On the propagation rate constants of cationic polymerizations

The concepts employed to explain polymerizations by ionizing radiations are used for a critical examination of the concepts involved in interpreting the kinetics of chemically initiated cationic polymerizations. It is explained how the interactions of the propagating carbenium ions with the solvent, monomer, and anion can result in the formation of up to six distinct unpaired species and several kinds of ion pairs; therefore, the consumption of the monomer can be governed simultaneously by many rate constants. Only one of these can have any general theoretical use, and suggestions are made for how it can be measured. For the first time, it is shown that the ion‐pairing process must involve a ligand displacement and so resembles the amination of the Ag⁺ ion, for example, in an aqueous solution by NH₃, rather than an association of inert ions of unchanging identity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2537–2544, 2002     

Effect of a complex formation on the calculated low-pressure rate constant of a bimolecular gas-phase reaction governed by tunneling

Many important bimolecular hydrogen-transfer processes that take place in the atmosphere proceed via a potential energy minimum (hydrogen-bonded complex) that precedes along the minimum energy path the unique saddle point of the reaction, the one corresponding to the hydrogen transfer. It is clear that the one-step low-pressure rate constant of such a reaction does not depend on the existence of any complex along the minimum energy path below the reactant if the reaction takes place by thermal activation over a transition state that lies quite above the reactants (for instance 10 kcal/mol). However, we have quantitatively shown in this article that the scenario notoriously changes if the reaction involves significant tunneling. In this work, we have theoretically calculated the rate constants and their temperature dependence for the reaction HO+HOH→HOH+OH by means of a canonical variational transition state theory and a canonical unified statistical theory (when necessary). Multidimensional tunneling effects have been included with a semiclassical transmission coefficient. Two kinds of modified potential energy surfaces (PESs), obtained from an original ab initio potential energy surface, previously calculated by us, have been used. The Eckart-modified PESs serve to model the hydrogen-abstraction profiles with no complexes along the path, while the Gaussian-modified PESs model the energy profiles with two complexes along the path symmetrically distributed at each side of the abstraction saddle point. Our results show that the existence of those complexes reduces the thickness of the classically forbidden region for energies below the adiabatic barrier, and then tunneling is promoted and the reaction is accelerated. The effect of the complex formation in several kinetic magnitudes, as the Arrhenius parameters and the kinetic isotope effect has also been analyzed. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1685–1692, 1999     

Solvent Effect on the Kinetic Study of the Alkaline Hydrolysis of Formamide in Acetone-Water Mixtures

The specific rate constants for the alkaline hydrolysis of formamide were determined in a series of acetone-water mixtures ranging from 0.0% to 70% by weight of the organic solvent and at different temperature, 25°–50°. The rate was found to be larger in water. Addition of acetone appears to cause a change in the solvent structure as concluded from the variation of log k with either 1/D or log[H₂O]. The reactivity of the reactants and the activated state seems to be affected differently by a change in the solvent structure. The magnitude of such effect should be considered separately on both the reactants and the activated state in order to account for the increase of the rate as the dielectric constant of the medium is increased.     

Influence of media polarity on the rate of activation of “dormant” chains in nitroxide‐mediated radical polymerization

Rate constants of decomposition of “living” polymeric adducts polystyrene (PS)‐TEMPO, poly‐4‐vinylpyridine‐TEMPO, PS‐SG1, and polyacrylic acid‐SG1 in different solvents were determined by the method of a competitive inhibition by means of electron spin resonance. It was found that with the increase in polarity of solvent, the values of constants become higher for all systems studied. This effect opens a new way of activating chains in nitroxide‐mediated radical polymerization. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

The kinetics of enhanced spin capturing polymerization: Influence of the nitrone structure

