Emulsion polymerization. IV. Experimental verification of the theory based on slow termination rate within latex particles

A large body of data shows that the time dependence of conversion fits the equation P = At² + Bt in the interval where, according to the Smith-Ewart model, the relationship should be linear. For latexes of very small particle size the Smith-Ewart linear relationship (P = Bt) is often observed, and for latexes of very large particle size the conversion was found to be proportional to t². The experimental value of parameter B was in good agreement with independent theoretical predictions. From A and B the ratio between termination and propagation constants was calculated and was in the 5–200 range. Independent estimates of this ratio give the same order of magnitude. These independent estimates are from the literature and are obtained from the increase in conversion rate at catalyst post-addition during emulsion polymerization or from emulsion polymerization initiated by intermittent irradiation or from homogeneous polymerization in the presence of inert polymers of high viscosity. The conversion–time curves describing the whole conversion process generally have sigmoid shape. The molecular weight is often found to pass through a maximum as the conversion increases. In one experiment this maximum coincided with the calculated maximum in the average number of radicals per particle Q. The variation of experimental molecular weights with conversion accurately followed the theoretical predictions. The deviation from the Smith-Ewart model was often significant. The value of Q was not 0.5, as the Smith-Ewart model requires it to be, but often reached values much larger, as large as 10. The particle size distribution broadened with increasing conversion and became increasingly skew. Numerous data taken from the literature are in good quantitative or qualitative agreement with the theory proposed in Part III and for these data the observed deviations from the Smith-Ewart theory are readily explainable. The new data obtained with styrene, n-butyl methacrylate, and methyl methacrylate are also in quantitative agreement with the new theory. One experiment involving methyl methacrylate is analyzed in great detail. The variation of time, of Q, of molecular weight, of average particle size, and of particle size distribution with conversion are reported. The molecular weight distribution is also calculated from the conversion dependence of molecular weight.     

The growth of polymer colloids

The traditional theoretical approach to emulsion polymerization is extended to include effects due to the size of each polymer latex particle. Specific account can thus be taken of the particle size distribution in considering the growth of the colloid. Coupled partial differential equations are derived to describe the system and shown to reduce to the conventional Smith-Ewart equations under certain limits. Solutions are presented for simple models for the emulsion polymerization of styrene and vinyl acetate.     

PARTICLE SIZE DISTRIBUTION IN CONTINUOUS EMULSION POLYMERIZATION WITH FREE RADICAL DESORPTION

A mathematical model of particle size distribution in continuous emulsion polymerization which accounts for the free radical desorption from polymer particles is presented. The desorption rate is based on the diffusion theories which suggest the rate coefficient should be inversely proportional to the surface area of the polymer particles. The number density and total particle number are estimated by our model.

The average number of radicals per particle approaches Smith-Ewart case II In the range of large particle sizes. A means for predicting the nature of average desorption rate is proposed, and it seems to be influenced by concentrations of emulsifier and initiator, and residence times as well     

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 emulsion copolymerization of tetrafluoroethylene with propylene. IV. Effects of emulsifier concentration and dose rate

Radiation-induced emulsion copolymerization of tetrafluoroethylene with propylene was carried out by batch operation with an initial molar ratio of tetrafluoroethylene to propylene of 3.0 in the emulsifier concentration range of 0.1 to 3.0% and in the dose rate range of 2 × 10⁴ to 2 × 10⁵ R/hr. The effects of emulsifier concentration and dose rate on the polymerization rate and the number-average degree of polymerization are discussed in comparison with the Smith-Ewart theory. The polymerization rate is proportional to the 0.26 power of emulsifier concentration and to the 0.7 power of dose rate. The degree of polymerization is independent of the emulsifier concentration and the dose rate above the critical micelle concentration (CMC) of the emulsifier. These results are not in agreement with the Smith-Ewart theory. It is explained that the termination reaction is a degradative chain transfer of propagating radicals to propylene. On the other hand, the copolymerization in emulsion occurs either below the CMC or in the absence of emulsifier. Under these conditions, however, it is impossible to obtain a copolymer of high molecular weight at a high rate of polymerization because of the presence of a small number of polymer particles formed and the short interval of chain growth in the polymer particle.     

