Size of a polymer chain in an environment of quenched chains

We perform high‐coordination three‐dimensional (3D) lattice simulations of a single chain of N monomers embedded in matrices of quenched chains, at different concentrations ρ, using pruned‐enriched Rosenbluth sampling. The partition function is well‐described by the expression, , where is a universal constant, and is the concentration dependent lattice connectivity constant. For sufficiently long chains, , we find that the radius of gyration R varies nonmonotonically with ρ; R decreases gradually from its unperturbed dimensions R₀ until , after which it increases relatively rapidly due to repulsion between monomers. Motivated by the similarity in the shape of the curves, and results on Gaussian chains, we successfully superpose all the simulation data onto a single master curve. Finally, we test the relationship , suggested by a Flory‐type scaling model, where ρ_c is the critical percolation threshold, and is a universal constant. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1611–1619     

Variation of the strain rate during CSM nanoindentation of glassy polymers and its implication on indentation size effect

The indentation strain rate is currently assumed to remain unvaried during continuous stiffness measurement (CSM) nanoindentation where is imposed to remain constant. To probe the validity of this assumption for the nanoindentation of glassy polymers, a series of experiments have been performed at different set values on poly(methyl methacrylate) and polycarbonate using CSM technique. It is firstly shown that the actual value changes drastically at shallow indentation depths and it takes a considerable depth, which is material independent, for this parameter to attain a stabilized value. Furthermore, the strain rate is measured directly as the descent rate of the indenter divided by its instantaneous depth ( ), and indirectly via considering the variations of the load and hardness during the test. Both of these approaches reveal that the strain rate is considerably larger at shallow depths, and the depth beyond which it becomes constant is material and ratio dependent. Finally, by considering the relationship between the hardness and strain rate, it is observed that although the strain rate variation alters the hardness, its contribution is not able to justify the observed indentation size effect; hence, other contributing factors for this phenomenon are discussed for their possible effects. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2179–2187     

The “bound wavefunction” on the repulsive excited ( ) state of the HD+ molecule

The time‐independent Schrödinger equation for the HD+ molecule is solved beyond the Born–Oppenheimer (B‐O) approximation. In the adiabatic representation, the wavefunction of the ground vibrational eigenstate is found to contain two parts: One is on the ground ( ) state which is dominant, and the other is on the repulsive excited ( ) state in the range from R = 0.0 to R = 5.0 Bohr. This is because the nonadiabatic coupling between the ground ( ) and excited ( ) states is strong in that region. The influences of the nonadiabatic coupling on the vibrational eigenfunctions are discussed in detail.     

Triplet harvesting in poly(9‐vinylcarbazole) and poly(9‐(2,3‐epoxypropyl)carbazole) doped with CdSe/ZnS quantum dots encapsulated with 16‐(N‐carbazolyl) hexadecanoic acid ligands

Semiconductor quantum dots (QDs) can be used as alternative for transition metal complexes to harvest the nonemissive triplet excitons in organic light‐emitting diodes (OLEDs). In search for a QD‐based OLED material generating blue emission, poly(9‐vinylcarbazole) (PVK) and poly(9‐(2,3‐epoxypropyl) carbazole) (PEPK) are chosen as host for blue‐emitting CdSe/ZnS core/shell QDs. The QDs are encapsulated with 16‐(N‐carbazolyl) hexadecanoic acid (C16), a ligand terminated by a carbazole moiety. As alternative for PVK, PEPK, where the lower molecular weight and less extensive excimer formation could promise a better film formation and more extensive exciton hopping, is explored. The efficiencies of singlet ( ) and triplet ( ) energy transfer to the C16 capped QDs are estimated by combining stationary photoluminescence spectra and fluorescence decays of pristine polymer films with those of polymer films doped with the QDs. At a loading of 30 wt % of the QDs, increases from 12 ± 1% in PVK to 41 ± 2% in PEPK while increases from 37 ± 22% in PVK to 72 ± 48% in PEPK. The investigation of the film morphology by atomic force microscopy confirms that the main factor limiting the triplet transfer efficiency in the PVK matrix is the clustering of the C16 capped QDs. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 539–551     

The H,H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

The one electron systems H, H , and HeH confined by an impenetrable spheroidal cavity are revisited in the frame of the Lagrange‐mesh method. The Born–Oppenheimer approximation where the nuclei are clamped at the foci is considered. Benchmark results of the total energy are obtained as a function of the interfocal distance R and the eccentricity of the cavity . Dipole oscillator strengths are calculated for the molecular ions H and HeH .     

