The two-parameter taft equation in kinetics of free radical reactions

A new method was developed for the calculation of the resonance substituent constants of the two-parameter Taft equation log k_sub/k₀=ρ*σ*+r*σ^r. It is based on a relationship between the spin density in free radicals and the rate constants of radical substitution reactions of CH₃. Possibilities and limitations of the application of this correlation equation to the investigation of substitution and addition radical reactions are discussed.     

Ternary Copolymerization: Azeotropy and Pseudoazeotropy

An analysis of experimental data for ternary copolymerizations has been performed by an optimizing calculation method, resulting in the estimation of the r _ij copolymerization constants. The azeotrope calculation results have been compared to those based on the r _ij constants found for binary copolymerization. For each set of r _ij constants, the possibility of the ternary azeotropy was studied. The formation of quasihomogeneous ternary copolymers was studied subsequent to the determination of the ternary pseudoazeotropy domains occurring at the intersection of the partial pseudoazeotropy domains.     

Effect of counterions on photoprocesses of thiacarbocyanine in a binary solvent blend

A model describing the effect of counterion X⁻ (X = Cl, I) on the deactivation kinetics of the S ₁ state of thiacarbocyanine Cy⁺X⁻ is presented. According to the model, the ion pair Cy⁺X⁻ in a binary solution is characterized by a distribution function f(r) over interatomic distances r, which depends on the composition of the mixture. The assumption of kinetically independent local states of the ion pair, which decay with the rate constants k _i(r)(i = 1–4 is the index of the decay channel), is made. The statistic analysis of the experimental data in terms of the model permitted us to find the functions f(r) and to estimate the parameters of the constants k _i(r).     

Emulsion copolymerization of styrene and methyl methacrylate

Chain transfer constants to monomer have been measured by an emulsion copolymerization technique at 44°C. The monomer transfer constant (ratio of transfer to propagation rate constants) is 1.9 × 10^?5 for styrene polymerization and 0.4 × 10^?5 for the methyl methacrylate reaction. Cross-transfer reactions are important in this system; the sum of the cross-transfer constants is 5.8 × 10^?5. Reactivity ratios measured in emulsion were r₁ (styrene) = 0.44, r₂ = 0.46. Those in bulk polymerizations were r₁ = 0.45, r₂ = 0.48. These sets of values are not significantly different. Monomer feed compcsition in the polymerizing particles is the same as in the monomer droplets in emulsion copolymerization, despite the higher water solubility of methyl methacrylate. The equilibrium monomer concentration in the particles in interval-2 emulsion polymerization was constant and independent of monomer feed composition for feeds containing 0.25–1.0 mole fraction styrene. Radical concentration is estimated to go through a minimum with increasing methyl methacrylate content in the feed. Rates of copolymerization can be calculated a priori when the concentrations of monomers in the polymer particles are known.     

Evident solvent effect on propagation reactions during radical copolymerization of maleimide and alkene

The radical copolymerization of N-(2,6-dimethylphenyl)maleimide (DMPhMI) and 2,4,4-trimethylpentene (TP) was investigated in several solvents at 60°C. The copolymerization rate and the molecular weight of the resulting copolymers were dependent on the kind of solvent used. It was also revealed that the monomer reactivity ratios depended on the solvent; r₁ = 0.086 and r₂ = 0 in chloroform and r₁ = 0.25 and r₂ = 0 in benzene, where DMPhMI and TP are M₁ and M₂, respectively. The propagation rate constants were determined for the homopolymerization and copolymerization in chloroform and benzene using electron spin resonance spectroscopy. The homo- and crosspropagation rate constants (k₁₁ and k₁₂, respectively) were revealed to depend on the solvent: k₁₁ is 20 and 37 L/mol·s and k₁₂ is 230 and 150 L/mol·s in chloroform and in benzene, respectively. The interaction between the maleimide moiety and the solvent molecules was discussed based on the acceptivity of the solvents. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 1515–1525, 1997     

Relative rate constants for the reactions of trichloropropenyl radical. Application of the two-parameter Taft equation

The relative rate constants for the hydrogen atom abstraction by CCl₃CH?CH· radical from CH₂Cl₂, CHCl₃, CH₃COCH₃, CH₃CN, C₆H₅CH₃, C₆H₅OCH₃, CH₃CHO, and CH₃OH in the liquid phase at 20°C have been measured. It was shown that these reaction rate constants are correlated by the two-parameter Taft equation with ρ* = 0.726 ± 0.096, r* = 1.22 ± 0.16. A relationship between r* and bond dissociation energy D(R? H) has been found for the abstraction reactions of different free radicals.     

