Interpretation paradoxes in unimolecular heterolysis kinetics

The rate constant of the first-order rate equation w = k[RX] that is derived from the variation of the reaction product concentration or determined by the verdazyl method characterizes the lifetime of the transition state or that of the solvent-separated ion pair rather than the heterolysis rate. The diffusion rate constant is equal to the dissociation rate constant of the contact ion pair and to the reverse of the lifetime of the solvent-separated ion pair: k _D ≈ k = 1/τ ≈ 10¹⁰ s⁻¹.     

Electrochemical Impedance Spectroscopy and Cyclic Voltammetry of <Emphasis Type="Italic">cis</Emphasis>-[Cr(bipy)<Subscript>2</Subscript>(SCN)<Subscript>2</Subscript>]I (where bipy: 2,2′-Bipyridine) in Polar Solvents

Cyclic voltammetric studies (CV) on the complex cis-bis(2,2′-bipyridine)bis(thiocyanate)chromium(III) iodide [Cr(bipy)₂(SCN)₂]I (where bipy: 2,2′-bipyridine, C₁₀H₈N₂) were recorded on platinum (Pt) and glassy carbon (GC) electrodes in either acetonitrile (ACN) or acetone (ACE) solvent media including n-tetrabutylammonium hexafluorophosphate (NBu₄PF₆) as supporting electrolyte, at scan rates (v) ranging from 0.05 to 0.12 V⋅s⁻¹. In addition, electrochemical impedance spectroscopic (EIS) measurements in the frequency (f) range from 0.1 Hz to 50 kHz were carried out on GC and Pt electrodes. The half-wave potential (E _1/2) of the redox couple Cr(III)/Cr(II) was determined as −0.84 V and −0.79 V (versus Ag/AgCl) in ACN and ACE, respectively. The heterogeneous electron transfer rate constant (k _s) corresponding to the couple Cr(III)/Cr(II) was found to be greater on GC compared to the Pt electrode. The nature of the solvent medium also affects the kinetics of the investigated couple, to be exact, k _s increases remarkably upon replacement of ACE by ACN. The EIS results indicate that the GC electrode is a better capacitor and provides the smaller charge transfer resistance in ACN.     

Investigation of the Electrochemical Reduction of Benzophenone in Aprotic Solvents Using the Method of Cyclic Voltammetry

The reduction of benzophenone (Bzph) in 3-pentanone (PEN), acetone (ACE), N,N-dimethylacetamide (DMA), N,N-dimethylformamide (DMF), tetrahydrofuran (THF), acetonitrile (ACN) and dimethyl sulfoxide (DMSO) with n-tetrabutylammonium hexafluorophosphate (TBAPF₆) as background electrolyte was studied using the technique of cyclic voltammetry at the temperature of 263.15 K. The half-wave potentials (E _1/2) were extracted. The reduction of Bzph occurs in two successive one-electron steps to produce first the free radical anion Bzph⁻ and then the dianion Bzph²⁻. The results indicated that the radical anion Bzph⁻ is reoxidized to Bzph in all investigated solvent media whereas the dianion Bzph²⁻ is reoxidized to Bzph⁻ only in THF. The heterogeneous electron-transfer rate constants (k _s ) were evaluated by employing the electrochemical rate equation proposed by Nicholson. The rate of electron transfer for the Bzph/Bzph⁻ couple was found to be relatively slow in all investigated solvent media. Consequently, the electron-transfer processes can be recognized as quasi-reversible. The diffusion coefficients (D) of Bzph in the investigated solvent media have been calculated using the modified Randles-Sevcik equation. The effect of the physical and chemical properties of the solvent medium on the electrochemical behavior of Bzph has been examined.     

