Emulsion polymerization. III. Theoretical prediction of the effects of slow termination rate within latex particles

The Smith-Ewart theory predicts that there is an interval during an isothermal homopolymerization when the conversion varies linearly with time. This prediction rests on the assumptions that, during this interval II, the particle number is constant, the monomer concentration in the particles is constant, and the termination rate within the particles is instantaneous, so that the average number of radicals per particle Q is half. In this paper this latter assumption is abandoned. If the termination rate is slow, two or more radicals can coexist in a particle. The termination rate within a particle becomes a function of the particle size because of the decreased probability that two radicals meet for termination in a given time when the volume in which these radicals are located increases. It follows that with increasing conversion the termination rate decreases. Stockmayer's calculations based on this model neglected the variation of particle volume with time, and it was assumed that a steady state of radical concentration in particles exists. In the present calculations these restrictive assumptions were not used. Stockmayer calculated only how Q should vary with conversion. In the present paper several experimentally verifiable consequences of the model are shown. The new calculations show that the interval II conversion-time curve can be represented by the formula At² + Bt, where B is the Smith-Ewart rate and is proportional to the particle number and the parameter A is independent of the particle number and depends mainly on initiation and termination rates. From A and B and propagation and termination rate constants can be calculated. With the aid of parameters A and B the conversion dependence of molecular weight and of Q can also be predicted for interval II. In the theoretical calculations the distribution of radicals among particles is established. It is shown that for a given value of Q this distribution is unique, independent of the experimental conditions leading to this Q. This distribution was derived solely from kinetic considerations and is analogous to the statistical Poisson distribution. With increasing Q, i.e., with increasing conversion, this distribution broadens. Since each particle grows proportionally to the number of radicals in it, particles must grow at greatly varying rates if there is broad distribution of radicals among them. It follows that the particle size distribution has to broaden with increasing conversion, contrary to predictions based upon the Smith-Ewart model. At present it is not yet possible to predict quantitatively the shape of the conversion-time curve in interval III, the interval following the disappearance of monomer droplets. The reason for this is that the functional dependence of the termination rate constant upon monomer concentration in the particles is not known. However, once the conversion-time curve is experimentally determined, it is possible to calculate from it the interval III values of Q and of molecular weight.     

Emulsion polymerization. VI. Concentration of monomers in latex particles

Nonpolymerizing latex particles surrounded by an aqueous phase saturated with monomer absorb only a finite amount of monomer, even if the monomer is a good solvent for the polymer, because the surface energy of each particle increases on swelling. At equilibrium the change in surface energy and the free energy of mixing exactly balance. Equations based on this thermodynamic principle predict with good accuracy the saturation swelling of crosslinked and uncrosslinked latex particles and the partitioning of monomer between the aqueous phase and latex particles at partial saturation. The available experimental data on swelling of latex polymers with monomers are reviewed. Earlier papers assumed that during emulsion polymerization the monomer concentration in the latex particles is independent of conversion as long as monomer droplets are present. This assumption is shown to be a justifiable approximation. The thermodynamics of the swelling of latex particles with a blend of two monomers is presented. The calculations indicate that copolymerization in emulsion should define reactivity ratios differing from those of homogeneous copolymerization by not more than 40% if the solubility of the comonomers in water is low. The reactivity ratio scheme is strictly applicable to emulsion copolymerization if the solvent properties of the two comonomers are identical.     

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.     

