Hierarchical enumeration of Kekulé’s benzenes,Ladenburg’s benzenes,Dewar’s benzenes,and benzvalenes by using combined-permutation representations

The group hierarchy for each skeleton of ligancy 6 is formulated to be: point group (PG \({\varvec{G}}_{\sigma }\)) \(\subseteq \) RS-stereoisomeric group (RS-SIG \({\varvec{G}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) stereoisomeric group (SIG \(\widetilde{{\varvec{G}}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) isoskeletomeric group (ISG \(\widetilde{\widetilde{{\varvec{G}}}}_{\sigma \widetilde{\sigma }\widehat{I}}\) = \({\varvec{S}}^{[6]}_{\sigma \widehat{I}}\)), where we start from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{6h}\) for the Kekulé benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{3h}\) for the Ladenburg benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the Dewar benzene skeleton, or from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the benzvalene skeleton. After these groups are constructed as combined-permutation representations, the calculation of the respective cycle indices with chirality fittingness (CI-CFs) and the introduction of ligand-inventory functions are conducted to give generation functions for 3D-based enumerations (for PGs and RS-SIGs) and 2D-based enumerations (for SIGs and ISGs). The enumeration results are discussed by means of isomer-classification diagrams, in which equivalence classes under enantiomerism (for PGs), RS-stereoisomerism (for RS-SIGs), stereoisomerism (for SIGs), and isoskeletomerism (for ISGs) are illustrated schematically. The implicit connotations of the conventional terms “skeletal isomerism”, “positional isomerism”, and “constitutional isomerism” are discussed, where the effects of the concept of isoskeletomerism are emphasized.     

Quasi-classical trajectory insight into stereodynamics for reaction $$\hbox {He}+\hbox {D}_{2}^{+}\rightarrow \hbox {HeD}^{+}+\hbox {D}$$ with the improved potential energy surface

In this work, a theoretical study on the detailed vector correlation for the reaction \(\hbox {He}+\hbox {D}_{2}^{+}\rightarrow \hbox {HeD}^{+}+\hbox {D}~(\hbox {v}, \hbox {j})\) has been carried out at the collision energy of 23.06 kcal/mol with different rotational states of j \(=\) 0–5 and vibrational states v \(=\) 1–5 by use of the quasi-classical trajectory calculation on an improved potential energy surface. The features of \({{\varvec{P}}}\mathbf{(}{\varvec{\theta }}_{{\varvec{r}}}{} \mathbf{)}\) distributions describing k and \(\mathbf{j}^\prime \) correlations were discussed. In addition, in order to get full knowledge of stereodynamics of the system, the distributions of dihedral angle \({{\varvec{P}}}\mathbf{(}{\varvec{\varphi }}_{{\varvec{r}}}{} \mathbf{)}\) and the polarization-dependent differential cross-sections (PDDCSs) were also reported. It has been demonstrated that both product alignment and polarization are sensitive to the reagent vibrational and rotational number. Furthermore, the dynamics behavior of the reaction is independently changed with respect to j under a certain v except for the product alignment effect \(({\varvec{P}}({\varvec{\theta }}_{{\varvec{r}}}))\), while it exhibits a generally regular trend concerning v when j is invariable.     

Inclusion complexes of $$\hbox{cholesteryl-(}\varepsilon\hbox{-caprolactone})_{\overline{10}}$$ functionalized polymer with γ-cyclodextrin

An inclusion complex (IC) of γ-cyclodextrin with biodegradable \(\hbox{cholesteryl-(}\varepsilon\hbox{-caprolactone})_{\overline{10}}\) \(\hbox{(Chol-(CL)}_{\overline{10}})\) functionalized polymer was prepared by using a general method of mixing solution. The formation of \(\gamma \hbox{-CD-Chol-(CL)}_{\overline{10}}\) IC was determined by Fourier transform infrared (FTIR),¹H-NMR, differential scanning calorimetry (DSC), and wide angle X-ray diffraction (WAXD), respectively. The results indicated that the \(\hbox{oligo}(\varepsilon\hbox{-CL})_{\overline{10}}\) blocks as well as the end cholesteryl moiety of the functionalized polymer were included and covered by γ-CD in a single-stranded mode in the \(\gamma \hbox{-CD-Chol-(CL)}_{\overline{10}}\) ICs. Moreover, the \(\gamma \hbox{-CD-Chol-(CL)}_{\overline{10}}\) ICs had a channel-type crystalline structure similar to that formed between the poly(propylene glycol) (PPG) and γ-CD. Finally, TGA revealed that the ICs had better thermal stability than their free components due to the inclusion complexation.     

