Free-radical polymerizations theory

Chain-Length Dependent Bimolecular Termination in Free-Radical Polymerization Theory, Validation and Experimental Application of Novel Model-Independent Methods... 

Bagdasan yan, K. S., Theory of Free Radical Polymerization, Israel Program for Scientific Translations, Jerusalem, 1968. 

Despite numerous efforts, there is no generally accepted theory explaining the causes of stereoregulation in acryflc and methacryflc anionic polymerizations. Complex formation with the cation of the initiator (146) and enoflzation of the active chain end are among the more popular hypotheses (147). Unlike free-radical polymerizations, copolymerizations between acrylates and methacrylates are not observed in anionic polymerizations however, good copolymerizations within each class are reported (148). 

In the literature there is only one serious attempt to develop a detailed mechanistic model of free radical polymerization at high conversions (l. > ) This model after Cardenas and 0 Driscoll is discussed in some detail pointing out its important limitations. The present authors then describe the development of a semi-empirical model based on the free volume theory and show that this model adequately accounts for chain entanglements and glassy-state transition in bulk and solution polymerization of methyl methacrylate over wide ranges of temperature and solvent concentration. 

The theory of radiation-induced grafting has received extensive treatment [21,131,132]. The typical steps involved in free-radical polymerization are also applicable to graft polymerization including initiation, propagation, and chain transfer [133]. However, the complicating role of diffusion prevents any simple correlation of individual rate constants to the overall reaction rates. Changes in temperamre, for example, increase the rate of monomer diffusion and monomer... 

Generalization of Flory s Theory for Vinyl/Divinyl Copolvmerization Using the Crosslinkinq Density Distribution. Flory s theory of network formation (1,11) consists of the consideration of the most probable combination of the chains, namely, it assumes an equilibrium system. For kinetically controlled systems such as free radical polymerization, modifications to Flory s theory are necessary in order for it to apply to a real system. Using the crosslinking density distribution as a function of the birth conversion of the primary molecule, it is possible to generalize Flory s theory for free radical polymerization. 

Atactic PVAc prepared in a free-radical polymerization is crosslinked by means of benzoyl peroxide. The resulting elastomertic networks are studied in elongation, both unswollen and swollen with triethylbenzene, over the range 273 - 363 K. The most important experimental results obtained are values of the network birefringence, which is negative. Calculations carried out to interpret the birefringence are based on Monte-Carlo simulations of the atactic structure, and on the RIS theory. 

Theory of Compartmentalized Free-Radical Polymerization Reactions... 

They also tested (10) Case II for the free radical polymerization of styrene (Mi) and methyl methacrylate at 132°C. by the dilution technique. These data are also shown in Table I, where the good agreement between theory and experiment is apparent. The applicability of the theory to different mechanisms of polymerization is a nice verification of the statement that the composition is governed by end-state thermodynamics rather than by mechanism. 

Due to the nature of free radical polymerization, i.e., the reacting system is essentially a binary mixture composed of monomer and high polymer, another approach was used to calculate p d, and therefore tyu This alternate method is based on the free volume theory, which predicts a relationship between Tg and the volume fractions of polymer and monomer in a binary system ... 

Fig. 22. Extent of reaction at vitrification vs. reaction temperature for linear free-radical polymerization (styrene) for f = 0.5 and [II, = 0.10 mole/1. The solid line is for the results from the T,-mole-cular weight model [Eq. (21)] the dashed line is for the results from the free volume theory [Eq. (26)]. [Aronhime, M, T., Gillham, J. K. J. Coat. Tech. 56 (718), 35 (1984)]...

By using the free-volume theory, one can successfully monitor the whole course of free-radical polymerization. It is commonly accepted that the presence of autoacceleration and limiting conversion in the polymerization reaction are due to the diffusion-controlled kt and kp, respectively. The initiation efficiency, f, will behave in a way similar to kp. 

The primary objective of the theory of compartmentalized free-radical polymerization reactions is to predict from the physicochemical parameters of e reaction system the nature of the locus population distribution. By this latter term is meant collectively the proportions of the total population of reaction loci which at any instant contain 0, l,2,...,i,... propagating radicals. The theory is concerned with the prediction of these actual populations and also with such characteristics of the locus population distribution as the average number of propagating radicals per reaction locus and the variance of the distribution of locus populations. 

The theory also has relevance to the so-called seeded " emulsion polymerization reactioas- In these reactions, polymerization is initial in the presence of a seed latex under conditions such that new particles are unlikely to form. The loci for the compartmentalized free-radical polymerization that occurs are therefore provided principally by the particles of the initial seed latex. Such reactions are of interest for the preparation of latices whose particles have, for instance, a core-shell" structure. They are also of great interest for investigating the fondamentals of compartmentalized free-radical polymerization processes. In this latter connection it is important to note that, in principle, measurements of conversion as a function of time during nonsteady-state polymerizations in seeded systems offer the possibility of access to certain fundamental properties of reaction systems not otherwise available. As in the case of free-radical polymerization reactions that occur in homogeneous media, investigation of the reaction during the nonsteady state can provide information of a fundamental nature not available through measurements made on the same reaction system in the steady state. 

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. 

Flory Statistics of the Molecular Weight Distribution. The solution to the complete set (j - I to j = 100,000) of coupled-nonlinear ordinary differential equations needed to calculate the distribution is an enormous undertaking even with the fastest computers. However, we can use probability theory to estimate the distribution. This theory was developed by Nobel laureate Paul Floty. We have shown that for step ipolymeiization and for free radical polymerization in which termination is by disproportionation the mole fraction of polymer -with chain length j is... 

Determination of Quotient kp/kf. Theory of Pre- and Aftereffect (3). kp is the absolute propagation constant of the chain propagation reaction in free radical polymerization corresponding to... 

Copolymers of 2,3-epoxypropyl methacrylate and butadiene prepared by solution free radical polymerization were tested as potential candidates for electrom negative resists.The sensitivity of the copolymers to ionizing radiation was determined with a linear accelerator.The experimental data were treated according to the Saito-Inokuti statistical theory.The calculated crosslinking yield values, G(x),were dependent an... 

Most early thermoplastics, e.g., PVC or PS, were obtained in the free radical polymerization, initiated either by heat or by sunlight. The first systematic studies of the free radical chemistry commenced 80 years later [Ostromislensky, 1911, 1915, 1916]. Fikentscher empirically determined which one of the 30-or-so monomers liked or disliked to copolymerize with each other. The advantage of latex-blending was also established. The theory of the free radical copolymerization was finally developed in the 1940 s [Alfrey et al, 1952]. 

C. A. Spade and V. A. Nopperp, Linear stability analysis of non-adiabatic free-radical polymerization waves. Combust. Theory Modelling, 5 (2001), pp. 21-39. 

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