Kinetic Investigation of the Electrochemical Oxidation of Bis(benzene)chromium(0) in Diethyl ketone/N,N-Dimethylformamide

The cyclic voltametric technique utilizing a platinum working electrode was applied for the investigation of the electrochemical oxidation of bis(benzene)chromium(0), (C₆H₆)₂Cr to bis(benzene)chromium(I), (C₆H₆)₂Cr⁺ in diethyl ketone (DEK), N,N-dimethylformamide (DMF), and DEK/DMF binary mixtures containing n-tetrabutylammonium hexafluorophosphate (TBAPF₆) as the supporting electrolyte at T=298.15 K. The half-wave potentials (E _1/2) of the (C₆H₆)₂Cr^+/0 redox couple in DEK, DMF and DEK/DMF binary mixtures, were determined. The variation of E _1/2 with the solvent composition was found to be almost linear. The E _1/2 results were analyzed in terms of the electron-donating power of the solvent medium. The diffusion coefficients, D, were calculated using the Randles-Sevcik equation. The kinetics of the electrode reaction were investigated through the determination of the heterogeneous electron-transfer rate constants, k _s, according to the electrochemical rate equation proposed by Nicholson. Furthermore, the activation Gibbs energies for the electron-transfer process (ΔG ^≠) were also calculated. The results indicate that the redox couple (C₆H₆)₂Cr^+/0 exhibits an electrochemically reversible and diffusion-controlled process in all the investigated solvent media.     

Measuring the ignition delay time for hydrogen-oxygen mixtures behind the front of an incident shock wave

The delay time τ has been measured for the formation of the ^·OH radical in igniting hydrogenoxygen mixtures diluted with argon (79–97%). The experiments have been carried out under incident shock wave conditions at temperatures of 900–3000 K, pressures of 0.5–2.5 atm, and H₂/O₂ ratios of 0.2–20. The dependence of τ on the pressure P _s of the stoichiometric part of the combustible mixture (2H₂-O₂) has been investigated for different mixture compositions. Under the above conditions, τ depends practically linearly on 1/P _s at P _s = 0.02−0.1 atm, irrespective of the mixture composition. This allows the measured τ data to be converted to one quantity, τP _s. The temperature dependence of τP _s in the P _s range from 0.02 to 0.1 atm is Arrhenius-like. For the hydrogen-rich mixtures (H₂/O₂ = 2–20), this dependence appears as τP _s= 0.057 + 0.0256exp(7470/T) μs atm; for the lean mixtures (H₂/O₂ = 0.125–1), τP _s = 0.021 + 0.0069exp(7470/T) μs atm. The length of the shock-heated gas plug in the incident shock wave poses limitations on the ignition delay time measurements at T < 900 K.     

Electrochemistry on Multi-walled Carbon Nanotubes in Organic Solutions

The oxidation of ferrocene (FeCp₂) to ferrocenium cation (FeCp₂⁺\mbox{FeCp}_{2}^{+}) (where Cp: cyclopentadienyl anion, C₅H₅^-\mbox{C}_{5}\mbox{H}_{5}^{-}) was investigated by means of cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) on either a glassy carbon (GC) electrode or a film consisted of multi-walled carbon nanotubes (MWCNT) in acetone (ACE), methanol (MeOH) and ACE/MeOH binary mixtures. The half-wave potentials (E _1/2), the diffusion coefficients (D) and the heterogeneous electron transfer rate constants (k _s) of the redox couple FeCp₂^+/0\mbox{FeCp}_{2}^{+/0} were determined. On both electrodes tested, the electron transfer process was found to be quasi-reversible and diffusion controlled in all investigated solvent mixtures. The E _1/2 values were shifted toward less positive potentials with the enrichment of mixtures in MeOH, due probably to the larger Lewis basicity of the MeOH molecules. Furthermore, values of both D and k _s diminish with the increase of MeOH content following the progressive increase of viscosity of the solvent medium. Among the electrodes probed, GC provides faster electrochemical process since it affords less charge-transfer resistance (R _ct), and consequently, an insignificant barrier for interfacial electron transfer.     