Special function representations of the Poisson kernel on hyperbolic spaces

In this paper we compute explicit formulae for the Poisson kernels on the hyperbolic upper half-space \(\mathbf {H}^{n}\) and the Poincaré unit ball \(\mathbf {D}^{n}\). We first construct an associated Legendre function expression for eigenfunctions of the Laplacian and use superposition principle to get a solution for the Laplace equation on \(\mathbf {H}^{n}\). The Poisson kernel on \(\mathbf {D}^{n}\) is obtained from that on \(\mathbf {H}^{n}\) by letting the hyperbolic distance \(\rho =d(w,w')\) \((w,w'\in \mathbf {H}^{n})\) tend to infinity. These Poisson kernels, apart from being interesting in their own right lead to various identities that seem to be novel in the context of special functions.     

Dinormal graphs

A novel type of graph is described, where the graph G has an orientation \({\stackrel{\rightarrow}G}\) and reverse orientation \({\stackrel{\leftarrow}G}\) such that \({G={\stackrel{\rightarrow}G\cup\stackrel{\leftarrow}G}}\) and the adjacency matrices \({A(\stackrel{\rightarrow}G)}\) and \({A(\stackrel{\leftarrow}G)}\) of \({\stackrel{\rightarrow}G}\) and \({\stackrel{\leftarrow}G}\) commute. Some general characterization and examples are given, e.g., for toroidal graphs.     

Solubility Thermodynamics of CyMe$$_{}$$-BTBP in Various Diluents Mixed with TBP

The two organic ligands 6,6′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydrobenzo[1,2,4]triazin-3-yl)[2,2′]bipyridine (CyMe\(_{4}\)-BTBP) and tri-butyl phosphate (TBP) have previously been investigated in different diluents for use within recycling of used nuclear fuel through solvent extraction. The thermodynamic parameters, \(K_{\mathrm{S}}\), \(\Delta C_{p}\), \(\Delta H^{0}\) and \(\Delta S^{0}\), of the CyMe\(_{4}\)-BTBP solubility in three diluents (cyclohexanone, octanol and phenyl trifluoromethyl sulfone) mixed with TBP have been studied at 288, 298 and 308 K, both as pristine solutions and pre-equilibrated with 4 mol\(\cdot \)L\(^{-1}\) nitric acid. In addition, the amount of acid in the organic phase and density change after pre-equilibration have been measured. The solubility of CyMe\(_{4}\)-BTBP increases with an increased temperature in all systems, especially after acid pre-equilibration. This increased CyMe\(_{4}\)-BTBP solubility after pre-equilibration could be explained by acid dissolution into the solvent. Comparing the \(\Delta H^{0}\) and \(\Delta S^{0}\) calculated using \(\Delta C_{p}\) with the same parameters derived from a linear fit indicates temperature independence of all three thermodynamic systems. The change in enthalpy is positive in all solutions.     

Nested wreath groups and their applications to phylogeny in biology and Cayley trees in chemistry and physics

Nested wreath product groups arise from looped or recursive structures that contain repeated copies of the same structure one within the other. Phylogeny trees in biology, Cayley trees, Bethe lattices, NMR graphs of non-rigid molecules, ammoniated ammonium ions are all examples of structures that exhibit such nested wreath product automorphism groups. We show that the conjugacy classes, irreducible representations and character tables of these nested group structures can be generated using multinomial generating functions cast in terms of matrix types that can be simplified into generalized cycle type polynomials. The nested wreath product groups rapidly increase in orders, for example, a simple wreath product group \(\hbox {S}_{7}[\hbox {S}_{7}]\) consists of \((7!)^{8}\) or \(4.1633\times 10^{23}\) operations, 481,890 conjugacy classes, spanning a 481,891 \(\times \) 481,891 character table that would occupy 232,217,972 pages. We have obtained powerful recursive relations for the conjugacy classes, character tables and the orders of various conjugacy cases of any nested wreath product \(\{[\hbox {S}_{\mathrm{n}}]\}^{\mathrm{m}}\) or \(\hbox {S}_{\mathrm{n}}[\hbox {S}_{\mathrm{n}}[\hbox {S}_{\mathrm{n}}{\ldots }.[\hbox {S}_{\mathrm{n}}]]{\ldots }.]\) with order \(\left( {n!}\right) ^{a_m},\,\hbox {a}_{\mathrm{m}}=(\hbox {n}^{\mathrm{m}}-1)/(\hbox {n}-1)\). We have obtained the character tables of phylogenetic trees of any order, character tables of Cayley trees of degrees 3 and 4 and for Cayley trees of larger degrees, we have derived exact analytical expressions for the conjugacy classes and IRs for up to \(\{[\hbox {S}_{7}]\}^{\mathrm{m}}\) with order \((7!)^{137257}\) for \(\hbox {m}=7\). Applications to colorings of phylogenic trees in biology are considered.     

