Shear melting of a hexagonal columnar crystal by proliferation of dislocations

A hexagonal columnar crystal undergoes a shear-melting transition above a critical shear rate or stress. We combine the analysis of the shear-thinning regime below the melting with that of synchrotron x-ray scattering data under shear and propose the melting to be due to a proliferation of dislocations, whose density is determined by both techniques to vary as a power law of the shear rate with a 2/3 exponent, as expected for a creep model of crystalline solids. Moreover, our data suggest the existence under shear of a line hexatic phase, between the columnar crystal and the liquid phase.     

A concave–convex problem with a variable operator

We study the following elliptic problem \(-A(u) = \lambda u^q\) with Dirichlet boundary conditions, where \(A(u) (x) = \Delta u (x) \chi _{D_1} (x)+ \Delta _p u(x) \chi _{D_2}(x)\) is the Laplacian in one part of the domain, \(D_1\), and the p-Laplacian (with \(p>2\)) in the rest of the domain, \(D_2 \). We show that this problem exhibits a concave–convex nature for \(1<q<p-1\). In fact, we prove that there exists a positive value \(\lambda ^*\) such that the problem has no positive solution for \(\lambda > \lambda ^*\) and a minimal positive solution for \(0<\lambda < \lambda ^*\). If in addition we assume that p is subcritical, that is, \(p<2N/(N-2)\) then there are at least two positive solutions for almost every \(0<\lambda < \lambda ^*\), the first one (that exists for all \(0<\lambda < \lambda ^*\)) is obtained minimizing a suitable functional and the second one (that is proven to exist for almost every \(0<\lambda < \lambda ^*\)) comes from an appropriate (and delicate) mountain pass argument.     

Fibronectin and bovine serum albumin adsorption and conformational dynamics on inherently conducting polymers: a QCM-D study

Quartz crystal microbalance with dissipation monitoring (QCM-D) was employed to characterize the adsorption of the model proteins, bovine serum albumin (BSA) and fibronectin (FN), to polypyrrole doped with dextran sulfate (PPy-DS) as a function of DS loading and surface roughness. BSA adsorption was greater on surfaces of increased roughness and was above what could be explained by the increase in surface area alone. Furthermore, the additional mass adsorbed on the rough films was concomitant with an increase in the rigidity of the protein layer. Analysis of the dynamic viscoelastic properties of the protein adlayer reveal BSA adsorption on the rough films occurs in two phases: (1) arrival and initial adsorption of protein to the polymer surface and (2) postadsorption molecular rearrangement to a more dehydrated and compact conformation that facilitates further recruitment of protein to the polymer interface, likely forming a multilayer. In contrast, FN adsorption was independent of surface roughness. However, films prepared from solutions containing the highest concentration of DS (20 mg/mL) demonstrated both an increase in adsorbed mass and adlayer viscoelasticity. This is attributed to the higher DS loading in the conducting polymer film resulting in presentation of a more hydrated molecular structure indicative of a more unfolded and bioactive conformation. Modulating the redox state of the PPy-DS polymers was shown to modify both the adsorbed mass and viscoelastic nature of FN adlayers. An oxidizing potential increased both the total adsorbed mass and the adlayer viscoelasticity. Our findings demonstrate that modification of polymer physicochemical and redox condition alters the nature of protein-polymer interaction, a process that may be exploited to tailor the bioactivity of protein through which interactions with cells and tissues may be controlled.     

The revised structure, total synthesis, and absolute configuration of streptophenazine A

A total synthesis of both diastereomers of the originally proposed structure for streptophenazine A (1) has been achieved. However, both synthetic compounds are different from the natural product. Re-examination of NMR data reported for streptophenazine A and a concise total synthesis of both diastereomers of 17 (17a and 17b) led to the structural revision of streptophenazine A to 17b. Asymmetric synthesis of (-)-streptophenazine A was also conducted, and its absolute configuration was determined to be 1'S,2'R.     

Inhomogeneous flows in sheared complex fluids

Using dynamic light scattering in heterodyne mode, we measure velocity profiles in two complex fluids known to exhibit stress plateau behaviour under shear: a wormlike micelle solution and a lamellar phase. In both cases, our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap. We point out that the position of the interface between the two structures is stable at a fixed local shear stress *.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

Entropic phase separation in polymer-microemulsion networks

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first-order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase behavior of the system is extremely robust and is independent of the detailed properties of either polymers or drops.     

A concurrent algorithm for parallel calculation of eigenvalues and eigenvectors of real symmetric matrices

Elementary Jacobi Rotations are used as the basic tools to obtain eigenvalues and eigenvectors of arbitrary real symmetric matrices. The proposed algorithm has a complete concurrent structure, that is: every eigenvalue-eigenvector pair can be obtained in any order and in an independent way from the rest. Examples based on diagonally dominant real symmetric matrices are given.