Thermodynamics of propagation

Propagation in TXN polymerization is reversible but cannot be described by the equation  

The equilibrium concentration of pentamers and higher oligomers is very low. Consequently, these species will not be discussed further. 

we are left with the following reversible reactions  

Moreover, in real systems (bulk or solution polymerization), polymerization proceeds in the crystalline state. Thus, thermodynamic parameters of phase transition are superimposed on thermodynamic parameters of chemical reactions (cf. Chap. 2 of this volume). 

Calculated from the results given above, the hypothetical equilibrium monomer concentrations in a homogeneous polymerization is 90)  

The basic approach to thermodynamics of propagation was outlined by Dainton and Ivin179) and the subject was comprehensively reviewed by Ivin189). This step of addition polymerization is described by the scheme 

For a sufficiently long polymeric chain, Kp is independent of its degree of polymerization since the above reaction converts a monomer into a monomeric segment placed in the midst of a long polymeric chain. Hence, this process may be symbolically described as 

In conventional addition polymerizations the growing chains are formed by some initiation processes and destroyed by some virtually irreversible terminations. The conversion of monomer into polymer eventually could be quantitative, provided that the initiation continues throughout the process. In the absence of termination or chain transfer the growing polymers remain living and then the polymerizing system ultimately has to attain a state in which the living polymers are in equilibrium with their monomer. The equilibrium concentration of the monomer, Me, provides valuable information leading to the determination of the appropriate Kp. To clarify this point, let us consider the equilibria 

Although Kj need not be equal to K2, and neither need K2 be equal to K3, it is obvious that for larger t s K,- = K, + x = = Kp. Without loss of generality we may assume that Kx K2 = K( = Kp, since this assumption does not alter the essence of the forthcoming conclusions. Furthermore, let us restrict our consideration to ideal systems when activities are equal to concentrations. Under those assumptions the following relations are valid  

The equilibrium concentration of the monomer depends, therefore, not only on Kp but also on the initial concentrations of the monomer and initiator. Alternatively, Me is given by the relation 

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This chapter is primarily concerned with the chemical microstructure of the products of radical homopolymerization. Variations on the general structure (CHr CXY) are described and the mechanisms for their formation and the associated Tate parameters are examined. With this background established, aspects of the kinetics and thermodynamics of propagation are also considered (Section 4.5). 

Another important factor affecting molecular weight distribution arises from reversibility of propagation. Its influence was discussed earlier in the section dealing with the thermodynamics of propagation, see p. 25 and Ref. 205. 

Propagation reactions in radical polymerization and copolymerization arc generally highly exothermic and can be assumed to be irreversible. Exceptions to this general rule arc those involving monomers with low ceiling temperatures (Section 4.5.1). The thermodynamics of copolymerization has been reviewed by Sawada.85... 

The first basic approach to the thermodynamics of addition polymerization was presented in 1948 by Dainton and Ivin (7) and developed in their review paper (2) published ten years later. In their exposition, they stressed the significance of the propagation step in addition polymerization, emphasizing its critical role in the whole process. This is the step whereby the macromolecule is gradually formed by the sequence of reactions... 

Ya.B. s studies of combustion and detonation are diverse and multidirectional. They include the chemical thermodynamics of combustion, propagation of exothermic chemical transformation fronts, deflagration and detonation theory, thermo-diffusion and chemo-kinetic processes in combustion and at high temperatures in general, and gasdynamics of flows in the propagation of non-uniform flame fronts and in detonation. 

In contrast to an explosive capable of detonating, this gas is in a state of complete thermodynamic equilibrium. Propagation of a wave occurs only as a result of external action, for example, the motion of a piston in a tube filled with gas. 

Worsfold and Bywater 212) have proposed that propagation through non-aggregated chains is kinetically (and not thermodynamically) controlled and yields only the carbanion having the cis conformation this can isomerize to the trans form unless the geometry is locked in by a further act of propagation ... 

Chain growth can only occur under suitable thermodynamic conditions. For the chains to have required properties, some chemical conditions must also be fulfilled. The possibility of the technical control of propagation depends on the rates of the respective reactions, i. e. on the kinetics of the process. 

The degenerative nature of propagation results in reformation of the same active species, but with monomer consumption and chain growth. Although the monomer s thermodynamic polymerizability is independent of the mechanism, the mechanism and structure of the active species determines the rate of monomer conversion. The structure of the active species involved in carbocationic polymerizations was discussed in Section II detailed information on the reactivities of model species was presented in Chapter 2, with the conclusion that covalent precursors do not react directly with alkenes, but must first ionize to sp2-hybridized carbenium ions. Only the resulting carbenium ions can add to double bonds. 

The effect of solvent on rates and thermodynamics of reactions can be understood to propagate through macromolecular processes to an influence of solvent on higher levels of organization. 

The computerized aqueous chemical model of Truesdell and Jones (, 3), WATEQ, has been greatly revised and expanded to include consideration of ion association and solubility equilibria for several trace metals, Ag, As, Cd, Cu, Mn, Ni, Pb and Zn, solubility equilibria for various metastable and(or) sparingly soluble equilibrium solids, calculation of propagated standard deviation, calculation of redox potential from various couples, polysulfides, and a mass balance section for sulfide solutes. Revisions include expansion and revision of the redox, sulfate, iron, boron, and fluoride solute sections, changes in the possible operations with Fe (II, III, and II + HI), and updating the model s thermodynamic data base using critically evaluated values (81, 50, 58) and new compilations (51, 26 R. M. Siebert and... 

The fourth major parameter which defines a system after the monomer, the initiator(s) and the solvent, is the temperature at which the polymerisation is conducted. The effect of temperature upon the position of the propagation-depropa tion equilibrium (ceiling temperature) is not directly relevant and too well-known to be discus here. We are obviously more interested in discussing the specific role of temperature in the reactions leading to the formation of chain carriers. The following considerations are pertinent to the kinetics of such interactions and to the thermodynamics of the reailting equflibria. 

Anionic polymerization carried out under suitable conditions results in the formation of living poly-mers—i.e. species which may grow further, if a suitable monomer is present in the system. This characteristic feature of living polymers, which arises from the elimination of all the termination steps, permits the following preparation of block polymers, polymers possessing two terminal functional groups, monodispersed polymers, etc. studies of the thermodynamics of the propagation step—i.e. determination of A / < cl aS of the... 

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