Estimation of molecular weight distribution based on chain length dependence of termination rate

When a chain length dependence of polymer-polymer termination is given by k_t,ns = const. (n^?2a + s^?2a) where n and s are the chain lengths for the polymer radicals and a is parameter, an instantaneous weight fraction of the non-reacting polymers is derived as: where h and k? are the kinetic parameters, p is a parameter depending on a, and p_n is instantaneous number-average chain length. Such a weight fraction corresponds to the experimental one over a wide range of conversion in the polymerization of styrene. On the scope of this correspondence, the polymer-polymer termination rate is estimated as: k?_t = 8πR₀D₁/100 ( = 4πR_sD_s) where R₀ is reaction radius between monomer radicals and D₁ is the diffusion coefficient of the monomer; R_s is reaction radius between segment radicals with n ? 100 and D_s is the diffusion coefficient of the segment. The Fujita-Doolittle theory applies to such a rate. Further, the rate also yields 1.5 × 10⁷1./mole-sec, which is the observable extent at conversions less than 0.2.     

Collision between polymeric radicals for termination rate constants

The motion of each polymeric radical during a collision between the polymeric radicals with the same radius is treated as completely random motion. The result obtained is: k_t = 0.250k_s (where k_t is the chain-termination rate constant and k_s is the reaction rate constant between radical chain ends). On taking the motion of the primary radical during a collision between a primary radical and a large polymeric radical to be completely random, the result obtained is: k_ti = 0.250k_si (where k_ti is the primary radical termination rate constant and k_si is the reaction rate constant between primary radical and radical chain end). On substituting k_s for k_si in the second equation, the rate constant obtained becomes the chain termination rate constant between the very small polymeric radical and the very large polymeric radical, and identical to the former equation. This identity indicates that the effect of the difference of the size of the polymeric radicals on the collision process relating to the chain termination rate constant should not be large.     

Studies on anionic polymerization of lactams. Part II. Effect of cocatalysts on the polymerization of pyrrolidone

The rates of addition of pyrrolidonate magnesium bromide (PyMgBr) to N-benzoyl-, N-acetyl-, and N-methylpyrrolidone were measured in solution in tetrahydrofuran (THF). The values found for the rate constants at 25°C. were 9.5 × 10^?2, 2.8 × 10^?2, and 5 × 10^?4 l./mole-sec., respectively. The rate constant for addition of PyMgBr to pyrrolidone was also measured and found to be 3 × 10^?9l./mole-sec. Possible causes for the large difference between the values of these constants are discussed.     

Solvent‐Mediated Functionalization of Benzofuroxan on Electron‐Rich Ruthenium Complex Platform

An unprecedented reactivity profile of biochemically relevant R‐benzofuroxan (R=H, Me, Cl), with high structural diversity and molecular complexity on a selective {Ru(acac)₂} (acac=acetylacetonate) platform, in conjugation with EtOH solvent mediation, is revealed. This led to the development of monomeric [Ru^III(acac)₂(L^1R)] ( 1 a – 1 c ; L^1R=2‐nitrosoanilido derivatives) and dimeric [{Ru^II(acac)₂}₂(L^2R)] ( 2 a – 2 b ; L^2R=(1E,2E)‐N¹,N²‐bis(2‐nitrosophenyl)ethane‐1,2‐diimine derivatives) complexes in one pot with a change in the metal redox conditions. The functionalization of benzofuroxan in 1 and 2 implied in situ reduction of N=O to NH^? in the former and solvent‐assisted multiple N?C coupling in the latter. The aforesaid transformation processes were authenticated through structural elucidation of representative complexes, and evaluated by their spectroscopic/electrochemical features, along with C₂D₅OD labeling and monitoring of the impact of substituents (R) in the benzofuroxan framework on the product distribution process. The noninnocent potential of newly developed L¹ and L² in 1 and 2 , respectively, was also probed by spectroelectrochemistry in combination with DFT calculations.     

Polymer reactions. V. Kinetics of autoxidation of polypropylene

The rate constants for the autoxidation of polypropylene were determined by a combined ESR, volumetric, and chemical method. The values of k_i, k_p, and k_t at 110°C. are 3 × 10^?4 sec.^?1, 1.9 l./mole-sec., and 3 × 10⁶ l./mole-sec., respectively. The values of k_i and its activation energy are the same as those for the decomposition of polypropylene hydroperoxide, thus identifying the latter as the principal initiation process. The values of the temperature-independent k_t suggest that secondary peroxy radicals are the terminating species. The rate constants are compared with rate constant ratios for initiated autoxidations of squalane and other related systems.     