Unusual dynamics of ring probes in linear matrices

We perform Monte Carlo simulations of ring and linear polymers in linear matrices, and investigate the diffusivity of the probes. As the matrix chain length N_m is increased from 10 to 300 monomers, the diffusivity D_l of a linear probe (N_l = 300) decreases monotonically, while that of a ring probe D_r varies non‐monotonically, with a peak around . We perform additional simulations with a single probe molecule ( ) in a linear matrix ( ). The non‐monotonicity in D_r persists even after ring–ring interactions are eliminated. Topology dependent differences in the short‐time dynamics of the probes are observed; unlike linear probes, mean‐squared displacements of ring probes depend on N_m. Primitive path analysis suggests that the difference in dynamics originates from differences in entanglement structure. For linear probes, the degree of entanglement is independent of N_m. For ring probes, we observe two regimes: when N_m is small, the number of threadings decreases as N_m increases, eventually transitioning to a plateau. In the small N_m regime, the change in the degree of entanglement offsets the change in the mobility of the matrix chains, leading to a non‐monotonic variation in D_r. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 169–177     

Influence of the crystallization on the molecular mobility and ionic DC conductivity behaviors of relaxor ferroelectric P(VDF‐TrFE‐CTFE) terpolymers

The dynamics of semicrystalline poly(vinylidene fluoride‐trifluoroethylene‐chlorotrifluoroethylene) (P(VDF‐TrFE‐CTFE)) terpolymers were fully investigated as a function of temperature and frequency, by means of broadband dielectric spectroscopy. Four types of relaxation regimes were observed over the full dielectric spectroscopy, namely (second) relaxation in the sub‐glass state, (segmental dynamics) in the rubbery state, the Curie transition and space charge carrier motion at high temperatures. Constrained segmental dynamics were observed in the terpolymer containing the highest crystalline fraction for which a narrow relaxation time distribution was found. These results indicate a decreasing average size of the cooperative rearranging region over the crystalline fraction. A decrease of the strength index values also implied a more fragile behavior for terpolymers with a higher degree of crystallinity. An exceptional increase in dielectric strength was found as the crystallinity increased. This behavior could be explained by an enhanced interphase (constrained amorphous phase). The Curie transition showed an accelerating relaxation rate for a more fragile terpolymer. Moreover, a motion of the space charge carrier ions was observed in the higher temperature range. Finally, there was evidence that the segmental dynamics in the amorphous phase was responsible for the motion of the space charge carrier ions. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1645–1657     

Enthalpy of fusion of poly(3‐hexylthiophene) by differential scanning calorimetry

The enthalpy of fusion for a perfect, infinite poly(3‐hexylthiophene) (P3HT) crystal () must be known to evaluate the absolute crystallinity of P3HT. This value, however, is still ambiguous as different values have been reported using various experimental techniques. Here, we extrapolate the enthalpy of fusion for extended chain crystals of oligomeric P3HT to infinite molecular weight and obtain a value of 42.9 ± 2 J/g employing differential scanning calorimetry with a correction based on grazing incidence small angle X‐ray scattering data. Also, we define the onset of chain folding within P3HT crystallites at a chain length of 5 Kuhn segments. Knowledge of allows calculation of P3HT percent crystallinity in thin films for applications such as organic field effect transistors and solar cells. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1469–1475     

Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

An accurate semianalytic wavefunction is proposed for the Hookium and two‐electron atoms for varying strength of where is the strength parameter and is coulomb interaction between two electrons. The wavefunction leads to energies that are as accurate as those from the Coupled cluster singles and doubles (CCSD) calculations. Using this wavefunction, we construct the external potential such that the density of the system remains unchanged as is varied. The work thus gives a unified picture of adiabatic connection for these systems based on an easy to use wavefunction and complements the past investigations done in this direction. Using the potential obtained, we explicitly calculate the energy of the corresponding positive ions and show that the chemical potential—calculated as the difference between the energies of the two‐electron system and its positive ion—is equal to the experimental ionization energy and remains unchanged as is varied. Furthermore, using total energies of these systems as a function of , we provide a new perspective into a variety of hybrid functionals.     

Rate Constants for the Gas‐Phase Reactions of Ozone and Nitrate Radicals with the Sesquiterpenes: Valencene and Farnesol

Sesquiterpenes are constituents of a variety of essential oils that are used in flavorings, perfumes, personal care, and cleaning products. Two sesquiterpenes that are commonly used as indoor fragrances are valencene and farnesol. Knowing the reaction rate constants of these chemicals with ozone (O₃) and nitrate radical () is an important factor in determining their fate indoors. In this study, the bimolecular rate constants of , , , and were measured using the relative rate technique at 297 ± 3 K and 1 atm total pressure. Using the rate constants reported here and measured/modeled indoor concentrations of O₃ and (20 ppb and 1 ppt, respectively), pseudo–first‐order‐rate lifetimes , , , and were determined.     

