Sphere packing, helices and the polytope {3, 3, 5}

The packing of tetrahedra in face contact is well-known to be relevant to atomic clustering in many complex alloys. We briefly review some of the structures that can arise in this way, and introduce methods of dealing with the geometry of the polytope {3, 3, 5}, which is highly relevant to an understanding of these structures. Finally, we present a method of projection from S₃ to E₃ that enables coordinates for the key vertices of the collagen model of Sadoc and Rivier to be calculated. Received 27 March 2001     

微波辐照对胶原蛋白三股螺旋结构的影响

胶原蛋白的三股螺旋结构是其不同于其他蛋白质的特殊结构，也是其具有特殊功能的基础，然而，胶原的三股螺旋结构易在外界条件的影响下被破坏。目前微波已被越来越多的应用于胶原蛋白的提取和改性过程，但是关于微波辐照对胶原蛋白结构影响的研究还相对较少。首先从牛跟腱中提取胶原蛋白，然后采用0.5 mg·mL-1的胶原蛋白溶液在30 ℃下以微波辐照保温为实验样，水浴加热和未经加热处理为对比样，最后采用紫外-可见光谱、傅里叶变换红外光谱、圆二色谱以及荧光发射光谱等方法，对不同加热方法中胶原蛋白的三股螺旋结构和超分子结构进行表征，研究了微波辐照对胶原蛋白结构的影响。实验结果表明，在低于胶原变性温度的条件下，无论是微波辐照还是水浴加热都不会破坏胶原蛋白的三股螺旋结构，也不会使胶原蛋白变性。但是，与水浴加热相比，微波辐照会对胶原蛋白的聚集行为产生抑制作用。微波辐照对胶原蛋白的作用既有与常规加热相同的热效应，又有常规加热过程中不存在的非热效应，非热效应表现为抑制胶原蛋白的聚集行为。研究结果可为微波场中胶原蛋白结构和性质的变化提供科学依据。     

The interplay between surface micro-topography and -mechanics of type I collagen fibrils in air and aqueous media: An atomic force microscopy study

Calf skin type I collagen fibrils were regenerated from acidic solution and imaged with contact mode atomic force microscopy in air, water, and buffer solution. When imaged in air at a contact force of 20-150 nN, collagen fibrils exhibited a distinct transverse banding pattern with a period of 65 nm, consisting of high ridges and shallow grooves. The force dependence of the images suggests that such banding pattern is attributed to the transverse contraction of the fibril upon dehydration during sample preparation, which reflects the tangential mass density across the fibril. Imaging in water and phosphate buffer solution at a contact force of 15-80 nN revealed hydrated collagen fibrils with smooth surfaces. The rigidity of the collagen fibrils decreased considerably upon hydration. Scanning the cantilever tip in an aqueous medium at a contact force of 90-280 nN enabled us to probe subunit arrangement in the bulk region of the collagen fibril. The results indicate that the molecular assembly in the hydrated fibril is akin to that in the intact form. The image resolution was improved by stabilizing the collagen molecules through crosslinking with glutaraldehyde, which served to resolve microfibril-like structure on the fibril surface. Received 28 March 2000 and Received in final form 15 June 2001     

From selective to wide-band light reflection: a simple thermal diffusion in a glassy cholesteric liquid crystal

Due to their helicoidal structure, cholesteric liquid crystals exhibit remarkable optical properties. Selective light reflection occurs when the pitch (repeat distance) is of the order of the wavelength of incident light propagating along the helix axis. The wavelength bandwidth, due to the optical anisotropy, is typically limited to 50 nm which is insufficient for some applications (full-colors displays, for example). By introducing a pitch gradient in the helix during a novel two-step process in a cholesteric glass, we show that reflection may occur over a wavelength bandwidth greater than 300 nm. First, the reflection bandwidth is adjusted by thermal annealing. Then, the optical properties are permanently stored by quenching the viscous material to a glass at room temperature. The two steps, pitch gradient establishment and film hardening, are independently controlled. The present process exhibits some reversibility and properties intrinsic to the glassy state are gained: laser-writing high resolution full-color images on solid films for image recording or high-density optical data-storage are indeed conceivable. Received 17 December 1998     

