Computational Study of Supramolecular Bis-porphyrin “Molecular Tweezers”

A computational study of a series of space separated bis-porphyrin “molecular tweezers” using semiempirical (AM1) and DFT (B3LYP and PBE1PBE) methods has been carried out. It was found that polynorbornane bis-porphyrin systems are significantly less rigid than previously thought. The variation of the metal–metal separation distance between the two porphyrin centers does not cause a significant energy change thus enabling these molecules to easily adjust to the optimal coordination distance required for complexation by various bidentate 4-pyridyl ligands inside the cavity of these “tweezers”. Article 54, ECCC-10, April 1-30 2005, http://www.eccc.monmouth.edu     

A Longitudinal Analysis of an Out‐of‐School Science Experience

A phenomenological approach was used to investigate the longitudinal recollections of participants of an out‐of‐school science program. The experience was a field trip to the Shenandoah National Park (USA) conducted in the fall of 2004. The science topic was geologic history and features related to the Shenandoah Valley. Two major themes relating to the participants' long term recollection of the out‐of‐school science field trip were identified after the interview data was analyzed. First, recollections were highly influenced by actions taken by the students, and, second, program content / subject matter were retained by all of the students to varying degrees. The interactive experiences that aided in memory retrieval from this study closely relates to the interactive experiences associated with memory and learning theory associated with the psychological domain. This linkage and its impact on how students learn in out‐of‐school science experiences are discussed.     

Synthesis of cyclic azobenzene analogues

Reaction of 2,2′-dinitrodibenzyl with lead metal powder in the presence of a basic triethylammonium formate buffer gave a cyclic azoxybenzene, 11,12-dihydrodibenzo[c,g][1,2]diazocine-5-oxide. The latter compound was converted into cyclic azobenzene and analogues (chloro-, bromo-, and cyano-) through subsequent transformations. Hydrolysis of the cyano cyclic azobenzene gave the corresponding carboxylic acid. This carboxylic acid was finally reacted with d-threoninol to give the corresponding amide, which readily undergoes photoisomerization upon illumination with light.     

The temperature‐dependent ballistic performance and the ductile‐to‐brittle transition in polymer networks

The temperature dependence of the ballistic impact performance of a series of transparent polymer networks is evaluated. A systematic series of homogeneous epoxy/propylene‐oxide‐based thermosets, a nanoscale phase‐separated epoxy/dual amine thermoset, and two homogeneous, completely aliphatic materials synthesized via ring‐opening metathesis polymerization are examined. The Vogel temperature (T_o) and the Kauzmann temperature (T_K) are critical parameters for scaling the temperature‐dependent ballistic impact performance of each class of materials. The ductile‐to‐brittle transition temperature in a series of propylene‐oxide amine‐cured epoxies occurs at the material T_K, corresponding to a sharp drop in fracture toughness and ballistic impact performance. Two aliphatic, ring‐opening metathesis polymerized materials are found to exhibit no clear transition from purely ductile to purely brittle behavior, but the temperature dependence is still scaled to a single curve when normalized by T_o. The cooperatively rearranging region (CRR) or the volume of this region is related to the breadth of temperatures over which these materials exhibit purely ductile deformation both quasi‐statically and at higher rates. The temperature‐dependent performance is discussed in the context of the configurational entropy. The breadth of the ductility window is related to the size of the CRR, calculated from calorimetric measurements at the resin T_g. Published 2019. This article is a U.S. Government work and is in the public domainin the USA. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 511–523     

Homogeneous Poisson Structures on Symmetric Spaces

We calculate, in a relatively explicit way, the Hamiltoniansystems that arise from the Evens–Lu construction of homogeneousPoisson structures on both compact- and noncompact-type symmetricspaces. A corollary is that the Hamiltonian system arising inthe noncompact case is isomorphic to the generic Hamiltoniansystem arising in the compact case. In the group case, thesesystems are also isomorphic to those arising from the Bruhat–Poissonstructure on the flag space, and hence, by results of Lu, canbe completely factored.     

Exotic smooth structures on small 4-manifolds with odd signatures

Let M be (2n-1)\mathbbCP²#2n[`(\mathbbCP)]<sup>2</sup>(2n-1)\mathbb{CP}^{2}\#2n\overline{\mathbb{CP}}{}^{2} for any integer n≥1. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structures when M is \mathbbCP<sup>2</sup>#4[`(\mathbbCP)]²\mathbb{CP}{}^{2}\#4\overline {\mathbb{CP}}{}^{2} or 3\mathbbCP²#k[`(\mathbbCP)]²3\mathbb{CP}{}^{2}\#k\overline{\mathbb{CP}}{}^{2} for k=6,8,10.     

Generalizations of Polya's urn Problem

We consider generalizations of the classical Polya urn problem: Given finitely many bins each containing one ball, suppose that additional balls arrive one at a time. For each new ball, with probability p, create a new bin and place the ball in that bin; with probability 1–p, place the ball in an existing bin, such that the probability that the ball is placed in a bin is proportional to $ m^\gamma $, where m is the number of balls in that bin. For p=0, the number of bins is fixed and finite, and the behavior of the process depends on whether is greater than, equal to, or less than 1. We survey the known results and give new proofs for all three cases. We then consider the case p>0. When =1, this is equivalent to the so-called preferential attachment scheme which leads to power law distribution for bin sizes. When >1, we prove that a single bin dominates, i.e., as the number of balls goes to infinity, the probability that any new ball either goes into that bin or creates a new bin converges to 1. When p > 0 and < 1, we show that under the assumption that certain limits exist, the fraction of bins having m balls shrinks exponentially as a function of m. We then discuss further generalizations and pose several open problems.AMS Subject Classification: 05D40, 60C05, 60G20, 68R10, 91C99.     

Transparent and UV-Reflective Photonic Films and Supraballs Composed of Hollow Silica Nanospheres

For an optically transparent, UV-reflective film, hollow silica nanospheres smaller than the visible wavelength (<λ_vis) are prepared and assembled into colloidal glasses, of which interstices are then backfilled with a polymer. The polymer refractive index is matched with the silica shell to minimize backscattering in the visible range, and the average distance between the hollow silica particles is adjusted by tuning the shell thickness to satisfy the interference resonance condition for a UV selective reflection. The resulting composite film shows a strong UV reflection as expected, but it is translucent in visible light due to non-negligible backscattering, which may be caused by large defects or fluctuation of the particle concentration. In order to avoid such backscattering, another polymer is introduced of which the refractive index is matched with the average refractive index of the hollow nanospheres. This allows an optically transparent film that selectively reflects the UV light. Furthermore, spherical aggregates of hollow silica nanospheres called “supraballs” are prepared and their average refractive index is matched with a solvent by adjusting the mixture ratio of water and ethylene glycol, which yields an optically transparent solution, selectively reflecting UV.