Intra- and intermolecular chain transfer to macromolecules with chain scission. The case of cyclic esters

Chain transfer to macromolecules with chain scission is the most often observed “side” reaction in the polymerization of heterocyclics. In our previous works we analysed quantitatively the intramolecular chain transfer to the own macromolecule (back-biting). This paper gives a general treatment of the kinetics of polymerization with propagation and intermolecular chain transfer to macromolecules, accompanied with chain scission. The numerical solution developed allows determining the k_p/k_tr ratio from the dependence of m̄_w/m̄_n on monomer conversion. This treatment was applied to the polymerization of L,L-lactide and k_p/k_tr ratios were measured for covalent alcoholate active species bearing Al, Fe, Ti, Sm, and La. In this way selectivities of active species (expressed with k_p/k_tr) were for the first time measured and finally correlated with the atomic number of the corresponding metal atoms, related to the strength of the bond involved in the monomer addition.     

Synthesis of poly(N‐isopropylacrylamide) with a low molecular weight and a low polydispersity index by single‐electron transfer living radical polymerization

The single‐electron transfer living radical polymerization (SET‐LRP) method in the presence of chain transfer agent was used to synthesize poly(N‐isopropylacrylamide) [poly(NIPAM)] with a low molecular weight and a low polydispersity index. This was achieved using Cu(I)/2,2′‐bipyridine as the catalyst, 2‐bromopropionyl bromide as the initiator, 2‐mercaptoethanol as the chain transfer agent (TH), and N,N‐dimethylformamide (DMF) as the solvent at 90 °C. The copper nanoparticles with diameters of 16 ± 3 nm were obtained in situ by the disproportionation of Cu(I) to Cu(0) and Cu(II) species in DMF at 22 °C for 24 h. The molecular weights of poly(NIPAM) produced were significantly higher than the theoretical values, and the polydispersities were less than 1.18. The chain transfer constant (C_tr) was found to be 0.051. Although the kinetic analysis of SET‐LRP in the presence of TH corroborated the characteristics of controlled/living polymerization with pseudo‐first‐order kinetic behavior, the polymerization also exhibited a retardation period (k > k_tr). The influence of molecular weight on lower critical solution temperature (LCST) was investigated by refractometry. Our experimental results explicitly elucidate that the LCST values increase slightly with decreasing molecular weight. Reversibility of solubility and collapse in response to temperature well correlated with increased molecular weight of poly(NIPAM). © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Non-ideality in vinyl polymerization—IV. Kinetics of polymerization of vinyl acetate in benzene initiated by azo-bis isobutyronitrile (AIBN)

Vinyl acetate was polymerized in bulk and in benzene at 50°C using a wide range of concentrations of azobisisobutyronitrile. Values of f_k (the efficiency of initiator) and k_prt/k_ik_p (the characteristic constant of primary radical termination) were found to be 0.53 and 2.00 × 10⁴ respectively from data for bulk polymerization. In solution polymerization, the initiator exponent is a function of initiator concentration ranging from 0.35 at high concentration to- about 0.65 at low concentration. This result has been explained on the basis of degradative chain transfer to solvent and primary radical termination. The results have been treated according to mathematical formulations already developed; the characteristic constant of degradative chain transfer and the transfer constant of the solvent have been determined. The results have been compared with literature values and discrepancies explained.     

Intermolecular chain transfer to polymer with chain scission: general treatment and determination of kp/ktr in L,L-lactide polymerization

A general kinetic treatment of the system with intermolecular chain transfer followed by fast reinitiation is given. It leads to the broadening of the molecular weight distribution (MWD), the number of growing chains being invariable. Thus, this system can be considered as a special case of living polymerization. A general method has been elaborated allowing the determination of the ratio of the rate constant of propagation (k_p) to the rate constant of the bimolecular transfer (k⁽²⁾_tr) from the dependence of the MWD on monomer conversion. Numerical values of k_p/k⁽²⁾_tr equal to ≈ 10² and 25 were thus determined for the polymerization of L , L -lactide (L , L -dilactide) initiated with aluminium tris(isopropoxide) trimer ({Al(OⁱPr)₃}₃) and tributyltin ethoxide (ⁿBu₃SnOEt), respectively.     

