Particle nucleation in emulsion polymerization. IV. Nucleation in monomer droplets

Nucleation in finely dispersed monomer emulsions in competition with homogeneous and micellar mechanism was studied. The emulsions were prepared with a high-pressure homogenizer under varying homogenizing conditions and made stable by the addition of hexadecane to the monomer. Sodium dodecyl sulfate was used as emulsifer. The number of particles in latexes polymerized with potassium persulfate and benzoyl peroxide initiators was measured and plotted as a function of the free emulsifier concentrations. With persulfate initiator the particle number achieved a minimum in the transition region between droplet and water phase–micellar nucleation mechanisms. With very fine emulsions Smith–Ewart case II kinetics with n = 0.5 applied. The reaction rate, which differed from conventional emulsion polymerizations, decreased with time up to the point at which n began to increase. In these runs the particle size distribution became nearly monodisperse.     

Particle nucleation in emulsion polymerization. II. Nucleation in emulsifier-free systems investigated by seed polymerization

Experiments with seeded polymerization in emulsifier-free systems were carried out with styrene in order to test the theory of particle nucleation presented in the first article in this series. The effect of amount, size, and surface charge density of the seed particles on the formation of new particles was investigated. An expression for the capture rate of oligomeric radicals from the water phase was evaluated in which the rate of capture was considered to be governed by the absorption of oligomers with chain length one less than the critical chain length for precipitation of the oligomer. Coagulation of primary particles was also included in the expression for the number of new particles obtained in the system. Limited coagulation of primary particles with already formed particles and with seed particles was found to play an important role in determining the final number of new particles found at the end of the runs.     

A molecular theory for particle nucleation: primary particle formation in emulsion polymerization

Homogeneous nucleation is fundamentally important in emulsion polymerization. A molecular theory is proposed to quantify primary particle formation in the process. The proposed model divides a polymerization system into three portions: the domains formed by growing radicals, their surrounding aqueous solution, and dispersed monomer droplets. In general, the total free energy of the domains is contributed from the mixing among the molecules including monomer and water, the elasticity of oligomeric radical chains, and the transferable free energy of electrolytes; while that of the outer solution is from the mixing of monomer and water molecules and the transferable energy of electrolytes. Application of this theory to vinyl acetate emulsion polymerization has shown that the critical degree of polymerization (j(cri)) predicted is in a good agreement with the value derived from experimental data reported in literature. Furthermore, this model can also estimate the concentrations of VAc and water in the domain at the degrees of polymerization around j(cri).     

Particle nucleation in emulsion polymerization. III. Nucleation in systems with anionic emulsifier investigated by seeded and unseeded polymerization

Studies of seeded and unseeded polymerization of styrene using sodium dodecylsulfate as emulsifier have been carried out in order to investigate the mechanism of particle nucleation in such systems and to test the theory presented in Part I of this series. The rate of capture of water-soluble oligomeric radicals was considered to be governed by absorption of oligomers with chain length one less than the critical chain length. It was concluded that the micelles became the dominating loci for particle nucleation above CMC for the emulsifier. A complete nonsteady-state model for particle initiation above CMC which takes into account radical desorption and reabsorption has been developed. It was indicated that, even for styrene, desorption of radicals may play a role in controlling the radical and particle number of interval I under certain conditions. The model also showed that the efficiencies of particles in absorbing radicals could be calculated from physical parameters, such as diffusion constants and surface charge densities, which are available for the system.     

Tests of the homogeneous nucleation theory with molecular-dynamics simulations. I. Lennard-Jones molecules

Two kinds of the homogeneous nucleation theory exist at the present: the classical nucleation theory and the semiphenomenological model. To test them, we performed molecular-dynamics (MD) simulations of nucleation from vapor to liquid with 5000-20,000 Lennard-Jones-type molecules. Simulations were done for various values of supersaturation ratios (from 2 to 10) and temperatures (from 80 to 120 K). We compared the size distribution of clusters in MD simulations with those in the theoretical models because the number density of critical clusters governs the nucleation rate. We found that the semiphenomenological model achieves excellent agreements in size distributions of the clusters with all MD simulations we done. The classical theory underestimates the number density of the clusters in the temperature range of 80-100 K, but overestimates in 100-120 K. The semiphenomenological model also predicts well the nucleation rate in MD simulations, while the classical nucleation theory does not. Our results confirmed the validity of the semiphenomenological model for Lennard-Jones-type molecules.     

