Effects of diffusion in the oxidative degradation of vulcanized rubbers. I. Rate of chain scission in the steady state

The effects of diffusion in the oxidation of cis-1,4-polyisoprene vulcanizates were investigated by means of the stress relaxation method. It was assumed that the diffusion of oxygen is coupled with first-order oxygen consumption and that the rate of chain scission is proportional to the rate of oxygen consumption. The diffusion equation of this process was solved under the steady-state condition to give a simple relation between the rate of chain scission and the film thickness. The experimental results were in good agreement with the theoretical treatment. The true activation energy as well as the ratio of the rate of oxidation k to the diffusion constant D could be estimated.     

Photodynamic Therapy Efficacy Enhanced by Dynamics: The Role of Charge Transfer and Photostability in the Selection of Photosensitizers

Progress in the photodynamic therapy (PDT) of cancer should benefit from a rationale to predict the most efficient of a series of photosensitizers that strongly absorb light in the phototherapeutic window (650–800 nm) and efficiently generate reactive oxygen species (ROS=singlet oxygen and oxygen‐centered radicals). We show that the ratios between the triplet photosensitizer–O₂ interaction rate constant (k_D) and the photosensitizer decomposition rate constant (k_d), k_D/k_d, determine the relative photodynamic activities of photosensitizers against various cancer cells. The same efficacy trend is observed in vivo with DBA/2 mice bearing S91 melanoma tumors. The PDT efficacy intimately depends on the dynamics of photosensitizer–oxygen interactions: charge transfer to molecular oxygen with generation of both singlet oxygen and superoxide ion (high k_D) must be tempered by photostability (low k_d). These properties depend on the oxidation potential of the photosensitizer and are suitably combined in a new fluorinated sulfonamide bacteriochlorin, motivated by the rationale.     

Aminolysis of aryl dithio-2-thiophenates and dithio-2-furoates in acetonitrile

The aminolyses of the title substrates with anilines and benzylamines are investigated in acetonitrile. A clean second-order kinetics is obtained with a first-order rate law in the amine concentration, which is uncomplicated by the fast proton transfer step. The large magnitude of ρ_Z (ρ_1g) as well as ρ_X (ρ_nuc) together with relatively large positive ρ_XZ values is consistent with a stepwise mechanism in which thiophenolate ion expulsion from the intermediate is rate limiting. For the reactions of aryl dithio-2-thiophenates with benzylamines the magnitude of ρ_X and ρ_Z values is relatively smaller suggesting that both the addition and expulsion of thiophenolate are partially rate determining. Relatively large secondary kinetic isotope effects, k_H/k_D≥1.7, with deuterated nucleophiles, support involvement a concurrent proton transfer to the departing thiophenolate ion in the transition state. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 849–857, 1998     

Diffusion-controlled reaction. V. Effect of concentration-dependent diffusion coefficient on reaction rate in graft polymerization

The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problem can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the v power of the monomer concentration C, in which the proportionality constant a = k_pR/k, where k_p and k_t are the propagation and termination rate constants, respectively, and R_i is the initiation rate. The values of v, w, and z depend on the particular reaction system. The results of our earlier work were generalized by allowing a non-Fickian diffusion rate, obtained from an extension of the Fujita free-volume theory, which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient, D = D₀ [exp(δC/M)], where M is the saturation concentration. It was shown that a reaction system is characterized by the three dimensionless parameters v, δ, and A = (L/2)[aM^(v?1)/D₀]^1/2, where L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as A increases. Larger values of δ and v cause a reaction system to behave closer to the diffusion-free regime. The transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is w order in initiation rate, v order in monomer, and independent of film thickness, the diffusion-controlled rate is w/2 order in initiator rate and inverse first-order in film thickness. The dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system.     

A study of dimethylferrocene diffusion and electrode kinetics using microelectrode voltammetry in poly(ethylene glycol) solvent

The heterogeneous electron transfer rate constant (k _s) of dimethylferrocene (DMFc) was estimated using cyclic voltammetric peak potential separations taken typically in a mixed diffusion geometry regime in a polyelectrolyte, and the diffusion coefficient (D) of DMFc was obtained using a steady-state voltammogram. The heterogeneous electron transfer rate constant and diffusion coefficient are both smaller by about 100-fold in the polymeric solvent than in the monomeric solvent. The results are in agreement with the difference of longitudinal dielectric relaxation time (τ_L) in the two kinds of solvents, poly(ethylene glycol) (PEG) and CH₃CN, indicating that k _s varies inversely with τ_L; k _s is proportional to D of DMFc. Both D and k _s of DMFc in PEG containing different supporting electrolytes and at different temperatures have been estimated. These results show that D and k _s of DMFc increase with increasing temperature in the polyelectrolyte, whereas they vary only slightly with changing the supporting electrolyte. Received: 5 February 1998 / Accepted: 23 July 1998     