Copper‐mediated initiators for continuous activator regeneration atom transfer radical polymerization of acrylonitrile

Initiators for continuous activator regeneration atom transfer radical polymerization technique was first accessed to acrylonitrile by using CuBr₂/2,2′‐bipyridine as the catalyst, ethyl 2‐bromoisobutyrate as the halogen initiator, and azobis(isobutyronitrile) as the free radical initiator. The key to success is ascribed to the facile achievement of the rapid equilibrium between active species and dormant species. Effects of ligand, catalyst concentration, free radical initiator concentration, and reaction temperature on the polymerization reaction and molecular weight (MW) as well as polydispersity index (PDI) were investigated in detail. The polymerization proceeded in a controlled/living fashion even though the concentration of copper catalyst decreased to 50 ppm, which is evident in pseudo first‐order kinetics of polymerization, linear increase of molecular weight, low PDI, and high chain‐end functionality of the generated polymer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Effect of triphenyl phosphite on the radical polymerization of styrene and methyl methacrylate

The effects of triphenyl phosphite (TPP) on the radical polymerization of styrene (St) and methyl methacrylate (MMA) initiated with α,α,-azobisisobutyronitrile (AIBN) was investigated at 50°C. The rate of polymerization of St and MMA at a constant concentration of TPP was found to be proportional to the monomer concentration and the square root of the initiator concentration. The rate of polymerization and the degree of polymerization of both St and MMA increased with increasing TPP concentration. The accelerating effect was shown to be due to the decrease of the termination rate constant k_t with an increase in the viscosity of the polymerization systems. The chain transfer constant C_tr of TPP in St and MMA systems was determined from the degree of polymerization system. The C_tr of TPP was almost zero in the St system and 6.5 × 10^?5 in the MMA system.     

Fast copper catalyzed living radical polymerization of acrylonitrile utilizing a high concentration of radical initiator

This article first reports a fast and controlled living radical polymerization (LRP) of acrylonitrile, evidenced by 81.3% monomer conversion within 40 min and well‐defined the polymers with a narrow polydispersity index (PDI) range of 1.14?1.38. This was achieved by utilizing azobis(isobutyronitrile) as radical initiator with a high concentration up to 190 mM and CuBr₂ as catalyst with a very low concentration down to 50 ppm. The polymerization displayed typical LRP characteristics, including pseudo first‐order kinetics of polymerization, the linear increase of number‐average molecular weights (MWs), low PDI values. The influence of various experimental components, radical initiator concentration, catalyst concentration, and reaction temperature, on the polymerization reaction and MW as well as PDI has been investigated in detail. ¹H NMR and gel permeation chromatography analyses as well as chain extension reaction confirmed the very high chain‐end functionality of the resultant polymer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Metallocene-methylaluminoxane catalysts for olefin polymerization. V. Comparison of Cp2ZrCl2 and CpZrCl3

The ethylene polymerization by Cp₂ZrCl₂/MAO (Cp = η⁵: cyclopentadienyl; MAO = methyl aluminoxane) and CpZrCl₃/MAO have been studied. The MW and PD (= M _w/M _w) of polymers obtained after 2.5-60 min are the same, which indicate short chain lifetime. The values of rate constants for Cp₂ZrCl₂ at 70°C are: k_p = 168?1670 (M s)^?1 and k_tr^A1 = 0.012-0.81 s^?1 depending upon [Zr] and [MAO,] k_tr^β = 0.28 s^?1, and k_tr^H = 0.2 M^?1 torr^?1/2 s^?1. These chain transfer rate constant values are two to three orders of magnitude greater than the corresponding values found for MgCl₂ supported titanium catalysts. One significant difference between the heterogeneous and homogeneous catalysts is that the former decays according to an apparent second order kinetics, whereas the latter decay is simple first order at 0°C and biphasic first order at higher temperatures. The productivity of the catalysts depends weekly on temperature while the MW decreases strongly with increase of temperature above 30°C. All the active species were formed upon mixing Cp₂ZrCl₂ with MAO while it took up to 20 min for the CpZnCl₃/MAO system. The productivity of the former increase more strongly with the decrease of [Zr] than the latter. Otherwise, the two catalyst systems have all their kinetic parameters differing less than a factor of two.     

