders are found. It is shown that by combining the Padé approximant with an appropriate analytic expression an accurate 3-parameter equation of state results.     

Monte Carlo study of the equimolar mixture of hard spheres and spherocylinders

Using the Monte Carlo simulation technique the behaviour of the equimolar mixture of hard spheres and prolate spherocylinders of the length-to-breadth ratio equal to two was studied for the case in which both components had the same breadth. The surface-to-surface and the center-to-center correlation functions and the compressibility factor were computed and the results compared with theoretical predictions. Effect of non-sphericity of one component is shortly discussed.     

Analytic Calculation of B 4 for Hard Spheres in Even Dimensions

We exactly calculate the fourth virial coefficient for hard spheres in even dimensions for D = 4, 6, 8, 10, and 12.     

Critical properties of non-spherical molecule fluids from the virial expansion

Critical constants of pure fluids (as important reference data in constructing vapour-liquid phase diagrams and basic input of various estimation methods) were determined for systems of non-spherical Kihara molecules; values of the critical temperature, density, compression factor and pressure of fluids composed of prolate and oblate molecules were evaluated from the fourth-order virial expansion. The second and third virial coefficients of the Kihara molecules were determined by applying the recently proposed method in which the effect of molecular core geometry and functional dependence of a pair interaction on the surface-surface distance are factorized and the former contribution determined from a formula for the corresponding hard convex body virial coefficient. The virial expansion for non-spherical Kihara molecules is applied to determine the critical constants of n-alkanes (methane to octane) and cyclic hydrocarbons (cyclopentane, cyclohexane, benzene and naphthalene); a fair agreement with experimental data was found.     

Fluids of general hard triatomic molecules

The second, third, and fourth virial coefficients, B_i , of a fluid of general symmetric hard triatomic molecules (fused hard spheres) have been calculated both numerically and theoretically for a variety of potential parameters. It has been found that: (i) for B₂ a valency angle ω_c exists such that for ω>w_c, B ₂ is independent of ω, (ii) B ₃ is very flat for ω>w_c, and (iii) B ₄ exhibits a maximum at ω～π/2. Theoretical calculations employing an assigned convex body fit very well the second and fairly well the third virial coefficients, but fail for the fourth except in the case of a linear molecule.     

Equilibrium properties of hard non-sphere fluids

Derivation of the thermodynamic properties of fluids of hard non-spherical molecules of arbitrary symmetry is based on the decoupling approximation. Theoretical expressions are given and calculations made for the equation of state and virial coefficients for hard ellipsoids. These results are compared with Monte Carlo values and show fair agreement in all cases. The theoretical predictions for the equation of state for binary mixtures are compared with the Monte Carlo results for hard spheres and hard prolate spherocylinders. Theoretical expressions for the first order quantum correction to the free energy, pressure and virial coefficients are also given. The quantum effects increase with increase of density and with increase of anisotropy parameter.     

Two Hard Spheres in a Spherical Pore: Exact Analytic Results in Two and Three Dimensions

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a relation valid for any dimension between these partition functions, second virial coefficient for inhomogeneous systems in a spherical pore, and third virial coefficients for polydisperse hard spheres mixtures. Using the established relation we were able to evaluate the cluster integral b ₂(V) related with the second virial coefficient for the Hard Disc system into a circular pore. Finally, we analyse the behaviour of the obtained expressions near the maximum density.     

Evidence for shape coexistence in186Pt

High-spin states in¹⁸⁶Pt have been populated by the¹⁸⁸Os (α, 6n) reaction and were investigated with the OSIRIS spectrometer. A shape coexistence at high spins was established in the nucleus¹⁸⁶Pt, which lies on the border between light prolate and heavy oblate Pt nuclei. Two bands corresponding to predominantly prolate shapes and one band of predominantly oblate shape have been observed. For prolate shapes a (π h _9/2)² alignment and for oblate shapesa (vi _13/2)² alignment has been found.     

