Dependence of the Constant of the Mark‐Houwink Equation under Theta Conditions on the Bulk of Substituents for Hydrocarbon Polymers

The logarithm of the constant K _θ in the Mark‐Houwink equation under theta conditions was found to be proportional to the molar volume of the substituent groups in the case of vinyl‐ and vinylidene‐type hydrocarbon polymers. This simple empirical relation can be used to estimate K _θ for such polymers.     

New biocidal metal complexes of bisphenol-A formaldehyde polymer containing piperazine

The polymeric ligand (BFP) was synthesized by condensation of bisphenol-A, formaldehyde, and piperazine in alkaline medium at 70–80°C. The polymer–metal complexes were synthesized by the reaction of BFP with Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) acetates in 1?:?0.5 (ligand?:?metal) molar ratio. All the synthesized polymers were characterized by elemental, spectral (infrared, ¹H-NMR, and UV-Vis), magnetic moment measurements, and thermal (TGA) analysis. The ligand-field and nephelauxetic parameters have been determined from UV-Vis spectra using ligand-field theory. Elemental analyses indicate the association of water with metal for Mn(II), Co(II), and Ni(II), which is also supported by TGA. The antimicrobial activities of the synthesized polymers were studied by agar well diffusion methods against Bacillus subtilis, Bacillus megaterium, Staphylococcus aureus, Escherichia coli, Salmonella typhi, Pseudomonas aeruginosa, and Shigella boydii. The antimicrobial activity and thermal stability of Cu(II)–polymer were higher than the other polymer–metal complexes due to the higher stability constant of Cu(II).     

On a discretization process of fractional-order Logistic differential equation

In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos.     

Nanoporous polyimide film from poly(ethylene glycol-co-imide) using a one-step heat calcination process

Polyamic acid (PAA) made from 3,3, 4,4-biphenyltetracarboxylic dianhydride and 4,4-diaminodiphenyl ether was synthesized and used as the backbone of nanoporous polyimide. Thermally labile polyethylene glycol (PEG) at 10, 20 or 30 wt% was introduced to the end group of PAA. Self-assembled PAA-b-PEG micelle-like nanoparticles could be formed as a result of amphiphilic characteristics of hydrophobic PAA and hydrophilic PEG. Thermal imidization and degradation of spin-coated amphiphilic PAA-b-PEG film were performed sequentially through one-step heat treatment to obtain polyimide film with nanopores. Pore sizes decreased with increasing amount of PEG block and their dielectric constants decreased from 2.71 ± 0.13 to 2.38 ± 0.11.     

Heat-resistant and soluble fluorinated poly(amide imide)s based on non-coplanar ortho-linked diimide-dicarboxylic acid

A series of novel fluorinated heat-resistant poly(amide imide)s (PAIS) based on non-coplanar diimide-diacid monomer (DIDA) were synthesized and characterized. The poly(amide imide)s were obtained in high yields and possessed inherent viscosities in the range of 0.47-0.91 dL g⁻¹. All of the polymers were amorphous in nature, showed outstanding solubility and could be readily soluble in common organic solvents such as N,N-dimethylacetamide, N-methyl-2-pyrrolidinoned, dimethyl sulfoxide, N,N-dimethylformamide, pyridine and tetrahydrofuran. Glass transition temperatures were in the range of 221-263 °C, as determined by differential scanning calorimetry. Degradation temperatures for 10% weight loss occurred all above 520 °C and char yields was more than 50% at 700 °C in nitrogen atmosphere. Moreover, these PAIs possessed low refractive indexes (n = 1.58-1.59), birefringence (Δn = 0.008-0.013), and dielectric constants (? ≈ 2.5) due to the trifluoromethyl pendent groups and ortho-catenated aromatic rings that interrupt chain packing and increase free volume.     

