离子半径的质量和电量综合因子的标度

根据作者曾建立的万有引力势与电势的关系式和系统的对比质电比(单位电量的质量)Sr的物理意义, 研究了离子半径r与Sr的关系: 对于相同电子构型的阳离子, 离子半径与lgSr呈线性关系; 对于相同电子构型的阴离子, 离子半径与Sr的关系满足Michealis-Menten 数学模型. 采用回归分析方法, 拟合出周期表中94种元素108种阳离子的半径和16种阴离子的半径. 从相关系数R和回归方程的显著性检验(F)都说明r与Sr密切相关, 其中102种阳离子半径数据与具有代表性的离子半径参考值相比平均绝对误差仅0.9 pm, 相对误差1.1%. 同时给出一条获取离子半径(包括复杂离子)数据的新途径.     

离子质电比和相差异因子对离子半径的综合标度

根据万有引力势与电势的关系式和系统的质电比(单位电量的质量)Sr的物理意义, 研究了离子半径r与离子的Sr和相差异因子的关系. 对于阳离子, r与lgSr和相差异因子呈线性关系; 对于稳定构型阴离子, r与Sr和相差异因子也存在定量关系. 采用回归分析方法, 给出稳定构型和非稳定构型阳离子半径计算公式, 以及稳定构型阴离子半径计算公式. 从相关系数R和回归方程的显著性检验(F)都可说明r与Sr和相差异因子密切相关, 其中拟合的96种元素的138种阳离子半径数据与具有代表性参考值相比, 平均绝对误差为2.0 pm, 相对误差为2.5%. 并预测出较为合理的稀有气体等30种离子半径数据. 同时给出一条获取离子半径(包括复杂离子)数据的新途径.     

Concerning atomic radii

The identification of the atomic radius with the distance from the nucleus to the position of the minimum in the internuclear electronic density is studied. It is shown that a set of statistically significant radii may be defined for the atoms of a given column of the periodic table bound to any of the atoms of another column. Sets of radii calculated by modified Anderson-Parr relations are presented. The values obtained are consistent with radii obtained using a minimum in electronic density criterion with electron densities calculated from molecular orbital wave functions or approximated by a sum of atomic densities.     

A nearly complete system of average crystallographic ionic radii and its use for determining ionization potentials

Available systems of empirical (crystallographic) ionic radii are compared. All these systems turn out to be compatible if the O^2? radius is taken to be 0.140 nm. The choice of the oxygen ionic radius is dictated by the equality of the metal ion-oxygen ion distances in oxide crystals and the metal ion-oxygen atom distances in crystal hydrates and concentrated aqueous solutions. In all systems of empirical ionic radii under consideration, the uncertainty of determination of ionic radii is 0.002–0.005 nm. A new method of determination of the ionic radii of elements in unusual valence states is suggested: from the empirical dependence of the electron density at an atom in a given valence state on the atomic radius, a two-parameter equation relating the ionic radii of Period 4–7 elements in two valence states is derived, which allows one to calculate the ionic radius that cannot be determined by crystallography because of the lack of stable compounds in this valence state. Ionic radii are calculated for all Period 4–7 elements in all valence states. They constitute a nearly complete system of ionic radii. There is a linear relationship between the atomic nucleus charge and the inverse ionic radius. It is shown that the square root of the ionization potential is a linear function of the inverse ionic radius. The as yet experimentally unknown ionization potentials of 78 ions of different elements are estimated.     

Covalent radii revisited

A new set of covalent atomic radii has been deduced from crystallographic data for most of the elements with atomic numbers up to 96. The proposed radii show a well behaved periodic dependence that allows us to interpolate a few radii for elements for which structural data is lacking, notably the noble gases. The proposed set of radii therefore fills most of the gaps and solves some inconsistencies in currently used covalent radii. The transition metal and lanthanide contractions as well as the differences in covalent atomic radii between low spin and high spin configurations in transition metals are illustrated by the proposed radii set.     

Measurement of the hydrodynamic radii of PEE-G dendrons by diffusion spectroscopy on a benchtop NMR spectrometer

Benchtop nuclear magnetic resonance (NMR) spectroscopy is a useful tool for the rapid determination of the self-diffusion coefficient and the hydrodynamic radius of dendrons. The self-diffusion coefficients of the first four generations of poly ethoxy ethyl glycinamide (PEE-G) dendrons are measured by diffusion-ordered spectroscopy (DOSY) on a benchtop NMR equipped with diffusion gradient coils. The hydrodynamic radii of the dendrons are calculated via the Stokes–Einstein equation. The effects of solvent and pH are determined with the hydrodynamic radius increasing with generation and decreasing upon neutralization of an acidic solution. These measurements provide valuable information for biological and pharmaceutical applications of dendrons.     

