Rigidity of colloidal alloys as studied by reflection spectroscopy in sedimentation equilibrium

Rigidities of colloidal alloys of binary mixtures of colloidal silica spheres (CS82; 103 nm in diameter) with larger silica spheres (CS91; 110 nm, CS121; 136 nm and CS161; 184 nm) have been measured by reflection spectroscopy in sedimentation equilibrium. Substitutional-solid-solution-type alloy structures are formed for mixtures of CS82 and CS91 and for CS82 and CS121. A superlattice, probably MgCu₂ type, is formed for CS82 and CS161 mixtures. The rigidities of the colloidal crystals of the single component of the spheres increase as the sphere size increases at the same number density of spheres. The rigidities of the colloidal alloys decrease when a comparatively small number of the larger spheres are mixed with the small spheres at the same total sphere number density. Received: 14 June 2000 Accepted: 3 November 2000     

Gapped gapless packing structures

The assumption of a gapless packing structure has previously been used to obtain the density and partial coordination numbers of a random mixture of hard spheres in the maximally dense regime. Here we extend the notion of a gapless packing structure to allow the determination of the characteristics of a packing away from maximal density by adding an appropriate number of void spherical elements. A gapless packing is then considered in which the void and solid spherical elements are assumed to be indistinguishable except for the purposes of calculating packing fraction and coordination number. We utilize the notion of specific volume to generate a one-parameter family of void distributions to obtain a set of coupled integral equations, which are solved numerically. Monodisperse and bi-disperse packings are investigated for packing fractions ranging from rho=0.26 to 0.78. Results are shown to be comparable to experiments and the effect of varying packing fraction on coordination numbers is shown to be invariant with respect to number distribution. A linear relationship between coordination number and packing fraction is elucidated for moderate to low packing fractions. Maximum and minimum random packing fractions are also discussed.     

Thermo-sensitive colloidal crystals of silica spheres in the presence of large spheres with poly (N-isopropyl acrylamide) shells

Thermo-sensitive colloidal crystals are prepared simply by mixing colloidal silica spheres and large thermo-sensitive gel spheres. The thermo-reversible change in the lattice spacing of colloidal crystals of monodisperse silica spheres (CS82, 103 nm in diameter) depends on the size of the admixed temperature-sensitive gel spheres. For spheres with sizes less and greater than that of the silica spheres, the lattice spacing upon temperature increase above the lower critical solution temperature of poly(N-isopropyl acrylamide) decreases (cf. Okubo et al. Langmuir 18:6783, 2002) and increases, respectively. A mechanism, which is able to explain these experimental findings, is proposed. Moreover, crystal growth rates and the rigidities of the thermo-sensitive colloidal crystals are studied.     

Coordination numbers for rigid spheres and local compositions

The coordination numbers of rigid spheres were simulated on a computer to obtain an improved empirical equation when surrounding spheres are of uniform size. In the case of two different species of surrounding spheres, the coordination numbers vary as a function of local composition and radius ratios. By fitting simulation results, correlations were proposed, which are expected to be of practical use in thermodynamic of real solutions.     

Cu(II)-脱乙酰壳聚糖配位聚合物的配位数

IR,ESR和XPS的测试结果表明,脱乙酰壳聚糖(简记CS)膜在铜氨水溶液浸渍过程中Cu(II)既与CS发生配位反应形成Cu(II)-CS配位聚合物,也产生吸附作用。ESR谱示出CuCl~2.2H~2O与Cu(II)-CS膜中的Cu(II)均含有一个单电子,可以利用XPS的Shake-up效应研究Cu(II)-CS配位聚合物的配位数,所得结果为4。又以同样的方法研究Cu(II)-聚乙烯醇(简记PVA)配位聚合物的配位数,发现Cu(II)是以低自旋状态的dsp^2杂化空轨道与PVA的羟基氧配位,其配位数也是4,这与资料所报道的一致,从而间接地验证了此方法研究Cu(II)-CS配位聚合物配位数的可靠性。     

