Diffusion-controlled reaction. VI. Radiation graft polymerization of styrene to polyethylene

The radiation graft polymerization of styrene to polyethylene was studied under diffusion-controlled conditions of radiation intensity I, monomer concentration M₁, and polymer sample thickness L. The results of the present study together with previous work under diffusion-free conditions verify our theoretical model for the diffusion-controlled reaction. The grafting rate is inverse first order in L for diffusion-controlled reaction and independent of L for diffusion-free reaction. The order of dependence of grafting rate on radiation intensity for diffusion-controlled reaction is one-half that for diffusion-free reaction. Diffusion control leads to a decrease in the order of dependence of grafting rate on monomer concentration. The decrease is greater than theoretically predicted; possible reasons for this effect are described.     

Classical kinetic energy,quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson’s stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsäcker term and an (N?1)-electron kinetic correlation term. We further show that the Weizsäcker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. We then write the N-electron classical kinetic energy as the sum of the (one-electron) classical kinetic energy and another (N?1)-electron kinetic correlation term. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsäcker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase, and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases. Finally, we underline that, although our aim in this paper is conceptual rather than practical, our results are potentially useful for the construction of improved kinetic-energy functionals.     

BRANCHING PATHWAYS IN THE PHOTOCYCLE OF BACTERIORHODOPSIN

Abstract— The pulsed laser photolysis of light-adapted bacteriorhodopsin (BR₅₇₀) is carried out over the temperature range between 25°C and—92°C in neutral and alkaline water-glycerol solutions. The results arc indicative of considerable complexity, introduced by two temperature dependent branching reactions associated with the intermediates K₆₁₀, L₅₅₀ and M₄₁₂, of the BR₅₇₀ photocycle. (a) At relatively low temperatures the primary photoproduct K-₆₁₀ equilibrates with a blue-shifted species, K_p. Both K₆₁₀ and the new intermediate subsequently decay into another species, K'_r, in a process which competes with the formation of L₅₅₀. Finally, K'_p converts very slowly to L₅₅₀. This branched pathway delays the formation of L₅₅₀ and thus of M₄₁₂, without affecting the final yield of either species, (b) A thermal back-reaction regenerating BR₅₇₀ takes place at the stage of L₅₅₀, inhibiting the formation of M₄₁₂. The reaction which also predominates at low temperatures, is relatively inefficient at high pH when the forward L₅₅₀→ M₄₁₂ step is highly catalyzed. It is the superposition of both branching mechanisms, (a) and (b), which accounts for the complex effects of temperature and pH on the photo-cycle of BR₅₇₀. Mechanism (b) is accounted for by a molecular scheme in which deprotonation of a tyrosine moiety at the stage of L₅₅₀ constitutes a prerequisite for deprotonation of the retinal-lysine schiff-base as required for forming M₄₁₂. This scheme appears to be directly related to the proton pump. Mechanism (a) introduces additional complexity in the photocycle at low temperatures but its molecular aspects are still unclear.     

Dependence of viscosity of concentrated polymer solutions upon molecular weight and concentration

Molecular weight M and concentration c dependencies of the zero-shear viscosity (η) were measured over wide ranges of M and c for concentrated solutions of linear and branched poly(vinyl acetate) as well as of polystyrene under θ conditions. The log η versus log M and log η versus log c curves for a given system can be superposed by the horizontal shift along the abscissa, giving smooth master curves. From the shift factors the ratio of two exponents β and α, which appear in the following equation, can be evaluated: η = K′(cρ)^αM^β, where ρ is the density of the solution and K′ is a constant at constant temperature. The evaluated values of β/α for the systems under θ conditions are equal to or very close to 0.50 as was anticipated from the previous work. The above superposition method was also applied to available viscosity data, and it was found that β/α had a good correlation with a in [η] = KM^a. This indicates that the individual molecules in concentrated solutions maintain the same individuality as in dilute solutions, and might be a positive support to the packed sphere model proposed previously by the authors. The effect of solvent on the molecular weight and the concentration dependencies of viscosity was also discussed.     

Diffusion-controlled reaction. VI. Radiation graft polymerization of 4-vinylpyridine to polyethylene

The radiation-initiated graft polymerization of 4-vinylpyridine to high-density polyethylene was studied over a wide range of reaction conditions of radiation intensity I, monomer concentration M₁, and polymer film thickness L. The conditions included both diffusion-free and diffusion-controlled graft polymerizations. The results corroborate our previous theoretical predictions on the effect of I, M₁, and L on the experimental grafting rate. The grafting rate is inverse first order in L for diffusion-controlled reaction and independent of L for diffusion-free reaction. The dependence of grafting rate on radiation intensity decreases from 1/2 to 1/4 order for diffusion-controlled reaction. Diffusion control results in a decrease in the dependence of rate on monomer concentration. The observed decrease is somewhat greater than theoretically predicted.     