Novel twist grain boundary smectic-C phases

Several new kinds of smectic-C twist grain boundary phases (TGBC) have been observed during the last few years. These pure compounds or mixtures exhibit unusual textures with polygonal lattices (square or hexagonal grids) in the plane normal to the TGB helix. The structure of these new phases seems to be complex and different from reported and predicted TGBC phases. In this article, we review the main results obtained on these different new phases, and we propose new TGBC structures based on the well-known splayed polarization --twisted director structures adopted by chiral smectic-C's in planar aligned (bookshelf) cells. The observed square or hexagonal lattices are made of superimposed pairs of unwinding lines due to the suppression of the helix within smectic-C blocks by the grain boundaries (unwinding walls). A lattice-free TGBC occurs if the helix within smectic-C blocks is suppressed completely. Received 15 March 2001     

Electron diffraction and microscopy of single-wall carbon nanotube bundles produced by different methods

The atomic structure of single-wall carbon nanotube bundles produced by three different techniques (laser ablation, electric arc discharge and catalytic chemical vapor deposition (CCVD)) has been characterized by electron diffraction and microscopy. Information on the helicity and the lattice packing has been obtained. Concerning the helicity, small bundles produced by CCVD exhibit only one or two tube helicities within a single bundle. The diffraction patterns of laser-ablation produced bundles also present well-defined but more diversified chiralities within a single bundle. By contrast the data acquired on bundles formed by arc discharge show a more diffuse pattern, characteristic of a random chirality dispersion within a single bundle. Concerning the lattice packing, informations are obtained via a detailed study of the equatorial line of the diffraction pattern for bundles produced by the three techniques. This electron diffraction study is completed by high-resolution electron microscopy. Received 8 August 2001 and Received in final form 14 March 2002     

Experimental study of the porosity of loose stacks of stiff cylindrical fibres: Influence of the aspect ratio of fibres

The aim of this work is to study the porosity of three-dimensional and two-dimensional packing of stiff cylindrical fibres according to their aspect ratio. First, we have carried out an experimental study of the porosity for 3D and 2D packing. In this last case, the elementary representative surfaces have been determined. Then, an attempt of interpretation of the porosity variations for 2D stacks has been realized on the basis of the excluded volume theory and a variation law has been proposed. To conclude, we have studied the relevance of a simplified packing model based on a single geometry of the defects. Received 12 April 1999 and Received in final form 4 August 1999     

Study of the symmetry of single-wall nanotubes by electron diffraction

Determining precisely the atomic structure of single-wall carbon nanotubes is essential since it tailors electronic properties of this new carbon material. Here, we present a quantitative electron diffraction study of electric-arc produced single-wall carbon nanotube bundles, combined with simulations based on the kinematic theory and with real-space images. We stress the importance of the twist of the bundle in the interpretation of our data and we analyze both packing lattice parameters and chirality distribution. We show that, within a given bundle, no chirality is favoured whereas SWNT diameters are almost uniform. Received 5 February 1999     

Elastic energy of tilt and bending of fluid membranes

Tilt of hydrocarbon chains of lipid molecules with respect to membrane plane is commonly considered to characterize the internal structure of a membrane in the crystalline state. However, membranes in the liquid state can also exhibit tilt resulting from packing constraints imposed on the lipid molecules in diverse biologically relevant structures such as intermediates of membrane fusion, pores in lipid bilayers and others. We analyze the energetics of tilt in liquid membranes and its coupling with membrane bending. We consider three contributions to the elastic energy: constant tilt, variation of tilt along the membrane surface and membrane bending. The major assumption of the model is that the core of a liquid membrane has the common properties of an elastic continuum. We show that the variation of tilt and membrane bending are additive and that their energy contributions are determined by the same elastic coefficient: the Helfrich bending modulus, the modulus of Gaussian curvature and the spontaneous curvature known from previous studies of pure bending. The energy of a combined deformation of bending and varying tilt is determined by an effective tensor accounting for the two factors. In contrast, the deformation of constant tilt does not couple with bending and its contribution to the elastic energy is determined by an independent elastic constant. While accurate determination of this constant requires additional measurements, we estimate its value using a simplified approach. We discuss the relationships between the obtained elastic Hamiltonian of a membrane and the previous models of membrane elasticity. Received 10 February 2000 and Received in final form 19 June 2000     