Additivity in kramers pairs symmetry: Multiplets with up to four unpaired electrons

Many fermions Kramers pairs formalism is considered from the prospective of the sum of individual single fermion time‐reversal operators. The obtained many fermions “pseudo Kramers pairs operator” ( ), as well as its square ( ), have formally the same structure as the many fermion spin operators and . Nevertheless, the shape of eigenfunctions with respect to and is different. Herein all Kramers adapted eigenfunctions of for cases of up to four unpaired fermions are compiled, and their properties with respect to further advocated. It will be shown that degeneracy of the multiplets recovers the proper behavior with respect to Pascal's triangle. A projection operator for obtaining the “high spin” Kramers adapted eigenfunctions is suggested. Noncommutation of with spin and angular momentum operators and degeneracy is discussed at last. © 2016 Wiley Periodicals, Inc.     

Geometry of the canonical Van Vleck transformation

Bloch's transformation from the zeroth‐order space for a perturbation problem to the corresponding space of exact eigenvectors, was found as a geometrically defined alternative to the algebraically constructed Van Vleck transformation. Klein's theorem of uniqueness transferred some of this geometrical interpretation to its canonical form . Quite recently Kvaal has taken a large step further by writing as a product of commuting planar rotations, obtained by describing and in terms of certain principal vectors and canonical angles. Kvaal's approach is now developed further, using a new commutation relation which simplifies algebraic manipulations substantially. It allows for a simple definition of an operator for the angle between and which has Kvaal's vectors and angles as eigenvectors and eigenvalues. Klein's theorem is refined in various ways. The impact of the approach on a number of previous results is considered. © 2015 Wiley Periodicals, Inc.     

Synthesis of gradient copolysiloxanes by simultaneous copolymerization of cyclotrisiloxanes and mechanism for kinetics inverse between anionic and cationic ring‐opening polymerization

Trifluoropropylmethylsiloxane–phenylmethylsiloxane gradient copolysiloxanes were synthesized by anionic and cationic ring‐opening polymerization (ROP) of 1,3,5‐tris(trifluoropropylmethyl)cyclotrisiloxane ( ) and phenylmethylcyclotrisiloxane ( ). The analysis of reactivity ratios revealed that the reactivity of toward anionic ROP was higher than that of ; however, exhibited lower reactivity compared with during the cationic ROP. AB and BAB type gradient copolymers were obtained because of a difference in the reactivity of the monomers. The microstructure of copolymers was characterized by ²⁹Si NMR spectroscopy, gel permeation chromatography, and differential scanning calorimetry. Furthermore, the mechanism for kinetics inverse of copolymerization was proposed based on the results of the optimized molecular configuration. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 835–843     

Ruthenium(II) complexes bearing pyridine‐based tridentate and bidentate ligands: catalytic activity for transfer hydrogenation of aryl ketones

Ru(II) complexes of the general formula [RuCl₂(′′)(L)] (1: ′N = N_b, L = MeOH; 2: ′N = N_b, L = CH₃CN; 3: ′N = N_d, L = CH₃CN; 4: ′N = N_p, L = CH₃CN), [Ru(p‐cymene)(_a–b)Cl]Cl (5a: N N_a = 2,2′‐bipyridine; 5b: N N_b = 4,4′‐dimethyl–2,2′‐bipyridine), [Ru(′′)(_a–b)Cl]Cl (6a: ′N = N_b, _a = 2,2′‐bipyridine; 6b: ′N = N_b, _b = 4,4′‐dimethyl‐2,2′‐bipyridine; 7a: ′N = N_d, _a = 2,2′‐bipyridine; 7b: ′N = N_d, _b = 4,4′‐dimethyl‐2,2′‐bipyridine; 8a: ′N = N_p, _a = 2,2′‐bipyridine; 8b: ′N = N_p, _b = 4,4′‐dimethyl‐2,2′‐bipyridine) and [Ru(′′)(_a)Cl]BF₄ (9a: ′N = N_b; _a = 2,2′‐bipyridine) were synthesized from the corresponding [RuCl₂(p‐cymene)]₂ dimer, ′′ and _a–b ligands. The compounds were characterized by elemental analysis, IR and NMR. Complex 9a was studied by X‐ray diffraction, confirming its cationic‐mononuclear [RuCl(_bb)(_a)]⁺ nature. The synthesized Ru(II) complexes (1–8) were employed as catalysts for the transfer hydrogenation of ketones to secondary alcohols in the presence of KOH using 2‐propanol as a hydrogen source at 82°C. The rates of the transfer hydrogenation reactions strongly depended on the type of and ancillary ligands. Copyright © 2012 John Wiley & Sons, Ltd.     