Ten-Electron Central Field Problem: An Inhomogeneous Electron Liquid

Abstract

Recent work has been carried out on the exchange energy density epsive;_x(r) of a ten-electron atomic ion in the (bare Coulomb) limit of large atomic number Z [Howard, I. A. et al (2000). Phys. Rev. A, 62, 062512]. This analytical study of epsive; x(r) was made possible by the existence of a closed form of the first-order (idempotent) density matrix (IDM).

Here, some generalizations are effected to a central potential energy V(r) which (a) localizes the ten electrons and (b) yields closed K and L shells for these ten electrons occupying the lowest eigenstates with spin compensation. In particular, it is shown that p-shell properties alone determine the IDM in this example of a confined inhomogeneous electron liquid.     

Density functional theory study of calix[4]arene‐N‐azacrown‐5, calix[4]arene‐N‐phenyl‐azacrown‐5, and their complexes with alkali‐metal cations: Na+, K+, and Rb+

Theoretical studies of 1,3‐alternate‐25,27‐bis(1‐methoxyethyl)calix[4]arene‐azacrown‐5 ( L₁ ), 1,3‐alternate‐25,27‐bis(1‐methoxyethyl)calix[4]arene‐N‐phenyl‐azacrown‐5 ( L₂ ), and the corresponding complexes M⁺/ L of L₁ and L₂ with the alkali‐metal cations: Na⁺, K⁺, and Rb⁺ have been performed using density functional theory (DFT) at B3LYP/6‐31G* level. The optimized geometric structures obtained from DFT calculations are used to perform natural bond orbital (NBO) analysis. The two main types of driving force metal–ligand and cation–π interactions are investigated. The results indicate that intermolecular electrostatic interactions are dominant and the electron‐donating oxygen offer lone pair electrons to the contacting RY* (1‐center Rydberg) or LP* (1‐center valence antibond lone pair) orbitals of M⁺ (Na⁺, K⁺, and Rb⁺). What's more, the cation–π interactions between the metal ion and π‐orbitals of the two rotated benzene rings play a minor role. For all the structures, the most pronounced changes in geometric parameters upon interaction are observed in the calix[4]arene molecule. In addition, an extra pendant phenyl group attached to nitrogen can promote metal complexation by 3D encapsulation greatly. In addition, the enthalpies of complexation reaction and hydrated cation exchange reaction had been studied by the calculated thermodynamic data. The calculated results of hydrated cation exchange reaction are in a good agreement with the experimental data for the complexes. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A method for the construction of orthogonal spin eigenfunctions

A method for the construction of the essentially idempotent and Hermitian diagonal elements of the matric algebra of the permutation group S_n is proposed. For the irreducible representation [λ] = [λ₁, λ₂] characterising a spin state S of an n-electron system, it is found that this method generates the complete set of spin projections from the appropriate primitive spin functions. The method is applied to a 7-electron system in the spin state S = M_S = 1/2 and the results are listed in the Appendix.     

Photodimers of cinnamic acid and related compounds. A stereochemical study by NMR

¹H NMR spectra of photodimers of cinnamic acid, chalcone and related compounds were analysed, and the spectral parameters and all the coupling constants were obtained. A clear differentiation among the head-to-head and head-to-tail stereoisomers can be obtained by considering the values of K, L, M and N parameters. The different types of hh and ht isomers can be immediately assigned by considering the relative values of the three-bond couplings. An authentic example of an A₂B₂ spin system is reported.     

Investigation of natural rubber composites with addition of montmorillonite fillers using thermal analysis

This paper is devoted to the investigation of the properties of the natural rubber composites prepared using the cation exchanged-montmorillonite fillers. The characteristics of the montmorillonite fillers were studied by Fourier transform infrared spectroscopy (FTIR) and thermogravimetry (TG). These characterized fillers were used to preparation of the natural rubber composites, which were submitted to measurements of dynamic-mechanical thermal analysis (DMTA) and vulcanizing characteristics (M _H, M _L, t _s, t _c(90), R _v) as well as physico-mechanical properties (tensile strength, modulus at 300 elongation—M ₃₀₀, tensibility).     