Several nitrones and one nitroso compound have been evaluated for their ability to control the molecular weight of polystyrene via the recently introduced radical polymerization method of enhanced spin capturing polymerization (ESCP). In this technique, molecular weight control is achieved (at ambient or slightly elevated temperatures) via the reaction of a growing radical chain with a nitrone forming a macronitroxide. These nitroxides subsequently react rapidly and irreversibly with propagating macroradicals forming polymer of a certain chain length, which depends on the nitrone concentration in the system. Via evaluation of the resulting number‐average molecular weight, M_n, at low conversions, the addition rate coefficient of the growing radicals onto the different nitrones is determined and activation energies are obtained. For the nitrones N‐tert‐butyl‐α‐phenylnitrone (PBN), N‐methyl‐α‐phenylnitrone (PMN), and N‐methyl‐α‐(4‐bromo‐phenyl) nitrone (pB‐PMN), addition rate coefficients, k_ad,macro, in a similar magnitude to the styrene propagation rate coefficient, k_p, are found with spin capturing constants C_SC (with C_SC = k_ad,macro/k_p) ranging from 1 to 13 depending on the nitrone and on temperature. Activation energies between 23.6 and 27.7 kJ mol⁻¹ were deduced for k_ad,macro, congruent with a decreasing C_SC with increasing temperature. Almost constant M_n over up to high monomer to polymer conversions is found when C_SC is close to unity, while increasing molecular weights can be observed when the C_SC is large. From temperatures of 100 °C onward, reversible cleavage of the alkoxyamine group can occur, superimposing a reversible activation/deactivation mechanism onto the ESCP system. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1098–1107, 2009     

Effect of LiClO4 on the radical polymerization of Di-2-[2-(2-methoxyethoxy)ethoxy]ethyl itaconate

The effect of LiClO₄ on the polymerization of di-2-[2-(2-methoxyethoxy)ethoxy]ethyl itaconate (DMEI) with dimethyl 2,2′-azobisisobutyrate (MAIB) was investigated in methyl ethyl ketone (MEK) kinetically and by ESR. The polymerization rate (R_p) at 50°C, where the concentrations of DMEI and MAIB were 1.00 and 5.00 × 10⁻² mol/L, increased with increasing [LiClO₄]. Marked acceleration was observed at higher [LiClO₄]s than 1.0 mol/L. The molecular weight of resulting polymer (ca. 10,000) was relatively insensitive to [LiClO₄], indicating occurrence of chain transfer. IR analysis of mixtures of LiClO₄/DMEI and LiClO₄/poly(DMEI) indicated complexation of LiClO₄ with DMEI and its polymer. The rate constants of propagation (k_p) and termination (k_t) were determined by ESR. k_p (1.7–10.5 L/mol s at 50°C) increased with [LiClO₄]. k_t (5.2–1.0 × 10⁴ L/mol s at 50°C) showed remarkable decrease at higher [LiClO₄]s than 1.0 mol/L. R_p of polymerization of equimolar complex of LiClO₄/DMEI with MAIB at 50°C in MEK was expressed by R_p = k[MAIB]^0.5[DMEI]^2.4. k_p increased and k_t decreased with [DMEI]. The activation energies of overall polymerization, propagation and termination were estimated to be 34.5, 8.0, and 59.4 kJ/mol. Copolymerization of DMEI with styrene was also profoundly affected by the presence of LiClO₄. Such large effects of LiClO₄ on the homo- and copolymerization of DMEI are explicable in term of association of LiClO₄-complexed DMEI monomers. © 1997 John Wiley & Sons, Inc.     

