Radiation-induced polymerization of acrylic acid in aqueous solution

Aqueous acrylic acid in the presence of cupric chloride has been subjected to γ-irradiation under various reaction conditions and the molecular weights of the resultant poly(acrylic acid) measured. The results, taken in conjunction with previous findings on the dependence of the rate of polymerization on intensity, monomer concentration, and cupric chloride concentration, indicate chain termination solely by cupric ion (rate constant k_tCu) and chain transfer to polymer (rate constant kf). Values have been obtained for k_tCu/k_p, k_f/k_p and G(radical) of acrylic acid. On the basis of these data a theoretical chain-length distribution has been derived which agrees well with distribution measured by gel-permeation chromatography.     

Monte Carlo simulation of kinetics and chain-length distribution in radical polymerization

In this paper, the Monte Carlo method for numerically simulating the kinetics and chain-length distribution in radical polymerization is described. Because the Monte Carlo method is not subject to the assumption of steady-state, it is particularly suitable for studying the kinetic behaviour before the steady-state has been reached and for systems in which the steady-state assumption may be violated. Illustrative applications of the algorithm given in this paper not only demonstrate convincingly both the feasibility and usefulness of the algorithm, but also provide some new insight into the illustrative examples. For the case of pseudostationary radical polymerization such as rotating-sector and pulsed-laser initiations, we have found that the pseudostationary radical concentration can be reached after two or three initiation periods. However, the number-average chain-length x̄_n reaches the pseudostationary value much slower than the radical concentration. It is oscillatively reaching the pseudostationary value, and the amplitudes of the oscillations are decreasing with time. We have also found that the chain-length distribution of the resulting polymer in the case of pseudostationary radical polymerization with termination by combination has stronger periodic modulation. Hence, it should be easier to locate the points of inflection in practice. Therefore, the rate constant of propagation, k_p, can be determined precisely for systems which are dominated by a combination-type of termination.     

New aspects of pseudostationary polymerization and their application

Contrary to the stationary state little thought has been given so far to the general principles of the pseudostationary state. In this discourse an attempt is made to demonstrate that — within wide limits — arbitrary initiation profiles may be used to determine k_p/k_t (k_p = rate constant of chain propagation, k_t = rate constant of chain termination) from the frequency dependence of rate of polymerization (in analogy to the rotating-sector technique) as well as to evaluate k_p from the chain-length distribution (CLD) of samples prepared under pseudostationary conditions. Adverse factors like nonspontaneous transformation of absorbed photons into primary radicals do not invalidate this result. The existence of a universal relationship (independent of the initiation profile) is proved to exist for the second moment of the CLD of samples prepared under pseudostationary initiation conditions for constant (chain-length independent) k_t. Pseudostationarity, however, might be also achieved if not the initiation but the termination is periodically varied. In this case the CLD has a completely different shape but allows determination of k_p likewise. Finally, the case of chain-length dependent k_t is shortly discussed in connection with pulsed-laser initiation. Although the general equation for the second moment of the CLD does not apply any longer for this case some generality appears to exist under these conditions, too.     

Chain-length dependent termination in pulsed-laser polymerization, 2. On the prospects of determining the bimolecular termination constant kt from the second moment of the chain-length distribution

The correct (event weighted) average of k_t, 〈k_t〉, has been calculated for pseudostationary laser-induced polymerization for a kinetic scheme with chain-length dependent termination and compared to the average k̄_t obtained by formally solving for k_t the expression for the second moment of the chain-length distribution valid for chain-length independent termination (represented by the product of rate of polymerization ν_p and weight average degree of polymerization P̄_w). It is shown that there is a fair agreement between the two quantities. This may be used to recover experimentally the power-law governing the dependence of k_t on chain-length, especially its exponent.     

New aspects of chain-length dependent termination

A survey is given on a selection of recently developed methods for the evaluation of the rate coefficient k_t of termination and its chain-length dependence. In particular these are the time-resolved single-pulse pulsed laser polymerization (TR-SP-PLP), the single pulse pulsed laser polymerization in combination with the analysis of the molecular weight distribution produced (SP-PLP-MWD), the methods yielding an average k_t either from the second moment of the chain-length distribution (CLD) or from the rate of polymerization, and a method focusing on the chain-length dependence of k_t consisting in an analysis of the CLD resulting from PLP experiments carried out at low pulse frequencies (LF-PLP). The results obtained by these methods are compared and discussed. The role of the shielding of the two radical chains by their appendant coils is emphasized.     

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.     

The incorporation of side reactions into pseudostationary polymerization, 3. The closed solution of a kinetic scheme for pulsed-laser polymerization comprising concomitant continuous initiation

A procedure is developed that allows the calculation of chain-length distributions of polymers prepared by periodic modulation of the initiation process considering concomitant continuous initiation. For the case of a (pseudostationary) laser-pulse initiated polymerization process a closed solution could be derived for the pseudostationary radical concentration and for the chain-length distribution of dead polymer terminated by disproportionation or stabilized by chain-transfer to monomer or solvent. The analysability of the characteristic peaks appearing in the chain-length distributions of laser-pulse initiated polymers (which is the key for determining the rate constant k_p) is only moderately influenced by continuous thermal radical formation if the extent of this side reaction is not pathologically large, i.e. as long as the amount of primary radicals created by the laser-pulse appreciably exceeds that produced in the dark reaction.     

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.     

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.     