Volumetric Investigations on Molecular Interactions of Glycine/<Emphasis Type="SmallCaps">l</Emphasis>-alanine in Aqueous Citric Acid Solutions at Different Temperatures

Apparent molar volumes \((\phi_{V})\) of glycine/l-alanine in water and in aqueous citric acid (CA) solutions of varying concentrations, i.e. (0.05, 0.10, 0.20, 0.30, 0.40 and 0.50) mol·kg^?1 were determined from density measurements at temperatures T?=?(288.15, 298.15, 308.15, 310.15 and 318.15) K and at atmospheric pressure. Limiting partial molar volumes \((\phi_V^{\text{o}})\) and their corresponding partial molar volumes of transfer \((\Delta_{\text{tr}} \phi_{V} )\) have been calculated from the \(\phi_{V}\) data. The negative \(\Delta_{\text{tr}} \phi_{V}\) values obtained for glycine/l-alanine from water to aqueous CA solutions indicate the dominance of hydrophilic–hydrophobic/hydrophobic–hydrophilic and hydrophobic–hydrophobic interactions over ion/hydrophilic–dipolar interactions. Further, pair and triplet interaction coefficients, i.e. \((V_{\text{AB}} )\;{\text{and}}\; (V_{\text{ABB}} )\) along with hydration number \((n_{\text{H}} )\) have also been calculated. The effect of temperature on the volumetric properties of glycine/l-alanine in water and in aqueous CA solutions has been determined from the limiting partial molar expansibilities \((\partial \phi_{V}^{\text{o}} /\partial T)_{p}\) and their second-order derivative \((\partial^{2} \phi_{V}^{\text{o}} /\partial T^{2} )_{{P}}\). The apparent specific volumes \((\nu_{\phi} )\) for glycine and l-alanine tend to approach sweet taste behavior both in the presence of water and in aqueous CA solutions. The \(\nu_{\phi}\) values for glycine/l-alanine increase with increase in concentration of CA at all temperatures studied. This reveals that CA helps in enhancing the sweet taste behavior of glycine/l-alanine which also supports the dominance of hydrophobic–hydrophobic interactions.     

Symmetry-itemized enumeration of RS-stereoisomers of allenes. I. The fixed-point matrix method of the USCI approach combined with the stereoisogram approach

After the RS-stereoisomeric group \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) of order 16 has been defined by starting point group \(\mathbf{D}_{2d}\) of order 8, the isomorphism between \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) and the point group \(\mathbf{D}_{4h}\) of order 16 is thoroughly discussed. The non-redundant set of subgroups (SSG) of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) is obtained by referring to the non-redundant set of subgroups of \(\mathbf{D}_{4h}\) . The coset representation for characterizing the orbit of the four positions of an allene skeleton is clarified to be \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}(/\mathbf{C}_{s\widetilde{\sigma }\widehat{I}})\) , which is closely related to the \(\mathbf{D}_{4h}(/\mathbf{C}_{2v}^{\prime \prime \prime })\) . According to the unit-subduced-cycle-index (USCI) approach (Fujita, Symmetry and combinatorial enumeration of chemistry. Springer, Berlin 1991), the subduction of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}(/\mathbf{C}_{s\widetilde{\sigma }\widehat{I}})\) is examined so as to generate unit subduced cycle indices with chirality fittingness (USCI-CFs). Then, the fixed-point matrix method of the USCI approach is applied to the USCI-CFs. Thereby, the numbers of quadruplets are calculated in an itemized fashion with respect to the subgroups of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) . After the subgroups of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) are categorized into types I–V, type-itemized enumeration of quadruplets is conducted to illustrate the versatility of the stereoisogram approach.     

