Fitch theory

Schuler, Robert M. and John G. Fitch. Theory and context of the didactic poem some classical, mediaeval and later continuities. Florilegium 5 (1983) 1-43. 

Considering that polymerization takes place in particles, as shown by results concerning copolymer composition, these results seem surprising. The possibility of continuous nucleation is quite normal and explained through the Fitch theory (12) but questionable points are ... 

The basic principle of the Fitch theory is that the formation of primary particles will take place up to a point where the rate of formation of radicals in the aqueous phase is equal to the rate of disappearance of radicals by capture of radicals by particles already formed. According to the Fitch theory of homogeneous particle nucleation, the addition of emulsifier does not lead to any... 

The first is diffusion capture. This theory was originally proposed by Fitch and Tsai (13) for the aqueous polymerization of methyl methacrylate. According to this theory, any oligomer which diffuses to an existing particle before it has attained the critical size for nucleation is irreversibly captured. The rate of nucleation is equal to the rate of initiation minus the rate of capture. The rate of capture is proportional to both the surface area and the number of particles. 

A paper by Fitch (53) gives an analysis of existing theories and identifies the domains in which the various models which have been proposed give reasonable approximations to observed behaviour. 

In 1965 Dunn and Taylor confirmed the theory for vinyl acetate polymerization (15), and proposed, in the light of the presumed importance of rapid coagulation during the earliest stages of reaction, that the "DLVO" theory for colloid stability (16) be applied. Fitch proposed a kinetic basis for a quantitative theory and observed that for observation of particle formation kinetics, "fast" reaction techniques must be used because "particle formation occurs in a matter of seconds or even less (17)". 

The first attempt to formulate a homogeneous nucleation theory to predict the absolute number concentration of particles, N, was made by Fitch and Tsai in 1970 (21). This was supported by a large number of experiments on the polymerization of MMA. 

It was further developed the following year (22), and was based primarily on the scheme of Priest (12) with an idea from Gardon (9d). The latter suggested that the rate of capture of oligomeric radicals in solution by pre-existing particles, R, should be proportional to the collision cross-section, or tfie square of the radius of the particles, r. This has been called the "collision theory" of radical capture. In 1975 Fitch and Shih measured capture rates in MMA seeded polymerizations and came to the conclusion that R was proportional to the first power of the radius, as would e predicted by Fick s theory of diffusion (23). In his book, K. J. Barrett also pointed out that diffusion must govern the motions of these species in condensed media (10). 

According to the aggregative and coagulative nucleation mechanisms which have been derived originally from the homogeneous nucleation theory of Fitch and Tsai [128], the most important point in the reaction is the instant at which colloidally stabilized particles form. After this point, coagulation between similar-sized particles no longer occurs, and the number of particles present in the reaction is constant. As shown in Fig. 6, the dispersion copolymerization with macromonomers is considered to proceed as follows. (1) Before polymerization, the monomer, macromonomer, and initiator dissolve completely into the... 

The description of phase 1 of the SE theory was refined by Gardon [133] and Harada et al. [134] the effect of particles in which polymerization has been terminated by radical entrance is included. Paris et al. [135] and Sautin et al. [136] calculate the balance of micelles and of the growing and dead particles. Pismen and Kuchanov [137] and Sundberg and Eliassen [138] included the effect of particle size distribution in their calculations. According to Fitch and Tsai [134] and Roe [140], the monomer swollen particles are produced by the polymerization of the monomer which is dissolved in water. 

Fitch-Roe approach. (At lower than critical emulsifier concentrations, micelles are not generated. With increasing amount of emulsifier, the physical properties of aqueous medium discontinuously change in the vicinity of its critical concentration. The critical emulsifier concentration is an important material constant.) Roe [140] proved that the two theories can be described by very similar quantitative relations. This latter theory stress the importance of dissolution equilibria for the equilibrium monomer concentration in the aqueous phase. 

The method is applicable for unflocculated pulps or those in which the ionic characteristics of the solution produce a flocculent structure. If polymeric flocculants are used, the floccule size will be highly dependent on the feed concentration, and an approach based on the Kynch theory is preferred. In this method, the test is carried out at the expected feed solids concentration and is continued until underflow concentration is achieved in the cylinder. To determine the unit area, Talmage and Fitch (op. cit.) proposed an equation derived from a relationship equivalent to that shown in Eq. (18-45) ... 

Fitch and Tsai applied their theory to describe homogeneous particle... 

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. 

More detailed and complete theories on particle nucleation have been published by Fitch et al. (General References and and by Hansen and Ugelstad (12). These publications consider several mechanisms for particle nucleation, and they present mathematical models that account for these various mechanisms. The present state of the art, however, will not permit one to compute N from a knowledge of the recipe ingredients and reaction conditions, except for special cases. Thus, most product and process development work should probably include the measurement of N as a function of the important variables. 

Fitch RM, Tsai CH. Particle formation in polymer colloids, III Prediction of the number of particles by a homogeneous nucleation theory. In Fitch RM, editor. Polymer Colloids. New York Plenum Press 1971. p 73. 

Fitch and Shih [8S] elaborated Garden s calculation of the rate at which radicals generated in the aqueous phase would collide with latex particles. They found that the electrostatic barrier between a latex particle stabilized only by ionic end-groups and a similarly charged radical was negligible. But experimental results indicated that the rate of radical entry was not proportional to the cross-section of the particles as required by the collision theory instead it was proportional to particle radius as predicted for diffusional entry. 

Crothers, DM, Kallenback NR, Zimm BH (1965) The melting transition of low-molecular-weight DNA theory and experiment. J Mol Biol 11 802-820 Felsenstein J (1987) Estimation of hominoid phylogeny from a DNA hybridization data set. J Mol Evol 26 123-131 Felsenstein J (1988) Phylogenies from molecular sequences inference and reliability. Ann Rev Genet 22 521-565 Fitch WM, Margoliash E (1967) Construction of phylogenetic trees. Science 155 279-284... 

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 ... 

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". 

Fitch R.M, Tsai C.H (1971) Particle Formation in Pol3rmer Colloids. HI. Prediction of the Number of Particles by Homogeneous Nucleation Theory. In Fitch R.M editor. Pol)nner Colloids. Newyork Plenum Press, pp. 73-102. 

Fitch, B. 1975. Current theory and thickening design. Parts 1-3. Filtration and Separation 12 355 59,480-i88,636-638. 

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