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Book reviews

     

Iterative Algorithms for Multiscale State Estimation, Part 2: Numerical Investigations

Usually, direct methods are employed for the solution of linear systems arising in the context of optimization. However, motivated by the potential of multiscale refinement schemes for large problems of dynamic state estimation, we investigate in this paper the application of iterative solvers based on the concepts developed in Ref. 1. Specifically, we explore the effect of different system reductions for various Krylov-space iteration methods as well as three concepts of preconditioning. The first one is the normalization of states and outputs, which also favors error analysis. Next, diagonal scale-dependent preconditioners are compared; they all bound the condition numbers independently of the refinement scale, but exhibit significant quantitative differences. Finally, the effect of the regularization parameter on condition numbers and iteration numbers is analyzed. It turns out that a so-called simplified Uzawa scheme with Jacobi preconditioning and suitable regularization parameter is most efficient. The experiments also reveal that further improvements are necessary.     

Selbstheilende Polymere

Even though the field of self‐healing is rarely known so far – self healing materials are already present at our market. Nevertheless just due to modern scientific concepts we are now able to understand the basic mechanistic steps in a more detailed way. Further progress on this field will open access to materials with a wide range of adjustable properties. Therefore, applications of such self healing materials are not limited – assuming the market‐price is competitive and the elongated lifetime delivers an appropriate advantage. Already demonstrated for concrete and clear coatings for cars, the investigations done so far have generated materials with improved properties and prolonged durability.     

Spherical polymer brushes under good solvent conditions: molecular dynamics results compared to density functional theory

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions by molecular dynamics methods and density functional theory. With increasing chain length, the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Finally, a brief discussion of the experiment is given.     

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where “surface fields” may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.     

Polymer-brush lubricated surfaces with colloidal inclusions under shear inversion

We characterize the response of compressed, sheared polymer-brush bilayers with colloidal inclusions to highly nonstationary inversion processes by means of molecular dynamics simulations and scaling theory. Bilayers with a simple (dimeric) solvent reveal an overshoot for the shear stress, while simulations of dry brushes without explicit solvent molecules fail to display this effect. We demonstrate that mechanical instabilities can be controlled by the inclusion of macromolecular structures, such as colloids of varying softness. Based on a recently developed theory, we suggest a scaling approach to determine a characteristic time for conformational and collective responses.     

Analysis of the cluster formation in two-component cylindrical bottle-brush polymers under poor solvent conditions. A simulation study

Two-component bottle-brush polymers, where flexible side chains containing N = 20, 35 and 50 effective monomers are grafted alternatingly to a rigid backbone, are studied by Molecular Dynamics simulations, varying the grafting density s \sigma and the solvent quality. Whereas for poor solvents and large enough s \sigma the molecular brush is a cylindrical object with monomers of different type occupying locally the two different halves of the cylinder, for intermediate values of s \sigma an axially inhomogeneous structure of “pearl-necklace” type is formed, where microphase separation between monomers of different type within a cluster takes place. These “pearls” have a strongly non-spherical ellipsoidal shape, due to the fact that several side chains cluster together in one “pearl”. We discuss the resulting structures in detail and we present a comparison with the single-component bottle-brush case.     

Comparing nanoparticle risk perceptions to other known EHS risks

Over the last decade social scientific researchers have examined how the public perceives risks associated with nanotechnology. The body of literature that has emerged has been methodologically diverse. The findings have confirmed that some publics perceive nanotechnology as riskier than others, experts feel nanotechnology is less risky than the public does, and despite risks the public is optimistic about nanotechnology development. However, the extant literature on nanotechnology and risk suffers from sometimes widely divergent findings and has failed to provide a detailed picture of how the public actually feels about nanotechnology risks when compared to other risks. This study addresses the deficiencies in the literature by providing a comparative approach to gauging nanotechnology risks. The findings show that the public does not fear nanotechnology compared to other risks. Out of 24 risks presented to the participants, nanotechnology ranked 19th in terms of overall risk and 20th in terms of “high risk.”     

Biaxial ordering of terminal diene groups in lipid membranes: an infrared linear dichroism study

The molecular order within the hydrophobic core of membranes of the diene lipid di-tetradecadienoylphosphatidylcholine was studied by means of infrared spectroscopy on multibilayer assemblies which orient macroscopically on the surface of an attenuated total reflection crystal. The relative humidity and temperature were used as variable parameters to demonstrate that there were profound differences in the melting transition of lipids possessing predominantly cis and trans diene groups. The cis isomer undergoes the phase transition at a vapor pressure which is increased by 0.15 GPa when compared with that of the trans isomer. The methylene wagging band progression gives no indication of differences between the acyl chain conformation of the cis and trans forms in the gel state. The frequencies of a number of absorption bands of the diene groups reveal that these moieties are predominantly in the s-trans conformation to accommodate a favorable packing within the bilayer. The linear dichroism of selected in-plane and out-of-plane vibrations of the diene groups gives indications of the biaxial ordering of these moieties. We present the basic equations for the quantitative analysis of IR dichroism data of lamellar structures in terms of transverse and longitudinal molecular order parameters. It turns out that the planes of the rigid diene groups orient preferentially in a perpendicular direction with respect to the bilayer surface and parallel to each other forming in this way a layer of well-aligned diene groups in the bilayer center. This finding is confirmed by the results of X-ray measurements. We suggest that the partial interdigitation of the diene groups of the sn-1 acyl chains promotes the formation of the inverse H_II phase and/or enables the formation of covalent bonds between both the monolayers upon polymerization of diene lipids.