Phase Behavior of Gradient Copolymer Melts with Different Gradient Strengths Revealed by Mesoscale Simulations

Design and preparation of functional nanomaterials with specific properties requires precise control over their microscopic structure. A prototypical example is the self-assembly of diblock copolymers, which generate highly ordered structures controlled by three parameters: the chemical incompatibility between blocks, block size ratio and chain length. Recent advances in polymer synthesis have allowed for the preparation of gradient copolymers with controlled sequence chemistry, thus providing additional parameters to tailor their assembly. These are polydisperse monomer sequence, block size distribution and gradient strength. Here, we employ dissipative particle dynamics to describe the self-assembly of gradient copolymer melts with strong, intermediate, and weak gradient strength and compare their phase behavior to that of corresponding diblock copolymers. Gradient melts behave similarly when copolymers with a strong gradient are considered. Decreasing the gradient strength leads to the widening of the gyroid phase window, at the expense of cylindrical domains, and a remarkable extension of the lamellar phase. Finally, we show that weak gradient strength enhances chain packing in gyroid structures much more than in lamellar and cylindrical morphologies. Importantly, this work also provides a link between gradient copolymers morphology and parameters such as chemical incompatibility, chain length and monomer sequence as support for the rational design of these nanomaterials.

Effect of Deformation Temperature on the Microstructure of Hard Magnetic Fecr22co15 Alloy Subjected to Tension Combined with Torsion Deformation Modes

The paper presents the results of microstructure evolution studies of hard magnetic FeCr22Co15 alloy deformed until destruction by tension and torsion in the temperature range 725-850ºC. The temperatures and deformation rates resulted from the condition of superplasticity occurrence in the Fe-Cr-Co alloys. Observations of the longitudinal sections of the deformed samples in the scanning electron microscope showed the formation of a weak gradient microstructure with the highest grain refinement in the surface layer of the material. Increasing the deformation temperature from 725 to 850_C increased the homogeneity of the deformation along the tensile axis of the sample. It also brought about the increase of grain size and slight increase of the thickness of fine grains in the surface layer. The precipitation of the intermetallic σ-phase was also observed with its maximum amount in the zones of the highest deformation.

Microstructure of Hard Magnetic FeCr22Co15 Alloy Subjected to Tension Combined with Torsion at High Temperatures

The paper presents the results of microstructure evolution studies of hard magnetic FeCr22Co15 alloy, destructed by tension and torsion at 800 and 850°C. The temperatures and deformation rates corresponded to the condition of superplasticity of Fe-Cr-Co alloys. Observations of longitudinal section of deformed samples in scanning electron microscope showed a formation of weak gradient microstructure with highest grain refinement in the surface layer of material. Precipitation of intermetallic σ-phase was also observed, with its maximum amount in zones of the highest deformation.

Harmonic Coordinates on Fractals with Finitely Ramified Cell Structure

We define sets with finitely ramified cell structure, which are generalizations of post-critically finite self-similar sets introduced by Kigami and of fractafolds introduced by Strichartz. In general, we do not assume even local self-similarity, and allow countably many cells connected at each junction point. In particular, we consider post-critically infinite fractals. We prove that if Kigami’s resistance form satisfies certain assumptions, then there exists a weak Riemannian metric such that the energy can be expressed as the integral of the norm squared of a weak gradient with respect to an energy measure. Furthermore, we prove that if such a set can be homeomorphically represented in harmonic coordinates, then for smooth functions the weak gradient can be replaced by the usual gradient. We also prove a simple formula for the energy measure Laplacian in harmonic coordinates.