Rovibrational spectra of bounded diatomic molecules

Spectra of a bounded diatomic molecule is studied numerically. Shifted Deng–Fan oscillator potential has been used to model the molecule. The accurate five‐point finite difference method has been used to solve the Schrödinger equation for rovibrational motion of the molecule. The energies of the bound states as well as free states of the molecule have been calculated. In addition, radial matrix elements like , n = 1, 2, and 3 have been calculated. These have been used to calculate the ‐pole static polarizabilities. The variation of bound state energies, matrix elements and ‐pole static polarizabilities with the boundary radius has also been studied. The Stark effect in case of this bounded system has also been investigated.     

and Au6 clusters: Superatomic molecules bearing an SP3‐hybrid Au6 core

The octahedral Au₆ core is explored for the formation of novel SP³‐hybrid superatomic molecules by considering and Au₆ clusters (X= F, Cl, Br, I). The bonding between the four capping atoms and the Au₆ core requires a combination of 1S and 1P shells of the core leading to a set of four equivalent hybrid orbitals. Thus, combining the superatom concept with both the Lewis structure model and VSEPR theory contributes to the rationalization of structure and bonding in metal clusters. For example, our results consider the Au₆ clusters as analogues of the simplest perhalogenated hydrocarbon, CX₄.     

Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules

In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector at the origin of the coordinate system and by the polar vector , assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector . The electronic interaction energy of these molecules in nonordered media is a cross term, coupling and via , one third of the trace of the anapole magnetizability a_αβ tensor, that is, . Both and W^BC have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals. © 2016 Wiley Periodicals, Inc.     

Dealing with the shifted and inverted Tietz–Hua oscillator potential using the J‐matrix method

The tridiagonal J‐matrix approach has been used to calculate the low and moderately high‐lying eigenvalues of the rotating shifted Tietz–Hua (RSTH) oscillator potential. The radial Schrödinger equation is solved efficiently by means of the diagonalization of the full Hamiltonian matrix, with the Laguerre or oscillator basis. Ro–vibrational bound state energies for 11 diatomic systems, namely , , , NO, CO, , , , , , and NO⁺, are calculated with high accuracy. Some of the energy states for molecules are reported here for the first time. The results of the last four molecules have been introduced for the first time using the oscillator basis. Higher accuracy is achieved by calculating the energy corresponding to the poles of the S‐matrix in the complex energy plane using the J‐matrix method. Furthermore, the bound states and the resonance energies for the newly proposed inverted Tietz–Hua IRSTH‐potential are calculated for the H₂‐molecule with scaled depth. A detailed analysis of variation of eigenvalues with n, quantum numbers is made. Results are compared with literature data, wherever possible. © 2015 Wiley Periodicals, Inc.     

Photodetachment of hydrogen negative ion near inelastic surfaces: Arbitrary laser polarization direction

The photodetachment of hydrogen negative ion near different inelastic surfaces is investigated by the semiclassical closed orbit theory for arbitrary laser polarization direction . A two‐term formula of photodetachment cross section consisting of a smooth background term and an oscillatory term is derived. The oscillatory term contains an extra angular factor that describes the dependence of oscillations in total cross section on the laser polarization direction. It is observed that the amplitude of oscillations in cross section reaches maximum at when laser polarization is parallel to the z‐axis and it approaches zero as the laser polarization direction becomes perpendicular to the z‐axis. It is also observed that as the reflection coefficient , which accounts for the inelastic behavior of the surfaces, increases the amplitude of oscillation also increases. © 2015 Wiley Periodicals, Inc.     

Reliability of Orientational Order Parameters Determined from Two‐dimensional X‐ray Diffraction Patterns: A Simulation Study

The orientational order parameter is one of the most important quantities to describe the degree of long‐range orientational ordering of liquid crystals. There are several approaches to experimentally measure this order parameter of liquid crystalline phases but every method includes substantial simplifications and assumptions. We present a simulation‐based approach to elucidate the reliability of the method of Davidson, Petermann and Levelut to measure via 2D X‐ray experiments. We have found that this method slightly underestimates by an absolute value of only 0.05 and thus provides reliable measures of by X‐ray diffraction.