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4-3f Molecular Weight and Particle Size Distributions Theoretical considerations indicate that compartmentalization of radicals in polymer particles does not change the polydispersity index PDI X w =X n in emulsion polymerization from its value of 2 in homogeneous polymerization when termination takes place by transfer to monomer, chain-transfer agent, or other substance [Butte et al., 2002a,b; Giannetti et al., 1988; Gilbert, 1995; Lichti et al., 1980, 1982; Mendizabal et al., 2000]. However, emulsion polymerization results in molecular weight broadening when termination involves bimolecular reaction between radicals. While short propagating chains are likely to couple or disproportionate with longer chains in homogeneous polymerization (PDI 1:5 and 2 for coupling and disproportionation, respectively) (Sec. 3-11), any two chains that undergo bimolecular termination in emulsion polymerization are not random. The broadening of PDI in emulsion polymerization is greater for disproportionation than for coupling. For case 2 behavior, coupling of the propagating chain in a polymer particle with the low-molecular-weight entering radical does not greatly affect PDI. Such coupling is equivalent to termination by chain transfer and PDI has a value of 2 compared to 1.5 for homogeneous polymerization. When termination is by disproportionation, PDI has a value of 4 at " 0:5 compared to 2 for n homogeneous polymerization [Butte et al., 2002a,b]. Low-molecular-weight radicals entering the polymer particles disproportionate with propagating radicals and increase the number of low-molecular-weight molecules; X n is decreased while X w is essentially unchanged and X w =X n increases. When " > 0:5 (case 3), the tendency toward molecular weight broadn ening decreases as the size of the radicals undergoing coupling or disproportionation

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become more nearly the same size PDI tends toward the values in homogeneous polymerization (15 and 2 for coupling and disproportionation, respectively) as " increases n from 05 to 2 The preceding discussion relates primarily to polymerization in stage II of an emulsion polymerization Since this constitutes the major portion of an emulsion polymerization and the reaction conditions (N, Ri , kp , [M]) are relatively constant during stage II, the molecular weight distribution is considerable narrower than in homogeneous polymerization [Cooper, 1974; Lin and Chiu, 1979] However, there is molecular weight broadening with conversion as reaction proceeds through stage III where various reaction parameters are no longer constant Also, the molecular weights produced during stage I are not the same as in stage II The PDI for a batch polymerization taken to complete conversion can be as high as 5 7 [Butte et al.

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, 2002a,b], which is still lower than for a typical homogeneous polymerization In addition to the molecular-weight distribution, there is a particle size distribution in emulsion polymerization [Chen and Wu, 1988; Gardon, 1977; Lichti et al, 1982] The particle size distribution (PSD) is expressed, analogously to the molecular weight distribution, as the ratio of the weight-average particle size to number-average particle size (Different particle sizes are calculated depending on whether one uses the particle radius, diameter, or volume as the measure of particle size) The particle size distribution is a consequence of the distribution of times at which different polymer particles are nucleated The polydispersity is maximum during interval I and narrows considerably during the subsequent period.

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There has been an effort to produce narrow-particle-size distributions (PSD) by controlling the nucleation process, choice and amount of surfactant, temperature and other reaction variables, and the use of seed emulsion polymerization Narrow particle size distributions are useful in applications such as calibration of electron microscope, ultracentrifuge, aerosol counting, and light-scattering instruments and the measurement of pore sizes of lters and membranes Narrow particle distributions, with PSD values of 11 and lower, have been obtained by choosing reaction conditons with short nucleation times (short interval I relative to intervals II and III), increased latex stability (to prevent coagulation), and decreased interval III times 4-3g Surfactant-Free Emulsion Polymerization.

This de nition of correlation functions ensures that they vanish if the points r1 ; r2 ; . . . ; rp are not inside a common sphere of radius (see proof in [1 4]). We also need the FT of the correlation function as mentioned below: h k1 ; k2 ; . . . ; kp 1 2p 3p h r1 ; r2 ; . . . ; rp expf i k1 r1 . . . kp rp gd3 r1 d3 rp 3:18

The presence of surfactant is a disadvantage for certain applications of emulsion polymers such as those involving instrument calibration and pore size determination. The presence of adsorbed surfactant gives rise to somewhat variable properties since the amount of adsorbed surfactant can vary with the polymerization and application conditions. Removal of the surfactant, either directly or by desorption, can lead to coagulation or occulation of the destabilized latex. Surfactant-free emulsion polymerization, involving no added surfactant, is a useful approach to solving this problem [Chainey et al., 1987; Li and Salovey, 2000; Ni et al., 2001]. The process uses an initiator yielding initiator radicals that impart surface-active properties to the polymer particles. Persulfate is a useful initiator for this purpose. Latexes prepared by the surfactant-free technique are stabilized by chemically bound sulfate groups of the SO -initiating species derived from persulfate ion. Since the surface-active groups are 4 chemically bound, the latexes can be puri ed (freed of unreacted monomer, initiator, etc.) without loss of stability, and their stability is retained over a wider range of use conditions than the corresponding latices produced using surfactants. A characteristic of surfactant-free emulsion polymerization is that the particle number is generally lower by up to about 2 orders of magnitude compared to the typical emulsion polymerization, typically 1012 versus 1014 particles per milliliter. This is a consequence of the lower total particle surface area

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