The fifth virial coefficients of fused hard sphere fluids

The virial coefficients up toB ₅ of 34 fused hard sphere models have been computed using about (4–10)×10⁵ trial configurations of a modified Monte Carlo integration method. The principle of the conformal behaviour of hard particle systems is tested against these data. It is found that while for the fourth coefficient the principle is satisfied in all the cases, the fifth coefficients exhibit more complicated behaviour and do not conform, in general, to this principle.     

Third virial coefficient of hard spheroids

The third virial coefficient B ₃ of a fluid of spheroids is calculated by direct integration using the method of 2-point measures of convex body geometry. Calculations are performed for aspect ratios up to 10 for both prolate and oblate spheroids. The infinite set of 2-point measures has five indices. The three numerical ones, L, Lι and m, are standard quantities in the theory of the rotation group. These new calculations use truncation at the L = L = 2 level. The results show dramatic improvement over previous results at the L = Lι = 1 level and are in excellent agreement with existing Monte Carlo calculations of B ₃.     

Wetting layer and size effects on the nonlinear optical properties of semi oblate and prolate Si0.7Ge0.3/Si quantum dots

Semi oblate and semi prolate are among the most probable self-organized nanostructures shapes. The optoelectronic properties of such nanostructures are not just manipulated with the height and lateral size but also with the wetting layer element. The practical interest of derivatives of germanium and silicon has a great important role in optoelectronic devices. This study is a contribution to the analysis of linear and nonlinear optical properties of Si_0.7Ge_0.3/Si. In the framework of the effective mass approximation, we solve numerically the Schrödinger equation relative to one particle confined in Si_0.7Ge_0.3/Si semi prolate and semi oblate quantum dots by using the finite element method and by taking into consideration the effect of the wetting layer. The energy spectrum of the lowest states and the dipolar matrix for the fourth allowed transitions are determined and discussed. We also calculate the detailed optical properties, including absorption coefficients, refractive index changes, second and third harmonic generation as a function of the quantum dot sizes. We found that with the change in the size of prolate and oblate quantum dots, there is a shift in the resonance peaks for the absorption coefficient and refractive index. It is due to the modification in the energy levels with changing size. The study proves a redshift in the second harmonic generation and third harmonic generation coefficients with an increase in the height/radius of the oblate/prolate quantum dot, respectively. We also demonstrated the variation of wavefunction inside the quantum dot with the change in wetting layer thickness.     

Crystal field and microscopic spin Hamiltonians approach including spin-spin and spin-other-orbit interactions for d and d ions at low symmetry C3 symmetry sites: V in Al2O3

A new module has been developed within the CFA/MSH computer package, which is applicable for d² and d⁸ ions at sites of trigonal symmetry type I (C_3v,D₃,D_3d) and type II (C₃,C_3i), including the ‘imaginary’ CF term. For the first time the spin-spin (SS) and spin-other-orbit (SOO) interactions have also been included in the Hamiltonian. This module enables to study the contributions to the energy levels and the spin Hamiltonian parameters, i.e. zero-field splitting D and g-factors: g_∥ and g_⊥. The contributions arising from the spin-orbit (SO), SS, and SOO interaction as well as those due to the low symmetry CF effects induced by the distortion angle ?, which describes the difference between C₃ and C_3v symmetry, can be studied. As an application of the new module, calculations have been carried out for V³⁺(3d²) ions in α-Al₂O₃ crystal, taking into account for the first time the SS and SOO interactions, and the low symmetry CF effects. The results show that (i) the contributions from the SS and SOO interactions to the energy levels are larger for free V³⁺ ions than those for V³⁺ ions in α-Al₂O₃ crystal, (ii) both the contributions to the SH parameters and the energy levels arising from the SOO interaction are larger than those arising from the SS interaction, (iii) the contributions due to the low symmetry CF effects induced by the distortion angle ? are in general significant, (iv) D and g_⊥ are sensitive to the distortion angle ?, whereas g_∥ is insensitive to ?, and (v) the influence of the lattice distortions on the spectroscopic properties of V³⁺ ion in α-Al₂O₃ is pronounced. It appears important for similar ion-crystal cases to consider the lattice distortions in detailed calculations, which take into account the relevant contributions from the SO, SS and SOO interactions. A good agreement between the theoretical and experimental results has been obtained.     