Cu(Ⅱ)脱乙酰壳聚精配位聚合物的配位数

IR,ESR和XPS的测试结果表明,脱乙酰壳聚糖(简记CS)膜在铜氨水溶液浸渍过程中Cu(Ⅱ)既与CS发生配位反应形成Cu(Ⅱ)-CS配位聚合物,也产生吸附作用.ESR谱示出CuCl_2·2H_2O与Cu(Ⅱ)-CS膜中的Cu(Ⅱ)均含有一个单电子,可以利用XPS的Shake-up效应研究Cu(Ⅱ)-CS配位聚合物的配位数,所得结果为4.又以同样的方法研究Cu(Ⅱ)-聚乙烯醇(简记PVA)配位聚合物的配位数,发现Cu(Ⅱ)是以低自旋状态的dsp~2杂化空轨道与PVA的羟基氧配位,其配位数也是4,这与资料所报道的一致,从而间接地验证了此方法研究Cu(Ⅱ)-CS配位聚合物配位数的可靠性.     

Effect of inclining strain on the crystal lattice along an extended series of lanthanide hydroxysulfates Ln(OH)SO4 (Ln = Pr-Yb, except Pm)

A series of trivalent lanthanide hydroxysulfates, Ln(OH)SO(4), (Ln = Pr through Yb, except radioactive Pm) has been synthesized via hydrothermal methods from Ln(2)(SO(4))(3)·8H(2)O by reaction with aqueous NaOH at 170 °C in Teflon lined Parr steel autoclaves, and were characterized by single crystal X-ray diffraction and FT-IR spectroscopy. Two types of arrangements were found in the solid state. The lighter (Ln = Pr-Nd, Sm-Gd) and heavier lanthanide(III) hydroxysulfates (Tb-Yb) are each isostructural. Both structure types exhibit the monoclinic space group P2(1)/n, but the unit cell content is doubled with two crystallographically distinct LnO(8) polyhedra for the heavier lanthanide compounds. The lighter complexes maintain the coordination number 9, forming a three-dimensional extended lattice. The heavier counterparts exhibit the coordination number 8, and arrange as infinite columns of two crystallographically different LnO(8) polyhedra, while extending along the "c" axis. These columns of LnO(8) polyhedra are surrounded and separated by six columns of sulfate ions, also elongating in the "c" direction. The rigid sulfate entities seem to obstruct the closing in of the lighter LnO(9) polyhedra, and show an inclining degree of torsion into the "ac" layers. The crystal lattice of the lighter 4f complexes can sufficiently withstand the tension buildup, caused by the decreasing Ln(3+) radius, up to Gd(OH)SO(4). The energy profile of this structural arrangement then seems to exceed levels at which this structure type is favorable. The lattice arrangement of the heavier Ln-analogues seems to offer a lower energy profile. This appears to be the preferred arrangement for the heavier lanthanide hydroxysulfates, whose crystal lattice exhibits more flexibility, as the coordination sphere of these analogues is less crowded. The IR absorbance frequencies of the hydroxide ligands correlate as a function of the Ln(3+) ionic radius. This corresponds well with the X-ray single crystal analysis data.     

Theoretical prediction of the coordination number, local composition, and pressure-volume-temperature properties of square-well and square-shoulder fluids

By assuming a Boltzmann distribution for the molecular equilibrium between local and bulk environments, a general model is derived for the prediction of coordination numbers and local compositions of square-well and square-shoulder fluids. The model has no empirical parameter fitted from the data of square-well and square-shoulder fluids, but is valid from the low-density limit to the high-density limit. The applicable width of well or shoulder covers the commonly used range varying from 1.0 to 2.0. The model can accurately predict the coordination numbers of pure square-well and square-shoulder fluids, so the equation of state derived from it is superior to other equations of state based on the existing coordination number models. The model also accurately predicts the local compositions of mixtures in wide ranges of density and size ratio (1.0-8.0), as well as the configuration energy of lattice gases and highly nonideal lattice mixtures. It is remarkable that the model correctly predicts temperature-dependent coordination numbers and local compositions for both equal- and unequal-sized mixtures at close packing, which cannot be predicted by the existing coordination number models. Our derivation demonstrates that the energy parameters in local composition models should represent the potential difference of a molecule between the local and bulk environments, not the pair-interaction potential, and depend on the system conditions and different kinds of pair-interaction parameters. This result is very useful for the development of local composition and activity coefficient models and the mixing rules of equations of state.     

