Propagation thermodynamics

Takesue [takes87] defines the energy of an ERCA as a conserved quantity that is both additive and propagative. As we have seen above, the additivity requirement merely stipulates that the energy must be written as a sum (over all sites) of identical functions of local variables. The requirement that the energy must also be propagative is introduced to prevent the presence of local conservation laws. If rules with local conservation laws spawn information barriers, a statistical mechanical description of the system clearly cannot be realized in this case. ERCA that are candidate thermodynamic models therefore require the existence of additive conserved quantities with no local conservations laws. A total of seven such ERCA rules qualify. ... 

Lack of termination in a polymerization process has another important consequence. Propagation is represented by the reaction Pn+M -> Pn+1 and the principle of microscopic reversibility demands that the reverse reaction should also proceed, i.e., Pn+1 -> Pn+M. Since there is no termination, the system must eventually attain an equilibrium state in which the equilibrium concentration of the monomer is given by the equation Pn- -M Pn+1 Hence the equilibrium constant, and all other thermodynamic functions characterizing the system monomer-polymer, are determined by simple measurements of the equilibrium concentration of monomer at various temperatures. 

Projections, linearly independent, 293 Propagation, of polymerization, 158 Propane, hydrate, 10, 33, 43, 46, 47 hydrate thermodynamic data and lattice constants, 8 + iodoform system, 99 Langmuir constant, 47 water-hydrogen sulfide ternary system, 53... 

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). 

Rate constants for ring-opening of dioxolan-2-yl radicals have been measured by Barclay et a/.241 as 103-104 s 1 at 75 °C (Scheme 4.29). There is also evidence that ring-opening is reversible.24 244 Thus, isomerization of the initially formed product to one more thermodynamically favored is possible if propagation is slow. 

Polymerization thermodynamics has been reviewed by Allen and Patrick,323 lvin,JM [vin and Busfield,325 Sawada326 and Busfield/27 In most radical polymerizations, the propagation steps are facile (kp typically > 102 M 1 s l -Section 4.5.2) and highly exothermic. Heats of polymerization (A//,) for addition polymerizations may be measured by analyzing the equilibrium between monomer and polymer or from calorimetric data using standard thermochemical techniques. Data for polymerization of some common monomers are collected in Table 4.10. Entropy of polymerization ( SP) data are more scarce. The scatter in experimental numbers for AHp obtained by different methods appears quite large and direct comparisons are often complicated by effects of the physical state of the monomei-and polymers (i.e whether for solid, liquid or solution, degree of crystallinity of the polymer). 

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... 

Thus with aMeSt, the kinetic chain is relatively short, monomer is consumed mainly by initiation and propagation, and chain transfer by the HSiCCHj CH H C Q initiator is unfavorable (see Sect. III.B.3.b.i.). In contrast, with isobutylene the kinetic chain may live longer because it is sustained by thermodynamically favorable chain transfer by the initiator. Scheme 5 illustrates the mechanism of isobutylene polymerization by the HSi(CH3)2CH2CH29>CH2Cl/Me3Al system. The kinetic chain is sustained by chain transfer loops shown on the left margin of the Scheme. 

As shown by the data in Fig. 31, the chain transfer constant of this initiator, Q = 1.0. In this context it is of interest to remember that the effect of initiator concentration on the molecular weight of HSi-PaMeSt was negligible, probably because of unfavorable thermodynamics (Sect. III.B.3.b.iv.). In contrast, with isobutylene chain transfer from the propagating carbenium ion to initiator is thermodynamically favorable (see Sect. IH.B.4.b.i.). Thus it is not surprising to find a large Q. The chain transfer mechanism has been illustrated in Scheme 5. 

For this kind of cooperative processes, it is characteristic that the formation of the nucleus is thermodynamically more difficult than for further propagation steps (positive cooperativity). This implies that the elementary transition step of an individual chain segment (tripeptide unit) is influenced by the state of adjacent segments through intramolecular interactions. 

As already mentioned, the enthalpy change A//° involved in an elementary propagation step corresponds to the equilibrium constant S. The parameter a, however, is purely entropically influenced mainly due to the steric restrictions during the formation of a helical nucleus. The determination of a, since it is related to the same power (3n - 2) of s, requires the consideration of the dependence of the thermodynamic parameters on the chain length (Eq. (9 a)). 

The following example shows that the influence of statistical thermodynamical calculations on qualitative assertions is often insignificant. The reactions (3) <5) describe three of the first propagation steps of the cationic copolymerization of ethene and isobutene. 

At the initial stage of bulk copolymerization the reaction system represents the diluted solution of macromolecules in monomers. Every radical here is an individual microreactor with boundaries permeable to monomer molecules, whose concentrations in this microreactor are governed by the thermodynamic equilibrium whereas the polymer chain propagation is kinetically controlled. The evolution of the composition of a macroradical X under the increase of its length Z is described by the set of equations ... 

The Thermodynamics Research Center staff have assigned an uncertainty value to each observed and recommended density value listed in the tables. The tme value of the property has a 95% probability of being in the range covered by + or - the uncertainty about the reported value. Assignment of uncertainty is a subjective evaluation based upon what is known about the measurement when the value is entered into the database, and includes the effects of all sources of experimental error. The errors have been propagated to the listed density at the reported temperature. Uncertainties reported by the investigators are considered but not necessarily adopted. Often, investigators report repeatability, but they usually do not provide uncertainty. 

Thus propagation must be much faster than isomerization, and the product will be determined by thermodynamics, rather than by reaction kinetics. The net results of the two processes may be quite similar, however, in that polymers of unexpected structures may be obtained, and copolymers may be prepared by polymerization of a single monomer. 

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