Berechnung der Form kolloider Teilchen aus Röntgen-Kleinwinkeldiagrammen

From the low angle X-ray scattering diagrams of monodisperse dilute solutions of particles (protein molecules, virus particles) the moments of the intersect distribution functions and the characteristic constants can be determined. By means of a given set of equations it is possible to determine the particle shape. The characteristic constants were calculated for prolate and oblate ellipsoids of revolution.     

Die Bestimmung des mittleren Elektronenabstandes ā von in Lösung befindlichen Makromolekülen aus Röntgen-Kleinwinkeldiagrammen

From a low-angle X-ray scattering diagram of a dilute monodisperse solution the mean distance ā between two electrons within the molecules investigated is predictable. The calculation is possible either with the help of integral transformations of the scattering curve or from the initial slope of the slight-smeared scattering curve. For spheres and hollow spheres, for prolate and oblate spheroids of revolution and for agglomerates of spheres, the calculation of the mean electron distance ā has been carried out.     

Elastic constants of nematics. Comparison between molecular theory and computer simulations

We compare the ratios of the Frank elasticity coefficients calculated within a recently developed molecular theory, based on the approximation of perfect local orientational order, with the results of computer simulations presented by Frenkel, Allen, Tjipto-Margo and Evans for fluids of hard prolate and oblate ellipsoids. Good agreement is found for high densities, which correspond to those of thermotropic nematics, and for realistic values of the axial ratio. By constrast, at lower densities the approximation of perfect local order appears to be inadequate and the results of computer simulations follow the predictions of mean-field-like theories.     

Elastic constants of nematics. Comparison between molecular theory and computer simulations

Abstract

We compare the ratios of the Frank elasticity coefficients calculated within a recently developed molecular theory, based on the approximation of perfect local orientational order, with the results of computer simulations presented by Frenkel, Allen, Tjipto-Margo and Evans for fluids of hard prolate and oblate ellipsoids. Good agreement is found for high densities, which correspond to those of thermotropic nematics, and for realistic values of the axial ratio. By constrast, at lower densities the approximation of perfect local order appears to be inadequate and the results of computer simulations follow the predictions of mean-field-like theories.     

Role of the shape of various bacteria in their separation by Microthermal Field-Flow Fractionation

The steady-state movement of the spherical and non-spherical particles, such as prolate or oblate rotational ellipsoids, cylinders, or parallelepipeds, suspended in a liquid and exposed to a unidirectional temperature gradient, is analyzed theoretically. The differences in the ratios of the rotational to translational diffusion coefficients of the non-spherical to spherical particles, the heterogeneity of thermal conductivity of the particle body, and the heterogeneity in surface chemical nature make possible to separate the particles according to differences in shape. Preliminary experimental separations of Gram-positive and Gram-negative, nearly spherical and rod-shaped bacteria performed by Microthermal Field-Flow Fractionation confirmed that the fractionation of the cells according to differences in shape is possible.     

Correlation between Small-Angle X-ray Scattering spectra and apparent diffusion coefficients in the study of structure and interaction of sodium taurodeoxycholate micelles

Small-Angle X-ray Scattering (SAXS) and Dynamic Light Scattering (DLS) measurements were carried out on aqueous micellar solutions of the ionic biological detergent sodium taurodeoxycholate (NaTDC). Apparent diffusion coefficients (D(app)) and SAXS spectra of NaTDC 0.1 M solutions at different ionic strengths (0.1-0.3 M NaCl) were reported. A comparative analysis of SAXS spectra and D(app) data was performed to infer information on particle structure and interaction potential. Uniform particles with a spherical, an oblate, and a prolate symmetry were used to model the micelles in the data interpretation. A hard-core interaction shell of suitable thickness and a screened Coulomb potential of the electric double layer (EDL potential) were alternatively used to represent the long-range repulsive tail of the interaction potential. The Percus Yevick and the Rescaled Mean Spherical Approximation were applied. To compare the data of the two techniques, for each sample, a D(app) was calculated from the SAXS best-fitting geometrical parameters and interparticle structure factor of the micelles. Hence, a fitting procedure involving both the scattering and D(app) data was performed. The interpretation of SAXS spectra does not allow the discrimination between the oblate and the prolate symmetries of the aggregates. On the other hand, the comparison of calculated and experimental D(app) values indicates that the prolate ellipsoid is better suited to represent the micelle shape. Moreover, the agreement between calculated and experimental D(app) values is sensitively better at the lowest NaCl concentration when the EDL potential is used. A rodlike micellar growth and a progressive screening of the electrostatic interactions is testified by the trends of best-fitting parameters as a function of the added electrolyte.     