基于二维红外技术研究氧化羧甲基纤维素钠/胶原的相互作用及热稳定性

采用氧化羧甲基纤维素钠(OCMC)作为交联剂,对胶原溶液进行改性并采用二维红外技术分析OCMC与胶原之间的相互作用及其对胶原热稳定性的影响。一维红外图谱显示OCMC交联改性对胶原的主要特征吸收峰即酰胺Ⅰ,Ⅱ和Ⅲ带的峰位与强度无明显影响;改性前后胶原的酰胺Ⅲ带与1 455 cm-1处吸光度的比值A_Ⅲ/A_{1 455}均接近于1.000,以上结果显示交联键的引入不会破坏胶原的三股螺旋结构,但无法获知胶原与OCMC之间的相互作用及胶原结构的变化。以OCMC用量为外扰条件建立二维红外相关图谱,进一步分析两者间相互作用。结合胶原结构与OCMC中基团的响应强度及顺序可知：OCMC首先通过羧基与胶原中精氨酸的胍基或赖氨酸的氨基发生静电作用,随后醛基与胶原氨基之间发生希夫碱反应;两者之间相互作用以希夫碱反应为主。由于静电作用与交联键的引入,改性后胶原的热稳定性得到提升。随着温度的升高,纯胶原与改性胶原的特征吸收峰均发生红移且A_Ⅲ/A_{1 455}值不断降低,说明两者在升温过程中其氢键不断减弱,导致三股螺旋发生解旋,但与纯胶原相比,改性胶原特征吸收峰的红移程度与A_Ⅲ/A_{1 455}值降低幅度较小,证实了改性后胶原的热稳定性有所提高。胶原与改性胶原在升温过程中结构变化的分析结果表明：改性前后胶原二级结构的崩塌均表现为三股螺旋结构被破坏转变成无规卷曲结构;然而在测试温度范围内,三股螺旋结构对温度的敏感度及响应顺序发生明显变化：（1）对于纯胶原,对温度最为敏感的结构是胶原的螺旋结构,而改性胶原的无规卷曲结构是最为敏感的、最不敏感的结构是胶原螺旋结构,反映出改性后胶原的螺旋结构得到稳定;（2）改性后胶原螺旋结构对温度的响应发生滞后,进一步证实胶原的稳定作用主要归功于三股螺旋结构的加固。     

The Laguerre polyhedral decomposition: application to protein folds

An extension of the Voronoi tessellation, the Laguerre polyhedral decomposition, is introduced and applied to the analysis of the packing geometry of amino-acids in folded proteins. This method considers an ensemble of points with different weights and therefore it is well suited for a geometrical analysis of a set of objects with a wide size distribution. With this method it is shown that the true volumes occupied by the amino-acids inside a protein is better described than with the standard Voronoi procedure. This method allows defining unambiguously (without cut-off distance) the neighborhood for each amino-acid in a given protein and contact matrices can be established which contain all topological informations on the internal structure. Finally, a statistical analysis of the geometrical characteristics of the polyhedra attached to each amino-acid is done over a collection of 35 proteins. Received 20 November 2002 / Received in final form 26 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: sadoc@lps.u-psud.fr     

A multi-reference exponential expansion for the electronic wave function

The expansion structure of a CI vector as combination of excitations from a model-space reference determinant is investigated. It is shown that between the linear and the exponential expansions there is a relation which is similar to the single-reference case, if the internal excitations are adsorbed into the reference vector. Moreover, expansions with respect to different determinants are related by a set of linear equations. By using these two properties, a State-Specific Coupled-Cluster formalism is proposed. Received 2 November 2000 / Received in final form 1st March 2002 Published online 28 June 2002     

Calculation of partial structure factors of a less-simple binary alloy

The partial static structure factors, using the Faber-Ziman (FZ) theory, have been calculated for Ag-In alloy. For 20% Ag at 623 K and 70% Ag at 973 K, the interionic pair potential based on the Bretonnet-Silbert (BS) formalism are calculated and the hard sphere diameters for the component elements are estimated from the potential profile using the linearised Weeks-Chandler-Andersen (LWCA) method. The average number densities are calculated on the assumption that the atomic volumes are simply additive. The calculated structure factors are compared with the experimental values. The partial structure factors for Ag-Ag at 20% Ag and In-In at 70% Ag appear to be slightly out of phase with the calculated values particularly in large q-region. From the calculations it appears that this discrepancy is related to the process of derivation of the experimental structure factors from the total one, and the Ag-In alloy can be described by a mixture of hard spheres. Received 31 October 2001 and Received in final form 10 January 2002     