Emulsion polymerization. I. Recalculation and extension of the Smith-Ewart theory

The most important assumptions underlying the Smith-Ewart theory are that the locus of chain propagation is the monomer-swollen latex particle, polymeric chains are initiated by radicals entering from the water phase into the particles, chain termination is an instantaneous reaction between two radicals within one particle, and particles are nucleated by radicals absorbed into monomer-swollen soap micelles. Right or wrong, these and other assumptions used by Smith and Ewart are retained in this paper. The newly derived and experimentally verifiable equations contain only such parameters which can be determined by experiments not involving emulsion polymerization. The proportionality constant between the particle number and the appropriate powers of soap and initiator concentrations is defined in terms of these independent parameters. Absolute rate equations are presented for the intervals before and after the completion of particle nucleation. To calculate these rates it is not necessary to have prior knowledge of the experimental particle number. The conversion at which particle nucleation is complete is calculated. The molecular weight is defined in terms of independent parameters. Predictions are made for the particle size distribution. It is shown that the validity of the theory is confined to specifiable intervals of conversion, to a certain range of monomer/water ratio, and to soap concentrations whose upper and lower limits are given.     

Emulsion polymerization. VII. Effects of instantaneous chain termination during the interval of particle nucleation

In the Smith-Ewart treatment of particle nucleation all particles were assumed to grow as if they contained exactly one radical. Modification of particle growth rate by chain termination in growing particles and reinitiation of nongrowing particles by radicals entering them was neglected in this interval although such effects were taken into account after the particle number became constant. The present theory eliminates this inconsistency for the case where chain termination is instantaneous. This refinement does not change previous predictions for the final number of particles, the steady state rate or the particle radius. Unlike the old theory, the present theory predicts continuous decay of the average number of radicals per particle from the initial value of unity to the steady-state value of one half. It also provides new theoretical predictions for the shape of the conversion-time curve at the initial stages of the reaction. Experimental data are reviewed in the context of the theory. Experimental particle sizes, steady-state conversion rates, and conversions at completion of particle nucleation were often in good quantitative agreement with the theoretical predictions. The predicted maximum in the conversion rate at the time when particle nucleation became completed was observed in a few instances. The theoretically predicted initial shape of the conversion-time curve may not be always observable due to experimental difficulties mainly associated with induction effects.     

Evolution of the termination rate coefficient in styrene polymerization

Styrene bulk polymerization was conducted at 70 °C with a high initiator concentration, and this ensured that the dominant chain‐stopping mechanism was the combination of free radicals. The evolution of the molecular weight distribution (MWD) of the polymer was measured via the periodic removal of samples during the course of the reaction and their analysis with gel permeation chromatography. The overall termination rate coefficient was independent of the conversion in the dilute regime, as observed from cumulative MWDs. In the middle of the conversion range, the observed trend was compatible with a translational‐diffusion‐controlled mechanism for the termination step. A bimodal distribution of the molecular weights was also found at high conversions and could be explained in terms of an increase in the free‐radical concentration and a very low termination rate coefficient. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 178–187, 2005     

Polymerization in nonuniform latex particles. II. Kinetics of two-phase emulsion polymerization

A new theory, based on the concept of nonuniform distribution of free radicals in polymerizing latex particles, has been developed for the kinetics of two-phase emulsion polymerization reactions. This theory also takes into account the diffusion controlled termination and propagation reactions to describe the gel effect and limiting conversion. The kinetic model permits prediction of the distribution of free radicals in the two polymer phases and rate of polymerization as a function of reaction conditions. Experimental data for polystyrene/polymethyl methacrylate and polymethyl methacrylate/polystyrene (postformed polymer/preformed polymer) in the literature have been used to assess the proposed idea of nonuniform distribution of free radicals in the latex particle.     

Gamma radiation-initiated polymerization of styrene at high pressure. IV. Emulsion polymerization with nonionic emulsifier

The effects of pressure, irradiation dose rate, and emulsifier concentration on the rate of polymerization of styrene emulsions stabilized with a nonionic surfactant, Teric GX13, were investigated. Results differed from those previously obtained with anionic surfactants and did not follow Smith–Ewart kinetics. The controlling influence of the surfactant at the particle–water interface on the reaction was demonstrated and results could be interpreted in terms of the Medvedev equation. Using this equation, we determined a value for the activation volume for chain propagation, ΔV, as ?18.7 cm³ mol^?1. This value is the same as that for pure styrene and emulsions that follow Smith–Ewart kinetics.     

