Improved convergence in block copolymer self-consistent field theory by Anderson mixing

A modification to real space polymeric self-consistent field theory algorithms that greatly improves the convergence properties is presented. The method is based on Anderson mixing [D. G. Anderson, J. Assoc. Comput. Mach. 12, 547 (1965)], and each iteration computed takes negligibly longer to perform than with other methods, but the number of iterations required to reach a high accuracy solution is greatly reduced. No a priori knowledge of possible phases is required to apply this method. We apply our approach to a standard diblock copolymer melt, and demonstrate iteration reductions of more than a factor of 5 in some cases.     

Elastic deformation of polycrystals

We propose a framework to model elastic properties of polycrystals by coupling crystal orientational degrees of freedom with elastic strains. Our model encodes crystal symmetries and takes into account explicitly the strain compatibility induced long-range interaction between grains. The coupling of crystal orientation and elastic interactions allows for the rotation of individual grains by an external load. We apply the model to simulate uniaxial tensile loading of a 2D polycrystal within linear elasticity and a system with elastic anharmonicities that describe structural phase transformations. We investigate the constitutive response of the polycrystal and compare it to that of single crystals with crystallographic orientations that form the polycrystal.     

The Cavity Method for the Rigidity Transition

In order to motivate an analogy between the rigidity theory and combinatorial optimization, we have used the cavity method to study the floppy to rigid transition in a 2-dimensional (2D) random graph as well as in a 3D small world chain. Our analytic results are in excellent agreement with numerical studies using the pebble game algorithm. We also illustrate that a transfer matrix method is equivalent to the cavity method at the replica symmetric level     

Pinning frequencies of the collective modes in alpha-uranium

Uranium is the only known element that features a charge-density wave (CDW) and superconductivity. We report a comparison of the specific heat of single-crystal and polycrystalline alpha-uranium. In the single crystal we find excess contributions to the heat capacity at 41 K, 38 K, and 23 K, with a Debye temperature ThetaD = 265 K. In the polycrystalline sample the heat capacity curve is thermally broadened (ThetaD = 184 K), but no excess heat capacity was observed. The excess heat capacity Cphi (taken as the difference between the single-crystal and polycrystal heat capacities) is well described in terms of collective-mode excitations above their respective pinning frequencies. This attribution is represented by a modified Debye spectrum with two cutoff frequencies, a pinning frequency V0 for the pinned CDW (due to grain boundaries in the polycrystal), and a normal Debye acoustic frequency occurring in the single crystal.     

Hierarchical microstructure in structural phase transitions

We consider a model in the context of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential in local deviatoric (rectangular) strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation-induced strain gradient terms. The last term favors branching of domain walls which enables communication between macroscopic and microscopic regions essential for shape memory. Below the transition temperature (T₀) we obtain the conditions under which branching of twins is energetically favorable. Above T₀ a hierarchy of branched domain walls also stabilizes tweed formation (criss-cross patterns of twins). External stress or pressure modulates (“patterns”) the spacing of domain walls. Results based on 2D time-dependent Ginzburg-Landau simulations are shown for twins, tweed and hierarchy formation.     

A Paper‐Based Platform for Long‐Term Deposition of Nanoparticles with Exceptional Redispersibility,Stability, and Functionality

Although nanoparticles (NPs) can be carefully engineered to have maximal stability and functionality desirable for use in diverse applications, they are generally not suitable for long‐term storage in solution. It is also difficult to store NPs in a dry state because dried NPs generally become aggregated and cannot easily be redispersed. Thus, a new strategy allowing long‐term storage of NPs with high stability, redispersibility, and functionality is highly demanded. By passivating the 13 nm gold nanoparticle (AuNP) surface with stabilizing agents and treating a paper substrate with both bovine serum albumin and sucrose after coating with a hydrophobic polyvinyl butyral layer, it is possible to fully redisperse (≈100%) dried AuNPs with colloidal stability comparable to that of as‐prepared AuNPs. Furthermore, AuNPs physically stabilized with polyvinylpyrrolidone can react with thiol‐containing compounds, such as 1,4‐dithiothreitol (DTT). Taking advantage of the oxidation reaction of hypochlorous acid with DTT, it is possible to demonstrate a paper‐based colorimetric sensor for detection of residual chlorine in water. Since this strategy is applicable to large‐sized AuNPs (30–90 nm), silver NPs, oleic acid‐capped magnetic NPs, and cetrimonium bromide‐passivated gold nanorods, it can be used for diverse NPs requiring long‐term storage for many applications.     

Energy minimization related to the nonlinear Schrödinger equation

In this the window of the Sobolev gradient technique to the problem of minimizing a Schrödinger functional associated with a nonlinear Schrödinger equation. We show that gradients act in a suitably chosen Sobolev space (Sobolev gradients) can be used in finite-difference and finite-element settings in a computationally efficient way to find minimum energy states of Schrödinger functionals.     

Effect of nitrogen addition on hydrogen incorporation in diamond nanorod thin films

The effect of nitrogen addition in the feed gas on the finally incorporated amount of hydrogen in the diamond nanorods (DNRs) thin films has been investigated. The Raman spectroscopy measurements helped to understand the structural and quality changes with increasing nitrogen gas flow rate during CVD deposition. The hydrogen concentration was measured with 3.0 MeV He²⁺ beam using elastic recoil detection analysis technique and it was found that with the addition of nitrogen, the hydrogen concentration was increased. The results of non-Rutherford backscattering spectroscopy (NRBS) used to measure the amount of nitrogen in the DNRs thin films have shown that the incorporated nitrogen is below the detection limit of NRBS technique. Our results suggested that the addition of nitrogen has affected the overall quality of diamond films in two ways; increasing the thickness of diamond films by increasing the non-diamond carbon content and increasing the hydrogen impurity incorporation. The role of nitrogen additive on diamond growth and hydrogen incorporation is discussed.