The primary electroviscous effect,free solution electrophoretic mobility,and diffusion of dilute prolate ellipsoid particles (minor axis = 3 nm) in monovalent salt solution

The principal objective of the present work is the modeling of the primary electroviscous effect of charged prolate ellipsoid models of low axial ratio. Other transport properties examined include (free solution) electrophoretic mobilities and translational diffusion constants. A numerical boundary element method is employed to solve the coupled Poisson, low Reynolds number Navier-Stokes, and ion transport equations. The methodology is first applied to the primary electroviscous effect of spheres with a centrosymmetric charge distribution and excellent agreement with independent theory is obtained. Specific model studies are also carried out for prolate ellipsoid models with axial ratios less than 4 and a minor axis equal to 3 nm. Most studies are carried out in aqueous NaCl solution (2 to 50 mM) at 20 degrees C for a range of different particle charges, although limited results are also presented in LiCl and KCl solution. The primary electroviscous effect for weakly charged prolate ellipsoids is smaller than that of a sphere under similar conditions. These studies are also carried out at high absolute particle charge. A comparison is made between the primary electroviscous effect and electrophoretic mobilities of prolate ellipsoids and corresponding spherical models.     

Chlorpromazine and sodium dodecyl sulfate mixed micelles investigated by small angle X-ray scattering

Small-angle X-ray scattering (SAXS) studies are reported on the interaction of chlorpromazine (CPZ) with micelles of anionic surfactant sodium dodecyl sulfate (SDS). Isotropic solutions of SDS (40 and 100 mM) at pH 4.0, 7.0, and 9.0 in the absence and presence of CPZ (2-25 mM) were investigated at the National Laboratory of Synchrotron Light (LNLS, Campinas, Brazil). The data were analyzed through the modeling of the micellar form factor and interference function. The results evidence a micellar shape transformation from prolate ellipsoid to cylinder accompanied by micellar growth and surface charge screening as the molar ratio CPZ : SDS increases in the complex. Small ellipsoids with axial ratio nu=1.5+/-0.1 at 40 mM SDS grow and reassemble into cylinder-like aggregates upon 5 mM drug incorporation (1 CPZ : 8 SDS monomers) with a decrease of the micelle surface charge. At 10 mM CPZ : 40 mM SDS cylindrical micelles are totally screened with an axial ratio nu approximately 2.5. The data also indicate the presence of small prolate ellipsoids (nu=1.7+/-0.1) in solutions of 100 mM SDS (no drug) and micellar growth (nu approximately 2.0 and 4.0) when 10 and 25 mM CPZ are added to the system. In the latter case, the aggregate is also better represented by a cylinder-like form. Therefore, our results demonstrate that the axial ratio and shape evolution of the surfactant : phenothiazine complex are both SDS concentration and drug : SDS molar ratio dependent. The drug location close to the SDS polar headgroup region without disrupting in a significant way both the paraffinic hydrophobic core and the polar shell thickness is inferred. SAXS data made it possible to obtain the shapes and dimensions of CPZ/SDS aggregates.     

Dielectric Properties and Structure of Aqueous Decaoxyethylene p-Isononylphenyl Ether Solutions

The static permittivity _s of aqueous decaoxyethylene p-isononylphenyl ether (NOP-10 grade) solutions is measured at surfactant concentrations of 1.14 and 4.97 wt % within 275–351 K temperature range; at concentrations of 9.96, 20, and 30 wt %, within 275–313 K range. Data on _s are analyzed, using the models of dilute disperse systems of oil–water type containing spherical particles, oblate and prolate spheroids. At 30, 20, and 9.96 wt % NOP-10 content, fragments of hexagonal mesophase are still retained in the isotropic phase near the interface, where there is a certain orientation of micelles acquiring the shape of prolate spheroids instead of cylindrical micelles. Upon heating up to 313 K, micelles are disoriented and their shape changes in prolate spheroid spherical micelle oblate spheroid sequence. With a further rise in water content, the fragments of lamellar mesophase appear in the isotropic phase at 4.97 and 1.14 wt % NOP-10 near the melting points of these solutions. They can exist with equal probability as the regions where either spherical micelles are located in the nodes of cubic lattice or oblate spheroidal micelles are distributed at random. As the temperature approaches the cloud point of dilute solutions, the randomly oriented oblate spheriodal micelles tend to acquire the disc-like shape.     