Polymerization in nonuniform latex particles. III. Kinetics of grafting in emulsion polymerization

The concept of nonuniform distribution of free radicals in polymerizing latex particles has been incorporated into the development of a kinetic model for grafting reactions. This theory permits prediction of grafting efficiency as a function of reaction conditions. It can also be used for evaluation of rate constants for grafting reactions. Experimental data for emulsion polymerization of styrene in the presence of polybutadiene seed latex have been used to assess the proposed grafting theory. The predominant grafting reaction appears to be the attack of growing polystyrene chains on the allyl hydrogen atoms of polybutadiene. The results further reinforce the hypothesis that the entering oligomeric free radicals do not distribute uniformly within the particle volume.     

Diffusion-controlled vinyl polymerization. IV. Comparison of theory and experiment

Bulk polymerization data of methyl methacrylate, ethyl methacrylate, ethyl acrylate, n-propyl acrylate, vinyl acetate, and styrene were compared with the predictions of the theory proposed in the earlier parts of this series (I-III). This theory of polymerization kinetics uses the concepts of free volume and chain entanglements to describe the relationship between chain mobility and chain length dependent termination reactions. Excellent agreement was found between the predictions of the theory and the polymerization rate and molecular weight data of the six polymerization systems studied. Emphasis was placed on the ability to explain the development of higher order molecular weight averages (M?_w, M?_z, etc.) because they provide the most crucial tests for such a model. No changes were required in the model as it was applied to the different polymerization systems for a variety of reaction conditions. The theory offers a unified understanding of the diverse polymerization behavior displayed by such systems.     

Stability of the polymerizable surfactant stabilized latex particles during semibatch emulsion polymerization

The effect of the polymerizable surfactant, sodium dodecyl allyl sulfosuccinate (JS-2), on the stability of polybutyl acrylate latex particles during semibatch emulsion polymerization was investigated in this work. Experimental data show that the ionic strength is the most important parameter in determining the latex stability during the reaction. Both the amount of coagulum produced by intensive coagulation and percentage of the particle volume change (ΔV) caused by limited flocculation increase with increasing electrolyte concentration. The parameter Δ V increases significantly when the concentration of JS-2 in the initial reactor charge ([JS-2]_i) increases. The amount of coagulum increases rapidly when the agitation speed is increased from 400 to 800 rpm. Experiments of coagulation kinetics were carried out to study the stability of latex products toward added salts. The experimental data show that the chemical stability of the latex product increases with increasing pH. Furthermore, the critical coagulation concentration and diffuse potential increase with increasing [JS-2]_i. It is postulated that the increasing electrostatic attraction force between two approaching particles due to the increased [JS-2] _i can increase the apparent magnitude of Hamaker constant.     

Evaluation of polymerization rate by chain length dependence on polymer–polymer termination and primary radical termination in radical polymerization

In order to analyze the polymerization rate at high initiation rate and/or low monomer concentration, the rate equations are derived by a rate formulated previously for polymer–polymer termination and another rate for primary radical termination, which is formulated here (both rates depend on chain length of polymer radical). Such equations would be applicable to the kinetic data in the polymerizations of styrene and methyl methacrylate. This shows that the assumption that both rates are independent of chain length overestimates the rate of primary radical termination.     

Monodisperse micron-sized crosslinked polystyrene particles. IV. Effect of network structure on polymerization procedure

Monodisperse micron-sized polystyrene particles crosslinked using urethane acrylate were produced by dispersion polymerization in ethanol solution and the effect of the crosslinked network structure on the polymerization procedure was studied. The influences of the concentrations of the initiator and urethane acrylate on the particle diameter (D _n), the particle number density (N _p), and the polymerization rate (R _p) were found to obey the approximate relationships D _n ∝ [initiator]^0.43 [urethane acrylate]^0.05, N _p ∝ [initiator]^−1.30 [urethane acrylate]^0.19, and R _p ∝ [initiator]^{0.24 ± 0.02}. The power-law dependence of D _n and N _p on the initiator concentration showed a similar trend to that of linear polystyrene reported in the literature. Especially, it was found that urethane acrylate does not have a serious effect on D _n and N _p of the particles produced. The dependence of R _p on the initiator concentration was observed to be higher than that of linear polystyrene, suggesting that there is still competition between heterogeneous polymerization and solution polymerization because of the crosslinked network structure of the primary particle. Received: 1 April 1999 Accepted in revised form: 29 June 1999     