Communication: A dynamical theory of homogeneous nucleation for colloids and macromolecules

Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal system in the strong damping limit the most likely path for nucleation can be determined by gradient descent in density space governed by a nontrivial metric. This is illustrated by application to low-density/high-density liquid transition of globular proteins in solution where it is shown that nucleation process involves two stages: the formation of an extended region with enhanced density followed by the formation of a cluster within this region.     

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     

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.     

Theory of colloid stability and particle nucleation kinetics in emulsion polymerization

The DLVO theory of colloid stability is applied to the uncatalyzed and catalyzed agglomeration of small primary particles formed in the earliest stages of emulsion polymerization in the manufacture of a carboxylic styrene/butadiene latex. The inverse 6th-power relationship between the stability ratio and the cation concentration revealed experimentally in an earlier work can be confirmed theoretically using variable Stern potentials. The Stern potential changes as parabolic function of log cation concentration. From the viewpoint of DLVO and Stern theory it is suggested that a spacer effect is crucial for the activity of the catalyst used.Presented at the 5th European and Interface Society Conference together with the 35th meeting of the Deutsche Kolloidgesellschaft on Trends in Colloid and Interface Science September 25–28, 1991, Maiz, FRG     

A kinetic model for nonisothermic homogeneous nucleation

A model for isothermal homogeneous nucleation is proposed that improves the classical model. A quasiequilibrium distribution of clusters was calculated on a basis of the Frenkel’-Lothe-Pound theory. The dependence of the free energy of clusters on their size was represented by an interpolation formula relating the free energy of dimers and large clusters to which a notion of macroscopic surface tension is applicable. The nucleation rate and the dependence of the cluster temperature on their size were calculated by balance equations describing the heating of from a cluster due to the condensation of monomers and its cooling due to collisions with an ambient gas. It is shown that the nucleation rate in excess buffer gas is higher than for the pure condensing gas by approximately two orders of magnitude. The model adequately describes the experimental data for the nucleation of methanol supersaturated vapor.     

Free radical exit in emulsion polymerization. I. Theoretical model

The exit or desorption of free radicals from latex particles is an important kinetic process in an emulsion polymerization. This article unites a successful theory of radical absorption (i.e., initiator efficiency), based on propagation in the aqueous phase being the rate determining step for entry of charged free radicals, with a detailed model of radical desorption. The result is a kinetic scheme applicable to true “zero-one” systems (i.e., where entry of a radical into a latex particle already containing a radical results in instantaneous termination), which is still, with a number of generally applicable assumptions, relatively simple. Indeed, in many physically reasonable limits, the kinetic representation reduces to a single rate equation. Specific experimental techniques of particular significance and methods of analysis of kinetic data are detailed and discussed. A methodology for both assessing the applicability of the model and its more probable limits, via use of known rate coefficients and theoretical predictions, is outlined and then applied to the representative monomers, styrene and methyl methacrylate. A detailed application of the theory and illustration of the methodology of model discrimination via experiment is contained in the second article of this series. © 1994 John Wiley & Sons, Inc.     

To the theory of homogeneous nucleation: Cluster energy

An attempt is made to critically analyze the modern state of the theory of homogeneous nucleation as concerns its ability to describe experiments with high accuracy. An analysis of the experimental data led us to conclude that the dependence of the nucleation rate on supersaturation and temperature T was not described by the theory, which underestimates the critical cluster size compared with the Gibbs-Thomson equation. The possibility of applying density functional theory (one of the latest achievements in the theory of homogeneous nucleation) was questioned. Within this theory, the Gibbs-Thomson equation remains valid even outside the classic capillary approximation. It is suggested that, to bring theory in consistency with experiment, certain fundamental propositions of the theory of nucleation should be revised. The inclusion of an additional contribution to the Gibbs energy of a cluster caused by the size dependence of the specific heat capacity of the cluster decreases the critical cluster size compared with the value calculated by the Gibbs-Thomson equation. The calculated dependence of nucleation rate on supersaturation was in agreement with the experimental results.     

Simple correction to the classical theory of homogeneous nucleation

Formation of the new disperse phase via homogeneous nucleation plays a fundamental role wherever the first-order phase transitions occur. Inconsistent temperature dependence of the nucleation rates and poor agreement of theoretical critical supersaturations with experimental data for a number of substances are fundamental problems of the classical nucleation theory (CNT). Here we show that these problems can be solved with a simple empirical correction to CNT. Despite its simplicity, the corrected CNT (CCNT) accurately predicts temperature dependences and absolute values of the critical supersaturations for both organic and inorganic substances with widely varying properties at different ambient conditions and it works surprisingly well in a wide size range down to few molecules. The difference in predictions of CCNT and other versions of the classical nucleation theory commonly used in analyzing experimental data is discussed. It has been found that CCNT consistently gives better agreement with experimental data than other versions of classical nucleation theory.     