Very low-pressure pyrolysis. VIII. The decomposition of Di-t-amyl peroxide

The very low-pressure pyrolysis (VLPP) technique has been applied to the pyrolysis of di-t-amyl peroxide (DTAP) over the temperature range 523-633°K. VLPP yields a low-pressure rate constant, k_uni The conversion of k_uni to k_∞ which must be made to calculate the Arrhenius parameters, is accomplished via the RRKM theory. The transition state model used in the RRKM calculations was based on a transition state model which accurately reproduced the VLPP data for di-t-butyl peroxide for which the Arrhenius parameters are well known. For the decomposition of DTAP it was found that log k_∞(300°K) = 15.8 - 36.4/θ, where θ = 2.303RT, in kcal/mole, and the units of k_∞, are sec^?1.     

Ruthenium(III)-catalyzed mechanistic studies of oxidation of benzhydrols by sodium N-chloro-p-toluenesulfonamide in HCl medium

The kinetics of oxidation of benzhydrol and its p-substituted derivatives (YBH, where Y=H, Cl, Br, NO₂, CH₃, and OCH₃) by sodium N-chloro-p-toluenesulfonamide or chloramine-T (CAT), catalyzed by ruthenium(III) chloride, in the presence of hydrochloric acid in 30% (v/v) MeOH medium has been studied at 35°C. The reaction rate shows a first-order dependence on [CAT]_O and a fractional-order each on [ YBH]_O, [Ru(III)], and [H⁺]. The reaction also has a negative fractional-order (−0.35) behavior in the reduction product of CAT, p-toluenesulfonamide (PTS). The increase in MeOH content of the solvent medium retards the rate. The variation of ionic strength of the medium has negligible effect on the rate. Rate studies in D₂O medium show that the solvent isotope effect, k′H₂O/k′D₂O, is equal to 0.60. Proton inventory studies have been made in H₂O(SINGLEBOND)D₂O mixtures. The rates correlate satisfactorily with Hammett σ relationship. The LFE relationship plot is biphasic and the reaction constant ρ=−2.3 for electron donating groups and ρ=−0.32 for electron withdrawing groups at 35°C. Activation parameters ΔH^≠, ΔS^≠, and ΔG^≠ have been calculated. The parameters, ΔH^≠ and ΔS^≠, are linearly related with an isokinetic temperature β=334 K indicating enthalpy as a controlling factor. A mechanism consistent with the observed kinetics has been proposed. © 1997 John Wiley & Sons, Inc.     

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.     

Kinetics of thermal gas‐phase decomposition of 2‐bromopropene using static system

The gas phase elimination kinetics of 2‐bromopropene was studied over the temperature range of 571–654 K and pressure range of 12–46 Torr using the seasoned static reaction system. Propyne was the only olefinic product formed and accounted for >98% of the reaction. This product was formed by homogeneous, unimolecular pathways with high‐pressure first‐order rate constant k_∞ given by the equation k_∞ = 10^{13.47 ± 0.6} exp^{?208.2 ± 6.7} (kJ mol^?1)/RT. The error limits are 95% certainty limits. The observed Arrhenius parameters are consistent with the four centered activated complex. The presence of methyl group on α‐carbon lowers the activation energy by 41 kJ mol^?1. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 39: 1–5, 2007     

Facile Fabrication of a Graphene‐based Electrochemical Biosensor for Glucose Detection

A simple and effective glucose biosensor based on immobilization of glucose oxidase (GOD) in graphene (GR)/Nafion film was constructed. The results indicated that the immobilized GOD can maintain its native structure and bioactivity, and the GR/Nafion film provides a favorable microenvironment for GOD immobilization and promotes the direct electron transfer between the electrode substrate and the redox center of GOD. The electrode reaction of the immobilized GOD shows a reversible and surface‐controlled process with the large electron transfer rate constant (k_s) of 3.42±0.08 s^?1. Based on the oxygen consumption during the oxidation process of glucose catalyzed by the immobilized GOD, the as‐prepared GOD/GR/Nafion/GCE electrode exhibits a linear range from 0.5 to 14 mmol·L^?1 with a detection limit of 0.03 mmol·L^?1. Moreover, it displays a good reproducibility and long‐term stability.     