A mesoscale modelling study of nematic liquid crystals confined to ellipsoidal domains

Director configurations of nematic liquid crystalline molecules packed in ellipsoidal domains have been investigated using mesoscale modelling techniques. Interactions between the directors were described by the Lebwohl-Lasher potential. Four different ellipsoidal shapes (sphere, oblate spheroid, prolate spheroid, and ellipsoid) were studied under homogeneous and homeotropic surface anchoring conditions. The model has been characterized by computing thermodynamic and structural properties as a function of ellipsoidal shape (prolate and oblate) and size. The predicted director configuration in ellipsoids resulting from homeotropic surface anchoring is found to be very different from that in spherical domains. The bipolar configuration involving homogeneous surface anchoring is nearly identical in the four cases. The effect of an external electric field, applied at different orientations with respect to the major axis of the ellipsoid, has been probed as a function of the magnitude of the field and the ellipsoidal size and shape. The orientation of directors is most easily accomplished parallel and perpendicular to the major axis for the oblate and prolate spheroids, respectively, for homeotropic anchoring, and along the bipolar symmetry axis for homogeneous anchoring. In domains with homeotropic surface anchoring, the oblate spheroid and elongated ellipsoid are predicted to be the most efficient geometries for PDLC applications; for homogeneous anchoring conditions, the prolate spheroid and elongated ellipsoid are predicted to be the most efficient.     

A mesoscale modelling study of nematic liquid crystals confined to ellipsoidal domains

Director configurations of nematic liquid crystalline molecules packed in ellipsoidal domains have been investigated using mesoscale modelling techniques. Interactions between the directors were described by the Lebwohl-Lasher potential. Four different ellipsoidal shapes (sphere, oblate spheroid, prolate spheroid, and ellipsoid) were studied under homogeneous and homeotropic surface anchoring conditions. The model has been characterized by computing thermodynamic and structural properties as a function of ellipsoidal shape (prolate and oblate) and size. The predicted director configuration in ellipsoids resulting from homeotropic surface anchoring is found to be very different from that in spherical domains. The bipolar configuration involving homogeneous surface anchoring is nearly identical in the four cases. The effect of an external electric field, applied at different orientations with respect to the major axis of the ellipsoid, has been probed as a function of the magnitude of the field and the ellipsoidal size and shape. The orientation of directors is most easily accomplished parallel and perpendicular to the major axis for the oblate and prolate spheroids, respectively, for homeotropic anchoring, and along the bipolar symmetry axis for homogeneous anchoring. In domains with homeotropic surface anchoring, the oblate spheroid and elongated ellipsoid are predicted to be the most efficient geometries for PDLC applications; for homogeneous anchoring conditions, the prolate spheroid and elongated ellipsoid are predicted to be the most efficient.     

Statistical mechanical theory for discotic liquid crystals Discotic nematic-isotropic transition properties

A statistical mechanical theory is applied to study the equilibrium properties of discotic nematic liquid crystals. We report the calculation of thermodynamic properties for a model system composed of molecules interacting through angle-dependent pair potentials which can be broken up into rapidly varying short-ranged repulsions and weak long-range attractions. The repulsive interaction is represented by a repulsion between hard oblate ellipsoids of revolution and is a short-range, rapidly-varying, potential. The influence of attractive potentials, represented by dispersion and quadrupole interactions on a variety of thermodynamic properties is analysed. It is found that the thermodynamic properties for the discotic nematic-isotropic transition are highly sensitive to the form of effective one-body orientational perturbation potential. The discontinuity in the transition properties is more pronounced in the case of quadrupole interaction than for anisotropic dispersion interaction. A remarkable symmetry in the transition properties between prolate ellipsoids (ordinary nematic) and oblate ellipsoids (discotic nematic) is observed.     

Quantization on curved surfaces

After a short review of the existing methods for quantization of curved manifolds, the free particle motions or the so‐called geodesic flows on axisymmetrical prolate and oblate ellipsoids are quantized using the isomorphism established by Neumann of these systems and the harmonic oscillator restricted to the unit sphere. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Study of gelatin-agar intermolecular aggregates in the supernatant of its coacervate

Intermolecular interaction leading to formation of aggregates between gelatin, a polyampholyte, and agar, a polysaccharide was studied in the supernatant of the complex coacervate formed by these biopolymers. Electrophoresis, laser light scattering and viscometry data were used to determine the interaction and the physical structure of these intermolecular soluble complexes by modeling these to be prolate ellipsoids of revolution (rod-like structures with well defined axial ratio and Perrin's factor). Solution ionic strength was found to reduce the axial ratio of these complexes implying the presence of screened polarization-induced electrostatic interaction between the two biopolymers.     

