In situ spectroscopic ellipsometry of pH-responsive polymer brushes on gold substrates

The dynamic and reversible switching behaviour of polyelectrolyte brushes of poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) toward changes of the pH value was studied by in situ VIS-spectroscopic ellipsometry (SE). For this, PDMAEMA brushes with three different molecular weights were synthesized via the “grafting from” method using surface initiated atom transfer radical polymerization. In detail, the applicability of different SE data modelling to describe the optical properties of the different brush layers in the swollen and collapsed state was investigated. Especially for the PDMAEMA brushes with a high molecular weight, an improved optical modelling of the experimental data could be achieved and revealed an exponential distribution of the PDMAEMA fraction in the brush layer.

Solid-state assisted synthesis of oligobenzoates

The solid-state assisted synthesis opens an easy access to oligobenzoates end-capped with gallic acid, protocatechuic acid or 4-hydroxybenzoic acid etherified with long flexible chains – which are important precursors for liquid crystalline materials. The latter may consist of aliphatic, oligoethyleneoxy and semiperfluorinated chains. The rapid preparation of oligoesters with different peripheries is demonstrated.     

Crystallization statistics,thermal history and glass formation

The formal theory of transformation kinetics describes the volume fraction of a phase transformed in a given time at a given temperature. The basic concepts are extended for isotropic crystal growth in a material having a known thermal history T(r, t). A crystal distribution function ψ(r, t, R) is defined such that the number of crystallites in a volume dυ at r having radii between R and R + dR at time t is ψ(r, t, R) dυ dR. The function ψ contains essentially complete statistical information about the state of crystallinity of a material. Formal expressions for ψ are obtained. Applications are discussed, including predictions of crystallinity when T(r, t) is known; predictions of glass-forming tendencies; experimental determination of nucleation rates; and the determination of the thermal history of a sample from post mortem crystallinity measurements. As an example, ψ(r, t, R) is calculated for a lunar glass composition subjected to a typical laboratory heat treatment.     

The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential α, we consider the problem of restoring the metric g and the magnetic potential α from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Mañé action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of α.For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on α. We also show injectivity and stability for g and α in a generic class G including real analytic ones.For the nonlinear problem, we show rigidity for real analytic simple (g,α), rigidity for metrics in a given conformal class, and locally, near any (g,α)∈G. We also show that simple magnetic systems on two-dimensional manifolds are always rigid.     

Recovering singularities of a potential from singularities of scattering data

In this paper we show that the leading singularities of certain potentials can be determined from the leading singularities of the backscattering (as well as other determined sets of scattering data). The potentials in question are conormal with respect to smooth surfaces of arbitrary dimension; the restrictions on their orders allow for unbounded potentials in all dimension greater than or equal to three.Partially supported by NSF Grant DMS-9101298 and an Alfred P. Sloan Research FellowshipPartially supported by NSF Grant DMS-9100178     

Calcium phosphate mineralization with linear poly(ethylene imine): a time-resolved study

We have earlier shown that linear poly(ethylene imine) (LPEI) is an efficient growth modifier for calcium phosphate mineralization from aqueous solution (Shkilnyy et al., Langmuir, 2008, 24 (5), 2102). The current study addresses the growth process and the reason why LPEI is such an effective additive. To that end, the solution pH and the calcium and phosphate concentrations were monitored vs. reaction time using potentiometric, complexometric, and photometric methods. The phase transformations in the precipitates and particle morphogenesis were analyzed by X-ray diffraction and transmission electron microscopy, respectively. All measurements reveal steep decreases of the pH, calcium, and phosphate concentrations along with a rapid precipitation of brushite nanoparticles early on in the reaction. Brushite transforms into hydroxyapatite (HAP) within the first 2 h, which is much faster than what is reported, for example, for calcium phosphate precipitated with poly(acrylic acid). We propose that poly(ethylene imine) acts as a proton acceptor (weak buffer), which accelerates the transformation from brushite to HAP by taking up the protons that are released from the calcium phosphate precipitate during the phase transformation.     

Tensor tomography on surfaces

We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.     

Reconstruction of inclusions in an elastic body

We consider the reconstruction of elastic inclusions embedded inside of a planar region, bounded or unbounded, with isotropic inhomogeneous elastic parameters by measuring displacements and tractions at the boundary. We probe the medium with complex geometrical optics solutions having polynomial-type phase functions. Using these solutions we develop an algorithm to reconstruct the exact shape of a large class of inclusions including star-shaped domains and we implement numerically this algorithm for some examples.     

A Numerical Study of the Flow Around a Model Winged Seed in Auto-Rotation

In this study the flow around a winged-seed in auto-rotation is characterized using direct numerical simulations (DNS) at Reynolds number in the range 80–240, based on the descent speed and a characteristic chord length. In this range, the flow is approximately steady when observed from a reference frame fixed to the seed. For all cases, the flow structure consists of a wing tip vortex which describes a helical path, a vortex shed behind the nut of the seed and a stable leading edge vortex above the wing surface which merges with the tip vortex. With increasing Reynolds number, the leading edge vortex becomes more intense and gets closer to the wing surface. The simulation results also show the formation of a spanwise flow on the upper surface of the wing, moving fluid towards the wing tip in a region downstream and beneath the leading edge vortex. This spanwise flow is rather weak inside the core of the leading edge vortex, and the analysis of the streamlines show a very weak transport of vorticity along the vortex for the cases under consideration. The analysis of the flow suggests that the stabilization of the leading edge vortex is mainly due to non-inertial accelerations, although viscous effects may contribute, specially at lower Re. Furthermore, the leading edge vortex has been characterized by analysing the flow variables averaged along cross-sections of the vortex. While some quantities, like the spanwise velocity or the pressure inside the vortex, are rather insensitive to the threshold used to define the leading edge vortex, the same is not true for the circulation of the vortex or its averaged spanwise vorticity, due to the viscous nature of the vortex. Finally, it is observed that the spanwise vorticity scales with the angular rotation of the seed for the different Re.