An Ion-Exchangeable MOF with Reversible Dehydration and Dynamic Structural Behavior (NH4)2[Zn2(O3PCH2CH2COO)2]⋅5 H2O (BIRM-1)

(NH₄)₂[Zn₂(O₃PCH₂CH₂COO)₂]⋅5 H₂O (BIRM-1) is a new metal phosphonate material, synthesized through a simple hydrothermal reaction between zinc nitrate and 3-phosphonopropionic acid, using urea and tetraethylammonium bromide as the reaction medium. In common with other metal–organic framework materials, BIRM-1 has a large three-dimensional porous structure providing potential access to a high internal surface area. Unlike most others, it has the advantage of containing ammonium cations within the pores and has the ability to undergo cation exchange. Additionally, BIRM-1 also exhibits a reversible dehydration behavior involving an amorphization-recrystallization cycle. The ability to undergo ion exchange and dynamic structural behavior are of interest in their own right, but also increase the range of potential applications for this material. Here the crystal structure of this new metal phosphonate and its ion exchange behavior with K⁺ as an exemplar are studied in detail, and its unusual structure-reviving property reported.     

Estimation,dependence and stability of solutions of an iterative equation

Aequationes mathematicae - In this paper we study estimation, continuous dependence and Hyers–Ulam stability for continuous solutions of a second order iterative equation. First we give an...     

On the Optimal Design of Wall-to-Wall Heat Transport

We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject to various boundary conditions and intensity constraints, we prove that the maximal rate of transport scales linearly in the r.m.s. kinetic energy and, up to possible logarithmic corrections, as the one-third power of the mean enstrophy in the advective regime. This makes rigorous a previous prediction on the near optimality of convection rolls for energy-constrained transport. On the other hand, optimal designs for enstrophy-constrained transport are significantly more difficult to describe: we introduce a “branching” flow design with an unbounded number of degrees of freedom and prove it achieves nearly optimal transport. The main technical tool behind these results is a variational principle for evaluating the transport of candidate designs. The principle admits dual formulations for bounding transport from above and below. While the upper bound is closely related to the “background method,” the lower bound reveals a connection between the optimal design problems considered herein and other apparently related model problems from mathematical materials science. These connections serve to motivate designs. © 2019 Wiley Periodicals, Inc.     

Dynamic control of volume phase transitions of poly(N‐isopropylacrylamide) based microgels in water using hydrazide‐aldehyde chemistry

We demonstrate that the volume phase transition temperature (VPTT) of copolymer microgel particles made from N‐isopropylacrylamide (NIPAm) and methacryloyl hydrazide (MH) can be tailored in a reversible manner upon the reaction of the hydrazide functional groups with aldehydes. The microgels were synthesized by precipitation polymerization in water. Due to the water‐soluble nature of the MH monomer, the VPTT at which the microgel particles contract shifts to higher values by increasing the incorporated amounts of methacryloyl hydrazide from 0 to 5.0 mol %. The VPTT of the copolymer microgel dispersions in water can be fine‐tuned upon addition of hydrophobic/hydrophilic aldehydes, which react with the hydrazide moiety to produce the hydrazone analogue. This hydrazone formation is reversible, which allows for flexible, dynamic control of the thermo‐responsive behavior of the microgels. The ability to “switch” the VPTT was demonstrated by exposing hydrophilic streptomycin sulfate salt incubated microgel particles to an excess of a hydrophobic aldehyde, that is benzaldehyde. The temperature at which these microgels contracted in size upon heating was markedly lowered in these aldehyde exchange experiments. Transformation into benzaldehyde hydrazone derivatives led to assembly of the microgel particles into small colloidal clusters at elevated temperatures. This control of supracolloidal cluster formation was also demonstrated with polystyrene particles which had a hydrazide functionalised microgel shell. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1745–1754     

Screening Clouds and Majorana Fermions

Ken Wilson developed the Numerical Renormalization Group technique which greatly enhanced our understanding of the Kondo effect and other quantum impurity problems. Wilson’s NRG also inspired Philippe Nozières to propose the idea of a large “Kondo screening cloud”. While much theoretical evidence has accumulated for this idea it has remained somewhat controversial and has not yet been confirmed experimentally. Recently a new possibility for observing an analogous crossover length scale has emerged, involving a Majorana fermion localized at the interface between a topological superconductor quantum wire and a normal wire. We give an overview of this topic both with and without interactions included in the normal wire.