INDO Calculation of Spin Densities in Radical Cations of a Series of Substituted Nitro- and m-Dinitrobenzenes

The spin densities in radical cations of 22 substituted nitro- and m-dinitrobenzenes were calculated by the INDO method. For radical anions of substituted nitrobenzenes, a good linear correlation was obtained between the spin densities s_Ns_N and experimental hyperfine coupling constants with the nitrogen atoms of the NO₂ groups (a ^N): a ^N = K _N s _N s _N, where K _N = 428.58 (R ² = 0.96). For radical anions of substi- tuted m-dinitrobenzenes, no satisfactory agreement between the calculated and experimental a ^N constants was attained.     

Determination of propagation and termination rate constants for some methacrylates in their radical polymerizations

Rotating sector determinations of k_p and 2k_t for ten methacrylates undergoing radical polymerization were carried out at 30°C. Ester groups in the monomers were: isopropyl, ethyl, β-cyclohexylethyl, methyl, γ-phenylpropyl, β-phenylethyl, β-methoxyethyl, benzyl, β-chloroethyl, and phenyl. Values of k_p obtained were 121, 126, 1190, 141, 149, 228, 249, 1250, 254, and 411 l./mole-sec., respectively; values of 2k_t × 10^?6 were 4.52, 7.35, 32.8, 11.6, 0.813, 1.88, 9.30, 41.9, 6.71, and 11.9 l./mole-sec., respectively. Omitting the data for the β-cyclohexylethyl and benzyl esters, a Taft correlation, log k_p = (0.70 ± 0.18)σ* + 2.2, was established, where σ* denotes Taft's polar substitutent constants for the above-mentioned ester groups. The steric substituent constants E_s were found to have no influence on k_p. Combination of k_p with r₂ data from copolymerization studies with styrene or methyl methacrylate as M₁ comonomer revealed that the more reactive monomer gave rise to the more reactive polymer radical. Monomer viscosities and molar volumes of the ester groups were found to correlate with 2k_t.     

Spatially intermittent polymerization

A novel reactor has been designed which permits the precise determination of absolute rate constants in photoinitiated free-radical vinyl polymerization. A solution of monomer and initiator flows through a dark tubular reactor past regularly spaced slots through which light shines. The alternating dark and light regions produce spatially intermittent polymerization (SIP) and make the system analogous to the well-known rotating-sector technique. However, the SIP reactor has the advantage of producing large volumes of reaction product, at low conversion, suitable for analysis of both conversion and molecular weight. This supplies the necessary data, from a single set of experiments, for the simultaneous determination of the rate constants for propagation and termination. Experimental data are reported at 25°C for methyl methacrylate which indicate that k_p = 315 I./mole-sec, independent of polymer molecular weight, and k_t is dependent on molecular weight especially at low molecular weight, approaching a lower value of k_t = 30 × 10⁶ I./mole-sec at a molecular weight of 10⁶. For styrene, measurements being made only at high molecular weight, k_p = 74 ± 5 and k_t = 37 ± 0.3 × 10⁶ l./mole-sec at 25°C.     

Solvent effects on the radiation-induced graft polymerization of styrene onto poly(isobutylene oxide)

The graft polymerization of styrene onto preirradiated poly(isobutylene oxide) (PIBO) with methanol and benzene was studied. The order of grafting yield and of the number-average molecular weight of graft chains decrease in the order; undiluted styrene > styrene–methanol (1:1) solution > styrene–benzene (1:1) solution. A kinetic treatment to calculate rate constants from the rate of grafting and the molecular weight of the graft chain was proposed. The propagation rate constant k_p was 0.2–0.3 l./mole-sec and the termination rate constant k_t was 1.0–16.0 l./mole-sec. The ratio k_p/k_t in this heterogeneous system was larger than that in homogeneous system by a factor of about 10⁴–10⁵.     