Reversible addition‐fragmentation chain transfer polymerization of methacrylates containing hole‐ or electron‐transporting groups

The controlled/living radical polymerization of 2‐(N‐carbazolyl)ethyl methacrylate (CzEMA) and 4‐(5‐(4‐tert‐butylphenyl‐1,3,4‐oxadiazol‐2‐yl)phenyl) methacrylate (t‐Bu‐OxaMA) via reversible addition‐fragmentation chain transfer polymerization has been studied. Functional polymers with hole‐ or electron‐transfer ability were synthesized with cumyl dithiobenzoate as a chain transfer agent (CTA) and AIBN as an initiator in a benzene solution. Good control of the polymerization was confirmed by the linear increase in the molecular weight (MW) with the conversion. The dependence of MW and polydispersity index (PDI) of the resulting polymers on the molar ratio of monomer to CTA, monomer concentration, and molar ratio of CTA to initiator has also been investigated. The MW and PDI of the resulting polymers were well controlled as being revealed by GPC measurements. The resulting polymers were further characterized by NMR, UV‐vis spectroscopy, and cyclic voltammetry. The polymers functionalized with carbazole group or 1,3,4‐oxadiazole group exhibited good thermal stability, with an onset decomposition temperature of about 305 and 323 °C, respectively, as determined by thermogravimetric analysis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 242–252, 2007     

Fluoropolyethers end‐capped by polar functional groups. II. Effect of catalyst and reagents concentration,solvent nature,and temperature on reaction kinetics of α,ω‐bis(hydroxy)‐terminated fluoropolyethers with cycloalyphatic and aromatic diisocyanates

A comparative kinetic study of the dibutyltin dilaurate (DBTDL) and 1,4‐diazabicyclo[2,2,2]octane (DABCO) catalyzed reactions of α,ω‐bis(hydroxy)‐terminated fluoropolyethers (FPEs)—Z‐DOLs and Z‐DOL TXs—of various molecular weights and purity, with 4,4′‐dicyclohexylmethane diisocyanate (H₁₂MDI), isophorone diisocyanate (IPDI) and 2,4‐toluene diisocyanate (TDI) was carried out in different solvents. An analytical method was used to follow the kinetics of the reactions at four different temperatures. The rate of NCO disappearance measured by two independent methods—IR spectroscopy and chemical titration were found to be very close. Straight proportionality between rate constants k_cat and catalyst concentration was found. But in some cases for the DBTDL catalyzed reactions effect of catalyst saturation along with appearance of the limiting DBTDL concentration C_lim below which the rate of reaction was close to zero were observed. Reactivity of Z‐DOLs in the tin‐catalyzed urethane reactions was found to decrease with their storage time at RT due to the slow hydrolysis of the end  COOR groups impurities, which give the corresponding acids that act as a strong inhibitor of the DBTDL activity. These acid admixtures have no influence on the DABCO catalyzed reactions. For the DBTDL and DABCO catalyzed reactions of Z‐DOLs with IPDI the dependence of effective rate constants k_eff (where k_eff = k_cat · 0.01/[DBTDL] and catalyst concentration is taken in mol % based on IPDI) on total reagents concentration were found to be described by curves with a maximum. Critical reagents concentration, after which the relationship k_eff = f (C) changes from proportional to inverse proportional, seems do not substantially depend on the solvent nature. Hydrogenated analog poly(ethylene glycol) MW 400 (PEG‐400) differs greatly from Z‐DOLs: only steady decrease of k_eff was observed with increase of reagents concentration C from 5 up to 95 wt %. Activation energies for all the studied reactions are within the range of 10.8–16.7 kcal/mol. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2579–2602, 2000     

Modeling Termination Kinetics of Non‐Stationary Free‐Radical Polymerizations

Pulsed‐laser induced polymerization is modeled via an approach presented in a previous paper.^[1] An equation for the time dependence of free‐radical concentration is derived. It is shown that the termination rate coefficient may vary significantly as a function of time after applying the laser pulse despite of the fact that the change in monomer concentration during one experiment is negligible. For the limiting case of t ≫ c^–1 (k_pM)^–1, where c is a dimensionless chain‐transfer constant, k_p the propagation rate coefficient and M the monomer concentration, an analytical expression for k_t is derived. It is also shown that time‐resolved single pulse‐laser polymerization (SP–PLP) experiments can yield the parameters that allow the modeling of k_t in quasi‐stationary polymerization. The influence of inhibitors is also considered. The conditions are analyzed under which M (t) curves recorded at different extents of laser‐induced photo‐initiator decomposition intersect. It is shown that such type of behavior is associated with a chain‐length dependence of k_t.     