The Influence of Alkali Metal Ions on the Stability and Reactivity of Chromium(III) Superoxide Moieties Spanned by Siloxide Ligands

In recent years, it has become clear that the presence of redox-inactive Lewis acidic metal ions can decisively influence the reactivity of metal–dioxygen moieties that are formed in the course of O₂ activation, in molecular complexes, and metalloenzymes. Superoxide species are often formed as the primary intermediates but they are mostly too unstable for a thorough investigation. We report here a series of chromium(III) superoxide complexes [L₂Cr]M₂O₂(THF)_y (L=⁻OSiPh₂OSiPh₂O⁻, M⁺=Li⁺, Na⁺, K⁺ and y=4, 5), which could be accessed, studied spectroscopically and partly crystallized at low temperatures. They only differ in the two incorporated Lewis acidic alkali metal counterions (M⁺) and it could thus be shown that the nature of M⁺ determines considerably its interaction with the superoxide ligand. This interaction, in turn, has a significant influence on the stability and reactivity of these complexes towards substrates with OH groups. Furthermore, we show that stability and reactivity are also highly solvent dependent (THF versus nitriles), as donor solvents coordinate to the alkali metal ions and thus also influence their interaction with the superoxide moiety. Altogether, these results provide a comprehensive and detailed picture concerning the correlation between spectroscopic properties, structure, and behavior of such superoxides, that may be exemplary for other systems.     

Mechanistic Origin of Antagonist Effects of Usual Anionic Bases (OH−, CO32−) as Modulated by their Countercations (Na+, Cs+, K+) in Palladium‐Catalyzed Suzuki–Miyaura Reactions

The mechanism of the reaction of trans‐ArPdBrL₂ (Ar=p‐Z‐C₆H₄, Z=CN, H; L=PPh₃) with Ar′B(OH)₂ (Ar′=p‐Z′‐C₆H₄, Z′=H, CN, MeO), which is a key step in the Suzuki–Miyaura process, has been established in N,N‐dimethylformamide (DMF) with two bases, acetate (nBu₄NOAc) or carbonate (Cs₂CO₃) and compared with that of hydroxide (nBu₄NOH), reported in our previous work. As anionic bases are inevitably introduced with a countercation M⁺ (e.g., M⁺OH^?), the role of cations in the transmetalation/reductive elimination has been first investigated. Cations M⁺ (Na⁺, Cs⁺, K⁺) are not innocent since they induce an unexpected decelerating effect in the transmetalation via their complexation to the OH ligand in the reactive ArPd(OH)L₂, partly inhibiting its transmetalation with Ar′B(OH)₂. A decreasing reactivity order is observed when M⁺ is associated with OH^?: nBu₄N⁺> K⁺> Cs⁺> Na⁺. Acetates lead to the formation of trans‐ArPd(OAc)L₂, which does not undergo transmetalation with Ar′B(OH)₂. This explains why acetates are not used as bases in Suzuki–Miyaura reactions that involve Ar′B(OH)₂. Carbonates (Cs₂CO₃) give rise to slower reactions than those performed from nBu₄NOH at the same concentration, even if the reactions are accelerated in the presence of water due to the generation of OH^?. The mechanism of the reaction with carbonates is then similar to that established for nBu₄NOH, involving ArPd(OH)L₂ in the transmetalation with Ar′B(OH)₂. Due to the low concentration of OH^? generated from CO₃^2? in water, both transmetalation and reductive elimination result slower than those performed from nBu₄NOH at equal concentrations as Cs₂CO₃. Therefore, the overall reactivity is finely tuned by the concentration of the common base OH^? and the ratio [OH^?]/[Ar′B(OH)₂]. Hence, the anionic base (pure OH^? or OH^? generated from CO₃^2?) associated with its countercation (Na⁺, Cs⁺, K⁺) plays four antagonist kinetic roles: acceleration of the transmetalation by formation of the reactive ArPd(OH)L₂, acceleration of the reductive elimination, deceleration of the transmetalation by formation of unreactive Ar′B(OH)₃^? and by complexation of ArPd(OH)L₂ by M⁺.     

Understanding the eighteen-electron rule

It is pointed out that the preferred closed-shell electron structures, such as those in typical high-symmetry 18-electron systems, are driven both by the bonding contributions to the centre and by the kinetic-energy (nodal-structure) terms in the ligand subsystem, L_n. The latter imposes a filling order s < p < d, even for the ML_n complex. Then the 18e principle can be right for the right reasons even without any np contributions at the central atom.     