Microgel formation in emulsion copolymerization. I. Polymerization without seed latex

Microgel formation during emulsion copolymerization of methyl methacrylate and ethylene glycol dimethacrylate is investigated both experimentally and theoretically. It was found that the average crosslinking density is fairly high even from a very early stage of polymerization. The molecular weight distribution (MWD) development in emulsion crosslinking copolymerization is completely different from that in homogeneous polymerization. Because the maximum molecular weights allowed to exist is limited by the particle size, a comprehensive model for the MWD development in nonlinear emulsion polymerization must account for the size of polymerization locus properly. During the formation of microgels, a drastic change in the weight-average molecular weights, which is characteristic of gelation in homogeneous media, is not always required. In a typical microgel formation process where a large mole fraction of divinyl monomer is used, the average molecular weights may increase just linearly with conversion in which a sharp MWD shifts to higher molecular weights with the progress of polymerization. It is shown that the microgels formed in emulsion polymerization are characterized as intramolecularly crosslinked macromolecules that occupy a very large weight fraction in each polymer particle. © 1996 John Wiley & Sons, Inc.     

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.     

Determination of the number of particles/unit volume of latex during the emulsion polymerization of styrene

The variation of the number of particles/unit volume of latex (N) with conversion was determined during the emulsion polymerization of styrene. The results showed that, contrary to what is required by the Smith-Ewart theory, N increased during the constant rate period. This conclusion was supported by the variation of the particle size distribution with conversion. Further evidence that latex particles could form in the absence of micelles was given by using systems in which the soaps were below the CMC. The chain length of the soaps used had a marked effect on the rate of polymerization. This effect was shown not to be due to the variation of the CMC with chain length, but possibly to the stronger adsorption of the longer chain length soaps at the polymer–water interface.     

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.     

Relationships for determining the rate constant of the polymerization growth reaction by means of the emulsion polymerization method

Some simple equations for the emulsion polymerization system were derived on the basis of the Smith-Ewart theory. These are used in calculating the molar monomer concentration and rate of polymerization in units of moles per liter per second for the zero-order region with respect to the monomer as well as in calculating the rate constant of the growth reaction.     

The Effect of Residence Time Distribution on the Slurry‐Phase Catalytic Ethylene Polymerization: An Experimental and Computational Study

This work is focused on the development and validation of a model accounting for the impact of the reactor residence time distribution in well‐stirred slurry‐phase catalytic polymerization of ethylene. Particle growth and morphology are described through the Multigrain model, adopting a two‐site model for the catalyst and a conventional kinetic scheme. Particle size distribution and polymer properties (average molecular weights and polydispersity) are computed as a function of particle size through a segregated model, assuming that neither breakage nor aggregation occur. Reactors are modeled by means of fundamental mass conservation equations. The model is applied to a system constituted by a series of two ideal continuous stirred tank reactors, where the synthesis of polyethylene with bimodal molecular weight distribution is performed, employing the initial catalyst size distribution as the only adjustable parameter. The model provides insights at the single particle scale for each specific size, thus highlighting the inhomogeneity which arises from the synergic effects of chemical kinetics and residence time distributions in both reactors. The satisfactory agreement between model results and experimental data, in terms of particle size distribution and average molecular weights, confirmed the suitability of the model and underlying assumptions.     

Particle formation under monomer‐starved conditions in the semibatch emulsion polymerization of styrene. I. Experimental

Particle formation and particle growth compete in the course of an emulsion polymerization reaction. Any variation in the rate of particle growth, therefore, will result in an opposite effect on the rate of particle formation. The particle formation in a semibatch emulsion polymerization of styrene under monomer‐starved conditions was studied. The semibatch emulsion polymerization reactions were started by the monomer being fed at a low rate to a reaction vessel containing deionized water, an emulsifier, and an initiator. The number of polymer particles increased with a decreasing monomer feed rate. A much larger number of particles (within 1–2 orders of magnitude) than that generally expected from a conventional batch emulsion polymerization was obtained. The results showed a higher dependence of the number of polymer particles on the emulsifier and initiator concentrations compared with that for a batch emulsion polymerization. The size distribution of the particles was characterized by a positive skewness due to the declining rate of the growth of particles during the nucleation stage. A routine for monomer partitioning among the polymer phase, the aqueous phase, and micelles was developed. The results showed that particle formation most likely occurred under monomer‐starved conditions. A small average radical number was obtained because of the formation of a large number of polymer particles, so the kinetics of the system could be explained by a zero–one system. The particle size distribution of the latexes broadened with time as a result of stochastic broadening associated with zero–one systems. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3940–3952, 2001     