Calculations of Monomer Conversion and Radical Concentration in Reversible Addition‐Fragmentation Chain Transfer Radical Polymerization

Simple expressions are derived for the development of monomer conversion, as well as propagating radical, adduct radical, dormant chain, and dead chain concentrations in reverse addition‐fragmentation transfer polymerization (RAFT). The relations for the profiles of propagating radical concentration and conversion versus time are derived and depend on group parameters of rate constants and chemical recipe. The analytical equations are verified against numerical solutions of the mass‐balance differential equations. This derivation involves the steady‐state hypothesis for radical and RAFT agent concentrations. The errors introduced by these assumptions are negligible when the fragmentation rate constant, k_f, is higher than 10 s⁻¹ or when the cross‐termination rate constant, k_ct, is higher than 10⁵ L · mol⁻¹ s⁻¹.

Calculated concentration profiles (points: numerical, lines: analytical) of propagating radical R, adduct radical A, dormant T, and dead D (= P + P′) chains.     

Relationship between kinetic chain length and radical polymerization rate

In the copolymerization of monomers M₁ and M₂ which form polymer radicals of chain length n of N¹_n with electron on a M₁ type and N²_n with one on a M₂ type, it is assumed that the specific rates of termination between N¹_n and N¹_n and N¹_s, N¹_n and N²_s, and N²_n and N²_s are k_α(ns)^?a, k_β(ns)^?a, and k_γ(ns)^?a, respectively, where k_α, k_β, and k_γ are the rate constants of reaction between segment radicals in the respective termination, and a is constant. The relation between kinetic chain length n? and polymerization rate R_p is derived as: 1/n? = 1/n?₀ + const. (R_p)^A(a), where n?₀ is the kinetic chain length of the polymer formed by transfer and A (a) is unity (predominance of transfer) and 1/(1–2a) (no transfer). In the copolymerization between methyl methacrylate (M₁) and styrene (M₂) at 60°C, when R_p → 0, k_r12/k₁₂ + k_r21/k₂₁ = 5.9× 10^?5 is obtained, where k_r12 and k_r21 are the rate constants of transfer of N¹ to M₂ and N² to M₁, and k₁₂ and k₂₁ are the rate constants of propagation of N¹ to M₂ and N² to M₁. In the absence of transfer, the a value is found to be 0.065 ± 0.008, from the relation between n? and R_p, regardless of the monomer composition. Such a value is also estimated by setting b = 0.72 in a = 0.153 (2b–1), where b is the constant in the Mark-Houwink equation. Further, the value of k_β is found to be 1.18 × 10⁹l./mole-sec, which is comparable with the diffusion-controlled rate of reaction between small molecules. The rate of reaction between segment radicals is fivefold larger than the polymer-polymer termination when transfer predominates.     

Polymerization of Cyclosiloxanes. I. Kinetic Studies on Living Polymer—Octamethylcyclotetrasiloxane Systems

The kinetics of the anionic polymerization of octamethylcyclotetrasiloxane (D₄) initiated by α-methylstyrene living polymer in tetrahydrofuran was studied. The following kinetic scheme was postulated: Initiation: Propagation: where S^- and M represent the initiator and D₄, respectively. At a living end concentration of 0.0377 mole/l. and a monomer concentration of 1.5 mole/l. in tetrahydrofuran at 25°C. the following kinetic data were obtained: k₁ = 2.3 × 10^?4 l./mole-sec., k₂ < 2.3 × 10^?5 sec.^?1, k₃ = 2.75 × 10^?2l./mole-sec. k₄ ≈ 1.17 × 10^?2 sec.^?1, K₁ > 10 l./mole and K₂ ≈ 2.35 l./mole. The rate constants k₁ and k₃ were found to be dependent on the concentration of anions. This is attributed to the dissociation of ion pairs to free ions at lower concentration. Under the experimental conditions studied the majority of the anions were present in the form of ion pairs. The reactivity of the free ions is about 100 times greater than that of ion pairs. There is no temperature effect on K₂, indicating zero ΔH and positive ΔS in the propagation reaction.     

Reactivity ratios of styrene and methyl methacrylate at 90°C

From the conversion–composition data of Gruber and Elias, the reactivity ratios of styrene (M₁) and methyl methacrylate (M₂) were calculated to be r₁ = 0.55 ± 0.02 and r₂ = 0.58 ± 0.06 at 90°C. The least-squares method was then used on these and literature values at other temperatures to obtain the Arrhenius expressions: In r₁ = 0.04736 – (235.45/T), and ln r₂ = 0.1183 – (285.36/T). Using literature values for the homopolymerization steps, A₁₁ = 2.2 × 10⁷l./mole-sec., E₁₁ = 7.8 kcal./mole, and A₂₂ = 0.51 × 10⁷ l./mole-sec.^?1, E₂₂ = 6.3 kcal./mole, activation energies and frequency factors were then calculated for the cross-polymerization steps: A₁₂ = 2.1 × 10⁷ l./mole-sec., E₁₂ = 7.3 kcal./mole, and A₂₁ = 0.45 × 10⁷ l./mole-sec., E₂₁ = 5.7 kcal./mole.     