TEM observation of nonamphiphilic copolymer micelles

Light scattering and transmission electron microscope (TEM) measurements were preformed for micelles of a nonamphiphilic poly(vinylphenol)-block-polystyrene diblock copolymer (PVPh-b-PSt) to determine the shape of the micelles. The micelles were prepared by the self-assembly of the copolymer in 1,4-dioxane, a nonselective solvent, in the presence of 1,4-butanediamine. The logarithm of the normalized time correlation function of the scattered field, lnG₁(τ), linearly decayed versus the delay time, τ. The diffusion coefficient measured in the range of the scattering angles from 30° to 150° was almost independent of the square of the magnitude of the scattering vector. The linear decay of lnG₁(τ) vs τ and the angular-independence of the diffusion coefficient suggested that the monodisperse spherical micelles were formed by the micellization. The TEM observations confirmed the formation of uniform spheres.     

Role of mononuclear rare earth metal complexes in promoting the hydrolysis of p-nitrophenyl phosphate (NPP)

Two long-chain multidentate ligands: 2,9-di-(n-2′,5′,8′-triazanonyl)-1,10-phenanthroline (L₁) and 2,9-di-(n-4′,7′,10′-triazaundecyl)-1,10-phenanthroline (L₂) were synthesized. The hydrolytic kinetics of p-nitrophenyl phosphate (NPP) catalyzed by complexes of L₁ and L₂ with La(III) and Gd(III) have been studied in aqueous solution at 298 K, I = 0.10 mol · dm⁻³ KNO₃ at pH 7.5–9.1, respectively. The study shows that the catalytic effect of GdL1 was the best in the four complexes for hydrolysis of NPP. Its k_LnLH−1, k _LnL and pK _a are 0.0127 mol⁻¹ dm³ s⁻¹, 0.000022 mol⁻¹ dm³ s⁻¹ and 8.90, respectively. This paper expounds the result from the structure of the ligands and the properties of the metal ions, and deduces the catalysis mechanism.     

Soret Coefficients for Aqueous Polyethylene Glycol Solutions and Some Tests of the Segmental Model of Polymer Thermal Diffusion

A thermogravitational cell is used to measure Soret coefficients (s) for dilute binary aqueous solutions of ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, and polyethylene glycol (PEG) fractions with average molecular weights from 200 to 20,000 g-mol^–1. The cell design allows the top and bottom halves of the solution column to be withdrawn and injected into a high-precision HPLC differential refractometer detector for analysis. Previously reported mutual diffusion coefficients D and the measured Soret coefficients are used to calculate thermal diffusion coefficients D _T. s and D vary with the PEG molecular weight M as M ^+0.53 and M ^–0.52, respectively; hence, D _T = sD is essentially independent of M. The segmental model of polymer thermal diffusion predicts D _T = D_seg U _S/RT ², where D _seg is the segment diffusion coefficient, U _S the solvent activation energy for viscous flow, R the gas constant, and T the temperature. The predicted D _T values, although independent of M, are too large by a factor of five. Additional tests of the segmental model are provided using literature data for polystyrene + toluene, n-alkane + CCl₄, and n-alkane + CHCl₃ solutions. Agreement with experiment is not obtained. In particular, the measured D _T values for the alkane solutions are negative.     

Quasielastic light scattering study of chemically crosslinked gelatin solutions and gels

Quasielastic light scattering measurements are reported for experiments performed on mixtures of gelatin and glutaraldehyde (GA) in the aqueous phase, where the gelatin concentration was fixed at 5 (w/v) and the GA concentration was varied from 1×10⁻⁵ to 1×10⁻³ (w/v). The dynamic structure factor, S(q,t), was deduced from the measured intensity autocorrelation function, g ₂(τ), with appropriate allowance for heterodyning detection in the gel phase. The S(q,t) data could be fitted to S(q,t)=Aexp(−D _f q ² t)+Bexp(−t/τ_c)^β, both in the sol (50 and 60 ^∘C) and gel states (25 and 40 ^∘C). The fast-mode diffusion coefficient, D _f showed almost negligible dependence on the concentration of the crosslinker GA; however, the resultant mesh size, ξ, of the crosslinked network exhibited strong temperature dependence, ξ∼(0.5−χ)^1/5exp(−A/RT) implying shrinkage of the network as the gel phase was approached. The slow-mode relaxation was characterized by the stretched exponential factor exp(−t/τ_c)^β. β was found to be independent of GA concentration but strongly dependent on the temperature as β=β₀+β₁ T+β₂ T ². The slow-mode relaxation time, τ_c, exhibited a maximum GA concentration dependence in the gel phase and at a given temperature we found τ_c(c)=τ₀+τ₁ c+τ₂ c ². Our results agree with the predictions of the Zimm model in the gel case but differ significantly for the sol state. Received: 25 May 1999 /Accepted in revised form: 27 July 1999     