Kinetic modeling of controlled living microemulsion polymerizations that use reversible addition–fragmentation chain transfer

Reversible addition–fragmentation chain transfer (RAFT) polymerization is a useful technique for the formation of polymers with controlled architectures and molecular weights. However, when used in the polymerization of microemulsions, RAFT agents are only able to control the polymer molecular weight only at high RAFT concentrations. Here, a kinetic model describing RAFT microemulsion polymerizations is derived that predicts the reaction rates, molecular weight polydispersities, and particle size. The model predicts that at low RAFT concentrations, the RAFT agent will be consumed early in the reaction and that this will result in uncontrolled polymerization in particles nucleated late in the reaction. The higher molecular weight polydispersity that is observed in RAFT microemulsion polymerizations is the result of this uncontrolled polymerization. The model also predicts a shift in the conversion at which the maximum reaction rate occurs and a decrease in the particle size with increasing RAFT concentration. Both of these trends are also consistent with those observed experimentally. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6055–6070, 2006     

The polymerization rate of freshly nucleated particles during emulsion polymerization with micellar nucleation

A simple procedure was developed to account for the contribution of freshly nucleated particles to the total polymerization rate during micellar nucleation. It has been shown that the polymerization rate of the freshly nucleated particles cannot be described by a steady-state solution for a radical population balance over the particle size distribution, i.e., the classical Smith-Ewart recursion relation. Once nucleated, the particles grow for a significant period of time with one radical before either radical desorption or radical absorption, followed by instantaneous bimolecular termination, occur. For most emulsion polymerizations, radical desorption is the dominant process for radical loss of the freshly nucleated particles. A relation for the mean time that the freshly nucleated particles grow with one radical was derived. © 1996 John Wiley & Sons, Inc.     

Radiation and Chemical Grafting of Styrene to Polybutadiene Latex

Earlier studies of the gamma radiation and potassium persulfate grafting of styrene to uncrosslinked small particle size polybutadiene latices have been extended to a commercial cross-linked large particle size latex. The larger size particles and high gel content of the substrate latex was found to lead to a more complicated pattern of behavior. The conversion curves and the molecular weights were found to be complex functions of the initial monomer concentration, number of particles and temperature with both methods of initiation. The simple Smith-Ewart theory did not, in general, apply to these systems, and the k_p and E_p varied with conditions and were not in agreement with the generally accepted literature values. The molecular weights of the extracted polystyrene homopolymer were lower in the case of radiation initiation, in agreement with the previous work. This suggests that shorter but numerous grafted side chains are possible with radiation presumably due to the higher radical fluxes. (Some parallel experiments indicated that the molecular weights of the extracted homopolystyrene are similar to those of the grafted side chains.) This phenomenon also leads to somewhat lower graft efficiency with radiation initiation. Nevertheless, radiation was found to give grafting efficiencies of more than 80% under the best conditions. The conversions were also quite efficient with economical yields per radiation dose. These results, coupled with the ease of control and other features of radiation, make it a viable alternative method of initiation for industrial use.     

Chemical properties of water-soluble,nonionic azo compounds as initiators for emulsion polymerization

Four kinds of water-soluble, nonionic azo compounds were studied in terms of their decomposition rate and initiator efficiency in radical polymerization, and then used for emulsion polymerization. They had relatively low initiator efficiency from 0.09 to 0.46. It was attributed to the susceptibility to a cage effect, depending on their molecular size and hydrophobicity. Four azo compounds initiated emulsion polymerization but nonionic latex particles were not obtained unexpectedly. Methanol-containing medium results in the formation of a bimodal particle size distribution as well as a bimodal molecular weight distribution. © 1996 John Wiley & Sons, Inc.     