Vibratio nal assig nme nts,co nformatio nal a nalysis,a nd molecular structures of $$\left[ {\text{C}_{\text{ n}} \text{mim}} \right]\left[ {\text{NTF}_{\text{2}} } \right]$$C nmimNTF2 ( n = 2, 4, 6, a nd 8) imidazolium-based io nic liquids: a combi ned experime ntal a nd qua ntum chemical approach

This work is aimed at providing physical insights about the interactions of cations, anion, and ion pairs of four imidazolium-based ionic liquids of \(\left[ {{\text{C}}_{\text{n}} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) with varying alkyl chain lengths (n = 2, 4, 6, and 8) using both DFT calculations and vibrational spectroscopic measurements (IR absorption and Raman scattering) in the mid- and far regions. The calculated Mulliken charge distributions of \(\left[ {{\text{C}}_{\text{n}} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) ion pairs indicate that hydrogen-bonding interactions between oxygen and nitrogen atoms (more negative charge) on \(\left[ {{\text{NTF}}_{2} } \right]^{ - }\) anion and the hydrogen atoms (more positive charge) on the imidazolium ring play a dominating role in the formation of ion pair. Thirteen stable conformers of \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) were optimized. According to our results, the strongest and weakest hydrogen bonds were existing in \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) and \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), respectively. A redshift of 290, 262, 258, and 257 cm^?1 has been observed for cations involving \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]^{ + }\), \(\left[ {{\text{C}}_{4} {\text{mim}}} \right]^{ + }\),\(\left[ {{\text{C}}_{6} {\text{mim}}} \right]^{ + }\), and stretching vibrations of \({\text{C}}12{-}{\text{H}}3\), respectively. By increasing the chain length, the strength of hydrogen bonds decreases as a result of \({\text{C}}12{-}{\text{H}}3\) bond elongation and less changes are observed in stretching vibrations of \({\text{C}}12{-}{\text{H}}3\) compared to the free cations. To the best of our knowledge, this research is the first work which reports the far-IR of \(\left[ {{\text{C}}_{4} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), \(\left[ {{\text{C}}_{6} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), and \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) and the mid-IR of \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\).     

Compatibility of activity coefficients estimated experimentally and by Pitzer equations for the assessment of seawater pH

Calibration of pH meters is usually performed with reference pH buffer solutions of low ionic strength, I ≤ 0.1 mol kg^?1. For seawater pH measurements (I ≈ 0.7 mol kg^?1), calibration buffers in high ionic strength matrix are required. The Harned cell, in association with the Nernst equation and a model for estimating the chloride ion activity coefficient, \(\gamma_{{{\text{Cl}}^{ - } }} ,\) is the basis of the primary method for pH assignment to reference pH buffers. The semi-empirical Pitzer model is, in principle, adequate to estimate \(\gamma_{{{\text{Cl}}^{ - } }}\) of complex solutions, namely seawater. Nevertheless, no assessment of the validity of the model for this matrix is known to the authors. This work aims at estimating the adequacy of the Pitzer model by assessing the metrological compatibility of mean activity coefficients, in this case \(\gamma_{ \pm } = \sqrt {\gamma_{{{\text{H}}^{ + } }} \gamma_{{{\text{Cl}}^{ - } }} }\) estimated experimentally with the Harned cell, \(\gamma_{ \pm }^{\text{Exp}} ,\) and using the Pitzer model, \(\gamma_{ \pm }^{\text{Ptz}}\). The measurement uncertainty considered in the compatibility test was estimated using the bottom-up approach, where components were combined by the numerical Kragten method after checking its adequacy. The compatibility of the estimated \(\gamma_{ \pm }\) was assessed for solutions with increasing complexity and an ionic strength of 0.67 mol kg^–1. \(\gamma_{ \pm }^{\text{Exp}}\) and \(\gamma_{ \pm }^{Ptz}\) are metrologically compatible for a confidence level of 95 % where the relative standard uncertainty of their difference ranged from 1.1 % to 3.1 % in all chloride solutions to approximately 6.3 % when sodium sulfate was also present. This led to assume the validity of the Pitzer model equations to estimate \(\gamma_{{{\text{Cl}}^{ - } }} ,\) required to define reference pH values of buffer solutions with high ionic strength.     