Kinetic study on the radical polymerization of 2‐methacryloyloxyethyl phosphorylcholine

Polymerization of 2‐methacryloyloxyethyl phosphorylcholine (MPC) was kinetically investigated in ethanol using dimethyl 2,2′‐azobisisobutyrate (MAIB) as initiator. The overall activation energy of the homogeneous polymerization was calculated to be 71 kJ/mol. The polymerization rate (R_p) was expressed by R_p = k[MAIB]^0.54±0.05 [MPC]^1.8±0.1. The higher dependence of R_p on the monomer concentration comes from acceleration of propagation due to monomer aggregation and also from retardation of termination due to viscosity effect of the MPC monomer. Rate constants of propagation (k_p) and termination (k_t) of MPC were estimated by means of ESR to be k_p = 180 L/mol · s and k_t = 2.8 × 10⁴ L/mol · s at 60 °C, respectively. Because of much slower termination, R_p of MPC in ethanol was found at 60 °C to be 8 times that of methyl methacrylate (MMA) in benzene, though the different solvents were used for MPC and MMA. Polymerization of MPC with MAIB in ethanol was accelerated by the presence of water and retarded by the presence of benzene or acetonitrile. Poly(MPC) showed a peculiar solubility behavior; although poly(MPC) was highly soluble in ethanol and in water, it was insoluble in aqueous ethanol of water content of 7.4–39.8 vol %. The radical copolymerization of MPC (M₁) and styrene (St) (M₂) in ethanol at 50 °C gave the following copolymerization parameters similar to those of the copolymerization of MMA and St; r₁ = 0.39, r₂ = 0.46, Q₁ = 0.76, and e₁ = +0.51. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 509–515, 2000     

Solvent effects on complexation of crown ethers with LiClO4, NaClO4 and KClO4 in methanol and acetonitrile

The thermodynamic formation constants K_f for complexation of Li⁺, Na⁺ and K⁺ with the crown ethers 12C4 and 15C5 have been determined in methanol and acetonitrile at 25°C using precision conductivity data. The method permits evaluation of very small K_f values (e.g., K_f=6.98 mol^–1-dm³ for LiClO₄+12C4 in methanol) as well as fairly large values (e.g., K_f=2.73×10⁴ mol^–1-dm³ for NaClO₄+15C5 in acetonitrile). The determination of K_f values from conductivity data takes into consideration the often neglected ion pair formation of both the uncomplexed and the complexed cations. Our results for K_f are generally consistent with previously reported values based on potentiometry, calorimetry and polarography, but there are significant differences in several cases which we attribute to neglect of ion association both for the uncomplexed or free cation K_a and the macrocyclic complexed cation K_a2. Our results are also consistent with the well known concepts relating the magnitude of K_f to both the cavity diameter and ion-solvent interactions. Limiting molar conductivities ₂ ⁰ for the complex salt (M-crown ether) (ClO₄) in both solvents were generally found to be smaller or very close to the corresponding quantity ₁ ⁰ for the binary MClO₄-solvent system. However, in methanol, single ion limiting molar conductivities for the cationic complexes ₂ ⁰ exhibit anomalous behavior which is attributed to solvation differences between free cations and complexed cations.     

The second dissociation constant of sulfuric acid at various temperatures by the conductometric method

The thermodynamic second dissociation constant K₂ for sulfuric acid has been determined by conductivity measurements of aqueous sulfuric acid solutions at various temperatures. The data are treated by using two different methods developed with two independent assumptions due to Noyes et al. and Shedlovsky. Both methods require the knowledge of relevant ionic conductivities, which may be calculated from the Onsager limiting law. The values for K₂ obtained with these two methods show excellent agreement. The value of 0.0103 mol-L^–1 at 25°C agrees with the best literature value of 0.0102 mol-L^–1 within the experimental uncertainty, as also does the enthalpy of dissociation which is derived from the derivative of the temperature coefficient of K₂.     