Atom transfer radical polymerization of n‐butyl methacrylate in an aqueous dispersed system: A miniemulsion approach

Ultrasonication was applied in combination with a hydrophobe for the copper‐mediated atom transfer radical polymerization of n‐butyl methacrylate in an aqueous dispersed system. A controlled polymerization was successfully achieved, as demonstrated by a linear correlation between the molecular weights and the monomer conversion. The polydispersities of the polymers were small (weight‐average molecular weight/number‐average molecular weight < 1.5). The influence of several factors, including ultrasonication, the amount of the surfactant, and the nature of the initiator, on the polymerization kinetics, molecular weight, and particle size was studied. The polymerization rate and molecular weights were independent of the number of particles and only depended on the atom transfer equilibrium. The final particle size, however, was a function of all the parameters. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4724–4734, 2000     

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.     

Seeded semicontinuous emulsion copolymerization of methyl methacrylate,butyl acrylate,and phosphonated methacrylates: Kinetics and morphology

A series of methyl methacrylate, butyl acrylate, and phosphonated methacrylate (MAPHOS) copolymers were prepared by seeded semicontinuous emulsion polymerization under monomer‐starved conditions by varying the amount and nature of phosphonated methacrylates (diester, monoacid, and diacid). The effects on the kinetics, molecular weight distribution, and particle size distribution were investigated. The molecular weights and particle growth were affected by the amount of acidic MAPHOS in the recipe. Secondary nucleation occurred above a critical concentration of acidic MAPHOS (5 wt %). Characterization of the latices by elemental analysis provided information on the phosphonic acid location and showed that phosphonic oligomers were formed in the aqueous phase. Particle size data and electrophoretic behavior of the latex afforded a discussion on the particle surface morphology. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2469–2480, 2003     

Sterically and electrosterically stabilized emulsion polymerization. Kinetics and preparation

The principal subject discussed in the current paper is the radical polymerization in the aqueous emulsions of unsaturated monomers (styrene, alkyl (meth)acrylates, etc.) stabilized by non-ionic and ionic/non-ionic emulsifiers. The sterically and electrosterically stabilized emulsion polymerization is a classical method which allows to prepare polymer lattices with large particles and a narrow particle size distribution. In spite of the similarities between electrostatically and sterically stabilized emulsion polymerizations, there are large differences in the polymerization rate, particle size and nucleation mode due to varying solubility of emulsifiers in oil and water phases, micelle sizes and thickness of the interfacial layer at the particle surface. The well-known Smith-Ewart theory mostly applicable for ionic emulsifier, predicts that the number of particles nucleated is proportional to the concentration of emulsifier up to 0.6. The thin interfacial layer at the particle surface, the large surface area of relatively small polymer particles and high stability of small particles lead to rapid polymerization. In the sterically stabilized emulsion polymerization the reaction order is significantly above 0.6. This was ascribed to limited flocculation of polymer particles at low concentration of emulsifier, due to preferential location of emulsifier in the monomer phase. Polymerization in the large particles deviates from the zero-one approach but the pseudo-bulk kinetics can be operative. The thick interfacial layer can act as a barrier for entering radicals due to which the radical entry efficiency and also the rate of polymerization are depressed. The high oil-solubility of non-ionic emulsifier decreases the initial micellar amount of emulsifier available for particle nucleation, which induces non-stationary state polymerization. The continuous release of emulsifier from the monomer phase and dismantling of the non-micellar aggregates maintained a high level of free emulsifier for additional nucleation. In the mixed ionic/non-ionic emulsifiers, the released non-ionic emulsifier can displace the ionic emulsifier at the particle surface, which then takes part in additional nucleation. The non-stationary state polymerization can be induced by the addition of a small amount of ionic emulsifier or the incorporation of ionic groups onto the particle surface. Considering the ionic sites as no-adsorption sites, the equilibrium adsorption layer can be thought of as consisting of a uniform coverage with holes. The de-organization of the interfacial layer can be increased by interparticle interaction via extended PEO chains--a bridging flocculation mechanism. The low overall activation energy for the sterically stabilized emulsion polymerization resulted from a decreased barrier for entering radicals at high temperature and increased particle flocculation.