Polymerization behaviour of 2,5-dimethylene- 2,5-dihydrofuran

Spontaneous homopolymerization of 2,5-dimethylene-2,5-dihydrofuran (DDF) was studied. The polymerization rates in two different initial monomer concentrations of DDF were analyzed with the first-order and second-order kinetics, and the homopolymerization of DDF was found to obey the first-order kinetics. The Arrhenius plot of the apparent rate constants at 30, 40, 50, and 60° gave an overall activation energy of 68.0 kJ/mol for the polymerization of DDF. From the comparison of the apparent rate constants at –78° and the time (the so-called half-life time) to decrease in half the monomer concentration for DDF with the corresponding values for p-xylylene (QM), DDF was found to be a less reactive monomer than QM. The copolymerizations of DDF with vinyl monomers such as acrylonitrile (AN), α-chloroacrylonitrile (CIAN), diethyl fumarate (DEF), and fumaronitrile (FN) were carried out in chloroform at 50° in the presence of AIBN to obtain the monomer reactivity ratios r₁(DDF) = 30.0 ± 3.0 and r₂ (AN) = 0 for the DDF-AN system, r₁ (DDF) = 1.55 ± 0.2 and r₂(CIAN) = 0 for the DDF-CIAN system, r₁(DDF) = 3.88 ± 0.2 and r₂(DEF) = 0 for the DDF-DEF system, and r₁(DDF) = 2.41 ± 0.1 and r₂ (FN) = 0 for the DDF-FN system, respectively. As the monomer reactivity ratios of r₂ for all systems were zero, Q and e values of DDF were calculated from the combination of two r₁ (DDF) values of any two copolymerization systems to be the 7.64 to 6.63 ×10²¹ range for Q and the –0.70 to –6.31 range for e, indicating that DDF is a highly conjugative and electron-donating monomer. © 1995 John Wiley & Sons, Inc.     

Real-Time FTIR Monitoring of the Carbocationic Copolymerization of Isobutylene with Styrene

The carbocationic copolymerization of isobutylene (IB) and styrene (St) was investigated using real time FTIR monitoring. Depending on the concentration of the individual monomers, and their ratio in the feed, initial rapid monomer consumption was observed. Instantaneous reactivity ratios (r_IB(inst) and r_St(inst)) obtained from apparent rate constants of monomer consumption strongly depended on concentration.     

Can Propagation Reaction in Carbocationic Polymerization and Copolymerization of Styrene be Diffusion Controlled ?

Summary: The reactivity ratios r₁ and r₂ in copolymerizations of styrene and parasubstituted styrenes, for which r₁ = 1/r₂, are in contradiction with diffusion control for their propagation reactions. The cross propagation rate constants k_12copol in copolymerization of styrene with p-chlorostyrene, p-methylstyrene and p-methoxystyrene have been shown to increase with their nucleophilicity parameter N. This is also not compatible with diffusion controlled cross propagation and propagation, but agrees with similar rate constants of propagation for these monomers. The capping rate constants k_12capp of reactions of poly(p-methylstyrene)^± and poly(p-methoxystyrene)^± with π-nucleophiles also increase with N, but with a much larger selectivity. This shows that k_12copol and k_12capp are not identical. The k, from 10⁹ to 6 10⁹ L mol⁻¹ s⁻¹, obtained with p-chlorostyrene, styrene and p-methylstyrene by the Diffusion Clock (DC) method are not consistent with those derived from the ionic species concentration (ISC method) for indene, 2,4,6-trimethylstyrene and p-methoxystyrene of the order of 10⁴ – 10⁵ L mol⁻¹ s⁻¹, also measured for living polymerization. These last values are in agreement with those measured previously in nonliving systems, and with an approximate compensation between the reactivity of a monomer and that of the corresponding carbocation.     

