Copolymer equation reversible

Just as in the derivation of the copolymer equation for the terminal model, we start with a reversibility relationship P3 AAB = P3 BAA. Now we must use second-order Markovian statistics to write this in terms of conditional probabilities (Equation 6-64) ... 

Polymerization equilibria frequently observed in the polymerization of cyclic monomers may become important in copolymerization systems. The four propagation reactions assumed to be irreversible in the derivation of the Mayo-Lewis equation must be modified to include reversible processes. Lowry114,11S first derived a copolymer composition equation for the case in which some of the propagation reactions are reversible and it was applied to ring-opening copalymerization systems1 16, m. In the case of equilibrium copolymerization with complete reversibility, the following reactions must be considered. 

Polovinsky 86) gives equations describing the copolymer composition for matrix polymerization obtained with reversible binding of the active ends of the growing chain with the matrix taken into account ... 

More recently Durgaryan derived (5) a copolymer composition equation assuming reversibility of all propagation reactions, Equations 1-4. He expressed his solution as a pair of simultaneous equations in which the two unknowns (besides kinetic parameters and monomer feed) were copolymer composition and the ratio [(mi)2 ]/[mi)i S ]. At this writing no experimental tests of Durgaryan s equations have appeared. 

The copolymer composition equation with reversibility of all propaga-tion steps was derived as a complex function [298,299] ... 

Neutral lanthanide-series metallocenes exhibit the remarkable ability to polymerize polar monomers such as methyl methacrylate to highly stereoregular polymers of extremely narrow molecular weight distribution (Mw/Mn 1) (equation 14). It is possible to prepare block copolymers of ethylene and poly(methyl methacrylate) by first adding MMA to Cp 2SmMe to produce a PMMA segment followed by addition of ethylene the reverse order of addition fails to give block materials because the ethylene monomer cannot insert into the enolate. 

The reverse strategy consists of coupling a living polymer onto a second polymer that contains pendant electrophiles. This approach was used by Pitsikalis and coworkers, who synthesized PS-grq/f-PtBuMA (86) by treatment of poly(p-bromomethylstyrene) (84) with living anionic PtBuMA (85) (equation 66) °. The graft copolymer was purified by selective precipitation with hot methanol. Indeed, the graft copolymer was insoluble in this solvent, whereas the PtBuMA arms were soluble . ... 

Yamashita et al. [157] have derived a copolymer composition equation that includes the depropj ation reaction such as might be expected in the cationic copolymerization of BCMO and THF. They consider two models. For the first one it is assumed that monomer M2 adds reversibly to both active chain ends mf and m and that depropagation by detachment of an M1 unit is neglected. The elementary reactions are then... 

To simulate the effects of reaction kinetics, mass transfer, and flow pattern on homogeneously catalyzed gas-liquid reactions, a bubble column model is described [29, 30], Numerical solutions for the description of mass transfer accompanied by single or parallel reversible chemical reactions are known [31]. Engineering aspects of dispersion, mass transfer, and chemical reaction in multiphase contactors [32], and detailed analyses of the reaction kinetics of some new homogeneously catalyzed reactions have been recently presented, for instance, for polybutadiene functionalization by hydroformylation in the liquid phase [33], car-bonylation of 1,4-butanediol diacetate [34] and hydrogenation of cw-1,4-polybutadiene and acrylonitrile-butadiene copolymers, respectively [10], which can be used to develop design equations for different reactors. 

In solution Fe(II)TPP reacts rapidly and irreversibly with oxygen to form a (i-oxo dimer (Equation 13). Fe(II) supported on silica gel does not dimerize (691. On lightly cross-linked polystyrenes dimerization occurs (681. but with 20-30% cross-linked DF 0.01, macroporous copolymers of styrene and 4 aminostyiene, dioxygen binds reversibly (107.1081. Similarly, Fe(in)Pc(COOH)4 bound covalently to linear polystyrene (1091 and to linear poty(styrene-co-2-vinylpyridine) (1101 is active for catalase-like decomposition of hydros peroxide. 

