Initial stages of SBA-15 synthesis: an overview

This work presents an overview of the data obtained for SBA-15 synthesis under the reaction conditions using synchrotron based small angle X-ray scattering and small angle neutron scattering. Three major stages in the synthesis of SBA-15 materials proceeding according to the cooperative self-assembly mechanism have been identified, and the structures of the intermediates species have been established. Our in situ time-resolved neutron scattering experiments demonstrate that only spherical micelles of the templating agent are present in the synthesis mixture during the first stage of the reaction. According to the neutron scattering and X-ray scattering data, in the second stage of the reaction the formation of hybrid organic-inorganic micelles is accompanied with the transformation from spherical to cylindrical micelles, which takes place before the precipitation of the ordered SBA-15 phase. During the third stage, these micelles aggregate into a two-dimensional hexagonal structure, confirming that the precipitation takes place as the result of self-assembly of the hybrid cylindrical micelles. As the synthesis proceeds, the voids between the cylinders are filled with the silicate species which undergo condensation reactions resulting in cross-linking and covalent bonding, leading to the formation of highly ordered SBA-15 mesostructure. This work demonstrates that valuable structural information can be obtained from X-ray and neutron scattering characterisation of complex systems containing periodic phases with d-spacing values up to 30 nm, and that both techniques are powerful means for in situ monitoring of the formation of nanostructured materials.     

Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir–capillaries interface

In this article the Stokes equations are considered in a domain simulating a capillary bed system. The capillaries are supposed to be thin, parallel and periodic. An asymptotic approximation is constructed. The macroscopic pressure satisfies a Robin interface condition whose coefficients are calculated numerically through a finite element approximation of a boundary layer problem, which is inspired to a domain decomposition technique.     

Neutron reflection and small-angle neutron scattering studies of a fluorocarbon telomer surfactant

Dilute aqueous phase behavior of a novel tris(hydroxymethyl)acrylamidomethane (THAM)-derived telomer bearing a perfluorohexyl hydrophobic chain, F6THAM6, has been investigated. Fluorinated polyhydroxy surfactants of this kind find use in emerging biomedical applications. Neutron reflection (NR) and drop volume surface tension (DVT) methods have been used to determine the critical micelle concentration (cmc=4.7 x 10(-4) mol x dm(-3)) and surface adsorption parameters (at the cmc NR gives a molecular area a(cmc)=67.4 and 62 A(2) and surface excess gamma(cmc)=2.46 x 10(-6) mol x m(-2)). The aggregation structures were determined by small-angle neutron scattering (SANS), indicating globular (polydisperse spheres) micelles of radius approximately 30 A are present. These findings are compared with literature on surfactants with related structures, to identify how the unusual molecular structure of F6THAM6 affects surfactant properties.     

Convex Fung-type potentials for biological tissues

The anisotropic, non-linear elastic behavior of biological soft tissue is typically accounted for by the hypothesis of hyperelasticity, i.e., the existence of an elastic potential. Fung-type potentials, based on the exponential of a quadratic form in the components of the Green-Lagrange strain, have been widely used in soft tissue modeling, and have inspired potentials in which the exponential was replaced by other monotonically increasing functions. It has been shown that simple fitting of the parameters of a Fung-type potential to experimental stress-strain curves may lead to non-convexity, with undesirable effects on the reliability of the algorithms used in Finite Element simulations. In this paper, we prove that the necessary and sufficient condition for the strict convexity of a Fung-type potential is that the quadratic form in the exponential is positive definite. This result provides a clear physical meaning for the parameters featuring in the quadratic form, and their relationship with the small-strain elastic moduli. This consistency relationship must be respected in order to guarantee that the Fung-type potential correctly reduces to the quadratic potential of classic linear elasticity in the small-strain approximation. Furthermore, we show that, when the conditions of convexity and consistency with the linear theory are respected, Fung-type potentials become a one-parameter family, and we discuss the consequences of this result for when fitting experimental data. An erratum to this article can be found at