Chain transfer by addition–substitution–fragmentation mechanism. I. End–functional polymers by a single-step free radical transfer reaction: Use of a new allylic linear peroxyketal

A new chain transfer agent, ethyl 2-[1-(1-n-butoxyethylperoxy) ethyl] propenoate (EBEPEP) was used in the free radical polymerization of methyl methacrylate (MMA), styrene (St), and butyl acrylate (BA) to produce end-functional polymers by a radical addition–substitution–fragmentation mechanism. The chain transfer constants (C_tr) for EBEPEP in the three monomers polymerization at 60°C were determined from measurements of the degrees of polymerization. The C_tr were determined to be 0.086, 0.91, and 0.63 in MMA, St, and BA, respectively. EBEPEP behaves nearly as an “azeotropic” transfer agent for styrene at 60°C. The activation energy, E_atr, for the chain transfer reaction of EBEPEP with PMMA radicals was determined to be 29.5 kJ/mol. Thermal stability of peroxyketal EBEPEP in the polymerization medium was estimated from the DSC measurements of the activation energy, E_ath = 133.5 kJ/mol, and the rate constants, k_th, of the thermolysis to various temperature. © 1994 John Wiley & Sons, Inc.     

Kinetics of styrene emulsion polymerization above the critical micelle concentration: Effect of the initial monomer concentration on the molecular weight

The emulsion polymerization of styrene above the critical micelle concentration has been experimentally studied from a low final polymer content up to a high polymer content (～50%). A maximum in the molecular weight (M) evolution has been observed in all cases. The presence or absence of such a maximum depends on the relative values of the rate of free‐radical entry (ρ) and the rate of chain transfer to the monomer (K_trC_Mp, where K_tr is the chain transfer to monomer rate coefficient and C_Mp is the monomer concentration in particles). If ρ ? K_trC_Mp, M is constant and equal to K_p/K_tr (where K_p is the propagation rate coefficient), except at very low particles sizes typical of the early stages of the reaction, in which the chain length is limited by the particle size. On the other hand, if ρ ? K_trC_Mp, M is determined by both C_Mp and ρ. It is proposed that ρ is determined by the sum of the entry of the oligomeric radicals formed in the aqueous phase and those contained in particles that undergo limited coagulation. This coagulative entry can become very significant; therefore, reactor hydrodynamics can play a major role in the kinetic behavior observed. Disagreement between Clay and Gilbert's model and molecular weight distribution data can be ascribed, to a lesser or greater extent, to the degree of correctness of the quasi‐steady‐state and instantaneous‐termination approaches. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1963–1972, 2005     

Quantitative comparison of selectivities in the polymerization of cyclic esters

Chain transfer processes (k_tr) taking place in the polymerization (anionic and pseudoanionic) of cyclic esters (lactones) are reviewed. These reactions are mostly responsible for the departure of these systems from the fully controlled (living) polymerizations. The ratios of k_p/k_tr have been determined for a number of initiating systems and the structures of the growing species are related to their selectivity, expressed by k_p/k_tr. It has been shown that the less reactive and more sterically crowded active species polymerize more selectively.     