Tertiary Butyl Nitrite Triggered Nitration of Phenols: Solvent‐ and Structure‐Dependent Kinetic Study

Nitration of phenols with tertiary butyl nitrite (TBN) obeyed second‐order kinetics with a first‐order dependence on [TBN] and [phenol] under acid‐free conditions. Reaction rates were significantly altered by a change in the dielectric constant and other physical properties of solvent. The rate of nitration increased with an increase in temperature (303–323 K) in different solvent media (acetonitrile, dichloroethane, CCl₄, dimethyl formamide (DMF), and toluene). The rates of nitration (log k) could not fit into either Amis or Kirkwood plots [log k’ vs. (1/D) or [(D – 1)/(2D + 1)], but the trends were better explained by the basic form of multivariate linear solvent energy relationships (MLSER) suggested by the Koppel and Palm approach on the one hand and the Kamlet and Taft approach on the other hand. These observations probably substantiate that cumulative contributions of basic solvent parameters (equilibrium as well as frictional solvent effects) and solvent–solute interactions for solvation of transition state during nitration of phenols. Reaction rates accelerated with the introduction of electron‐donating groups and retarded with electron‐withdrawing groups. Accordingly, the reactivity of structurally different phenols was found to follow the following sequence: p‐OH > p‐MeO > p‐Me > H > m‐Me > p‐Cl > p‐Br > m‐Cl > p‐NO₂ > m‐OH. The results are interpreted by Hammett's theory of linear free energy relationship. The reaction constant (Hammett's ρ) is a measure of the sensitivity of the reaction toward the electronic effects of the substituent. The rho (ρ) values obtained from the present experiments are fairly large negative values (ρ < 0), indicating attack of an electrophile on the aromatic ring. An increase in temperature decreases the reaction constant (ρ) values. According to Exner, ρ values for a given reaction are influenced by the temperature according to the following relation: ρ = A [1 – β/T]. Obtained “isokinetic temperature (β)” values are in the range of 225–290. These values are far below the experimental temperature range (303–323 K), indicating that the entropy factors are probably more important in controlling the reaction. This point can be seen from the negative entropy values and linearity of multiple linear regression analysis (MLRA). Furthermore, in the present study, rate constants for TBN nitration of ortho‐substituted phenols could not fit into Taft's plots of log(k/k_CH3) versus σ* or, E_s or combined Taft's relationship. However, Charton's MLRA of the log k with polar, resonance, steric, hydrophobicity, and molar refractivity showing a very good linear relationship was obtained. It is of interest to note that when log k_exp values are correlated with log k_cal a perfect linearity is obtained with a correlation coefficient of unity, indicating the consonance between experimental and calculated rate constants in the present work.     

Electrocatalytic Oxidation of Nitrite at Gold Nanoparticle-polypyrrole Nanowire Modified Glassy Carbon Electrode

A novel chemically modified electrode based on the dispersion of gold nanoparticles on polypyrrole nanowires has been developed to investigate the oxidation behavior of nitrite using cyclic voltammetry, differential pulse voltammetry and chronoamperometry techniques. The diffusion coefficient (D), electron transfer coefficient (α) and charge transfer rate constant (k) for the oxidation of nitrite were determined. The modified electrode exhibited high electrocatalytic activity toward the oxidation of nitrite. The catalytic peak current was found to be linear with nitrite concentrations in the range of 8.0×10^?7?2.5×10^?3 mol·L^?1 with a detection limit of 1.0×10^?7 mol·L^?1 (s/n=3). The proposed method was successfully applied to the detection of nitrite in water samples with obtained satisfactory results. Additionally, the sensor also showed excellent sensitivity, anti‐interference ability, reproducibility and stability properties.     