Bioadsorption and ion exchange of Cr3+ and Pb2+ solutions with algae

Heavy metals can be removed from effluents and recovered using physico-chemical mechanisms as biosorption processes. In this work “Arribada” seaweed biomass was employed to assess its biosorptive capacity for the chromium (Cr³⁺) and lead (Pb²⁺) cations that usually are present in waste waters of plating industries. Equilibrium and kinetic experiments were conducted in a mixed reactor on a batch basis. Biosorption equilibrium and fluid-solid mass transfer constants data were analyzed through the concept of ion exchange sorption isotherm. The respective equilibrium exchange constants (K _eqCr=173.42, K _eqPb=58.86) and volumetric mass transfer coefficients ((k _mCr a)′=1.13×10⁻³ s⁻¹, (k _mPb a)′=0.89×10⁻³ s⁻¹) were employed for the dynamic analysis of Cr and Pb sorption in a fixed-bed flow-through sorption column. The breakthrough curves obtained for both metals were compared with the predicted values by the heterogeneous model (K _eqCr=171.29, K _eqPb=60.14; k _mCr a=7.81×10⁻² s⁻¹, k _mPb a=2.43×10⁻² s⁻¹), taking into account the mass transfer process. The results suggest that these algae may be employed in a metal removal/recovery process at low cost. An erratum to this article can be found at     

Highly hydrophobically modified polyelectrolytes: Field variables to control emulsion type

Highly hydrophobically modified (with n-dodecylamide chain) linear poly(acrylic acid)s (HHMPAAH) and poly(sodium acrylate)s (HHMPAANa) with various degrees of grafting (τ) were synthesized and used as emulsifiers of the n-dodecane/water system. The type of emulsion, oil in water (O/W) or water in oil (W/O), was investigated as a function of the polymer chemical structure (τ, salt or acid form of the copolymer) and aqueous phase electrolyte concentration (NaNO₃). Increasing τ and/or salt concentration was found to favor the formation of inverse emulsions. Direct liquid–liquid dispersions are more likely to form with poly(sodium acrylate)s than with poly(acrylic acid)s. Hence, field variables such as τ, pH and ionic strength are relevant parameters to control emulsion type. Moreover, a balanced polyelectrolyte neither soluble in oil nor in water was synthesized for the first time. With this original emulsifier, the dispersion type was found to change from O/W to W/O with polymer salting out. The work provides convenient model system for fundamental studies of polymer conformation at liquid–liquid interfaces. Received: 31 March 1998 Accepted: 30 April 1998     

Numerical modelling and simulation of Laviron treatment for poly-phenothiazine derivative-modified glassy carbon electrodes

Electropolymerization of a new phenothiazine derivative (bis-phenothiazin-3-yl methane, BPhM) on glassy carbon electrodes leads to electroactive and conducting layers of poly-BPhM. Based on the Laviron method, the kinetic parameters (the heterogeneous electron transfer rate constants k _s and transfer coefficients α) were calculated out of the experimental and theoretical data. The theoretical data have been obtained by using the analogical modelling and numerical simulating method. The modified electrodes present high values of k _s(~50s⁻¹) in phosphate buffer solutions of different pH values. A good correlation of mathematical and numerical simulated kinetic parameters has been obtained, with the experimental values and the norm of residuals being very close to zero.     