Phase diagram of subphtalocyanine ordering on Ag(111)

A model of subphtalocyanine molecules ordering on Ag(111) is proposed. We have demonstrated that the driving force of the ordering into honeycomb and hexagonal close packed patterns is a balance of intermolecular and subphtalocyanine-Ag interactions which can be generally expressed by a potential with infinite exclusion in a sufficiently large number of nearest coordination spheres of Ag(111) lattice and oscillatingly decaying behavior outside the sphere of exclusion. To cope with computational problems due to large size of the molecules compared to the substrate lattice period, we introduce the rescaling of Ag(111) lattice, and took into account an infinite exclusion of first, second, and third neighbors, attraction-of fourth and fifth, and repulsion-of sixth and seventh. The phase diagram is obtained by the lattice gas model using Monte Carlo simulations. Very strong first order phase transitions, causing the two-phase coexistence, were found between disordered and honeycomb as well as between disordered and hexagonal closed packed phases.     

壳聚糖镍和壳聚糖镧配位聚合物的配位数研究

从ＩＲ、ＥＳＲ和ＸＰＳ的测试结果可知,Ｎｉ＾２＋或Ｌａ＾３＋与壳聚糖（ＣＳ）键节单元上的氨基Ｎ和仲羟基Ｏ发生配位反应,形成ＣＳ－Ｎｉ＾２＋或ＣＳ－Ｌａ＾３＋配位聚合物膜。通过电导率研究其配位数,发现Ｎｉ＾２＋或Ｌａ＾３＋可与壳聚糖的３个或５个键节单元配位。根据以上的实验可推定中心离子Ｎｉ＾２＋与壳聚糖３个键节单元上的氨基Ｎ和仲羟基Ｏ结合,形成六配位的ＣＳ－Ｎｉ配位聚合物Ｌａ＾３＋与壳聚糖５个键节单     

模型高分子尾型链的构象统计理论

基于金刚石格点上受限于半空间的随机行走，借概率论中的反射原理推导出了模型高分子尾型链的构象分布．得到了链长为Ｎ的模型尾型链的允许构象数Ｃ１（Ｎ）和末端距分布函数．在四选择模型中，发现Ｃ１（Ｎ）／４Ｎ与Ｎ－１／２成正比．模型尾型链在与壁正交方向上的均方末端距分布与平行方向比较扩张至２倍，而后者与自由链对应的分量相等．这些解析结果得到了精确计数和ＭｏｎｔｅＣａｒｌｏ模拟计算机“实验”的支持．     

Inverted colloidal crystals as three-dimensional cell scaffolds

A new type of three-dimensional scaffold with inverted colloidal crystal geometry for the investigation of topological effects in cell cultures is introduced in this publication. The scaffolds are made by infiltration of the hexagonal crystal lattice of polystyrene spheres with sol-gel formulation and subsequent annealing. It possesses a relatively high degree of order among existing cell scaffolds and affords tight control over the scaffold porosity and tissue organization. The prepared scaffolds can be a convenient system for the investigation of cell-cell and cell-matrix interactions. Their biocompatibility is demonstrated for human hepatocellular carcinoma HEP G2 and human bone marrow HS-5 cell cultures. A preliminary effect of the scaffold topology on cell proliferation is observed. HEP G2 hepatocytes form a large number of 10-15 cell colonies on scaffolds made from 75-microm spheres, while their number diminishes for scaffolds from 10- and 160-microm spheres. Under similar conditions, HS-5 forms smaller colonies consisting of three to four cells in 90-microm cavities.     

On the caging number of two- and three-dimensional hard spheres

Local structural arrest in random packings of colloidal or granular spheres is quantified by a caging number, defined as the average minimum number of randomly placed spheres on a single sphere that immobilize all its translations. We present an analytic solution for the caging number for two-dimensional hard disks immobilized by neighbor disks which are placed at random positions under the constraint of a nonoverlap condition. Immobilization of a disk with radius r = 1 by arbitrary larger neighbor disks with radius r > or = 1 is solved analytically, whereas for contacting neighbors with radius 0 < r < 1, the caging number can be evaluated accurately with an approximate excluded volume model that also applies to spheres in higher Euclidean dimension. Comparison of our exact two-dimensional caging number with studies on random disk packing indicates that it relates to the average coordination number of random loose packing, whereas the parking number is more indicative for coordination in random dense packing of disks.     