Electrochemically Polymerized N,N-Dimethylaniline Films Containing Tris-(Bathophenanthroline Disulfonato)Iron(II/III) Complexes

The electropolymerization of N, N-dimethylaniline (DMA) was carried out in an aqueous CF₃COONa solution (pH 1.0) containing DMA in the presence of tris(bathophenanthroline disulfonato)iron(II), Fe(bphen)₃ ^4-. Poly(N, N-dimethylanilinium trifluoroacetate) (PDMA) film was formed on electrode surfaces and, at the same time, Fe(bphen)₃ ^4- ions were stably confined in the formed PDMA film by electrostatic interaction between them and the positively charged quaternary ammonium sites of the PDMA film. The PDMA-Fe(bphen)₃ ^4-/3- film thus prepared displayed well-defined reversible electroactivity and electrochromic properties ascribable to those of the Fe(bphen)₃ ^4-/3- couple confined in the film. The PDMA-Fe(bphen)₃ ^4- film is red, and the PDMA-Fe(bphen)₃ ^3- film is colorless. The response rate of the color change to a potential pulse was found to be correlated with the kinetic parameters characterizing the rate of the overall charge-transfer reaction at the PDMA-Fe(bphen)₃ ^4-/3- film-coated electrode, that is, the apparent diffusion coefficient (D _app) for the homogeneous charge-transport process within the film and the standard rate constant (k) of the heterogeneous electron-transfer reaction at the electrode/film interface. For the PDMA-Fe(bphen)₃ ^4-/3- film with larger k° and D _app values, the response rate of the color change was larger, Further, k°, D _app, and response rate depended on the concentration (C°) of the Fe(bphen)₃ ^4- (or Fe(bphen)₃ ^3-) confined in the PDMA film; and at a given film thickness, the lower C°, the higher were k°, D _app, and response rate. At a given C°, the thinner the film thickness, the greater was the response rate.     

Initiated oxidation of polyenes formed in the thermal degradation of PVC

Polyenes formed in the thermal degradation of PVC are readily oxidized in the liquid phase in the presence of a radical initiator. In pure oxygen at a constant rate of initiation, different length polyenes are consumed by a first-order reaction: the rate of consumption is proportional to the polyene length and to the square root of initiator concentration. Applying the relationships given by the theory of chain reactions, we determined the ratio of the rate constant of chain propagation calculated for one double bond k₂ to the square root of the chain-termination rate constant k₄. The value obtained, which is relatively high in comparison to other unsaturated hydrocarbons, reflects very well the high reactivity of polyenes of the degraded PVC sample towards oxidation. Intramolecular chain propagation steps are also likely to play a role in the oxidation of polyenes.     

Rate of decomposition of hexafluoroazomethane and the absolute rate of recombination of trifluoromethyl radical at higher temperatures

The unimolecular homogeneous decomposition of hexafluoroazomethane was studied in a VLPP apparatus in the temperature range 720–1050 K and is consistent with the following Arrhenius parameters: at 900 K, where the A factor was assumed to be the same as for 2,2′-azoisobutane. The homogeneous rate of recombination of ·CF₃ radicals at temperatures around 1000 K was also studied under VLPP conditions and was found to be in the fall-off region, corresponding to k/k^∞ = 8.5 × 10^?3 when a rotational transition-state model was used. This model predicts an essentially constant value of k_r^∞ of 10^9.7 over the temperature range 300–1000 K.     

Kinetics and mechanism of oxidation of some nickel(II)–imine–oxime complexes by peroxodisulfate in aqueous acidic solutions

The kinetics of the oxidation of [Ni(II)(H₂L¹)](ClO₄)₂, (H₂L¹ = 3,8-dimethyl-4,7-diaza-3,7-decadiene-2,9-dione dioxime) and [Ni(II)(HL²)]ClO₄, (H₂L² = 3,9-dimethyl-4,8-diaza-3,8-undecadiene-2,10-dione dioxime) by peroxodisulfate anion (PDS) in aqueous media at 298.0 K have been studied. The kinetics of oxidation of both Ni(II) complexes was found to be first order in the complex concentration. The dependence of the pseudo-first-order rate constant, k _obs, for both complexes showed first-order dependence on PDS concentration. The kinetics of oxidation of [Ni(II)(H₂L¹)]²⁺ complex showed a complex dependence on [H⁺] over the pH range of 4.98–7.50, whereas that of [Ni(II)(HL²)]⁺ is independent of pH over the pH range of 5.02–7.76. The value of k _obs, for both complexes, decreased with increasing ionic strength consistent with the involvement of oppositely charged ions in the rate-determining step. The effect of ionic strength is more pronounced for [Ni(II)(H₂L¹)]²⁺–PDS reaction than for [Ni(II)(HL²)]⁺–PDS reaction, confirming the higher charges of the latter.     