Electrostatic potentials and covalent radii

We begin with a brief overview of the electrostatic potential V(r) as a fundamental determinant of the properties of systems of electrons and nuclei. The minimum of V(r) along the internuclear axis between two bonded atoms is a natural and physically meaningful boundary point, at which the electrostatic forces of the two nuclei upon an element of charge exactly cancel. We propose that the distances from nuclei to V(r) bond minima provide the basis for a well-defined set of covalent radii. Density functional calculations at the B3PW91/6-311+G** level were carried out for 59 molecules to locate the V(r) minima in 95 bonds and use these as the basis for determining single- and multiple-bond covalent radii for eight first- and second-row atoms plus hydrogen. It was found to be unrealistic to assign a single covalent radius to each atom; different values are needed for bonds to first- and second-row atoms, as well as to hydrogen. Using these results, we are able to predict the bond lengths of 33 single and multiple bonds with average errors of less than 0.04 A relative to experimental data.     

Average electron radii in many-electron atoms

In many-electron atoms, the average electron radius r represents the mean distance of a single electron from the nucleus when all the interelectronic interactions are averaged. If the electron-electron interaction is explicitly considered, the average radius r splits into two different radii, inner radius r(<) and outer radius r(>). For the 102 atoms He through Lr in their ground states, the radii r(<) and r(>) are systematically examined at the Hartree-Fock limit level. The effect of electron correlations on r(<) and r(>) is also discussed for the He atom and its isoelectronic ions.     

Bounds to electron-pair relative and center-of-mass radii in many-electron atoms

When the electron-electron interaction is explicitly considered in many-electron atoms, the average electron radius (r) splits into the inner (r<) and outer (r>) radii. It is shown that the sum and difference of these radii constitute upper and lower bounds, respectively, to the electron-pair relative distance r(12)=(/r1-r2/). An analogous result is also derived for the electron-pair center-of-mass radius (R)=(/r1+r2//2). For the 102 atoms He through Lr in their ground states, the tightness of these bounds is numerically examined at the Hartree-Fock limit level. Good linear correlations are observed between (r12) and (r>), and between (R) and (r>)/2.     

Average inner and outer radii in singly-excited 1<Emphasis Type="Italic">snl</Emphasis> states of the He atom

Average inner < r _< > and outer < r _> > radii are studied for 28 singly-excited 1 snl singlet and triplet states (0 ≤ l ≤ n ≤ 5) of the He atom. In all the cases, the average inner radius < r _< > is close to 0.75 bohr, which indicates that one of the two electrons behaves like the 1s electron in He⁺. On the other hand, an analysis of the average outer radius < r _> > shows that the other electron of the 1snl states behaves approximately like an snl electron in the hydrogen atom. The average outer radius < r _> > reflects more diffuse character of the singlet electron distribution. This paper is dedicated to the late Professor Serafin Fraga for his great contribution to quantum sciences. Contribution to the Serafin Fraga Memorial Issue.     

Nodal,ionic, and atomic radii,in compounds

The distance in an atom from the nucleus to the final node in the wavefunction of a valence electron has been defined as the nodal radius. This parameter, in conjunction with a Thomas-Fermi pseudo-potential, is used to calculate the nearest-neighbor distance in some octet compounds. Calculated values of the atomic radii are compared with the semi-empirical ionic and tetrahedral radii for atoms in these compounds.     

Thermogravimetric analysis of selected group (II) carbonateminerals — Implication for the geosequestration of greenhouse gases

The precursors of carbonate minerals have the potential to react with greenhouse gases to form many common carbonate minerals. The carbonate bearing minerals, magnesite, calcite, strontianite and witherite, were synthesised and analysed using a combination of thermogravimetry and evolved gas mass spectrometry. The DTG curves show that as both the mass and the size of the metal cationic radii increase, the inherent thermal stability of the carbonate also increases dramatically. It is proposed that this inherent effect is a size stabilisation relationship between that of the carbonate and the metal cation. As the cationic radius increases in size, the radius approaches and in the case of Sr²⁺ and Ba²⁺ exceeds that of the overall size of the carbonate anion. The thermal stability of these minerals has implications for the geosequestration of greenhouse gases. The carbonates with the larger cations show significantly greater stability.     