Effects of iron(III) chloro complexes on the polymerization of styrene

The polymerization of styrene initiated by 2,2′-azobisisobutyronitrile has been studied in N,N-dimethylformamide solution at 60°C in the presence of hexakis(N,N-dimethylformamide) iron(III) tetrafluoroborate alone, and also in the presence of added lithium chloride. The presence of Fe(DMF)₆³⁺ ions in the polymerizing systems caused retardation, but iron(III) chloro complexes produced well defined inhibition periods. Velocity constants at 60°C for polystyryl radicals towards Fe(DMF)₆³⁺, Fe(DMF)₅Cl²⁺, Fe(DMF)₄Cl₂⁺, and FeCl₄^? ions were calculated to be 847, 4.15 × 10⁴, 6.55 × 10⁴, and 3.14 × 10⁴ l./mole-sec, respectively. Values of the initiator efficiency f for most systems investigated ranged from 0.59 to 0.62.     

Water-absorption properties of an acetal copolymer

The kinetics of sorption from the liquid phase to equilibrium and desorption were studied over the temperature range 0–80°C. Equilibrium uptake was found to increase linearly with concentration in this range. Sorption-desorption kinetics showed the diffusion coefficients to decrease with increasing concentration, although the extent of this dependence did not appear in itself to be temperature-dependent. The apparent diffusion coefficient obeyed the law D = D₀ exp {? E/RT} over the temperature range studied, giving E = 9.9 kcal./mole and D₀ = 0.45 cm.² sec.^?1. These values are compared with corresponding values for other polymers.     

Polymerization of vinyl acetate retarded by 4-methyl-2,6-di-tert-butylphenol: Kinetic and ESR studies

4-Methyl-2,6-di-tert-butylphenol strongly retards the free radical polymerization of vinyl acetate initiated by azobisisobutyronitrile. The chain transfer constant, estimated from rate data, is 0.020 ± 0.004 at 35°C and does not vary significantly with temperature. Molecular weight data lead to transfer constants of 0.023, 0.020, and 0.024 at 35, 45, and 55°C, respectively. A mean kinetic isotope effect of 9.8 ± 1.0 is observed for the phenol deuterated at the OH group, showing that the main attack of poly(vinyl acetate) radicals on the phenol involves hydrogen abstraction from this group. The activation energy for hydrogen abstraction is estimated to be 7.8 kcal/mole, and the rate constant at 50°C is 160 ± 40 1./mole-sec. The stationary concentration of 4-methyl-2,6-di-tert-butylphenoxyl in the polymerization mixture is proportional to the phenol concentration and is independent of the initiator concentration, as shown by electron spin resonance studies. Cross termination of poly(vinyl acetate) and phenoxy radicals occurs to a greater extent than mutual termination of these radicals. The rate constant for cross termination is close to 1 × 10⁸ 1./mole-sec at 50°C; the activation energy for cross termination is 2.9 ± 1.3 kcal/mole.     

Molecular weight distribution studies. I. Radiation-induced polymerization of liquid α-methylstyrene

The concentration of water in purified and BaO-dried α-methylstyrene was found to be 1.1 × 10^?4M. The radiation-induced bulk polymerization of the α-methylstyrene thus prepared was studied in the temperature range of ?20°C to 35°C. The polymerization rate varied as the 0.55 power of the dose rate. The theoretical molecular weights and molecular weight distribution were calculated from a proposed kinetic scheme and these values were then compared with those found experimentally. The agreement between these two was reasonably close, and therefore it was concluded that, from the molecular weight distribution point of view, the proposed kinetic scheme for the cationic polymerization of α-methylstyrene is an acceptable one. The rate constant for chain transfer to monomer k_f changed with temperature and was found to be responsible for the decrease in the molecular weight of the polymer with increase in temperature. k_f and k_p at 20°C were found to be 0.95 × 10⁴ l./mole-sec and 0.99 × 10⁶ l./mole-sec, respectively.     