Fragmentation of grains in a two-dimensional packing

A numerical model of fragmentation of a two-dimensional granular medium under pressure is investigated. The fragmentation process is found to be strongly dependent on the type of force used as the criterion for breaking the grains. The fragmentation mode affects the process less dramatically. There is a power-law divergence in the pressure when the medium approaches the full packing limit, . Both log-normal and power-law fragment-size distributions are found. Gravity is demonstrated to be an important factor. Received: 14 December 1997 / Accepted: 17 March 1998     

Stacking faults in close-packed clusters

Ground state geometries of small hard sphere clusters were studied using two different type of contact interaction, a pair-potential and a many-atom interaction. Monte Carlo method in an FCC lattice with all possible (111) stacking faults was used to obtain the minimum energy geometries for clusters up to 59 atoms. Due to the surface energy, FCC packing is generally favoured as opposite to the HCP structure. However, in most cluster sizes the ground state obtained with the many-atom interaction has one or more stacking faults. The most symmetric geometry is usually not the ground state. Clusters with 59 and 100 atoms were studied due the possibility of a high symmetry cluster with stacking faults in all four directions. The size dependence of the total energy has similarities with that of the average moment of inertia. Received 6 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

Phasons, sliding modes and friction

Aperiodic crystals may have additional low frequency modes related to the possibility to describe them in a higher-dimensional space. Dynamics associated with these degrees of freedom is called phasonic, but there are very different phenomena of this type. A discussion is given of the use of the term. The relation between phason modes, the crystal structure, and the modulation and sliding modes is discussed. Finally a relation with frictionless motion is studied. Received 4 April 2002 / Received in final form 22 July 2002 Published online 17 September 2002     

Giant electrical fluctuations in metallic disordered packings

We have experimentally studied granular arches through electrical measurements. The packing is composed of 2d metallic pentagons and is submitted to small taps. Large electrical fluctuations are observed and they are distributed along power laws. This indicates the presence of long-time memory effects even the packing density remains constant around a value ρ = 0.72±0.02. Large electrical fluctuations should be associated with the breaking/creation of granular arches. Received 3 October 2000     

Rheology of nanosized hairy grain suspensions

Suspensions of nanosized hairy grains have been prepared by grafting long polydimethylsiloxane chains (molecular weight ) onto silica particles (radius ), dispersed into a good solvent of PDMS. Depending on the particle volume fraction, different rheological behaviors are observed. In the very dilute regime, the suspensions are perfectly stable and the particles behave almost as hard spheres: flow penetration inside the corona is then very weak. When the particle volume fraction goes to the close packing volume fraction, the suspension viscosity does not diverge as for hard spheres due to the increase of flow penetration inside the corona and to corona entanglements. The particles have then the same behavior as polymer stars having an intermediate number of arms (). Finally, in the concentrated regime (), the suspensions form irreversible gels. We shown that this unexpected gelation phenomenon is related to the presence of the silica cores: grafted PDMS chains can adsorb onto different particles and form irreversible bonds between the cores. The viscosity and elastic modulus evolutions during gelation are well described by the scalar percolation model of sol-gel transition. Received 23 March 1998     

Scaling approach of the convective drying of a porous medium

We propose a simplified, theoretical approach of the evolution of liquid distribution during the convective drying of a granular packing. In the absence of gravity effects three regimes are distinguished according to the relative importance of surface evaporation, capillarity or evaporation from the interior of the sample. The evolution of the drying rate as a function of the saturation can be inferred from the characteristic velocities associated to each of these effects. We also carried out drying experiments of bead packings saturated with ethanol, at four different velocities of the boundary convection current, and with bead size ranging from 4.5 to 100 μm. The drying curves exhibit different regimes with a scaling as a function of particle radius and current velocity as predicted by the theory. Received 7 June 1999 and Received in final form 25 October 1999     

Dynamics and effective actions of BCS superconductors

We derive the effective dynamical theory for BCS superconductors, based on the effective action formalism. Both the metallic regime and the superconducting regime are studied in the clean and dirty limit. The full electrodynamics of the problem is formulated in a manifestly gauge-invariant and transparent way. Furthermore, we consider the effect of particle-hole asymmetry in the band structure, and discuss its consequences for vortex dynamics and the topological term in the effective action. The effective action is the starting point for treating (quantum-) dynamical problems involving BCS superconductors. Received 23 November 1998