Atomic radii scales and electron properties deduced from the charge density

A procedure to represent Hartree-Fock electron densities in atoms [L. Fernandez Pacios, J. Comp. Chem., 14 , 410 (1993)] defines ρ(r) as a reduced expansion of exponential functions. These analytically modeled densities (AMDs) are used in this article to develop a simple computational procedure for analyzing different atomic radii scales implemented in the commercial software system MATHEMATICA. The analysis is focused on the physical information associated to a given atomic radius as deduced from calculations depending on ρ(r). The amount of electron charge contained in the sphere of the given radius as well as the distinct contributions to the potential energy integrated up to that radius are obtained within the AMD formulation for main-group atoms H—Kr. The ASCII file needed to run the procedure within MATHEMATICA is also presented. © 1995 by John Wiley & Sons, Inc.     

Ionicity,atomic radii,and structure in the layered dichalcogenides of group IVb,Vb, and VIb transition metals

Pauling's electronegativities are introduced in considerations of bond lengths, lattice constants, atomic radii, charge densities, structures, and heats of formation of the layered dichalcogenides of Groups IVb, Vb, and VIb transition metals. Strong correlations are found between these and the fractional ionic character of the metal-chalcogen bonds as defined by Pauling. A critical effective radius ratio is defined that separates trigonal prismatic and octahedral compounds.     

流体力学半径对估算胶体微球聚集速率常数的影响

胶体粒子聚集速率常数实验值远低于理论值一直是被普遍关注的问题.聚集速率常数的理论推导是基于粒子的几何半径来考虑的,但决定粒子扩散速率及聚集速率的应该是粒子的流体力学半径(大于几何半径),因而它是使聚集速率常数实验值低于理论值的因素之一.影响流体力学半径的因素很多,其中,带电粒子在溶液中因表面存在双电层,会明显增大流体力学半径,造成聚集速率减慢.而双电层的厚度又随溶液中离子强度的不同而改变.本工作在聚集速率的公式中引入了修正因子,即几何半径与其流体力学半径之比,以修正由于用几何半径代替流体力学半径带来的误差.其中几何半径和流体力学半径可以分别用扫描电镜(SEM)和动态光散射(DLS)来测定.以两种粒径的聚苯乙烯带电微球为例,考察了在不同离子强度下,该误差的大小.结果发现,对于半径为30 nm的微球,用流体力学半径计算的慢聚集速率常数比理论值偏低约8%.该误差随离子强度增加而减少.对于快聚集情况,流体力学半径对聚集速率基本没有影响.     

Measuring the size of polymers with negative radii using MALS/QELS: an exploration of the thermodynamic radius

The concept of 'size' in polymer science can have several interpretations, including definitions that rely on either statistical or equivalent-hard-sphere measures of the spatial extent of macromolecules in solution. A definition such as that of the equivalent thermodynamic radius (R(T)), which relies on the second virial coefficient of the polymer solution, offers the possibility of a zero or even a negative size parameter for macromolecules, depending on whether the polymer solution is in a theta or poor thermodynamic state, respectively. Here, we present the results of multi-angle light scattering measurements of R(T) for polystyrene and poly(methyl methacrylate), showing positive, negative, and zero values for this radius, depending on dilute solution thermodynamics. These results are augmented with measurements of the hydrodynamic radius, using quasi-elastic light scattering, and with random-walk-based calculations of the root-mean-square and viscometric radii. Re-examination of the literature provides additional examples of negative radii of polymers and oligomers.     

正离子的边界半径

本文建议和讨论了离子的边界半径, 给出了一价正离子的边界半径的周期表以及某些常见正离子的边界半径。正离子的边界半径与SP半径、Pauling离子半径、晶体离子半径等有一定的关联, 显示了其合理性和可应用性。由这些关联性质, 还可以预言某些元素的难以测定的电离能。     

Orientation of a benzene molecule inside a carbon nanotube

Benzene molecules confined in carbon nanotubes of varying radii are employed as semiconductors in electronic nanodevices, and their orientation determines the electrical properties of the system. In this paper, we investigate the interaction energy of all the possible configurations of a benzene molecule inside various carbon nanotubes and then we determine the equilibrium configuration. We adopt the continuous approach together with the semi-empirical Lennard-Jones potential function to model van der Waals interaction between a benzene molecule and a carbon nanotube. This approach results in an analytical expression, which accurately approximates the interaction energy and can be readily used to generate numerical data. We find that horizontal, tilted and perpendicular configurations on the axis of the carbon nanotube are all possible equilibrium configurations of the benzene molecule when the radius of the carbon nanotube is less than 5.580 Å. However, when the radius of the carbon nanotube is larger than 5.580 Å an offset horizontal orientation is the only possible equilibrium configuration of the benzene molecule. In the limiting case, the orientation of a benzene molecule on a graphene sheet can be derived simply by letting the radius of the carbon nanotube tend to infinity.