Droplet nucleation

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

However, in the case of mini- and microemulsions, processing methods reduce the size of the monomer droplets close to the size of the micelle, leading to significant particle nucleation in the monomer droplets (17). Intense agitation, cosurfactant, and dilution are used to reduce monomer droplet size. Additives like cetyl alcohol are used to retard the diffusion of monomer from the droplets to the micelles, in order to further promote monomer droplet nucleation (18). The benefits of miniemulsions include faster reaction rates (19), improved shear stabiHty, and the control of particle size distributions to produce high soHds latices (20). 

The secondary source of fine particles in the atmosphere is gas-to-particle conversion processes, considered to be the more important source of particles contributing to atmospheric haze. In gas-to-particle conversion, gaseous molecules become transformed to liquid or solid particles. This phase transformation can occur by three processes absortion, nucleation, and condensation. Absorption is the process by which a gas goes into solution in a liquid phase. Absorption of a specific gas is dependent on the solubility of the gas in a particular liquid, e.g., SO2 in liquid H2O droplets. Nucleation and condensation are terms associated with aerosol dynamics. 

Turnbull and Cech [58] analyzed the solidification of small metal droplets in sizes ranging from 10 to 300 xm and concluded that in a wide selection of metals the minimum isothermal crystallization temperature was only a function of supercooling and not of droplet size. Later, it was found that the frequency of droplet nucleation was indeed a function of not only crystallization temperature but also of droplet size, since the probability of nucleation increases with the dimension of the droplet [76]. However, for low molecular weight substances the size dependence of the homogeneous nucleation temperature is very weak [77-80]. 

Polymerization of miniemulsions occurs by droplet nucleation only. 

In miniemulsion polymerization the nucleation of the particles mainly starts in the monomer droplets themselves. Therefore, the stability of droplets is a crucial factor in order to obtain droplet nucleation. The better the droplets are stabilized against Ostwald ripening, the higher is the droplet nucleation. 

It was found that the chain length of the resulting polymer is inversely proportional to the square root of the initiator concentration [66], underlining that the reaction in miniemulsion is rather direct and close to an ideal radical polymerization. It could be shown that the amount of initiator used for polymerizing the latex does not have an effect on the number of nucleated droplets which shows that droplet nucleation is by far the dominant mechanism over the whole range of initiator concentrations. 

The process of miniemulsion allows in principle the use of all kinds of monomers for the formation of particles, which are not miscible with the continuous phase. In case of prevailing droplet nucleation or start of the polymer reaction in the droplet phase, each miniemulsion droplet can indeed be treated as a small nanoreactor. This enables a whole variety of polymerization reactions that lead to nanoparticles (much broader than in emulsion polymerization) as well as to the synthesis of nanoparticle hybrids, which were not accessible before. 

Polymerization in miniemulsion is a very suitable technique to avoid this problem since each droplet acts as a nanoreactor. As a result, pure polyacrylonitrile (PAN) nanoparticles were obtained in the size range 100 nmwater phase. This is no restriction for a miniemulsion polymerization process, and the use of a hydro-phobic initiator 2,2 azobis(2-methylbutyronitrile) allows the preservation of the droplets as the reaction sites by droplet nucleation (see Fig. 12). Initiation of the... 

Deposition potential — is the required value to observe the appearance of a new phase in the course of a -> electrocrystallization process. See, - equilibrium forms of crystals and droplets, - nucleation and growth kinetics, -> nucleation overpotential. 

When a free radical growing in the aqueous phase enters a monomer droplet and polymerization proceeds therein (droplet nucleation). 

Usually particle formation by initiation in the monomer droplets droplet nucleation) is not considered important in conventional emulsion polymerization. This is because of the low absorption rate of radicals into the monomer droplets, relative to the other particle formation rates. However, when the monomer... 