Simulation of pseudostationary radical polymerization, 1. Chain-length distributions for arbitrary initiation profiles

A procedure is developed which allows to treat arbitrary periodic initiation profiles (asymmetric and symmetric triangle profiles, sinusoidal profiles, Gaussian profiles etc.) in pseudostationary radical polymerization. Using an iterative method these profiles are transformed into the (likewise periodic) radical profiles and into the chain-length distributions of the resulting polymer in case of termination by disproportionation. These distributions are analysed for the position of their inflection points which may be used for experimental determination of the elementary rate constant of chain propagation k_p. It turned out that for all profiles that have at least one discontinuity (e.g. asymmetric triangle profiles) the position of the point of inflection is a correct measure of k_p for a conveniently wide range of experimental parameters. In case of profiles without discontinuity (symmetric triangle profiles, sinusoidal and Gaussian profiles) the position of the inflection point is shifted to lower values which means that the k_p values determined on this basis will be a little too small. In most cases, however, the error introduced by this fact will not exceed the overall error of the experiment so that in practice the method of determining k_p in pseudostationary polymerization is not restricted to those profiles which exhibit discontinuities.     

Chain-length dependent termination in pulsed-laser polymerization, 1. Interaction with propagation

Using a new simulation procedure in which each individual propagation step is subjected to a Poisson process it was proved that in case of chain-length dependent termination the apparent rate of propagation no longer coincides with the true one. This is caused by the polydispersity of the chain-length distribution of the growing chains: shorter chains are removed preferentially. This effect is comparatively small although significant. The consequences for the determination of the rate constant of chain propagation k_p are nearly negligible.     

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.     

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.     

Polymerization and crosslinking of epoxides: Base-catalyzed polymerization of phenyl glycidyl ether

The anionic polymerization of 2,3-epoxypropyl phenyl ether initiated by sodium methoxide and dimsyl sodium in dioxane and in dimethyl sulfoxide has been studied. Kinetic and dielectric constant measurements have been recorded, and a mechanism for the initiation reaction with dimsyl sodium has been put forward. Polymerization initiated with dimsyl sodium revealed almost total absence of sulfur in the polymer by endgroup analysis. The reaction was shown to be inhibited by oxygen. Molecular weight determinations have indicated a reaction involving transfer to give polymers of lower than calculated M?_n and a ratio of k_p/k_tr ratio of approximately 73. Gel-permeation chromatography suggests a narrow molecular weight distribution in the polymers prepared.     

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.     

Photopolymerization of methyl methacrylate with azo-containing polydimethylsiloxane as photoinitiator: Effect of siloxane chain length

The kinetics of the free radical photopolymerization of methyl methacrylate (MMA) initiated by azo-containing polydimethylsiloxane (PSMAI) and azobisisobutyronitrile (AIBN) was investigated. The greater polymerization rate R_p in MMA/PSMAI systems may be due to the higher value of the initiation rate R_i and the lower value of the termination rate constant k_t than that in MMA/AIBN system. The reaction orders with respect to initiators PSMAI decreased with an increase in polydimethylsiloxane chain length (SCL) in PSMAI. The observed deviations in polymerization rate from rate equation could be explained in terms of primary radical termination. The photoinitiator efficiency Φ of initiators decreased with increase in SCL, while the ratio of the rate constants for chain termination and chain initiation by primary radical increased with SCL. The fraction β of primary radicals entering into termination in MMA/PSMAI systems were larger than that in MMA/AIBN system. © 1996 John Wiley & Sons, Inc.     

Molecular weight distribution in living polymerization proceeding with reshuffling of polymer segments due to chain transfer to polymer with chain scission, 1. Determination of kp/ktr ratio from DPw/DPn data. Ideal reproduction of polymer chain activities

The molecular weight distribution (MWD) curves for polymerization systems with chain transfer to polymer leading to reshuffling of polymer segments (and broadening of the MWD), but not changing chain functionalities, were simulated by the Monte Carlo method. The bimodality observed in some distributions was explained by different distribution functions of chains which did not undergo reshuffling and of those which underwent the chain transfer reaction. Using this observation, a numerical integration method for computing DP _w/DP _n (and the MWD curves) in the systems under consideration was devised. Plots relating DP _w/DP _n to monomer conversion and k_tr/k_p are presented and a method of determination of k_tr/k_p from the DP _w/DP _n data is proposed.     

The Importance of Chain-Length Dependent Kinetics in Free-Radical Polymerization: A Preliminary Guide

The effect of chain-length dependent propagation at short chain lengths on the observed kinetics in low-conversion free-radical polymerization (frp) is investigated. It is shown that although the values of individual propagation rate coefficients quickly converge to the high chain length value (at chain lengths, i, of about 10), its effect on the average propagation rate coefficients, 〈k_p〉, in conventional frp may be noticeable in systems with an average degree of polymerization (DP_n) of up to 100. Furthermore it is shown that, unless the system is significantly retarded, the chain-length dependence of the average termination rate coefficient, 〈k_t〉, is not affected by the presence of chain-length dependent propagation and that there exists a simple (fairly general) scaling law between 〈k_t〉 and DP_n. This latter scaling law is a good reflection of the dependence of the termination rate coefficient between two i-meric radicals, k, on i. Although simple expressions seem to exist to describe the dependence of 〈k_p〉 on DP_n, the limited data available to date does not allow the generalization of these expressions.     

Kinetic model of living radical polymerization

This work studies the kinetics of living radical polymerization by means of both the nonsteady state approach and the quasi-stationary state method. Expressions for the numberand weight-average degress of polymerization and the polydispersity index were derived. Numerical results show that the concentration of residual initiator seriously influences the polydispersity index of the resulting polymer. The calculated outcomes of the non-steady state approach are evidently different from those of the quasi-stationary state method when the magnitude of the rate constant of termination is comparable with that of the propagation rate constant, and the difference becomes negligible if the rate constant of the termination (k_t) is much larger than that of propagation (k_p). The polydispersity index of the resulting polymer increases with decreasing ratios of k_t to k_p or M_O to I_O (initial concentrations of monomer and initiator).     

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