The Radial Distribution of Ions and Electrons in RF Inductively Coupled H<Subscript>2</Subscript>/T<Subscript>2</Subscript>B Plasmas

A glow discharge polymer (GDP) was fabricated using trans-2-butene (T₂B) and hydrogen (H₂) via a plasma-enhanced chemical vapor deposition (PECVD) system. The uniformity of the GDP films was significantly affected by the radial distribution of the H₂/T₂B plasma parameters. The plasma properties while discharging by a multi-carbon gas source of mixed H₂/T₂B were investigated during the GDP deposition process. The main positive ions and ion energy distributions in inductively coupled H₂/T₂B plasmas were analyzed by energy-resolved mass spectrometer (MS), and the electron density and the effective electron temperature were mainly analyzed using a Langmuir probe. The MS results show that the main positive ions in the plasmas are \({\text{C}}_{ 2} {\text{H}}_{ 4}^{ + }\), \({\text{C}}_{ 2} {\text{H}}_{ 6}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 3}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 6}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 8}^{ + }\), \({\text{C}}_{ 4} {\text{H}}_{ 5}^{ + }\), \({\text{C}}_{ 4} {\text{H}}_{ 1 0}^{ + }\), \({\text{C}}_{ 5} {\text{H}}_{ 5}^{ + }\), and \({\text{C}}_{ 5} {\text{H}}_{ 7}^{ + }\) with mass-to-charge ratios (m/e) of 28, 30, 39, 42, 44, 53, 58, 65, and 67, respectively. For a normalized ion intensity, the relative intensities of saturated CH ions increase with increasing radial distance, while the unsaturated CH ions decrease with increasing radial distance. The ion energy distribution of \({\text{C}}_{ 2} {\text{H}}_{ 6}^{ + }\) (m/e = 30) presents a bimodal structure. Additionally, both the electron density and the effective electron temperature decrease with increasing radial distance.     

On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)

In our recent works (R. Szmytkowski, J. Phys. A 39:15147, 2006; corrigendum: 40:7819, 2007; addendum: 40:14887, 2007), we have investigated the derivative of the Legendre function of the first kind, P _ν(z), with respect to its degree ν. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, \({P_{\nu}^{\pm m}(z)}\), with respect to the degree ν, for \({m \in \mathbb{N}}\). At first, we establish several contour-integral representations of \({\partial P_{\nu}^{\pm m}(z)/\partial\nu}\). They are then used to derive Rodrigues-type formulas for \({[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}}\) with \({n \in \mathbb{N}}\). Next, some closed-form expressions for \({[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}}\) are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, \({Q_{n}^{\pm m}(z)}\); the explicit representations are suitable for use for numerical purposes in various regions of the complex z-plane. Finally, the derivatives \({[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}, [\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}}\) and \({[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}}\), all with m > n, are evaluated in terms of \({[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}}\). The present paper is a complementary to a recent one (R. Szmytkowski, J. Math. Chem 46:231, 2009), in which the derivative \({\partial P_{n}^{\mu}(z)/\partial\mu}\) has been investigated.     

Schrödinger equations on $${\mathbb{R}^3 \times \mathcal{M}}$$ with non-separable potential

We consider the problem of defining the Schrödinger equation for a hydrogen atom on \({\mathbb{R}^3 \times \mathcal{M}}\) where \({\mathcal{M}}\) denotes an m dimensional compact manifold. In the present study, we discuss a method of taking non-separable potentials into account, so that both the non-compact standard dimensions and the compact extra dimensions contribute to the potential energy analogously to the radial dependence in the case of only non-compact standard dimensions. While the hydrogen atom in a space of the form \({\mathbb{R}^3 \times \mathcal{M}}\) , where \({\mathcal{M}}\) may be a generalized manifold obeying certain properties, was studied by Van Gorder (J Math Phys 51:122104, 2010), that study was restricted to cases in which the potential taken permitted a clean separation between the variables over \({\mathbb{R}^3}\) and \({\mathcal{M}}\) . Furthermore, though there have been studies on the Coulomb problems over various manifolds, such studies do not consider the case where some of the dimensions are non-compact and others are compact. In the presence of non-separable potential energy, and unlike the case of completely separable potential, a complete knowledge of the former case does not imply a knowledge of the latter.     