Emulsion polymerization. II. Review of experimental data in the context of the revised Smith-Ewart theory

Tables are presented for convenient calculation of the basic parameters of the revised Smith-Ewart theory. For the methyl methacrylate (MMA)/sodium lauryl sulfate (SLS)/K₂S₂O₈, and for the styrene/SLS/K₂S₂O₈ reaction mixtures parameters are presented from which the absolute values of the following quantities can be conveniently calculated for any temperature, soap, and initiator concentration: particle number, particle radius, conversion where particle nucleation stops, rate and molecular weight in interval II, the interval after completion of particle nucleation and before the disappearance of monomer droplets. The theoretical predictions are compared to new experimental data and to those from the literature. The available data confirm the theoretical prediction that particle nucleation stops after a very small amount of polymer is formed, of the order of 0.01 cc. polymer/cc. water in most recipes. The theory and experiments are in good qualitative agreement for the conversion rate prior to completion of particle formation: the conversion rate rises with time and, when particle nucleation stops, it levels off. Excellent quantitative agreement can be obtained between theoretical and experimental particle size values. In the experiments of this laboratory the SLS concentration was varied 60-fold, the K₂S₂O₈ concentration was varied 140-fold and the difference between theoretical and experimental poly(MMA) particle radii was always less than about 20%. Similar good agreement was obtained for polystyrene over the temperature range 30–90°C. Some polystyrene data from the literature with carboxylic soaps give just as good fit as the data with SLS of this laboratory. The predicted proportionality between particle number and the product of 0.6 power of soap concentration and of 0.4 power of initiator concentration was observed for several monomers. The theoretical predictions for the rate and molecular weight obtained in interval II are valid only for relatively low initiator and high soap recipes. For recipes for MMA and styrene the rate data are in good agreement with those calculated from the theory. The theory also correctly predicts the order of magnitude of the experimental molecular weights. For several monomers the rate and molecular weight vary with initiator and soap concentrations in a manner close to theoretical predictions.     

Radiation-induced polymerization of glass-forming systems. IV. Effect of the homogeneity of polymerization phase and polymer concentration on temperature dependence of initial polymerization rate

The effect of homogeneity of polymerization phase and monomer concentration on the temperature dependence of initial polymerization rate was studied in the radiation-induced radical polymerization of binary systems consisting of glass-forming monomer and solvent. In the polymerization of a completely homogeneous system such as HEMA–propylene glycol, a maximum and a minimum in polymerization rates as a function of temperature, characteristic of the polymerization in glass-forming systems, were observed for all monomer concentrations. However, in the heterogeneous polymerization systems such as HEMA–triacetin and HEMA–isoamyl acetate, maximum and minimum rates were observed in monomer-rich compositions but not at low monomer concentrations. Furthermore, in the HEMA–dioctyl phthalate polymerization system, which is extremely heterogeneous, no maximum and minimum rates were observed at any monomer concentration. The effect of conversion on the temperature dependence of polymerization rate in homogeneous bulk polymerization of HEMA and GMA was investigated. Maximum and minimum rates were observed clearly in conversions less than 10% in the case of HEMA and less than 50% in the case of GMA, but the maximum and minimum changed to a mere inflection in the curve at higher conversions. A similar effect of polymer concentration on the temperature dependence of polymerization rate in the GMA–poly(methyl methacrylate) system were also observed. It is deduced that the change in temperature dependence of polymerization rate is attributed to the decrease in contribution of mutual termination reaction of growing chain radicals to the polymerization rate.     