Deletion and contraction identities for the resistance values and the Kirchhoff index

We establish identities, which we call deletion and contraction identities, for the resistance values on an electrical network. As an application of these identities, we give an upper bound to the Kirchhoff index of a molecular graph. Our upper bound, expressed in terms of the set of vertices and the edge connectivity of the graph, improves previously known upper bounds. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Direct dynamics study on mechanism and kinetics of the biradical self‐reaction of HOO

A theoretical study of the mechanism and the kinetics for the hydrogen abstraction reaction of the biradical hydroperoxy radical has been presented at the CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G(d,p) level of theory. Our theoretical calculations suppose a stepwise mechanism involving the formation of a postreactant complex in the triplet and singlet entrance channels. Four transition states of the six‐membered chain complexes (³TS1 and ¹TS1) and six‐membered ring complexes (³TS2 and ¹TS2) are located at the high dual level CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G(d,p) method. The rate constants of Path 1 ～ Path 4 at the CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G (d,p) level are calculated by means of the conventional transition state theory (TST) and canonical variational TST without and with small‐curvature tunneling (SCT) correction within the temperature range of 200–2,500 K. The calculated results show that the triplet channel is the dominating reaction channel and Path 2 is found to be the most favorable pathway. The rate constants of Path 2 are in good agreement with the experimental values at the experimentally measured temperatures. Moreover, the variational effect is not obvious in the low temperature range but is not neglectable in the high temperature range. The SCT plays an important role particularly in the low temperature range. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Spectrophotometric determination of the formation constants of some transition metal cations with a new synthetic Schiff base in dichloromethane and chloroform using rank annihilation factor analysis

The complex formation between a new synthesized Schiff base and the cations Ni²⁺, Co²⁺, Cu²⁺, Zn²⁺ in dichloromethane (DCM) and chloroform solutions was investigated spectrophotometrically using rank annihilation factor analysis (RAFA). The results of mole ratio plots and continuous variation data show the stoichiometry of complexation were found to be 1:1, and 2:1 metal ion to ligand. The stoichiometry was obtained as 1:1 metal ion to ligand ratio for Co²⁺, Ni²⁺ and Zn²⁺ in chloroform and 2:1 for Cu²⁺. In DCM the stoichiometry was obtained as 1:1 for Co²⁺ and 2:1 for Ni²⁺ and Zn²⁺ and a consecutive 2:1 metal ion to ligand ratio was obtained for Cu²⁺. Formation constants of these complexes were estimated by application of RAFA on spectrophotometric data. In this process the contribution of ligand was removed from the absorbance data matrix when the complex stability constant acts as an optimizing object and simply combined with the pure spectrum of the ligand, the rank of the original data matrix can be reduced by one by annihilating the information of the ligand from the original data matrix.     

Effect of ammonia,ammonia-water,and sulfuric acid on the HO2 + HO2 → H2O2 + 3O2 reaction in troposphere: Competition between stepwise and one-step mechanisms

A detailed theoretical study on the reaction mechanisms for the formations of H₂O₂ + ³O₂ from the self-reaction of HO₂ radicals under the effect of NH₃, H₃N···H₂O, and H₂SO₄ catalysts was performed using the CCSD(T)/CBS//M06-2X/aug-cc-pVTZ method. The rate constant was computed using canonical variational transition state theory (CVT) with small curvature tunneling (SCT). Our results indicate that NH₃-, H₃N···H₂O-, and H₂SO₄-catalyzed reactions could proceed through both one-step and stepwise routes. Calculated rate constants show that the catalyzed routes in the presence of the three catalysts all prefer stepwise pathways. Compared to the catalytic efficiency of H₂O, the efficiencies of NH₃, H₃N···H₂O, and H₂SO₄ are much lower due to their smaller relative concentrations. The present results have provided a definitive example of how basic and acidic catalysts influence the atmospheric reaction of HO₂ + HO₂ → H₂O₂ + ³O₂. These results further encourage one to consider the effects of basic and acidic catalysts on the related atmospheric reactions. Thus, the present investigation should have broad implications in the gas-phase reactions of the atmosphere.