Synthesis, π‐Face‐Selective Aggregation,and π‐Face Chiral Recognition of Configurationally Stable C3‐Symmetric Propeller‐Chiral Molecules with a π‐Core

The C₃‐symmetric propeller‐chiral compounds (P,P,P)‐ 1 and (M,M,M)‐ 1 with planar π‐cores perpendicular to the C₃‐axis were synthesized in optically pure states. (P,P,P)‐ 1 possesses two distinguishable propeller‐chiral π‐faces with rims of different heights named the (P/L)‐face and (P/H)‐face. Each face is configurationally stable because of the rigid structure of the helicenes contained in the π‐core. (P,P,P)‐ 1 formed dimeric aggregates in organic solutions as indicated by the results of ¹H NMR, CD, and UV/Vis spectroscopy and vapor pressure osmometry analyses. The (P/L)/(P/L) interactions were observed in the solid state by single‐crystal X‐ray analysis, and they were also predominant over the (P/H)/(P/H) and (P/L)/(P/H) interactions in solution, as indicated by the results of ¹H and 2D NMR spectroscopy analyses. The dimerization constant was obtained for a racemic mixture, which showed that the heterochiral (P,P,P)‐ 1 /(M,M,M)‐ 1 interactions were much weaker than the homochiral (P,P,P)‐ 1 /(P,P,P)‐ 1 interactions. The results indicated that the propeller‐chiral (P/L)‐face interacts with the (P/L)‐face more strongly than with the (P/H)‐face, (M/L)‐face, and (M/H)‐face. The study showed the π‐face‐selective aggregation and π‐face chiral recognition of the configurationally stable propeller‐chiral molecules.     

Intramolecular stacking interaction in mixed-ligand complexes containing ATP4- and aromatic N-heterocyclic ligands

The stability constants of the binary ML2+ and ternary M(ATP)L2- complexes,where L=Iq (isoquinoline) or BIm (benzimidazole) and M=Zn2+ or Cd2+,have been determined by poten-tiometric pH titration in aqueous solution at I=0.1 mol/L (NaClO4),T=25℃.The stability of the ternary complexes characterized by corresponding to the equilibrium M(ATP)2-+ML2+=M(ATP)L2-+M2+ is higher than what would be expected on statistical grounds.The increase may be related to the stacking interaction between the aromatic ring of the ligands L and the purine moiety of ATP4- 1H NMR studies of Zn2+/ATP4-/L confirm the presence of stacking in the ternary complexes.It is concluded that the strength of the intramolecular stacking interaction is dependent on the structure of the aromatic ring of the ligand L and the formation of a metal ion bridge.Possible implications are discussed briefly.     

An improved method to measure all rate constants in the simplest enzyme kinetics model

Since Adrian Brown and Victor Henri’s work, the simplest enzyme kinetics model, which contains only three rate constants k ₁, k ₂ and k ₋₁ in 1902, has been thoroughly explored in many directions. By using the Michaelis–Menten equation, K _M and k ₂ can be measured quickly. All the three rate constants can be derived by temperature jump method or transient state kinetics, but both methods need more complicated techniques and equipments. In our previous paper (Li et al. in J Math Chem 46:290–301, 2009), we gave a method to measure all the rate constants which does not require any additional equipment other than those needed for measuring K _M and k ₂. Here, we propose a new one which needs no additional equipment either. This method is based on a study of inflection points of integral curves. Numerical results show that the new one is much better than the previous one in two aspects: near the end of the reaction, the new one gives more accurate estimation; during the quasi-steady state of the reaction, it also gives good estimations while the previous one can not. Hence, this method not only advances the estimation accuracy, but also has more choices for measuring.     

Rhodium(III), palladium(II) and platinum(II) complexes of Bis(o-aminobenzenesulfonyl)ethylenediamine

New complexes of the formulae K₃[RhL ₃]·2 H₂O, [PdL]·H₂O and [M(LH₂)Cl₂] [whereM = Pd, Pt andLH₂ = bis(o-aminobenzenesulfonyl)ethylenediamine] have been prepared and characterized by conductivity measurements, thermogravimetric analysis, X-ray powder patterns and IR, Ligand Field and¹H-NMR spectroscopy.