球形拓扑中复杂形状生物膜泡的获得及其稳定性分析

通过在Surface Evolver软件中建立一些与目标形状相似的初始形状，经长时间演化后，得到了实验上已经观察到的具有D_2h和D_3h对称性的海星形生物膜泡.通过跟踪不同形状膜泡的Hessian矩阵的本征值，确定了双凹圆盘与海星形及哑铃形之间的相变是不连续的，其间所经历的三角扁盘及椭圆扁盘形中间相在SC模型中通常是不稳定的. 关键词： SC模型 生物膜泡 Surface Evolver     

A study of π states of H2 + in the one centre approach

The statistical theory of the elastic constants of nematic liquid crystals is applied to detailed calculations based on well-defined approximations for the direct correlation function of Ornstein and Zernike and for the singlet orientational distribution. The model of hard spherocylinders with superimposed r ^-6 attraction modulated by a Maier-Saupe P ₂(cos ?_{1 2}) term, is used. The dependence on temperature, on the order parameter and on the length to breadth ratio, of the reduced elastic constants K* _i (i=1, 2, 3), is discussed in some detail and comparison with experiment is included.     

Nuclear reorientation effects for the 26Mg, 28Si(12C, 12C′) reactions at E = 41 MeV

Angular distributions for elastic and inelastic scattering of 41 MeV ¹²C from ²⁶Mg and ²⁸Si have been measured. Corresponding angular distributions from coupled-channels calculations show significant differences depending on whether a prolate or an oblate intrinsic shape is assumed. The ²⁶Mg and ²⁸Si data are best described by calculations with prolate and oblate shapes, respectively, in agreement with previous Coulomb excitation rorientation measurements. The Hendrie scaling procedure fails to accurately predict the measured nuclear β₂ deformation for ²⁶Mg.     

Shape-excited states of28Si

The Hartree-Fock (HF) minima for the nucleus²⁸Si were obtained for the prolate, oblate and spherical shapes using the interaction obtained by Preedom and Wildenthal. The interaction gives rise to large energy separation between the prolate and the oblate shapes. The spherical solution is just 2 MeV above the lowest HF (oblate) minimum. The spectrum projected from the oblate HF state is in good agreement with the experimental spectrum. The transition probabilities for the different energy levels also agree reasonably well. The configuration mixing calculations performed on the basis of states projected from the three shapes indicate that there is no significant mixing of different projected states. The second 0 ₂ ⁺ state, thus obtained, corresponds to the third 0 ₃ ⁺ state in the experimental spectrum and stems dominantly from the spherical HF state. It is seen that the structure of the energy levels of²⁸Si, especially the second 0 ₂ ⁺ level is very sensitive to the two body interaction. The results are compared with those obtained using the renormalised interaction of Kuo.     

Smectic phases in hard particle mixtures: Koda's theory

Mixtures of parallel linear particles and spheres tend to demix upon compression. The linear species usually concentrates in regular layers, thus forming a smectic phase. With increasing concentration of spheres this ‘smectic demixing’ transition occurs at ever lower packing densities. For the specific case of hard spherocylinders and spheres Koda et al. [T. Koda, M. Numajiri, S. Ikeda, J. Phys. Jap., 65, 3551 (1996)] have explained the layering effect in terms of a second virial approximation to the free energy. We extend this approach from spherocylinders to other linear particles, namely fused spheres, ellipsoids and sphero-ellipsoids.