Molecular weight distribution in emulsion polymerization. I. The homopolymer case

A model for evaluating the instantaneous degree of polymerization distribution of homopolymers produced in emulsion, based on the mathematics of the Markov chains, is developed. The model accounts for any number of active chains per particle, as well as for the two fundamental mechanisms of chain termination: mono- and bi-molecular, both by combination and by disproportionation. The core of the model is the so called subprocessmain process treatment, which allows us to correctly evaluate the degree of polymerization of the chains growing in the polymer particles, by distinguishing between the events experienced by the polymer chain which imply a change of its degree of polymerization (subject transitions) and those which imply only a change in the particle state (environment transitions). This is obtained by properly defining the one-step transition probability matrix of the relevant Markov process. Once this is done, the evaluation of the distribution of the degrees of polymerization reduces to a few simple operations among matrices. Explicit expressions for the instantaneous probability density functions and the relative cumulative distributions are obtained. The application of such relationships is facilitated by the numerical procedures reported in the Appendices. The results of the model developed in this work are in agreement with those of earlier models in the range of parameter values of practical interest. In the limit of very low molecular weights, only the model developed in this work provides the correct answer. Moreover, a much more significant result is its applicability to the case of emulsion copolymerization, as it is shown in Part II.     

Control of surfactant level in starve-fed emulsion polymerization. I. Sulfate-containing oligomers: Preparation and application as surfactant in emulsion polymerization

It is well known that the amount of surfactant must be carefully controlled during starve-fed emulsion polymerization processes. Too little surfactant leads to emulsion instability and coagulation, while too much surfactant leads to secondary particle formation. Although these relationships are qualitatively understood in the art, there is little quantitative basis to guide the synthetic chemist, especially in multistep starve-fed emulsion polymerization processes to make larger supermicron particles. We have developed a method, which will be described in a companion article, to control the surfactant level by monitoring the surface tension during polymerization. In order to quantitatively predict how much surfactant to add at any given time, one needs to know in advance the adsorption characteristics of the soap. Further complicating the matter is the formation of “in situ” or oligomeric surfactant during polymerization with aqueous initiators such as ammonium persulfate. This work demonstrates how to prepare surface-active oligomers and how to make latex particles using them as surfactant. First, we established the mass balance for the initiator-derived sulfate groups in seed latexes by conductometric, potentiometric, and iodometric titrations. Based on the characterization of seed latexes, a method for determining the effective sulfate concentration has been developed. When surface-active oligomers were used as the only surfactant, we obtained a series of monodisperse, supermicron copolymer latex particles with diameters up to 3.22 μm. This is a similar result to that obtained with a commercially made anionic surfactant. © 1995 John Wiley & Sons, Inc.     

Radiation-induced emulsion polymerization of ethylene. I. Effect of reaction conditions on the polymerization

The effect of reaction conditions on the rate of radiation-induced emulsion polymerization of ethylene was studied by use of a 500-ml autoclave. Among various kinds of emulsifiers, a series of potassium salts of fatty acids gave high rates of the polymerization. The polymerization was inhibited by the presence of oxygen, but the rate of polymerization followed by the induction period was not influenced by the initial presence of oxygen. Stirring rate and the monomer: water ratio did not affect the rate of polymerization. The rate of polymerization was maximum at about 80°C, and number-average molecular weight was influenced by the temperature in a similar manner as the rate of polymerization. This suggests that the change of mobility of propagating radical in the polymer particle changes the rate of termination reaction. The rate of polymerization was proportional to the 1.7 power of the reaction pressure.     

On the kinetics of styrene emulsion polymerization above CMC. I. A mathematical model

A detailed mathematical model of the kinetics of styrene emulsion polymerization has been proposed. Its main features/assumptions are compartmentalization, micellar and homogeneous nucleation, particle formation by both initiator‐derived and desorbed radicals, dependence on the particle size of the rate coefficients, thermodynamic considerations, and aqueous phase kinetics. The model predicts that micellar nucleation dominates over homogeneous nucleation and that the evolution of the nucleation rate reaches a maximum, where desorbed radicals have an important contribution. Initiator‐derived radicals with only one monomeric unit have also a significant contribution on the rate of capture in particles. The results suggest that the correctness of the instantaneous termination approach depends not only on the size of the particle, but also on the type of entering radical (initiator‐derived or monomeric). © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2201–2218, 2000