The distinguishing feature of droplet nucleation as opposed to micellar or homogeneous nucleation is the nature of the particle at birth . Droplets, which are nucleated into particles, begin as nearly 100% monomer. Micellar or homogeneous nucleated particles start out with much lower monomer concentrations and eventually swell to around 60% (for MMA) in the presence of monomer droplets. This fundamental difference may lead to large differences between miniemulsion and macroemulsion polymerizations in radical desorption and/or intraparticle termination during Intervals I and II. 

If Ostwald ripening is retarded by using a costabilizer, predominant droplet nucleation can be achieved. This is the basis of miniemulsion polymerization. One of the first comprehesive studies of miniemulsion polymerization was done on styrene by Choi et al. [53]. 

Reimers and Schork [94, 95] report the use of PMMA to stabihze MM A miniemulsions enough to effect predominant droplet nucleation. Emulsions stabilized against diffusional degradation by incorporating a polymeric costabilizer were produced and polymerized. The presence of large numbers of small droplets shifted the nucleation mechanism from micellar or homogeneous nucleation, to droplet nucleation. Droplet diameters were in the miniemulsion range and reasonably narrowly distributed. On-hne conductance measurements were used to confirm predominant droplet nucleation. The observed reaction rates were dependent on the amount of polymeric costabilizer present. The latexes prepared with polymeric costabilizer had lower polydispersities (1.006) than either latexes prepared from macroemulsions (1.049) or from alkane-stabilized miniemulsions (1.037). 

Wang and Schork [73] used PS, PMMA and PVAc as the costabilizers in miniemulsion polymerizations of VAc with PVOH as the surfactant. They found that, while PMMA and PS were effective kinetic costabihzers (at 2-4%wt on total monomer) for this system, PVAc was not. While the polymeric costabilizers did not give true miniemulsions, Ostwald ripening was retarded long enough for predominant droplet nucleation to take place. 

Mouran et al. [105] polymerized miniemulsions of methyl methacrylate with sodium lauryl sulfate as the surfactant and dodecyl mercaptan (DDM) as the costabilizer. The emulsions were of a droplet size range common to miniemulsions and exhibited long-term stability (of greater than three months). Results indicate that DDM retards Ostwald ripening and allows the production of stable miniemulsions. When these emulsions were initiated, particle formation occurred predominantly via monomer droplet nucleation. The rate of polymerization, monomer droplet size, polymer particle size, molecular weight of the polymer, and the effect of initiator concentration on the number of particles all varied systematically in ways that indicated predominant droplet nucleation. 

In another paper, Blythe et al. [116] studied enhanced droplet nucleation when HD is used as the costabilizer. The enhancement in this case is much less. The authors conclude that, since HD is a very effective costabihzer (much more so than CA), the effect of the polymer in preserving the droplet number, if not the droplet size distribution, is not pronounced. Therefore, this effect appears to occur primarily in systems with CA (perhaps due to its polar nature, and so, its probable interfacial activity). Multiple investigators have reported effective (near 100%) droplet nucleation with HD and other costabilizers. 

If a miniemulsion could be run at 100% droplet nucleation (or near to this), then a very robust nucleation system would result. The number of particles could be determined by the number of initial monomer droplets, and this can be controlled by adjusting surfactant, costabilizer and shear levels. In this case, the number of particles would be independent of radical flux. In fact, the most compelling evidence for droplet nucleation is experimental evidence that the number of polymer particles is independent of the initiator level. (Once the radical flux is high enough to nucleate all, or nearly all of the droplets, then changes in radical flux caused by inconsistent initiator or unknown inhibitors will not affect the final particle number.) We will discuss the results of such robust nucleation later. 