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Rhodium(III), Palladium(II)- und Platin(II)-Komplexe mit Bis(o-aminobenzolosulfonyl)ethylendiamin (Kurze Mitteilung)

Zusammenfassung Neue Komplexe der allgemeinen Formeln K₃[RhL ₃]·2H₂O, [PdL]·H₂O und [M(LH₂)Cl₂] mitM = Pd, Pt undLH₂ = Bis(o-aminobenzolosulfonyl)ethylendiamin wurden dargestellt und mit Konduktionsmessungen, thermogravimetrischen Analysen, Röntgenstrukturanalysen, IR, Ligandfeld- und¹H-NMR-Spektroskopie charakterisiert.

     

Flexibility versus Rigidity: How Conformational Constraint,Steric Hindrance and Solvent Impact Binding between π-Electron Poor Tweezer-Type Hosts and π-Electron Rich Guests

Tweezer-type receptors that form π−π stacked supramolecular complexes are important components in functional polymeric materials and molecular machines. Herein, we study how varying specific structural components of tweezer-receptors impacts their binding. A library of tweezer receptors, each containing two π-electron poor receptor residues and differing by the nature of the linking unit which was either a flexible 2,2′-(ethylenedioxy)bis(ethylamine) residue or a rigid 3,3’’-diamino-m-terphenyl diamine structure, were synthesised. Each tweezer formed 1 : 1 supramolecular complexes with π-electron rich residues (1,5-dihydroxynapthalene and pyrene) as confirmed by UV/Vis and ¹H NMR spectroscopic studies. Binding constants were determined to be between 2.3×10⁻⁵ and 71 M⁻¹ in organic solvents and were one magnitude greater in aqueous solvents for water soluble systems. The nature of the linker had variable effects on the binding constants, showing the design of tweezer type supramolecular receptors with targeted K_a values is non-trivial and requires structural optimisation supported by binding constant determination studies.     

Synthesis and characterization of molecularly imprinted polymers for recognition of ciprofloxacin

A molecularly imprinted polymer (MIP), with special molecule recognition properties of ciprofloxacin (CIP), was prepared by thermal polymerization in which ciprofloxacin acted as template molecule, α-methacrylic acid (MAA) acted as functional monomer and trimethylolpropane trimethylacrylate (TRIM) acted as crosslinker. The optimized ratio was determined to be n(CIP): n (MMA):n(TRIM)51:6:16 by investigation of the effects of different concentrations of functional monomer and the crosslinker on the MIP’s recognition properties. Equilibrium binding experiment was used to investigate the adsorption dynamics, the binding ability to template molecule and the substrate selectivity. Scatchard analysis was used to study the MIP’s binding characteristic to template molecule. The results indicated that MIP has higher adsorption ability and selectivity. The equilibrium distribution coefficient K _D was 41.64 and the separation factor α was 1.62. Scatchard analysis showed that two different kinds of binding sites were produced in the polymer matrix and their dissociation constants were calculated to be K _d1 = 5.249 × 10⁻⁵ mol·L⁻¹, K _d2 = 2.237 × 10⁻³ mol·L⁻¹. __________ Translated from Chemistry, 2008, 71(2): 132–137     

Anion dependence of crown ether selectivities for alkali picrates and sulfonates in dioxane and toluene. A synergistic effect

The binding constants,K _N, of sodium and potassium 8-anilinonaphthalene-1-sulfonate (ANS) and of sodium 5-dimethylamino-1-naphthalenesulfonate (DNS) to benzo-18-crown-6 bound to a 2% cross-linked polystyrene network (RN18C6) were measured spectrophotometrically in dioxane and the results compared with those obtained for picrate salts. The network RN18C6 was then used to measure in dioxane and toluene by a competition method the equilibrium constant,K, of the reaction A^–M⁺N+CrA^–M⁺Cr+N.A^–M⁺N denotes the ionic solute (ANS, DNS, methyl orange or picrate salt) bound to the network RN18C6 (N) and A^–M⁺Cr is the solute bound to a soluble ligand Cr, where Cr represents a series of 18-crown-6 and 15-crown-5 compounds. Combining theK _N andK values the formation constants,K _L, of the crown ether complexes of the respective salts were obtained in dioxane. The data show a reversal in the complexation strength of the 18-crown-6 compounds in dioxane when sodium picrate is replaced by sodium ANS. The results were rationalized in terms of a synergistic effect exerted by dioxane, with dioxane forming a 1:1 dioxanate with the crown ion pair complex. This effect is especially strong with ANS and with a rigid planar crown ether like dibenzo-18-crown-6. The binding constants,K _N, of NaANS and NaDNS to RN18C6 in dioxane are nearly three times larger than for sodium picrate, and the same holds for the potassium salts. Differences in anion interactions with the network appear to be a plausible cause for the anion dependence ofK _N.