Magnetic nanoparticle design for medical applications

Magnetic nanoparticles have attracted attention because of their current and potential usefulness as contrast agents for magnetic resonance imaging (MRI) or colloidal mediators for cancer magnetic hyperthermia. This contribution examines these in vivo applications through an understanding of the involved problems and the current and future possibilities for resolving them. A special emphasis is made on magnetic nanoparticle requirements from a physical viewpoint (e.g. relaxivity for MRI and specific absorption rate for hyperthermia), the factors affecting their biodistribution and the solutions envisaged for enhancing their half-life in the blood compartment and targeting tumour cells. Then, the synthesis strategies developed in our group are presented and focused on covalent platforms capable to be tailor-derivatised by surface molecular chemistry. The opportunity of using more complex oxides than conventional magnetite for controlling the in vivo temperature is also discussed.     

Electronic structure of some mesoscopic systems: II. Electronic composites

We study the electronic properties of a mesoscopic system composed of an array of straight, infinite rods made of an isotropic medium and embedded in a regular way in an isotropic background. Such a composite system has two-dimensional periodicity in the plane perpendicular to the rods. Using a Fourier series expansion, the corresponding Schrödinger equation is solved within the effective-mass approximation. The electronic band structure is computed for the wave vector in the transverse plane, and is illustrated by dispersion curves along the principal directions of the two-dimensional Brillouin zone as well as by the histograms of the density of states. The main result is the appearance of absolute energy gaps in the two-dimensional band structure.     

Simple models of adsorbed polymers: Vibrational properties

The vibrational properties of polymers adsorbed on surfaces are investigated within the frame of two simple models. First the surface is modelled as a one-dimensional infinite harmonic chain. Polymeric “ molecules ” are represented as harmonic chains of finite length. The coupling between the polymers and the surface is treated within the frame of the Interface Response Theory. Upon adsorption of polymers, resonant vibrational modes appear as well defined peaks in the variation of the density of states of the system. The effect of the interaction between adsorbed polymers via phonons is investigated and shown to lead to antiresonances in the spectral density of states and the formation of gaps in the density of states as the surface coverage is increased. A second more realistic model is introduced where the same finite harmonic chains (polymers) are grafted on a two dimensional [001] surface cut through a cubic harmonic crystal. Again the variation in density of states exhibits resonant modes between the polymers and the substrate. However, in this case, the interaction between polymers is short range. Adsorption of a film of polymers produces resonant modes which remain well-defined features within the substrate bulk band.     

Planar and non-planar solidification of optically organised smectic films

This letter describes an original freezing process that yields homogeneous solid films at ambient temperature with preservation of the layered structure of the chiral smectic phase. One of the most remarkable features of the process is its ability to provide complexly bent films with arbitrary three-dimensional shapes. Their optical homogeneity is observed in the planar as well as in the bent films. The method is very simple. After forming the films by spreading the liquid crystal above a hole in a glass slice placed over a hot stage, the film is heated from below. The hot film is exposed to ambient temperature. Then, a solid object at room temperature with a specifically adapted shape is immersed in the liquid film. The mechanical constraints imposed by the object curves the film and stabilises various solid two- and three-dimensional structures. Their homogeneous optical properties are due to long-range organisation of the molecular orientation (tilt), which combines with a complex helical arrangement of the frozen smectic layers.     

Toward the Rational Design of Galactosylated Glycoclusters That Target Pseudomonas aeruginosa Lectin A (LecA): Influence of Linker Arms That Lead to Low‐Nanomolar Multivalent Ligands

Anti‐infectious strategies against pathogen infections can be achieved through antiadhesive strategies by using multivalent ligands of bacterial virulence factors. LecA and LecB are lectins of Pseudomonas aeruginosa implicated in biofilm formation. A series of 27 LecA‐targeting glycoclusters have been synthesized. Nine aromatic galactose aglycons were investigated with three different linker arms that connect the central mannopyranoside core. A low‐nanomolar (K_d=19 nm , microarray) ligand with a tyrosine‐based linker arm could be identified in a structure–activity relationship study. Molecular modeling of the glycoclusters bound to the lectin tetramer was also used to rationalize the binding properties observed.     

Elastic properties of finite three-dimensional solid phononic-crystal slabs

We study theoretically, by means of layer-multiple scattering techniques, the propagation of elastic waves through finite slabs of phononic crystals consisting of metallic spheres in polyester matrix, embedded in air. We focus on the study of modes localized on the surfaces of the structure, investigating the physical parameters which influence and determine their appearance. Our results reveal the existence of absolute phononic frequency gaps in these finite structures, and point out the possibility, under an appropriate choice of the parameters, of tunable regions of frequency free of propagating and/or surface-localized modes. This could be very useful in the design of devices related to frequency filtering, waveguiding, etc.     

Equilibrium schemes for scalar conservation laws with stiff sources

We consider a simple model case of stiff source terms in hyperbolic conservation laws, namely, the case of scalar conservation laws with a zeroth order source with low regularity. It is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced CFL condition and refined meshes required because of the lack of accuracy on equilibrium states. The source term should be taken into account in the upwinding and discretized at the nodes of the grid. In order to solve numerically the problem, we introduce a so-called equilibrium schemes with the properties that (i) the maximum principle holds true; (ii) discrete entropy inequalities are satisfied; (iii) steady state solutions of the problem are maintained. One of the difficulties in studying the convergence is that there are no estimates for this problem. We therefore introduce a kinetic interpretation of upwinding taking into account the source terms. Based on the kinetic formulation we give a new convergence proof that only uses property (ii) in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions. The computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that, in comparison with an usual upwind scheme, the corresponding equilibrium version is far more accurate. Furthermore, numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients.