A laser flash photolysis/IR diode laser absorption study of the reaction of chlorine atoms with selected alkanes

A high‐resolution IR diode laser in conjunction with a Herriot multiple reflection flow‐cell has been used to directly determine the rate coefficients for simple alkanes with Cl atoms at room temperature (298 K). The following results were obtained: k(Cl + n‐butane) = (1.91 ± 0.10) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + n‐pentane) = (2.46 ± 0.12) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + iso‐pentane) = (1.94 ± 0.10) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + neopentane) = (1.01 ± 0.05) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + n‐hexane) = (3.44 ± 0.17) × 10^?10 cm³ molecule^?1 s^?1 where the error limits are ±1σ. These values have been used in conjunction with our own previous measurements on Cl + ethane and literature values on Cl + propane and Cl + iso‐butane to generate a structure activity relationship (SAR) for Cl atom abstraction reactions based on direct measurements. The resulting best fit parameters are k_p = (2.61 ± 0.12) × 10^?11 cm³ molecule^?1 s^?1, k_s = (8.40 ± 0.60) × 10^?11 cm³ molecule^?1 s^?1, k_t = (5.90 ± 0.30) × 10^?11 cm³ molecule^?1 s^?1, with f( ? CH₂^? ) = f (? CH₂^? ) = f (?C?) = f = 0.85 ± 0.06. Tests were carried out to investigate the potential interference from production of excited state HCl(v = 1) in the Cl + alkane reactions. There is some evidence for HCl(v = 1) production in the reaction of Cl with shape n‐hexane. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 34: 86–94, 2002     

Initiator efficiency of 2,2′‐azobis(isobutyronitrile) in bulk dodecyl acrylate free‐radical polymerizations over a wide conversion and molecular weight range

An Erratum has been published for this article in J. Polym. Sci. Part A: Polym. Chem. (2004) 42(21) 5559 . The initiator efficiency, f, of 2,2′‐azobis(isobutyronitrile) (AIBN) in dodecyl acrylate (DA) bulk free‐radical polymerizations has been determined over a wide range of monomer conversion in high‐molecular‐weight regimes (M_n ? 10⁶ g mol^?1 [? 4160 units of DA)] with time‐dependent conversion data obtained via online Fourier transform near infrared spectroscopy (FTNIR) at 60 °C. In addition, the required initiator decomposition rate coefficient, k_d, was determined via online UV spectrometry and was found to be 8.4 · 10^?6 s^?1 (±0.5 · 10^?6 s^?1) in dodecane, n‐butyl acetate, and n‐dodecyl acetate at 60 °C. The initiator efficiency at low monomer conversions is relatively low (f = 0.13) and decreases with increasing monomer to polymer conversions. The evolution of f with monomer conversion (in high‐molecular‐weight regimes), x, at 60 °C can be summarized by the following functionality: f^{60 °C} (x) = 0.13–0.22 · x + 0.25 · x² (for x ≤ 0.45). The reported efficiency data are believed to have an error of >50%. The ratio of the initiator efficiency and the average termination rate coefficient, 〈k_t±, (f/〈k_t〉) has been determined at various molecular weights for the generated polydodecyl acrylate (M_n = 1900 g mol^?1 (? 8 units of DA) up to M_n = 36,500 g mol^?1 (? 152 units of DA). The (f/〈k_t〉) data may be indicative of a chain length‐dependent termination rate coefficient decreasing with (average) chain length. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5170–5179, 2004     

Addition–fragmentation chain transfer: Molecular weight distributions and retardation in the system methyl methacrylate/methyl α‐(bromomethyl)acrylate

A detailed investigation of addition–fragmentation chain transfer (AFCT) in the free‐radical polymerization of methyl methacrylate (MMA) in the presence of methyl α‐(bromomethyl)acrylate (MBMA) was carried out to elucidate mechanistic details with efficient macromonomer synthesis as an underlying goal. Advanced modeling techniques were used in connection with the experimental work. Curve fitting of simulated and experimental molecular weight distributions with respect to the rate coefficient for addition of propagating radicals to MBMA (k_add) over 60–120 °C resulted in E_add = 21.7 kJ mol^?1 and A_add = 2.18 × 10⁶ M^?1 s^?1 and a very weak temperature dependence of the chain‐transfer constant (E_add ≈ E_p). The rate coefficient for fragmentation of adduct radicals at 60 °C was estimated as k_f ≈ 39 s^?1 on the basis of experimental data of the MMA conversion and the concentration of 2‐carbomethoxy‐2‐propenyl end groups. The approach developed is generic and can be applied to any AFCT system in which copolymerization does not occur and in which the resulting unsaturated end groups do not undergo further reactions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2640–2650, 2004     

Olefin copolymerization with metallocene catalysts. II. Kinetics,cocatalyst, and additives

The kinetics of ethylene/propylene copolymerization catalyzed by (ethylene bis (indeyl)-ZrCI₂/methylaluminoxane) has been investigated. Radiolabeling found about 80% of the Zr to be catalytically active. The estimates for rate constants at 50°C are k₁₁ = 1104 (M_s)^?1, k₁₂ = 430 (M_s)^?1, k₂₂ = 396 (M_s)^?1,k₂₁ = 1020 (M_s)^?1, and k^A_tr,1 + k^A_tr.2 = 1.9 × 10^?3 s^?1. Substitution of trimethylaluminum for methylaluminoxane resulted in proportionate decrease in polymerization rate. The molecular weight of the copolymer is slightly increased by loweing the [Al]/[Zr] ratio, or addition of Lewis base modifier but at the expense of lowered catalytic activity and increase in ethylene content in the copolymer. Lowering of the polymerization temperature to 0°C resulted in a doubling of molecular weight but suffered 10-fold reduction in polymerization activity and increase of ethylene in copolymer.     

A new approach to electron diffraction analysis of symmetric triatomic molecules with large-amplitude bending motion: The equilibrium geometry,force field and vibrational frequencies of BaI2 as determined by electron diffraction

Diffraction data on BaI₂, analyzed by a new approach, indicate an anharmonic potential with a barrier of 71(12) cm^?1 at a linear geometry. The structural and vibrational parameters were found to be r_e^h(Ba-I_o) = 3.150(7)Å, ∠_eIBaI = 148.0(9) °, f_q = 0.69(8) mdyn/Å,f_qq= 0.14(6) mdyn/Å, k₂ = ?0.0075(15) mdyn/Å, k₄ = 0.0025(9) mdyn/ų, v₁ = 106(12) cm^?1 and v₃ = 145(21) cm^?1. The bending frequency v₂ is predicted to be near 16 cm^?1.     

Kinetic model of reversible addition‐fragmentation chain transfer polymerization in microemulsions

A simplified kinetic model for RAFT microemulsion polymerization has been developed to facilitate the investigation of the effects of slow fragmentation of the intermediate macro‐RAFT radical, termination reactions, and diffusion rate of the chain transfer agent to the locus of polymerization on the control of the polymerization and the rate of monomer conversion. This simplified model captures the experimentally observed decrease in the rate of polymerization, and the shift of the rate maximum to conversions less than the 39% conversion predicted by the Morgan model for uncontrolled microemulsion polymerizations. The model shows that the short, but finite, lifetime of the intermediate macro‐RAFT radical (1.3 × 10^?4–1.3 × 10^?2 s) causes the observed rate retardation in RAFT microemulsion polymerizations of butyl acrylate with the chain transfer agent methyl‐2‐(O‐ethylxanthyl)propionate. The calculated magnitude of the fragmentation rate constant (k_f = 4.0 × 10¹–4.0 × 10³ s^?1) is greater than the literature values for bulk RAFT polymerizations that only consider slow fragmentation of the macro‐RAFT radical and not termination (k_f = 10^?2 s^?1). This is consistent with the finding that slow fragmentation promotes biradical termination in RAFT microemulsion polymerizations. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 604–613, 2010     

Electrode kinetics of electroactive electropolymerized polymers deposited on graphite electrode surfaces

A kinetic examination of the charge-transport processes (i.e. (i) heterogeneous electron-transfer process of electrode/film interfaces and (ii) homogeneous charge-transport process within films) at electroactive electropolymerized film-coated electrodes was conducted by normal pulse voltammetry. The films employed were of poly(o-phenylenediamine), Poly(N-methylaniline) and poly(N-ethylaniline), which were prepared on electrodes as coating films by electrooxidative polymerization of the corresponding monomers in an acidic solution. It was found that process (i) obeys the conventional Butler-Volmer equation and that process (ii) can be treated as a Fickian diffusion process. In addition, the kinetic parameters characterizing processes (i) and (ii) (i.e. the standard rate constant (k°) and transfer coefficient (α) for process (i), and the apparent diffusion coefficient (D_app for process (ii)) were estimated: D_app = ca (1–4)×10⁻⁸ cm² s⁻¹ s⁻¹, k° = ca. (4–6)×10⁻⁴ cm s⁻¹, α_a (for anodic process) = 0.83–0.86 and α_c (for cathodic process)=0.13–0.23. The are compared with the data reported previously for other electroactive polymer films.     

Re‐formation Reaction of Cyclic Nitroxide‐Based Alkoxyamines: Steric and Polar/Stabilization Effects

In nitroxide‐mediated radical polymerization, the polymerization times decrease with the increasing re‐formation rate constant of the C? ON bond (→ alkoxyamine) between the growing polymer chain and the nitroxide radical. The factors influencing the re‐formation rate constant are of considerable interest, but up to now, the polar/stabilization effects have not been addressed thoroughly. The combination of new data with previously reported data now showed that the re‐formation rate constant k_c increases with the increasing polar character of the substituents attached to the nitroxide moiety. The polar/stabilization effects are weaker for the re‐formation than for the homolysis of the C? ON bond, and may be mainly attributed to the relocation of the odd electron onto the O‐atom of the N? O moiety, i.e., the stabilization of the nitroxide moiety. Hence, it is possible to predict the values of k_c by combining both the polar/stabilization (σ_I) and steric effects (E ), i.e., log(k_c/M ^?1 s^?1) = 9.86 + 0.57 ? σ_I + 0.40 ? E_s.     

Kinetics of polymerization rate based on the dependence of termination rate on chain length

When the structure of a primary radical resembles that of the chain end of the polymer radical, the rate of the primary radical termination is approximately the same as the termination rate between the oligomer radical and the polymer radical. The rate constant of termination between polymer radicals of chain length n and s, which involve the primary radicals, is k_t,ns = const.(ns)^?a. In the polymerization of methacrylonitrile initiated by 2,2′-azobisisobutyronitrile in dimethylformamide at 60.0°C, the value of a is found to be 0.091. From data obtained previously in the bulk polymerization of styrene initiated by 1-azobis-2-phenylethane at 60.0°C, the value of a is found to be 0.167. Because such a values are so large that they are not estimated by the excluded volume, the termination rates are discussed by adding the dependence of the diffusion of the segments to that for chain length.     

Cinetique de polymerisation du styrene en presence de peroxyde de benzoyle p,p′ bis-bromomethyle synthese de polymeres peroxydes

The free radical polymerization of styrene has been studied by using p,p′-bisbromomethyl benzoyl peroxide as initiator containing a chain transfer group. The rate constant of decomposition (k_d) of this peroxide has been determined at various temperatures, as well as the efficiency factor f and the transfer constant to initiator C₁. At 60°, f = 0·70 ± 0·05 and C₁ = 0·5. Polystyrene containing peroxide groups has been prepared by using this initiator. The highest yield in polymeric peroxide has been obtained for polymerization in emulsion at 40°.     

Radical and cationic polymerizations of 3‐ethyl‐3‐methacryloyloxymethyloxetane

3‐Ethyl‐3‐methacryloyloxymethyloxetane (EMO) was easily polymerized by dimethyl 2,2′‐azobisisobutyrate (MAIB) as the radical initiator through the opening of the vinyl group. The initial polymerization rate (R_p) at 50 °C in benzene was given by R_p = k[MAIB]^0.55 [EMO]^1.2. The overall activation energy of the polymerization was estimated to be 87 kJ/mol. The number‐average molecular weight (M?_n) of the resulting poly(EMO)s was in the range of 1–3.3 × 10⁵. The polymerization system was found to involve electron spin resonance (ESR) observable propagating poly(EMO) radicals under practical polymerization conditions. ESR‐determined rate constants of propagation (k_p) and termination (k_t) at 60 °C are 120 and 2.41 × 10⁵ L/mol s, respectively—much lower than those of the usual methacrylate esters such as methyl methacrylate and glycidyl methacrylate. The radical copolymerization of EMO (M₁) with styrene (M₂) at 60 °C gave the following copolymerization parameters: r₁ = 0.53, r₂ = 0.43, Q₁ = 0.87, and e₁ = +0.42. EMO was also observed to be polymerized by BF₃OEt₂ as the cationic initiator through the opening of the oxetane ring. The M?_n of the resulting polymer was in the range of 650–3100. The cationic polymerization of radically formed poly(EMO) provided a crosslinked polymer showing distinguishably different thermal behaviors from those of the radical and cationic poly(EMO)s. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1269–1279, 2001     

Radical polymerization behavior of trimethoxyvinylsilane

Trimethoxyvinylsilane (TMVS) was quantitatively polymerized at 130 °C in bulk, using dicumyl peroxide (DCPO) as initiator. The polymerization of TMVS with DCPO was kinetically studied in dioxane by Fourier transform near‐infrared spectroscopy. The overall activation energy of the bulk polymerization was estimated to be 112 kJ/mol. The initial polymerization rate (R_p) was expressed by R_p = k[DCPO]^0.6[TMVS]^1.0 at 120 °C, being closely similar to that of the conventional radical polymerization involving bimolecular termination. The polymerization system involved electron spin resonance (ESR) spectroscopically observable polymer radicals under the actual polymerization conditions. ESR‐determined apparent rate constants of propagation and termination were 13 L/mol s and 3.1 × 10⁴ L/mol s at 120 °C, respectively. The molecular weight of the resulting poly(TMVS)s was low (M_n = 2.0–4.4 × 10³), because of the high chain transfer constant (C_mtr = 4.2 × 10^?2 at 120 °C) to the monomer. The bulk copolymerization of TMVS (M₁) and vinyl acetate (M₂) at 120 °C gave the following copolymerization parameters: r_l = 1.4, r₂ = 0.24, Q₁ = 0.084, and e₁ = +0.80. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5864–5871, 2005     

Volume change of ion pair formation: Rubidium nitrate and thallium(I) nitrate in water

Density data for dilute aqueous solutions of RbNO ₃ and TlNO ₃ at 25°C lead to the following equations for the apparent molal volumes: RbNO₃: Φ_V = 43.0₇ + 2.46c ^1/2 + 0.15c (0?0.41M) TINO₃: Φ_V = 39.5₀ + 10.83c ^1/2 ? 25.46c + 26.0c ^3/2 (0.03?0.25M) From these expressions and a semiempirical equation for Φ_v of a completely dissociated 1:1 electrolyte, values of ΔΦ_v for ion pair formation at c=0.10 are calculated to be+5 ml-mole^?1 for RbNO ₃ and+12 ml-mole^?1 for TlNO ₃ . Comparison of ΔΦ_v with the electrostriction volume effect suggests that virtually all of the electrostriction is removed in the formation of the TlNO ₃ ion pair but only about half with RbNO ₃ . Values of ΔΦ_v are in poor agreement with those estimated from electrostatic theories of ion pair formation.     

Determination of electrochemical kinetic parameters by square-wave polarography: Polarographic reduction of Zn(II) in 1 M KCl,KBr, and KNCS solutions

A new method of determining electrochemical kinetic parameters by square-wave polarography was presented, in which the faradaic current at θ/2, θ being the half-period of superimposed square-wave voltage, was used for the analysis. The method gave the following kinetic parameters for the electrode reaction, Zn(II) + 2e(Hg), in aqueous solutions at 25° C: k_c^θ=0.0052 cm s^?1 and α_c=0.36 in 1 M KCl, k_c^θ=0.011 cm s^?1 and α_c=0.30 in 1 M KBr, and k_c^θ=0.020 cm s^?1 and α_c=0.52 in 1 M KNCS. Induced adsorption of Zn(II) on the dropping mercury electrode was suggested in solutions containing thiocyanate ions.     

Cavity ring‐down study of BrO radicals: Kinetics of the Br + O3 reaction and rate of relaxation of vibrationally excited BrO by collisions with N2 and O2

Cavity ring‐down (CRD) techniques were used to study the kinetics of the reaction of Br atoms with ozone in 1–205 Torr of either N₂ or O₂, diluent at 298 K. By monitoring the rate of formation of BrO radicals, a value of k(Br + O₃) = (1.2 ± 0.1) × 10⁻¹² cm³ molecule⁻¹ s⁻¹ was established that was independent of the nature and pressure of diluent gas. The rate of relaxation of vibrationally excited BrO radicals by collisions with N₂ and O₂ was measured; k(BrO(v) + O₂ → BrO(v − 1) + O₂) = (5.7 ± 0.3) × 10⁻¹³ and k(BrO(v) + N₂ → BrO(v − 1) + N₂) = (1.5 ± 0.2) × 10⁻¹³ cm³ molecule⁻¹ s⁻¹. The increased efficiency of O₂ compared with N₂ as a relaxing agent for vibrationally excited BrO radicals is ascribed to the formation of a transient BrO–O₂ complex. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 125–130, 2000     

Unitary group approach to spin-adapted open-shell coupled cluster theory

We show that the irreducible tensor operators of the unitary group provide a natural operator basis for the exponential Ansatz which preserves the spin symmetry of the reference state, requires a minimal number of independent cluster amplitudes for each substitution order, and guarantees the invariance of the correlation energy under unitary transformations of core, open-shell, and virtual orbitals. When acting on the closed-shell reference state with n_c doubly occupied and n_v unoccupied (virtual) orbitals, the irreducible tensor operators of the group U(n_c) ? U(n_V) generate all Gelfand-Tsetlin (GT) states corresponding to appropriate irreducible representation of U(n_c + n_v). The tensor operators generating the M-tuply excited states are easily constructed by symmetrizing products of M unitary group generators with the Wigner operators of the symmetric group S_M. This provides an alternative to the Nagel-Moshinsky construction of the GT basis. Since the corresponding cluster amplitudes, which are also U(n_c) ? U(n_s) tensors, can be shown to be connected, the irreducible tensor operators of U(n_c) ? U(n_v) represent a convenient basis for a spin-adapted full coupled cluster calculation for closed-shell systems. For a high-spin reference determinant with n, singly occupied open-shell orbitals, the corresponding representation of U(n), n=n_c + n_v + n_s is not simply reducible under the group U(n_c) ? U(n_s) ? U(n_v). The multiplicity problem is resolved using the group chain U(n) ? U(n_c + n_v) ? U(n_s) ? U(n_c) ?U(n_s)? U(n_v) ? U(n_v). The labeling of the resulting configuration-state functions (which, in general, are not GT states when n_c > 1) by the irreducible representations of the intermediate group U(n_c + n_v) ?U(n_s) turns out to be equivalent to the classification based on the order of interaction with the reference state. The irreducible tensor operators defined by the above chain and corresponding to single, double, and triple substitutions from the first-, second-, and third-order interacting spaces are explicitly constructed from the U(n) generators. The connectedness of the corresponding cluster amplitudes and, consequently, the size extensivity of the resulting spin-adapted open-shell coupled cluster theory are proved using group theoretical arguments. The perturbation expansion of the resulting coupled cluster equations leads to an explicitly connected form of the spin-restricted open-shell many-body perturbation theory. Approximation schemes leading to manageable computational procedures are proposed and their relation to perturbation theory is discussed. © 1995 John Wiley & Sons, Inc.     

Structural diversity of two novel complexes of Co(II) with bis-triazole ligand: From one-dimensional chain to two-dimensional porous network

Using two novel bis-triazole ligands, 2,6-bis(1,2,4-triazole-4-yl)pyridine (L¹) and 1,6-bis(1,2,4-triazole-1-yl)hexane (L²), one novel one-dimensional (1D) chain polymer [Co(NCS)₂(L¹)₂] _n (I) and one two-dimensional (2D) coordination polymer [Co(NCS)₂(L²)₂] _n (II) have been synthesized and structurally characterized. The crystal crystallizes in the triclinic system for I, space group $P\bar 1$ , a = 7.879(6), b = 8.830(7), c = 9.837(8)Å, α = 70.230(11)°, β = 115.474(6)°, γ = 85.591(12)°, Z = 1. The crystal crystallizes in the mo-noclinic system for II, space group $P\bar 1$ , a = 7.879(6), b = 8.830(7), c = 9.837(8) α = 70.230(11)°, β = 115.474(6)°, γ = 85.591(12)°, Z = 1. The structural diversity of these two new Co(II) complexes vary from 1D chain to 2D porous supramolecular network, which may be ascribed to ligand directing effects under similar synthetic conditions (L¹ contains rigid pyridine spacers while L2 contains flexible hexane spacers).     

Controlled radical polymerization of styrene mediated by the C‐phenyl‐N‐tert‐butylnitrone/AIBN pair: Kinetics and electron spin resonance analysis

Kinetics of the free radical polymerization of styrene at 110 °C has been investigated in the presence of C‐phenyl‐N‐tert‐butylnitrone (PBN) and 2,2′‐azobis(isobutyronitrile) (AIBN) after prereaction in toluene at 85 °C. The effect of the prereaction time and the PBN/AIBN molar ratio on the in situ formation of nitroxides and alkoxyamines (at 85 °C), and ultimately on the control of the styrene polymerization at 110 °C, has been investigated. As a rule, the styrene radical polymerization is controlled, and the mechanism is one of the classical nitroxide‐mediated polymerization. Only one type of nitroxide (low‐molecular‐mass nitroxide) is formed whatever the prereaction conditions at 85 °C, and the equilibrium constant (K) between active and dormant species is 8.7 × 10^?10 mol L^?1 at 110 °C. At this temperature, the dissociation rate constant (k_d) is 3.7 × 10^?3 s^?1, the recombination rate constant (k_c) is 4.3 × 10⁶ L mol^?1 s^?1, whereas the activation energy (E_a,diss.), for the dissociation of the alkoxyamine at the chain‐end is ～125 kJ mol^?1. Importantly, the propagation rate at 110 °C, which does not change significantly with the prereaction time and the PBN/AIBN molar ratio at 85 °C, is higher than that for the thermal polymerization at 110 °C. This propagation rate directly depends on the equilibrium constant K and on the alkoxyamine and nitroxide concentrations, as well. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1219–1235, 2007     

Effet sterique sur les vitesses de transfert protonique: cyclohexanols substitues dans le dimethylsulfoxyde

Steric effects on proton transfer from, and to, hydroxylic oxygen have been studied in a series of seventeen α-methyl and a-benzyl cyclohexanols in anhydrous DMSO, under both acid and base catalysed conditions, using dynamic MNR techniques. The protonation rate constants (k₁ ? 10⁶ M^-1 s^-1 at 25°C) obey a Taft-Ingold relationship, containing only a steric contribution E_s = E_s^OH + E_s^α, where: E_s^OH = 0 or 0.15 for an axial or equatorial hydroxyl respectively and E_s^α = ?0.070 (or ?0.115) for substituting an α-hydrogen by a methyl (or benzyl) group. An equatorial hydroxylic function is therefore 40% more reactive than its axial homologue. These kinetic data are fairly consistent with structural information resulting from IR spectroscopy (v_co and v_OH vibrations) and from NMR (hydroxylic chemical shifts and coupling constants).     

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.