Polystyrene–polyisoprene block copolymers in dilute solutions: Characterization of the conformation by small-angle neutron scattering

The variable-contrast method in small-angle neutron scattering has been applied to a study of the conformation of polystyrene–polyisoprene block copolymers in dilute solution. The experimental results reveal no intramolecular segregation effect in dilute solutions in toluene and cyclohexane.     

Molecular correlation functions for uniaxial ellipsoids in the isotropic state

We perform event-driven molecular dynamics simulations of a system composed by uniaxial hard ellipsoids for different values of the aspect ratio and packing fraction. We compare the molecular orientational-dependent structure factors previously calculated within the Percus-Yevick approximation with the numerical results. The agreement between theoretical and numerical results is rather satisfactory. We also show that, for specific orientational quantities, the molecular structure factors are sensitive to the particle shape and can be used to distinguish prolate from oblate ellipsoids. A first order theoretical expansion around the spherical shape and a geometrical analysis of the configurations confirms and explains such an observation.     

On the structure and the chain conformation of side-chain liquid crystal polymers

Abstract

Backbone anisotropy and the structure of the mesophases of a series of side-chain liquid crystal polymers have been studied in the bulk by neutron scattering. The backbone conformation is obtained by small-angle neutron scattering on mixtures of hydrogenous polymers with deuteriated backbones. The components of the radius of gyration parallel, R _⊥ and perpendicular, R ∥ to the magnetic field are determined as a function of temperature for both the nematic phase and the smectic phase. It is shown that the polymer backbone is deformed in both phases. When the polymer exhibits only a nematic phase, it adopts a prolate conformation, where the average backbone direction is more or less parallel to the aligned mesogenic groups. Upon transition from the smectic phase to a nematic phase, the backbone in the nematic phase assumes a slightly oblate shape. This tendency towards oblate shape is due to the smectic fluctuations which are always present in such nematic phases. The exentricity of the oblate backbone conformation in the smectic phase is always larger than in the nematic phase. This is attributed to a periodic distribution of the backbone between the mesophase layers. Then, the backbone anisotropy depends not only on the smectic structure (S_A1, S_Ad), but also on the temperature dependence of the density of aligned mesogenic groups in the layers. On the other hand, it is shown that the isotopic mixtures are no longer ideal when polymers deuteriated in the mesogenic moieties are mixed with the corresponding hydrogenous polymers.     

Lanthanide SMMs Based on Belt Macrocycles: Recent Advances and General Trends

Enhancement of axial magnetic anisotropy is the central objective to push forward the performance of Single-Molecule Magnet (SMM) complexes. In the case of mononuclear lanthanide complexes, the chemical environment around the paramagnetic ion must be tuned to place strongly interacting ligands along either the axial positions or the equatorial plane, depending on the oblate or prolate preference of the selected lanthanide. One classical strategy to achieve a precise chemical environment for a metal centre is using highly structured, chelating ligands. A natural approach for axial-equatorial control is the employment of macrocycles acting in a belt conformation, providing the equatorial coordination environment, and leaving room for axial ligands. In this review, we present a survey of SMMs based on the macrocycle belt motif. Literature systems are divided in three families (crown ether, Schiff-base and metallacrown) and their general properties in terms of structural stability and SMM performance are briefly discussed.     

Investigation of micelle formation in aqueous solution by laser-light scattering

The micellar properties of dilute solutions of two ionic detergents are investigated by quasielastic scattering of laser light. The interpretation of the results in terms of Tanford's theory shows that micelles have oblate ellipsoidal shape near the critical micelle concentration. Evidence for micelle polydispersity is presented, and an approximate evaluation of the spread of the size distribution function is given.     

Polymorphism and structure in different kinds of liquid crystal polymers and copolymers

We report a short outline of chain-conformation informations obtained by small angle neutron scattering (SANS) studies of different kinds of Liquid Crystalline Polymers (LCPs). We conclude that in the nematic phase the prolate shape of the chains are directly connected to the orientational order and the magnitude of the chain extension strongly depends on molecular parameters relative to the coupling mesogen-chain. The behavior is markedly different when the backbone anisotropy is oblate shape due to the chain confinement between the smectic layers.