Diffusion control in radiation graft polymerization with varying dependence of rate on monomer concentration

The quantitative effect of diffusion control on the rate of radiation-initiated graft polymerization has been studied theoretically for systems in which the diffusion-free reaction may show various dependencies of rate on monomer concentration other than the usual first-order dependence. The study is also very general in that it can be applied to systems involving a variety of different modes of initiation and termination. Whether the grafting process is diffusion-free or diffusion-controlled has been analyzed in terms of the interaction of the initiation rate R_i, the propagation and termination rate constants k_p and k_t, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, the diffusivity D of the monomer in the polymer, and the diffusion-free kinetic order of dependence v of the grafting rate on monomer concentration. The dependence of the grafting rate for both the diffusion-free and diffusion-controlled reactions on these parameters is expressed both by mathematical experssions and graphically. Diffusion control is shown to occur at a critical value of the parameter A which is proportional to L(k_pR_i^w/k_t^zD)^1/2M^(ε?1)/2 where w, z, and v have different values depending on the specific modes of initiation, propagation and termination in a particular grafting system. The grafting rate is shown to vary with the value of A according to specific mathematical expressions. In comparing diffusion-free to diffusion-controlled reaction, it is shown that the former is independent of L and D while the latter is directly dependent on L and inversely on D^1/2. Further, the change from diffusion-free to diffusion-controlled reaction involves a change in the dependence of rate on monomer from v-order to [(v ? 1)/2]-order. The nonsteady-state as well as the steady-state reaction rates have been analyzed.     

Diffusion with discontinuous swelling. V. Type II diffusion into sheets and spheres

Type II diffusion into uniform spheres (radius R) and sheets (thickness 2l) is calculated under the assumption that the glass-gel boundary proceeds at a constant velocity v from the surface towards the interior of the sample, that the diffusion coefficient D_g in the glass is constant and that the diffusion coefficient D_r of the rubbery gel is so much higher than vR or vl that practically no sorbate gradient is needed for the transport through the gel of the sorbate. The diffusion process is completed when this boundary reaches the center of the sample. The concentration profile of the sorbate in the glassy matrix in front of the boundary varies with time and velocity v. It does not, however, influence the boundary propagation velocity. Hence the often observed increase of the rate of the weight gain just at the end of the diffusion process is not considered at all. The relative weight gain of the sample W(t)/W_∞ as a function of time is the only quantity usually measured. From the ordinate intercept A and the initial slope B of the plot of W(t)/t^1/2W_∞ vs. t^1/2, one can calculate the characteristic transport properties, i.e., the diffusion coefficient D_g of the glass and the velocity v of the glass–gel boundary.     

Temperature dependence of rate constants for the reaction of atomic oxygen with hydrogen chloride

A phase-shift method has been used to determine the rate constant for the reaction of ground state oxygen atoms with HCl over the temperature range of 330–600 K. Oxygen atoms were generated by modulated mercury photosensitized decomposition of N₂O, and monitored by the chemiluminescence from their reaction with NO. After correction for diffusion of oxygen atoms from the viewing zone, the rate constants can be represented by the Arrhenius equation k₁ = (3.06 ± 1.43) × 10¹² exp[(?3160 ± 184)/T] cm³/mol·s. The indicated uncertainties are 95% confidence limits for 15 degrees of freedom. Also, the third-body efficiency of HCl relative to N₂O in the reaction O + NO + M ← NO₂ + M was determined to be 1.9 ± 0.2 over the temperature range of 298–360 K.     

Comment on the concentration and temperature dependences of the translational diffusion coefficient of flexible-coil macromolecules in solution: Poly(2-vinyl pyridine) in tetrahydrofuran

Concentration-dependence coefficients k_D^? of the mutual diffusion coefficient of poly(2-vinyl pyridine) in tetrahydrofuran in the temperature range 15–55°C are compared with predictions of recent theories of macromolecular diffusion. In this temperature range a change in local conformation of the polymer occurs. The accompanying changes in chain solvation and coil hydrodynamics result in a sizable decrease in the hydrodynamic interaction parameter X defined by Akcasu. The formulation of theory appropriate for comparison with frame-indifferent experimental diffusivities is discussed. We find that current theories predict qualitatively, but not quantitatively, the change in temperature dependence of k_D^? that occurs at the conformational transition. The discrepancies closely parallel those reported in recent independent comparisons of theoretical k_D^? versus experimental data for flexible-coil molecules. No theory can adequately predict k_D^? over a wide range of X.