Hansen-Ugelstad-Fitch-Tsai

Although iterative numerical solution of Equations (5.10)-(5.13) is trivial, insight can be obtained from the analytic solution obtained when it is assumed that kp,aq is independent of the degree of polymerization (note, however, that this simplification is not likely to be quantitatively accurate). The resulting formula was also obtained, in a somewhat different context, in the simplest version of the Hansen-Ugelstad-Fitch-Tsai (HUFT) theoiy for particle formation [26,27], and may be expressed either as the entry rate coefficient for radicals derived directly from initiator, or alternatively as the initiator efficiency, /mi, ... 

This type of single-chain precipitation was suggested by Fitch and Tsai [4, 57], and improved later by Ugelstad and Hansen [58]. According to the Hansen-Ugelstad-Fitch-Tsai (HUFT) theory, the rate of particle formation can be determined by ... 

Hansen-Ugelstad-Fitch-Tsai (HUFT) Model... 

The particle generation rate was calculated by a step mechanism, namely formation of primary precursor particles by homogeneous nucleation (JLQ.) followed by coagulation to latex particles (8-9). This homogeneous nucleation mechanism is often referred to as the HUFT mechanism for its originators Hansen, Ugelstad, Fitch, and Tsai. 

A related matter concerns the physical mechanism by which radicals (primary or oligomeric) are acquired by the reaction loci. One possibility, first proposed by Garden (1968) and subsequently developed by Fitch and Tsai (1971), is that capture occurs by a collision mechanism. In this case, the rate of capture is proportional to, inter alia, the surface area of the particle. Thus, if the size of the reaction locus in a compartmentalized free-radical polymerization varies, then a should be proportional to r, where r is the radius of the locus. A second possibility (Fitch, I973) is that capture occurs by a diffusion mechanism. In this case, the rate of capture is approximatdy proportional to r rather than to r. A fairly extensive literature now exists concerning this matter (see, e.g., Ugelstad and Hansen, 1976, 1978. 1979a, b). The consensus of present opinion seems to favor the diffusion theory rather than the collision theory. The nature of the capture mechanism is not. however, relevant to the theory discussed in this chapter. It is merely necessary to note that both mechanisms predict that the rate of capture will depend on the size of the reaction locus constancy of a therefore implies that the size of the locus does not change much as a consequence of polymerization. 

Other than micellar nucleation, many mechanisms have been proposed to explain the particle nucleation stage. The best-known alternative theory for particle nucleation is that of "homogeneous nucleation" which includes the formation of particle nuclei in the continuous aqueous phase. This theory is proposed by Priest, Roe and Fitch and Tsai, and extended by Hansen and Ugelstad (HUFT) describes the emulsion polymerization of water-solubble monomers such as vinyl acetate and acrylonitrile, their water solubility though low (< 3%) is much in excess of the amount of monomer which may be solubilized by the emulsifier [43-48]. It is also the only mechanism which can apply to monomers of low water-solubility, such as styrene, in emulsifier-free reaction system, and also in reaction system which contain a micellizing emulsifier but at such a concentration that is below the CMC. When the monomers are somewhat soluble in the continuous phase, emulsifier micelles have little influence on particle formation. Emulsifier may be required, however, to ensure colloidal stability of the product as it is formed and subsequently "on the shell". 

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