滴定量热法研究连串一级反应热动力学

本文用滴定量热法分别建立了滴定期和停滴反应期1-1级连串反应热动力学的数学模型。根据这两种模型,由非线性最小二乘法原理直接拟合单次实验结果可同时求得1-1级连串反应的速率常数（ k ₁和 k ₂）和摩尔反应焓。并用滴定量热法研究了丁二酸二乙酯皂化反应的热动力学,实验结果验证了两种数学模型的正确性。     

Equilibrium structure and spectroscopic constants of maleic anhydride

The quadratic, cubic, and semi-diagonal quartic force fields of maleic anhydride have been calculated at the MP2 level of theory employing the cc-pVTZ basis set. The spectroscopic constants derived from the force field are in excellent agreement with the corresponding experimental values. The semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational corrections calculated from the cubic force field. This semi-experimental equilibrium structure is in excellent agreement with the ab initio structures computed at the CCSD(T) level of theory and it is closer to the ab initio structure than the purely experimental (or empirical) structures r ₀, r _m⁽¹⁾, and r _m⁽²⁾ obtained by microwave spectroscopy as well as the equilibrium structure derived from gas-phase electron diffraction data.     

Treatments of cross-termination rate constants in radical copolymerization

In copolymerization, Arlman's equation was modified to where k_tab is an apparent cross-termination rate constant depending on a ratio f₁ = [A]/[B], and K_z (x = 1, 2, 3, 4) is the ratio of each cross-termination rate constant depending on the penultimate unit to the geometric mean K?_tab of two termination rate constants in homopolymerizations. The calculated values of (K₁ + K₂/r₁r₂) by using this equation were related to K₁ + K₂/r₁r₂ = 18/r₁r₂.     

Radical copolymerization of crotonyl compounds with styrene

The monomer reactivity ratios for the radical copolymerization of crotononitrile (CN), methyl crotonate (MC), and n-propenyl methyl ketone (PMK) with styrene (St) were measured at 60°C. in benzene and little penultimate unit effect was shown for these systems. The values obtained were: St–CN, r₁ = 24.0, r₂ = 0; St–MC, r₁ = 26.0, r₂ = 0.01; St–PMK, r₁ = 13.7, r₂ = 0.01. The rate of copolymerization and the viscosity of the copolymer decreased markedly as the molar fraction of the crotonyl compound in the monomer mixture increased. The Q–e values were also calculated to be as follows: CN, e = 1.13, Q = 0.009; MC, e = 0.36, Q = 0.015; PMK, e = 0.61, Q = 0.024. A linear relationship was obtained between the e values of the crotonyl compounds and their Hammett constants σ_m.     

Effect of the substituents on radical copolymerization of dialkyl fumarates with some vinyl monomers

Radical copolymerization of dialkyl fumarates (DRF) with various vinyl monomers was carried out in benzene at 60°C. The monomer reactivity ratios, r₁ and r₂, were determined from the comonomer-copolymer composition curves. The relative reactivity of DRFs with various ester substituents toward a polystyryl radical was revealed to depend on both steric and polar effects of the ester groups. It has also been clarified that α-substituents of the polymer radical have a significant role in addition of DRF, from the comparison of the monomer reactivity ratios determined in copolymerizations with monosubstituted and 1,1-disubstituted ethylenes. The absolute cross-propagation rate constants were also evaluated and discussed. © 1992 John Wiley & Sons, Inc.     

Polymer coupling and theory of on-random crosslinking: an analytical solution

Gel formation is an important feature in free-radical polymer coupling. Due to the different possible combination reactivities of each polymer backbone radical, polymer chains are crosslinked in a non-random manner. Equations of the moments have been derived to predict the pregel molecular weight development and the crosslink density at gel point. This work provides an analytical solution for the differential equations. The model agrees with the Flory-Stockmayer gelation theory under the condition of random crosslinking. The magnitude of deviations from the classical theory for non-random crosslinking depends on the product of the radical termination reactivity ratios (r₁r₂), the ratio of the rate constants of backbone radical generation (k), the ratio of the weight-average chain lengths of primary polymers (y), and the polymer weight fractions (w₂).     