Kinetic isotope effect in the reaction of oh radical with acetone-D6

The discharge-flow method with resonance fluorescence detection of OH radicals was applied to obtain the rate constant value of k _D = 1.95 ± 0.14 (1σ) 10¹⁰ cm³ mol^-1s^-1 at 298 K. Combination with k _H from our previous study gives the kinetic isotope effect of k _H / k _D = 5.33 ± 0.41. OH + CH₃C(O)CH₃ → Products (H) OH + CD₃C(O)CD₃ → Products(D) This revised version was published online in June 2006 with corrections to the Cover Date.     

Apparent Molar Volume and Viscosity Studies on Some Carbohydrates in Solutions

 The apparent molar volume (φ_v) and viscosity (η) of L(+)-arabinose, D(+)-galactose, D(−)-fructose, D(+)-glucose, sucrose, lactose, and maltose in water and in 0.1% and 0.3% water-Surf Excel solutions were measured as a function of solute concentrations at 308.15, 313.15, and 323.15 K, respectively. The apparent molar volume (φ_v) of the carbohydrates was found to be a linear function of the concentration. From a φ_v versus molality (b) plot, the apparent molar volume at infinite dilution (), which is practically equal to the partial molar volume at infinite dilutions () of these substances was determined. The viscosity coefficients B and D for the carbohydrates were calculated on the basis of the viscosity of the solutions and the solvent using the Jones-Dole equation. The activation free energy for viscous flow (ΔG ^≠) of the solutions was also calculated using the Eyring equation. The carbohydrates showed structure making behaviour both in water and in water-Surf Excel solutions. When water-Surf Excel solutions and pure water solutions containing carbohydrate molecules are compared, the former were found to be more structured. The behaviour of these solutes in water and in water-Surf Excel solution systems is discussed in the light of solute–solvent interactions.     

Termination rate constants in radical polymerization

A rate constant is generally derived by using Fick's equation corresponding to the spherical interdiffusion of particles. By using this rate constant, chain and primary radical termination rate constants can be approximated to rate constants for the bimolecular reactions between two radical chain ends, and primary radical and radical chain end, respectively. The former is given by k_s = 8πN_LD_sL_s exp { ? L_s/R_s} × 10^?3 1./mole-sec. The latter is given by k_si = 4πN_L(D_s + D_i)L_si exp { ? L_si/R_si} × 10^?3 1./mole-sec. Here, N_L is Avogadro's number; D_s and D_i are the diffusion constants of radical chain end and primary radical, respectively; L_s and L_si are, respectively, the distances between two radical chain ends and between a primary radical and a radical chain end at a thermal energy equal to the coulombic energy of interaction of the net charges; and R_s and R_si are, respectively, the average distances between two radical chain ends and primary radical on a collision.     

Diffusing probe measurements in Newtonian and elastic solutions

The diffusion coefficients of polystyrene latex spheres and hematite particles in both Newtonian and elastic liquids have been measured using dynamic light scattering. The diffusion coefficients of the latex particles measured in glycerol/water (Newtonian) solutions obey Stokes–Einstein behaviour over a range of solvent viscosities and temperatures. Two apparent diffusion coefficients for the particles are measured in visco-elastic polyacrylamide and polyacrylate solutions and are designated D_fast and D_slow. The apparent fast diffusion coefficients measured in the elastic solutions show an increase to a maximum, above that measured in the solvent water, with increasing polyelectrolyte concentration. At higher polyelectrolyte concentrations the observed D_fast values decrease below the value obtained in the solvent water. D_fast increases with the scattering vector squared (q²) while D_slow, is independent of q².     

Behavior of polyelectrolyte solutions in a wide range of solvent dielectric constant

We exploit the strong temperature dependence of dielectric constant of N-methylformamide to control the strength of electrostatic interactions in polyelectrolyte solutions of sodium polystyrene sulfonate, and investigate the dynamic properties of salt-free solutions over a broad temperature range, from 54 to −58 °C. The traditional fast and slow diffusion processes are observed. The ratio of diffusion coefficients, D_s/D_f, increases and the ratio of their amplitudes, A_s/A_f, decreases, both by a factor of about two in this temperature range confirming the expected temperature variation with the Bjerrum length.