Statistical analysis of random sphere packings with variable radius distribution

Many solid state systems can be modelled by means of packings of hard spheres of variable size. Therefore the spatial-statistical analysis of the geometrical structure of such packings is of great scientific interest. The present paper starts with the application of classical characteristics such as packing fraction, coordination number and pair correlation function for the characterization of sphere packings. Then, the application of tessellation-based methods follows, which includes the analysis of correlations between cell face and coordination numbers. Finally, a search method for crystalline sub-structures is presented.     

Compositions of nanoparticles of cubic symmetry

The formulas for calculation of the number of particles in structures of cubic symmetry O _h are reported. The numbers of atoms in the shells of cubic symmetry are determined by four structurally invariant numbers and the “quantum number” of the order n of the group. The classification of the shells of cubic symmetry is presented, and eight classes of shells are revealed. A key role in this classification is played by basic shells; in the case of close-packed spheres, these basic shells are repeated every six layers. The sum of all coordination numbers of all atoms of subshells is 24. The possibility of the existence of new fullerenes and nanoparticles of elemental boron and its oxides is considered.     

Isoglitter

A novel orthorhombic lattice is described that is generated upon a 1,4-cyclohexadieneoid motif, and is a model of a potential allotrope of C. The orthorhombic lattice (Ammm, space group #65) that is described, is called isoglitter as it is a structural relative of the tetragonal glitter lattice (P4₂/mmc, space group #131) first proposed in 1994 by Bucknum et?al. A geometrical optimization of the isoglitter lattice, employing the Cambridge Serial Total Energy Package (CASTEP) algorithm based upon density functional theory (DFT) was performed. The present report is an account of the CASTEP optimized isoglitter crystal structure, including an idealized drawing of the unit cell, and a set of optimized crystallographic coordinates for isoglitter. Results of an electronic band structure calculation, together with a density of states (DOS) profile for the lattice based upon CASTEP, are reported as well. The unit cell of isoglitter contains 8 C atoms and has a DFT modeled density of about 3.009 g/cm³. Isoglitter is comprised entirely of planar and chair-like 6-gons, and puckered 8-gons, in its structural pattern. The Wells point symbol for the network is cited here as (6³)(6⁵.8) and it is thus not a true graphene–diamond hybrid, where this point symbol translates to a Schlaefli symbol given as (6^2/9, 3^1/2). Based upon its connectivity, comprised of 3-connected trigonal planar vertices in a 1-to-1 stoichiometry with 4-connected tetrahedral vertices, the novel lattice is positioned midway between the graphene sheet, located at (6, 3), and the diamond lattice, located at (6, 4), in the topology mapping of structures described earlier by Wells.     

Dialkylindiumacetate R2InOOCCH3 (R = CH3, C2H5) Darstellung,Eigenschaften und Struktur

Dialkylindium Acetates R₂InOOCCH₃ (R = CH₃, C₂H₅). Preparation, Properties, and Structure. Dimethyl- and diethylindium acetate were prepared and the vibrational spectra (IR and RAMAN ) discussed. The X-ray structure determination shows that diethylindium acetate belongs to the orthorhombic space group Pnma. The unit cell with lattice constants a = 8.40, b = 7.41, c = 15.13 Å contains four molecules. Each indium atom forms with an acetate group a planar four-membered ring. The indium-oxygen distance within such a ring is only a little shorter than the distance of this oxygen to the indium of the next neighboured ring. Indium has therefore the coordination number six.     

Coordination numbers for rigid spheres of different size—estimating the number of next-neighbour interactions in a mixture

The maximum number of rigid spheres which can be attached to a central sphere of different diameter is calculated numerically. It is shown that this coordination number is not proportional to the surface ratio of the spheres, but roughly to power 1.2 of the diameter ratio. This has consequences for the methods by which averages of molecular properties are calculated; for several binary liquid mixtures it is shown that replacing molar fractions by contact fractions makes plots of excess properties versus concentration appear more symmetrical, thereby reducing the number of terms required in Redlich-Kister correlations.