Silyl enol ethers as monomer. I. Radical copolymerizability of α-trimethylsilyloxystyrene

α-Trimethylsilyloxystyrene (TMSST), the silyl enol ether of acetophenone, was not homopolymerized either by a radical or a cationic initiator. Radical copolymerization of TMSST with styrene (ST) and acrylonitrile (AN) in bulk and the terpolymerization of TMSST, ST, and maleic anhydride (MA) in dioxane were studied at 60°C and the polymerization parameters of TMSST were estimated. The rate of copolymerization decreased with increased amounts of TMSST for both systems. Monomer reactivity ratios were found as follows: r₁ = 1.48 and r₂ = 0 for the ST (M₁)–TMSST (M₂) system and r₁ = 0.050 and r₂ = 0 for the AN (M₁)–TMSST (M₂) system. The terpolymerization of ST (M₁), TMSST (M₂), and MA (M₃) gave a terpolymer containing ca. 50 mol % of MA units with a varying ratio of TMSST to ST units and the ratio of rate constants of propagation, k₃₂/k₃₁, was found to be 0.39. Q and e values of TMSST were determined using the values shown above to be 0.88 and ?1.13, respectively. Attempted desilylation by an acid catalyst for the copolymer of TMSST with ST afforded polystyrene partially substituted with hydroxyl groups at the α-position.     

The kinetics of complexation of nickel(II) and cobalt(II) with cinchomeronate in aqueous solution

The pressure-jump method has been used to determine the rate constants for the formation and dissociation of nickel(II) and cobalt(II) complexes with cinchomeronate in aqueous solution at zero ionic strength. The forward and reverse rate constants obtained are k_f = 2.27 × 10⁶ M^?1 s^?1 and k_r = 3.81 × 10¹ s^?1 for the nickel(II) complex and k_f = 1.23 × 10⁷ M^?1 s^?1 and k_r = 2.66 × 10² s^?1 for the cobalt(II) complex at 25°C. The activation parameters of the reactions have also been obtained from the temperature variation study. The results indicate that the rate determining step of the reaction is a loss of a water molecule from the inner coordination sphere of the cation for the nickel(II) complex and the chelate ring closure for the cobalt(II) complex. The influence of the pyridine ring nitrogen atom of the cinchomeronate ligand on the complexation of cobalt(II) ion is also discussed.     

Rates of copolymerization of acrylonitrile and ethylenesulfonic acid

Use was made of differential absorption in the near-infrared region to follow the rates of copolymerization of acrylonitrile (AN, M₁) with ethylenesulfonic acid (ESA, M₂) in aqueous zinc chloride solution. The concentrations of the monomers were followed separately and simultaneously. It was found experimentally that the ratios d log [M₁]/dt and d log [M₂]/dt were each constant. This was interpreted to mean that the product of the reactivity ratios of the two monomers (r₁,r₂) is unity and that the ratio of termination rate constants is equal to the propagation reactivity ratio. It was found that d log [M₁]/d log [M₂] = r₁ = 4.5₂. This value is in fair agreement with polymer composition data obtained independently. In the Q—e system the equality r₁r₂ = 1 is equivalent to the monomers having equal e values. Thus, in the AN—ESA system, P₁/P₂ = k₁₁/k₂₁ = k₁₂/k₂₂ = k_1T/k_2T, where P₁ is the resonance constant of polymer radicals ending in units of M₁; and k₁₁, k₁₂, and k_1T are the rate constants involving the reaction of this radical with M₁, M₂, and T (terminating agent), respectively. A gel effect was not observed even at M₁ conversions as high as 88%.     

Conformational Analysis of Biphenyl Derivatives. I. A Novel Steric Constant from the Internal Rotation Rate of 2,2′‐Bis‐(N‐Substituted Carbamoylmethyl)Biphenyl by Means of Dynamic NMR

A novel scale of steric substituent constant E_s^D is defined from the correlation of the logarithms of the internal rotation rate (k_r) at 393 K with Hancock (E_s^c) steric constant by means of dynamic NMR. In the inhibition of Pseudomona species lipase by 2,2′‐bis‐(N‐substituted carbamoylmethyl)biphenyls (1‐8), the logarithms of bimolecular rate constants are multiply correlated with both the Taft substituent constant σ* and E_s^D.     

Thermodynamic and kinetic characteristics of liquid phase hydrogenation of substituted nitrobenzenes

Quantum-chemical calculations of the thermodynamic characteristics of hydrogenation of nitrobenzoic acid isomers and nitrophenol in the gas phase and also in aqueous and alcoholic media were performed. Correlation dependences between the calculated Δ_r G ₂₉₈^○ values and rate constants for the reaction in various media were obtained.