In contrast to the simple copolymerization Equation (22-15), both monomer concentrations appear not only as ratios, but also alone in Equations (22-49) and (22-51). Thus, the copolymer composition at a given monomer ratio also depends on the total monomer concentration (Figure 22-7). This composition dependence shows that a reversible a-methyl styrene disequence depolymerization occurs in the free radical copolymerization of a-methyl styrene with methyl methacrylate at 60° C. In the corresponding copolymerization of acrylonitrile at 80° C, reversible depolymerization first begins with the a-methyl styrene trisequence. 

Because of the complicating effects of counterion and solvent associated with anionic polymerization, relatively few reactivity ratios have been determined for anionic systems. Typical reactivity ratios for the anionic copolymerization of styrene and a few other monomers are shown in Table 8.3. Most of the values were determined from the copolymer composition equation [Eq. (7.11) or (7.18)]. A dramatic effect of solvent is seen with styrene-butadiene copolymerization, where a change from the nonpolar hexane to the highly solvating THF reverses the order of reactivity. Again in the case of hydrocarbon solvent, the reaction temperature shows a minimal in uence on reactivity ratios, while in the case of polar solvents, such as THF, the reactivity ratios vary considerably, which has been rationalized by considering the solvation of carbon-lithium bond. Thus as the temperature is increased (from -78°C to 25°C), the extent of solvation by THF is expected to decrease, resulting in more covalent carbon-lithium bond. 

Three types of copolymerization can be expected (1) both monomers have high ceiling temperatures (2) one monomer has a low ceiling temperature (3) both monomers have low ceiling temperatures. The copolymer composition equation was modified for a system where reversible reactions are pronounced. 

Derives expressions for enthalpy and entropy of copolymerization, the chain sequence distribution of copolymers, and the Clapeyron equation for reversible polymerization... 

This is a three-part book with the first part devoted to polymer blends, the second to copolymers and glass transition tanperatme and to reversible polymerization. Separate chapters are devoted to blends Chapter 1, Introduction to Polymer Blends Chapter 2, Equations of State Theories for polymers Chapter 3, Binary Interaction Model Chapter 4, Keesome Forces and Group Solubility Parameter Approach Chapter 5, Phase Behavior Chapter 6, Partially Miscible Blends. The second group of chapters discusses copolymers Chapter 7, Polymer Nanocomposites Chapter 8, Polymer Alloys Chapter 9, Binary Diffusion in Polymer Blends Chapter 10, Copolymer Composition Chapter 11, Sequence Distribution of Copolymers Chapter 12, Reversible Polymerization. 

Some of the equilibrium copolymerizations of this type were kinetically analyzed by Lowry, Hazell and Ivin, Yamashita et al., and Wittmer, who derived equations for the composition of a copolymer in systems with reversibility of some reactions in triad (or some in dyad) model copolymerizations. Although the analyzed systems are concerned with... 

Another general treatment of the copoljnnetization equilibrium was provided by Szymanski, ° who used, while deriving his relationships, similarly as O Driscoll and co-workers, the reverse conditional probabilities (of a copolymer unit to be preceded by the same or a different unit). This treatment looks simpler than the one proposed earlier by Szwarc and Perrin, and similarly their equations can be applied to the systems of any number of comonomers and any average degree of polymerization. The proposed solution also applies to the systems of ideal copolymerization Besides, the... 

The concept of shelf life (shelf time) of a chain polymerization has been discussed by Szwarc. Shelf life in this context is defined as the time available to the operator to complete a given synthetic task, for example, block copolymer synthesis by sequential monomer addition, or end-capping (functionalization) of the polymer chains by reaction with a quenching agent. The equations dealing with chain breaking in the previous section may be used to demonstrate the concept of shelf life and how it is favorably affected by the operation of a reversible-deactivation equilibrium. 

However, with the exception of copolymerization of the three- and/or four-membered comonomers, the copolymerization of higher rings is expected to be reversible, such that four additional homo- or cross-depropagation reactions must be added (kinetic Equation 1.44). In such a situation, the traditional methods of kinetic analysis must be put on hold , as a numerical solving of the corresponding differential equations is necessary. Moreover, depending on the selectivity of the active centers, any reversible transfer reactions can interfere to various degrees with the copolymerization process. Thus, the kinetically controlled microstructure of the copolymer may differ substantially from that at equilibrium (cf Section 1.2.4). 

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