Catalytic chain transfer polymerization of isobutylene: The role of nucleophilic impurities

Fast polymerization of isobutylene (IB) initiated by tert‐butyl chloride using ethylaluminum dichloride·bis(2‐chloroethyl) ether complex (T. Rajasekhar, J. Emert, R. Faust, Polym. Chem. 2017, 8, 2852) was drastically slowed down in the presence of impurities, such as propionic acid, acetone, methanol, and acetonitrile. The effect of impurities on the polymerization rate was neutralized by using two different approaches. First, addition of a small amount of iron trichloride (FeCl₃) scavenged the impurity and formed an insoluble · impurity complex in hexanes. The polymerization rate and exo‐olefin content were virtually identical to that obtained in the absence of impurities. Heterogeneous phase scavenger (FeCl₃) exhibited better performance than homogenous phase scavengers. In the second approach, conducting the polymerization in wet hexanes, the fast polymerization of IB was retained in the presence of impurities with a slight decrease in exo‐olefin content. ¹H NMR studies suggest that nucleophilic impurities are protonated in the presence of water, and thereby neutralized. Mechanistic studies suggest that the rate constant of activation (k_a), rate constant of propagation (k_p), and rate constant of β‐proton elimination (k_tr) are not affected by the presence of impurities. To account for the retardation of polymerization in the presence of impurities, delay of proton transfer to monomer in the chain transfer step is proposed. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3697–3704     

The role of solvent polarity and cocatalyst structure in the cationic polymerization of 3,3-bis(chloromethyl) oxetane

In the cationic polymerization of 3,3-bis(chloromethyl)oxetane induced by BF₃ the solvent polarity (toluene, methylene chloride, ethylene chloride, nitrobenzene, and nitromethane) does not influence the k_tr/k_p ratio, where k_tr stands for the rate constant of chain transfer to polymer. Increase of the overall polymerization rate is due mainly to the increase of k_i. The application of the steady-state conditions in which the slow formation of the active centers is compensated by the unimolecular chain transfer to polymer allowed the determination of k_tr/k_p ratios for several chain-transfer agents of low molecular weight. Alcohols and ethers of different basicities were used. It was established that the k_tr/k_p ratio is a linear function of ?pK_a of the chain-transfer agents.     

Atom transfer radical copolymerization of acrylonitrile and ethyl methacrylate at ambient temperature

Copolymerization of acrylonitrile (AN) and ethyl methacrylate (EMA) using copper‐based atom transfer radical polymerization (ATRP) at ambient temperature (30 °C) using various initiators has been investigated with the aim of achieving control over molecular weight distribution. The effect of variation of concentration of the initiator, ligand, catalyst, and temperature on the molecular weight distribution and kinetics were investigated. No polymerization at ambient temperature was observed with N,N,N′,N′,N″‐pentamethyldiethylenetriamine (PMDETA) ligand. The rate of polymerization exhibited 0.86 order dependence with respect to 2‐bromopropionitrile (BPN) initiator. The first‐order kinetics was observed using BPN as initiator, while curvature in first‐order kinetic plot was obtained for ethyl 2‐bromoisobutyrate (EBiB) and methyl 2‐bromopropionate (MBP), indicating that termination was taking place. Successful polymerization was also achieved with catalyst concentrations of 25 and 10% relative to initiator without loss of control over polymerization. The optimum [bpy]₀/[CuBr]₀ molar ratio for the copolymerization of AN and EMA through ATRP was found to be 3/1. For three different in‐feed ratios, the variation of copolymer composition (F_AN) with conversion indicated toward the synthesis of copolymers having slight changes in composition with conversion. The high chain‐end functionality of the synthesized AN‐EMA copolymers was verified by further chain extension with methyl acrylate and styrene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1975–1984, 2006     

Advances in catalytic chain transfer polymerisation mediated by cobaloximes

Catalytic chain transfer copolymerisation of MMA and HEMA (70:30) has been carried out under semi‐continuous emulsion polymerisation conditions, using CoBF as catalyst. It has been shown that macromonomers of low molar mass can be synthesised with an apparent chain transfer constant, C_S^E, of ca. 1300 down to a threshold value of ca. 20 ppm of CoBF. Below this value an initial 20% shot of monomer/catalyst mixture was necessary to prevent events involved in the catalytic chain transfer process becoming diffusion controlled and to prevent the reaction to proceed under monomer starved conditions. Analysis of the Co(II) species by SQUID has been carried out. CoBF shows a value for its effective magnetic susceptibility of 1.77μ_B. It was found that a correction for the response of the sample container is essential for reliable data to be achieved. Diffusion ordered 2D‐NMR spectroscopy (DOSY) has been used as a method to study the catalyst diffusion dependence for the rate coefficient of chain transfer. However, the apparent values of the found diffusion coefficients are an order of magnitude above the natural limit for center of mass diffusion.     