Chain-length dependent termination in pulsed-laser polymerization, 3. On the prospects of determining the bimolecular termination constant kt from rate data

The correct (event-weighted) average of k_t, 〈k_t〉, has been calculated from simulation data for pseudostationary laser-induced polymerization for a kinetic scheme with chain-length dependent termination and compared to the average k̄_t which is obtained by employing the formal procedures, originally designed for the evaluation of individual rate constants from rate data in the case of chain-length independent termination. Satisfactory (and in fact excellent) results are obtained only if the complete equation for the conversion per laser pulse is solved for k̄_t. This leads to an almost perfect recovery of the power-law governing the dependence of k_t on chain-length, especially the exponent.     

Radiation-induced emulsion polymerization of ethylene. IV. Effect of pressure,temperature, and additives on rate in connection with number of polymer particles

The effects of pressure, temperature, and additives on the rate of radiation-induced emulsion polymerization of ethylene with FC-143 as emulsifier were studied kinetically. The rate of polymerization was proportional to the 2.5 power of ethylene fugacity, and the apparent rate constant (rate of polymerization/2.5 power of ethylene fugacity) was constant below 78°C. Above this temperature, the rate constant decreased with an apparent activation energy of ?8.2 kcal/mole. These facts can be interpreted in connection with the polymer structure and the change of rate of escape of radicals from the polymer structure and the change of rate of escape of radicals from the polymer particle into the aqueous phase. The rate of polymerization decreased on addition of a series of n-aliphatic alcohols due to the chain-transfer reaction and consequent escape of radicals to the aqueous phase. On the other hand, the addition of tert-butyl alcohol increased the rate of polymerization, probably because of its effect in increasing swelling of the polymer particles. Addition of electrolytes increased the rate of polymeriaztion as a result of the increase of the number of polymer particles.     

Emulsion polymerization of vinyl chloride, 2 potassium persulfats decomposition in the presence of PVC latex

The decomposition rate of potassium persulfate (KPS) in aqueous solutions, in the presence of sodium dodecyl sulfate (SDS) and poly(vinyl chloride) latex (PVC) was studied. The dissolved SDS increases the decomposition rate constant (k_d) while the SDS aggregation as micella and/or its adsorption on the polymer hydrophobic surface results in a decreasing k_d. The emulsifier - free surface of the polymer particles increases the decomposition rate. A reaction mechanism based on emulsifier - emulsifier and emulsifier - polymer hydrophobic interactions is put forward.     

Effect of viscosity on termination rate constant in radical polymerization at low conversion

By using the expression, k_t = A₁D_s for the chain termination rate constant (where A₁ is a constant and D_s is the diffusion constant of radical chain end), a familiar chain termination rate constant, k_t = A₂/η_s (where A₂ is a constant and η_s is solvent viscosity) was examined with variation of conversion x. It was found that the proportionality of chain termination rate constant and solution viscosity is a valid relation at conversion 0 but is approximate at conversion x_c ≥ x > 0. Here x_c denotes a critical conversion under the average distance around spherical polymers formed in polymerization solution is zero. At conversions above x_c, the inverse relation between chain termination rate constant and solution viscosity is not correct.     

Application of a calorimetric method in radiation-induced polymerization—IV: Determination of propagation and termination rate constants for cyclohexyl-methacrylate

A calorimetric method has been used to study the gamma-induced polymerization of cyclohexyl-methacrylate (CHMA) under non-stationary conditions. As for other methacrylates already studied in this laboratory, the polymerization rate of CHMA is proportional to (dose-rate)${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for all temperatures and dose rates examined. The rate constants for propagation and termination have been determined and the results compared with those for methyl, ethyl and n-butyl methacrylates. The $\text{M}$_w values of CHMA, formed in tetrahydrofuran at different dose rates, agree with the kinetic behaviour.