3D‐morphology reconstruction of nanoscale phase‐separation in polymer memory blends

In many organic electronic devices functionality is achieved by blending two or more materials, typically polymers or molecules, with distinctly different optical or electrical properties in a single film. The local scale morphology of such blends is vital for the device performance. Here, a simple approach to study the full 3D morphology of phase‐separated blends, taking advantage of the possibility to selectively dissolve the different components is introduced. This method is applied in combination with AFM to investigate a blend of a semiconducting and ferroelectric polymer typically used as active layer in organic ferroelectric resistive switches. It is found that the blend consists of a ferroelectric matrix with three types of embedded semiconductor domains and a thin wetting layer at the bottom electrode. Statistical analysis of the obtained images excludes the presence of a fourth type of domains. The criteria for the applicability of the presented technique are discussed. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1231–1237     

The formation of dead zones in nonisothermal porous catalyst with temperature-dependent diffusion coefficient

This paper considers the formation of dead zones in the porous catalyst pellets due to the chemical reaction and diffusion. We established and investigated the model with nonisothermal reaction of fractional order and activated temperature-dependent diffusivity. The effects of process parameters, catalyst shape, and reaction and diffusion parameters on the formation of the dead zone are studied numerically and characterized by the critical Thiele modulus. The lower bounds for the critical Thiele modulus are derived analytically in terms of process parameters for exothermic and endothermic reactions and verified numerically. The critical Thiele modulus increases with increasing Arrhenius number for diffusion and decreasing Arrhenius number for reaction in the case of exothermic reactions, whereas the opposite trends hold for the endothermic reactions. The critical Thiele modulus also increases with increasing fractional reaction order as well as with decreasing energy generation function, and increasing Biot numbers for heat and mass transfer. Moreover, the critical Thiele modulus is the highest for spherical pellets and the lowest for pellets with planar shape.     

The Dynamics of the Neuropeptide Y Receptor Type 1 Investigated by Solid-State NMR and Molecular Dynamics Simulation

We report data on the structural dynamics of the neuropeptide Y (NPY) G-protein-coupled receptor (GPCR) type 1 (Y1R), a typical representative of class A peptide ligand GPCRs, using a combination of solid-state NMR and molecular dynamics (MD) simulation. First, the equilibrium dynamics of Y1R were studied using ¹⁵N-NMR and quantitative determination of ¹H-¹³C order parameters through the measurement of dipolar couplings in separated-local-field NMR experiments. Order parameters reporting the amplitudes of the molecular motions of the C-H bond vectors of Y1R in DMPC membranes are 0.57 for the Cα sites and lower in the side chains (0.37 for the CH₂ and 0.18 for the CH₃ groups). Different NMR excitation schemes identify relatively rigid and also dynamic segments of the molecule. In monounsaturated membranes composed of longer lipid chains, Y1R is more rigid, attributed to a higher hydrophobic thickness of the lipid membrane. The presence of an antagonist or NPY has little influence on the amplitude of motions, whereas the addition of agonist and arrestin led to a pronounced rigidization. To investigate Y1R dynamics with site resolution, we conducted extensive all-atom MD simulations of the apo and antagonist-bound state. In each state, three replicas with a length of 20 μs (with one exception, where the trajectory length was 10 μs) were conducted. In these simulations, order parameters of each residue were determined and showed high values in the transmembrane helices, whereas the loops and termini exhibit much lower order. The extracellular helix segments undergo larger amplitude motions than their intracellular counterparts, whereas the opposite is observed for the loops, Helix 8, and termini. Only minor differences in order were observed between the apo and antagonist-bound state, whereas the time scale of the motions is shorter for the apo state. Although these relatively fast motions occurring with correlation times of ns up to a few µs have no direct relevance for receptor activation, it is believed that they represent the prerequisite for larger conformational transitions in proteins.     

On the number of popular differences

We prove that there exists an absolute constant c > 0 such that for any finite set A ⊆ ℤ with |A| ≥ 2 and any positive integer m < c|A|/ ln |A| there are at most m integers b > 0 satisfying |(A + b) \ A| ≤ m; equivalently, there are at most m positive integers possessing |A| −m (or more) representations as a difference of two elements of A.     

Sums and differences along Hamiltonian cycles

Given a finite abelian group G, consider the complete graph on the set of all elements of G. Find a Hamiltonian cycle in this graph and for each pair of consecutive vertices along the cycle compute their sum. What are the smallest and the largest possible number of distinct sums that can emerge in this way? What is the expected number of distinct sums if the cycle is chosen randomly? How do the answers change if an orientation is given to the cycle and differences (instead of sums) are computed? We give complete solutions to some of these problems and establish reasonably sharp estimates for the rest.