Macro- and miniemulsion polymerization in a PFR/CSTR train was modeled by Samer and Schork [64]. Since particle nucleation and growth are coupled for macroemulsion polymerization in a CSTR, the number of particles formed in a CSTR only is a fraction of the number of particles generated in a batch reactor. For this reason, their results showed that a PFR upstream of a CSTR has a dramatic effect on the number of particles and the rate of polymerization in the CSTR. In fact, the CSTR was found to produce only 20% of the number of particles generated in a PFR/CSTR train with the same total residence time as the CSTR alone. By contrast, since miniemulsions are dominated by droplet nucleation, the use of a PFR prereactor had a negligible effect on the rate of polymerization in the CSTR. The number of particles generated in the CSTR was 100% of the number of particles generated in a PFR/CSTR train with the same total residence time as the CSTR alone. 

Observation (i) above can be understood in terms of droplet nucleation and the lack of competition between nucleation and growth. A mechanistic understanding of observation (ii) above was provided by Samer and Schork [64]. Nomura and Harada [136] quantified the differences in particle nucleation behavior for macroemulsion polymerization between a CSTR and a batch reactor. They started with the rate of particle formation in a CSTR and included an expression for the rate of particle nucleation based on Smith Ewart theory. In macroemulsion, a surfactant balance is used to constrain the micelle concentration, given the surfactant concentration and surface area of existing particles. Therefore, they found a relation between the number of polymer particles and the residence time (reactor volume divided by volumetric flowrate). They compared this relation to a similar equation for particle formation in a batch reactor, and concluded that a CSTR will produce no more than 57% of the number of particles produced in a batch reactor. This is due mainly to the fact that particle formation and growth occur simultaneously in a CSTR, as suggested earlier. 

An approach similar to that taken by Nomura and Harada was used by Samer to quantify the effects of droplet nucleation on emulsion polymerization kinetics in a CSTR. In their simplified analysis, it was assumed that radical capture by particles and droplets is proportional to the ratio of particle and droplet diameters. This assumption is reliable at low to moderate residence times, when polymer particles still closely resemble monomer droplets with respect to composition and surface characteristics. For predominant droplet nucleation, the maximum particle generation is limited by the concentration of monomer droplets in the feed. In Fig. 11 the steady state particle generation is given as a function of the residence time and temperature. Nucleation efficiency is defined as the number of particles divided by the number of droplets in the... 

Reimers [95] used polymeric costabihzer to carry out miniemulsion polymerization of MMA. Droplet nucleation was found to be the dominant nucleation mechanism in the polymerization. As a result, the nucleation was more robust, and the polymerizations were less sensitive to variations in the recipe or contaminant levels. This was evident in the rates of polymerization and in the particle numbers. The miniemulsion polymerizations were subjected to changes in initiator concentration, water-phase retarder, and oil-phase inhibitor, and were shown to be significantly more robust. 

Batch miniemulsion polymerization of MMA using PMMA as the costabilizer was carried out with SLS as the surfactant and KPS as the initiator. Solids content was kept at -30%. A low surfactant level was used with the miniemulsions to ensure droplet nucleation. The initiator concentration of the polymer-stabilized miniemulsion polymerizations was varied from 0.0005 to 0.02 Mjq, based on the total water content. An aqueous phase retarder, (sodium nitrite) or an oil-phase inhibitor (diphenylpicrylhydrazol [DPPH]), was added to both the miniemulsions and the macro emulsions prior to initiation. Particle numbers and rates of polymerization for both systems were determined. 

Results from the polymer-costabilized miniemulsion polymerizations are shown in Table 2. Droplet sizes were found to vary between 115.1 and 121.0 nm. These are in accord with measurements made by Fontenot [140] for MMA miniemulsions stabilized with hexadecane. The sizes of the particles in the final products were close to the sizes of the droplets, ranging from 102.6 to 108.1 nm, with polydispersities ranging from 1.011 to 1.027. The ratio of the number of particles to the number of droplets (N /N ) was found to be between 0.95 and 1.08. Therefore, the majority of the droplets were nucleated to form polymer particles. Droplet nucleation led to polymerization rates comparable to those for the corresponding macroemulsions. For equal concentrations of initiator, 0.01 Maq, the rates are 0.199 and 0.233 gmol/min L q for the mini- and the macroemulsion polymerizations, respectively. 

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