Redox behavior of $${\text{VO}}^{2 + } / {\text{VO}}_{2}^{ + }$$ as a simulant of $${\text{NpO}}_{2}^{ + } / {\text{NpO}}_{2}^{2 + }$$NpO2+/NpO22+ in boiling nitric acid solution

To evaluate the redox behavior of \({\text{VO}}^{2 + } / {\text{VO}}_{2}^{ + }\) as a simulant of \({\text{NpO}}_{2}^{ + } / {\text{NpO}}_{2}^{2 + }\) in boiling nitric acid solution, i.e., typical operating conditions for nuclear fuel reprocessing plants, oxidation rate measurements for VO²⁺ in boiling and non-boiling nitric acid solutions, thermodynamic calculations, and kinetic calculations were performed. The results indicated that the apparent oxidation rate of VO²⁺ to \({\text{VO}}_{2}^{ + }\) is accelerated by a decrease in \({\text{NO}}_{2}^{ - }\) and HNO₂ concentrations owing to the boiling phenomena of nitric acid solution.     

Analysis on the removal of ammonia nitrogen using peroxymonosulfate activated by nanoparticulate zero-valent iron

Nanoparticulate zero-valent iron (Fe⁰) was used to activate peroxymonosulfate (PMS) to remove low concentration of ammonia nitrogen in the aqueous system. The removal process was investigated under various conditions. It was indicated that the removal of \({\text{NH}}_{4}^{ + }\) followed the pseudo-first-order kinetic model for the initial reactions. The removal rate increased with the ascending of pH and Fe⁰ dosage, while declined with the ascent of initial \({\text{NH}}_{4}^{ + }\) concentration. The existence of nitrogenous compounds would inhibit the reactions, especially for the compounds with carboxyl structure functional groups. The identification of free radical proved that \(\cdot {\text{SO}}_{4}^{ - }\) is the main radical in Fe⁰/PMS for the removal of ammonia nitrogen. The inorganic products including \({\text{NO}}_{2}^{ - }\), \({\text{NO}}_{3}^{ - }\), Fe²⁺ and Fe³⁺ were detected with the detailed mechanism proposed. The results demonstrated that Fe⁰/PMS process was more effective on ammonia removal compared to single Fe⁰, Fe⁰/persulfate and Fe⁰/H₂O₂. This study proposed a cost-effective process for \({\text{NH}}_{4}^{ + }\) removal at very low concentration of sulfate radicals.     

Base hydrolysis of tris(3-(2-pyridyl)-5,6-bis(4-phenyl sulphonic acid)-1,2,4-triazine)iron(II) in aqueous,SDS and CTAB media: kinetic and mechanistic study

The kinetics and mechanism of base hydrolysis of tris(3-(2-pyridyl)-5,6-bis(4-phenyl sulphonic acid)-1,2,4-triazine)iron(II), \({\text{Fe}}({\text{PDTS}})_{3}^{4 - }\) have been studied in aqueous, sodium dodecyl sulphate (SDS) and cetyltrimethyl ammonium bromide (CTAB) media at 25, 35 and 45 °C under pseudo-first-order conditions, i.e. \(\left[ {\text{OH}^{ - } } \right]\) ? \({\text{Fe}}({\text{PDTS}})_{3}^{4 - }\). The reaction is first order each in \({\text{Fe}}({\text{PDTS}})_{3}^{4 - }\) and hydroxide ion. The rate increases with increasing ionic strength in aqueous and SDS media, whereas this parameter has little effect in CTAB. In SDS medium, the rate-determining step involves the reaction between \(\left[ {\text{OH}^{ - } } \right]\) and \({\text{Fe}}({\text{PDTS}})_{3}^{4 - }\), whereas in CTAB medium, it involves reaction between a neutral ion pair, {\({\text{Fe}}({\text{PDTS}})_{3}^{4 - }\)·4CTA⁺} and \(\left[ {\text{OH}^{ - } } \right]\) ions. The specific rate constants and thermodynamic parameters (E _a, ΔH ^#, ΔS ^# and ΔG _35°C ^# ) have been evaluated in all three media. The near equal values of ΔG _35°C ^# obtained in aqueous and SDS media suggest that these reactions occur essentially by the same mechanism. Slightly lower ΔG _35°C ^# values in CTAB medium can be attributed to a higher concentration of reactants in the Stern layer. The reaction is inhibited in SDS medium but catalysed in CTAB. The former can be attributed to the anionic surfactant creating more repellent space between the reactants. Catalysis in CTAB medium is ascribed to electrophilic and hydrophilic interactions between hydroxide ion/substrate with the cationic Stern layer, resulting in increased local concentrations of both reactants.