烷基过氧化氢中氢提取反应类大分子体系的反应能垒与速率常数的精确计算

自由基与分子反应是一类具有负活化能的非基元反应,通常认为是通过反应复合物的两步过程,在大气化学和碳氢燃料燃烧机理中广泛存在,且在理论计算和实验上广泛研究.以碳氢燃料燃烧机理中重要反应类羟基自由基提取烷基过氧化氢α位氢的反应为研究对象,通过量化计算揭示其反应规律,计算得到其精确动力学参数.在所研究反应类中,定义第一步反应复合物的生成反应的标准摩尔吉布斯自由能变化等于零时所对应的温度为其转折温度T_c,并表明了当T >> T_c时可采用稳态近似法处理该类反应体系,得到总包反应速率常数.所有反应涉及的物种几何结构优化和频率分析均在BHandHLYP/6-311G（d,p）水平下得到,并在所研究反应类中选取了5个代表反应,通过CCSD（T）/CBS单点能计算,得到其最高转折温度为195.17 K,远远低于碳氢燃料燃烧模拟通常关注温度范围的最低温度650 K,表明用稳态近似法处理该类负活化能反应体系是合理的.计算还表明,该类反应的过渡态反应中心几何结构守恒,因此可将等键反应方法引入类反应,通过对低水平从头算得到的反应能垒进行校正,以得到高精度的结果.为了验证等键反应方法的可靠性,选取5个反应作为研究对象,将低水平BHandHLYP/6-311G（d,p）的校正结果和高水平CCSD（T）/CBS直接计算的结果进行比较,反应能垒最大绝对偏差由校正前的19.99 kJ·mol^－1降到校正后的1.47 kJ·mol^－1,表明用等键反应方法,只需在低水平从头算水平下就可以得到高水平的计算结果,从而可解决大分子体系精确动力学参数缺乏的问题.利用等键反应方法计算了20个反应的反应能垒,并结合过渡态理论计算得到了总包反应的速率常数,并揭示了该类反应只在低温段呈现负活化能关系.     

Influence of the size of the formed cycle on the reactivity of free radicals in cyclization reactions

Numerous experimental data for the cyclization of free radicals C·H₂(CH₂)_nCH=CH₂ cyclo-[(CH₂)_n+1CH(C·H₂)], and C·H₂(CH₂)_nCH=CHR cyclo-[(CH₂)_n+1C·HCHR] were analyzed in the framework of the parabolic model. The activation energy of thermoneutral (H _e = 0) cyclization E _e0 decreases linearly with an increase in the energy of cycle strain E _rsc: E _e0(n) (kJ mol–1) = 85.5 – 0.44E _rsc(n) (n is the number of atoms in the cycle). The activation entropy of cyclization S ^# also depends on the cycle size: the larger the cycle, the lower S ^#. A linear dependence of S ^# on the difference between the entropies of formation S° of cyclic hydrocarbon and the corresponding paraffin was found: S ^# = 1.00[S°(cycle) – S°(C_nH_2n+2)]. The E _e0 values coincide for cyclization reactions with the formation of the six-membered cycle and the bimolecular addition of alkyl radicals to olefins.     

Effect of temperature on the number of active sites and propagation rate constant at ethylene polymerization over supported bis(imino)pyridine iron catalysts

The inhibition of ethylene polymerization with radioactive carbon monoxide (¹⁴CO) was used to obtain data on the number of active sites (C_P) and propagation rate constant (k_P) at ethylene polymerization in the temperature range of 35–70 °C over supported catalysts LFeCl₂/Al₂O₃, LFeCl₂/SiO₂, and LFeCl₂/MgCl₂ (L: 2,6‐(2,6‐(Me)₂C₆H₃N = CMe)₂C₅H₃N) with activator Al(i‐Bu)₃. The values of effective activation energy (E_eff), activation energy of propagation reaction (E_P), and temperature coefficients of variation of the number of active sites (E_Cp = E_eff ? E_P) were determined. The activation energies of propagation reaction for catalysts LFeCl₂/Al₂O₃, LFeCl₂/SiO₂, and LFeCl₂/MgCl₂ were found to be quite similar (5.2–5.7 kcal/mol). The number of active sites diminished considerably as the polymerization temperature decreased, the E_Cp value being 5.2–6.2 kcal/mol for these catalysts at polymerization in the presence of hydrogen. The reactions of reversible transformations of active centers to the surface hydride species at polymerization in the presence and absence of hydrogen are proposed as the derivation of E_Cp. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6621–6629, 2008