Supported catalysts for stereospecific polymerization of propylene

Tetrabenzyltitanium (B₄Ti), tribenzyltitanium chloride (B₃TiCl), tetra(p-methylbenzyl)titanium (R₄Ti) and tri(p-methylbenzyl)titanium chloride (R₃TiCl) have been used as catalysts for ethylene and propylene polymerization activated by AlEt₂Cl. B₄Ti-AIEt₂Cl in solution polymerizes ethylene readily but its activity decays rapidly. B₄Ti was also supported on Cab-O-Sil, Alon C, and Mg(OH)Cl. The last support was found to give catalyst with longest lifetime with a rate of polymerization, R_p = 7.0 g/hr-mmole Ti-atm ethylene. ¹⁴CO counting techniques gave 1.13 × 10^?3 mole of propagating center per mole of B₄Ti; the rate constant of propagation, k_p = 540 l./mole-sec. None of the tetravalent titanium compounds polymerize propylene in solution. However, when supported on Mg(OH)Cl, Cab-O-Sil, Alon C, Cab-O-Ti, and charcoal, they all polymerize propylene. In this work the supports were characterized by various techniques, including the paramagnetic probe method, to determine the concentration and nature of surface hydroxyls. Those factors controlling the rate and stereospecificity of propylene polymerization were investigated. The system B₃TiCl–Mg(OH)Cl–AlEt₂Cl is the most active with R_p = 2.89 g/hr-mmole Ti-atm propylene. The concentration of propagation center is 0.9 × 10^?3 mole per mole of B₃TiCl; k_p = 32 l./mole-sec. This catalyst gave only about 70% stereoregular polymer. Diethyl ether is found to raise stereospecificity to 100%, but there is a concommittent tenfold decrease of activity. Other interesting catalyst systems are: (π-C₅H₅)TiMe₃–Mg(OH)Cl–AlEt₂Cl (1.56, 89.5); (π-C₅H₅)TiMe₂–Mg(OH)Cl–AlEt₂Cl (0.075, 94.5); and (π-C₅H₅)TiMe₃–Alon C–Al-Et₂Cl (0.08,97.2), where the first number in the parenthesis is R_p in g/mmole Ti-hr-atm and the second entry corresponds to percentage yield of stereoregular polypropylene. Hafnocene and titanocene supported on Mg(OH)Cl produce only oligomers of propylene.     

Experimental study of the kinetics of reaction of chlorine atoms with tetrahydrofuran and fully deuterated tetrahydrofuran

The overall rate constants for H-abstraction (k_H) from tetrahydrofuran and D-abstraction (k_D) from fully deuterated tetrahydrofuran by chlorine atoms in the temperature range of 298-547 K were determined. In both cases, very weak negative temperature dependences of the overall rate constants were observed, described by the expressions: k_H = (1.55 ± 0.13) × 10⁻¹⁰ exp(52 ± 28/T) cm³ molecule⁻¹ s⁻¹ and k_D = (1.27 ± 0.25) × 10⁻¹⁰exp(55 ± 62/T) cm³ molecule⁻¹ s⁻¹. The experimental results show that the value of the kinetic isotope effect (k_H/k_D), amounting to 1.21 ± 0.10, is temperature independent at 298-547 K.     

Alternating copolymerization of the styrene–methyl methacrylate system complexed with diethylaluminum chloride

The rate and molecular weight profiles were obtained for the spontaneous alternating copolymerizations conducted with diethylaluminum chloride. The rate formally fitted an expression, R = k_p[MMA][Sty], and the rate constant was established by two distinct methods: (1) from the yield versus time data and (2) from initial rate over a range of initial concentrations; it was determined as 5.4 × 10^?6 l./mole-sec with E_a = 4.2 kcal/mole. Molecular weights were determined by gel-permeation chromatography. No increase in molecular weight was observed with increased reaction time. Thus living centers or diradicals are not involved in the process. The M?_n shows a steady decrease with increase in monomer-diethylaluminum chloride concentration but the rate is maximum at equimolar monomer concentrations. The data are interpreted on a chain-transfer mechanism and show close agreement to a model in which the excess complexed acceptor monomer is the transfer agent. The chain-transfer constant of 7.1 × 10^?4 l./mole-sec is several orders of magnitude greater than for uncomplexed systems.