A density functional theory computational study of the role of ligand on the stability of CuI and CuII species associated with ATRP and SET‐LRP

Atom transfer radical polymerization (ATRP) and single electron‐transfer living radical polymerization (SET‐LRP) both utilize copper complexes of various oxidation states with N‐ligands to perform their respective activation and deactivation steps. Herein, we utilize DFT (B3YLP) methods to determine the preferred ligand‐binding geometries for Cu/N‐ligand complexes related to ATRP and SET‐LRP. We find that those ligands capable of achieving tetrahedral complexes with Cu^I and trigonal bipyramidal with axial halide complexes with [Cu^IIX]⁺ have higher energies of stabilization. We were able to correlate calculated preferential stabilization of [Cu^IIX]⁺ with those ligands that perform best in SET‐LRP. A crude calculation of energy of disproportionation revealed that the same preferential binding of [Cu^IIX]⁺ results in increased propensity for disproportionation. Finally, by examining the relative energies of the basic steps of ATRP and SET‐LRP, we were able to rationalize the transition from the ATRP mechanism to the SET‐LRP mechanism as we transition from typical nonpolar ATRP solvents to polar SET‐LRP solvents. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4950–4964, 2007     

Relativistic Dynamics in Basic Chemistry

This paper revisits the historical sequence in which some of the major developments of 20th-century physics occurred, and explores how theories could have turned out differently, if the sequence of developments had been different. It shows how a delay in founding special relativity theory until after (1) at least one puzzling problem in electromagnetic theory could be acknowledged, and (2) sat least some of the experimental observations pertinent to the development of quantum mechanics had become well known, could have resulted in a larger theory that covers both domains in a manner quite different from that of any of the theories we use today. The revised theory dispenses with a separate postulate introducing Planck’s constant h, identifying instead a physical mechanism that implies the constant. Some important aspects of quantum chemistry then follow. Editor, Galilean Electrodynamics, Proceedings of the Natural Philosophy Alliance; Visiting Industry Professor, Tufts University, retired     

Statistical mechanics of warm and cold unfolding in proteins

We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins. Received: 19 March 1998 / Revised and Accepted: 25 May 1998     

A partial differential equation which describes an interatomic surface

In this work we present a first-order partial differential equationwhich defines the topology of single ‘atomic entities’in multiatomic systems. Such an equation, obtained by R. F.W. Bader, is here analysed and discussed from a general mathematicalpoint of view; a method is then proposed for defining the initialor boundary condition. With this contribution we would liketo promote and stimulate a more detailed analysis which goesbeyond practical purposes and basic mathematical analysis inorder to have a deeper understanding of the theory behind theequation and its consequences for practical applications.     

宇宙学常数疑难

当代天文学的一系列观测事实都支持应该存在一个非零的正的宇宙学常数，但是，人们发现当前宇宙学常数值太小，而且宇宙学常数即真空能量密度与现在的物质密度巧合地具有相同的量级，然而现有物理学理论还无法给出合理的解释，因此宇宙学常数问题成为物理学和天文学上最重大的疑难之一。文章综述了近年来宇宙在加速膨胀这一重大的天文发现和宇宙学常数的观测结果以及当前理论物理学在宇宙学常数问题上的一些尝试。     

On Computability of Decaying and Nondecaying States in Quantum Systems with Cantor Spectra

We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection. The decay properties of the states in such systems depend on the nature of the dissection rate that can be characterized in terms of the algebraic number theory. We show that in spite of simplicity of the considered model the computational modeling of nondecaying states is in general impossible.     

Correct Evaluation of the Effect of Transverse Effective Charges on Phonons in AlAs Quantum Dots

An improved valence force field model (VFFM) is suggested to calculate the phonon modes in both bulk specimens and quantum dots (QDs) of AlAs taking account of the effect of transverse effective charges (TCs) correctly.The resultant dispersions of AlAs bulk phonons are in accord better with the results carefully fitted to the experimental data by using 11-parameters rigid-ion model, than those got by ordinary VFFM, especially in the region of near F point. For AlAs QDs, TCs are evaluated bond by bond for each phonon mode of QD and its effect on the change of the force on atoms is taken into account to modify further the phonon spectrum. The frequency spectra and densities of phonon states of different irreducible representations calculated by using improved VFFM are compared with the results of ordinary VFFM. The correct evaluation of the TCs is not only important in calculating the phonon spectrum of both bulk and QD specimens accurately, but is also in the further discussion of the electron-phonon (e-ph) interaction, which can be directly related to TCs of ions in QD.     

一维接触过程的光滑性与稳定性

本文证明了一维接触过程在适当的小扰动下，其极点平稳分布除在临界点λ＿ｃ处外总是光滑的．特别，一维接触过程本身的极点平稳分布关于其参数除在临界点处外总是光滑的．     

广义非简谐振子的多尺度微扰理论

应用多尺度微扰理论到广义非简谐振子, 得到了一阶经典和量子微扰解. 特别是 我们的量子解在极限条件下能方便地转变为经典解, 并且坐标和动量算符的对易 关系的简化十分自然. 与Taylor级数解相比较, 无论是在经典还是在量子解 中频率移动都出现在各阶振动表达式中, 所以多尺度微扰解是弱耦合非简谐振动的较好解法.     

Independence of the brittle–ductile transition from the rubber particle size for impact‐modified poly(vinyl chloride)

A series of acrylic impact modifiers (AIMs) with different particle sizes ranging from 55.2 to 927.0 nm were synthesized by seeded emulsion polymerization, and the effect of the particle size on the brittle–ductile transition of impact‐modified poly(vinyl chloride) (PVC) was investigated. For each AIM, a series of PVC/AIM blends with compositions of 6, 8, 10, 12, and 15 phr AIM in 100 phr PVC were prepared, and the Izod impact strengths of these blends were tested at 23 °C. For AIMs with particle sizes of 55.2, 59.8, 125.2, 243.2, and 341.1 nm, the blends fractured in the brittle mode when the concentration of AIM was lower than 10 phr, whereas the blends showed ductile fracture when the AIM concentration reached 10 phr. It was concluded that the brittle–ductile transition of the PVC/AIM blends was independent of the particle size in the range of 55.2–341.1 nm. When the particle size was greater than 341.1 nm, however, the brittle–ductile transition shifted to a higher AIM concentration with an increase in the particle size. Furthermore, the critical interparticle distance was found not to be the criterion of the brittle–ductile transition for the PVC/AIM blends. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 696–702, 2006