Polymerization and copolymerization of trioxane: Factors influencing molecular weight and end groups

In bulk polymerization and copolymerization of trioxane with ethylene oxide, it has been shown that p-chlorophenyldiazonium hexafluorophosphate is a superior catalyst as compared to boron trifluoride dibutyl etherate (BF₃ · Bu₂O). Polymers and copolymers of significantly higher molecular weight have been obtained. The higher molecular weight has been attributed primarily to less inherent chain transfer during propagation, which in turn can be attributed to the superior gegenion PF₆^?. The polymerization proceeds via a clear period followed by sudden solidification. Faster polymerization and higher molecular weight polymers have been observed for homopolymerization than for copolymerization. The polymer yield obtained after solidification is determined by both rate of polymerization and rate of crystallization of polymers. These rates, in turn, are dependent on the catalyst concentration. The molecular weight is determined both by polymer yield and extent of inherent chain transfer. In the range of monomer to catalyst mole ration [M]/[C] = (0.5–20) × 10⁴ investigated, it has been found that in the higher range, the polymer yield is independent of the catalyst concentration and the extent of inherent chain transfer is inversely proportional to the half power of catalyst concentration: [M]/[C] = (0.5–8) × 10⁴ for homopolymerization and (0.5–3) × 10⁴ for copolymerization with 4.2 mole % ethylene oxide. In the lower range, the yield decreases with catalyst concentration and the extent of inherent chain transfer is inversely proportional to higher power of catalyst concentration. The dependence of molecular weight of polymers on catalyst concentration has been shown to be a complex one. The molecular weight goes through a maximum as the catalyst concentration is decreased. The maximum molecular weights have been obtained at [M]/[C] ≈ 8 × 10⁴ for homopolymerization and ～3 × 10⁴ for copolymerization with 4.2 mole % ethylene oxide. Prior to reaching maximum the molecular weight is inversely proportional to the half power of catalyst concentration indicating it is primarily controlled by inherent chain transfer. Upon further decrease of catalyst, molecular weight decreases as a result of both a decrease in polymer yield and an increase in inherent chain transfer. In copolymerization of trioxane and ethylene oxide, it has been ascertained that methylene chloride exhibits a favorable solvating effect. Although higher inherent chain transfer takes place in copolymerization than in homopolymerization, the extent of chain transfer is independent of ethylene oxide concentration. The difference in polymer yield and molecular weight a t different ethylene oxide concentrations is attributed primarily to the difference in k_p/k_t ratio. It also has been demonstrated that end capping of polymer chains can be accomplished by the use of a chain transfer agent—methylal.     

Modeling the Effects of Primary Radicals in Free‐Radical Polymerization

The effects of non‐ideal initiator decomposition, i.e., decomposition into two primary radicals of different reactivity toward the monomer, and of primary radical termination, on the kinetics of steady‐state free‐radical polymerization are considered. Analytical expressions for the exponent n in the power‐law dependence of polymerization rate on initiation rate are derived for these two situations. Theory predicts that n should be below the classical value of 1/2. In the case of non‐ideal initiator decomposition, n decreases with the size of the dimensionless parameter α ≡ (k_tz /k_dz) √r_ink_t, where k_tz is the termination rate coefficient for the reaction of a non‐propagating primary radical with a macroradical, k_dz is the first‐order decomposition rate coefficient of non‐propagating (passive) radicals, r_in is initiation rate, and k_t is the termination rate coefficient of two active radicals. In the case of primary radical termination, n decreases with the size of the dimensionless parameter β ≡ k_t,s r_in^1/2/k_p,s M r_t,l^1/2, where k_t,s is the termination rate coefficients for the reaction of a primary (“short”) radical with a macroradical, k_t,l is the termination rate coefficients of two large radicals, k_p,s is the propagation rate coefficient of primary radicals and M is monomer concentration. As k_t is deduced from coupled parameters such as k_t /k_p, the dependence of k_p on chain length is also briefly discussed. This dependence is particularly pronounced at small chain lengths. Moreover, effects of chain transfer to monomer on n are discussed.