Thermodynamics of reversible polymerization

ATP HYDROLYSIS LINKED TO ACTIN POLYMERIZATION PERTURBS THE THERMODYNAMICS OF REVERSIBLE POLYMERIZATION... 

Some readers will be interested in the fact that Huang and Wang [75] in 1972 presented a newer theoretical treatment of the reaction kinetics of reversible polymerization in which this classic derivation of Dainton and Ivin is a special case. The thermodynamics of equilibrium polymerizations have recently been reviewed by Sawada [76]. 

Note 1 Thermodynamic processes that produce reversible changes in the physical structure of a polymeric material are termed physical aging. 

Interestingly, there have been repeated attempts to view such gradual structural changes due to chemical equilibria as phase transitions as well [262]. Instructive examples for such an analysis are living polymers — for example, in demixing solutions of polymers [263] and in sulfur [264], where the reversible polymerization process has been treated as a second-order phase transition. The experimental evidence for such an interpretation is, however, at best weak [265], and classical association models [266] describe the thermodynamic properties equally well. 

In addition to the physical state of reactants, it should be remembered that the ideal behavior is encountered only in the gaseous state. As the polymerization processes involve liquid (solution or bulk) and/or solid (condensed or crystalline) states, the interactions between monomer and monomer, monomer and solvent, or monomer and polymer may introduce sometimes significant deviations from the equations derived for ideal systems. The quantitative treatment of thermodynamics of nonideal reversible polymerizations is given in Ref. 54. 

Thermodynamics of free-radical polymerization. The free energy of polymerization, AGp, is given by the first and second laws of thermodynamics for a reversible process as... 

In homogenous media, most of the transacylation reactions are reversible and as soon as the first polymer amide groups are formed, the same kind of reactions can occur both at the monomer and at the polymer amide groups. Unless the active species are steadily formed or consumed by some side reaction, a set of thermodynamically controlled equilibria is established between monomer, cyclic as well as linear oligomers and polydisperse linear polymer. The existence of these equilibria is a characteristic feature of lactam polymerizations and has to be taken into account in any kinetic treatment of the polymerization and analysis of polymerization products. The equilibrium fraction of each component depends on the size of the lactam ring, substitution and dilution, as well as on temperature and catalyst concentration. 

Lactam polymerization comprises the conversion of a cyclic lactam unit into a linear one without the formation of any new chemical bonds. The term polymerizability involves both the thermodynamic feasibility and a suitable reaction path to convert the cyclic monomer into a linear polymer. Sometimes, a slight confusion arises when the term polymerizability is used as a synonym for both the rate of polymerization and the thermodynamic instability of the lactam. Due to the reversible nature of the polymerization of most lactams, eqns. (1)—(3), their polymeriz-abilities cannot be expressed in terms of the rate of polymerization only, but the rate of both polymerization and monomer reformation must be compared. 

The values for the thermodynamic parameters in the formation of polymers can be used for the characterization of depolymerization reactions. The formation of monomers in a polymer decomposition reaction (depolymerization) is relatively common (see Table 2.1.1). Depolymerization can be considered a reverse polymerization, the two reactions having equal absolute values for the heats of reaction but with opposite signs. Therefore, the heats of polymerization can be used for the thermodynamic characterization of pyrolytic reactions with formation of monomers (kinetic factors are also very important in pyrolytic reactions as further shown in Section 2.3). 

In summary, chain propagation involves alternating reversible carbon monoxide insertion in Pd-alkyl species and irreversible insertion of the olefin in the resulting Pd-acyl intermediates. The overall exothermicity of the polymerization is caused predominantly by the olefin insertion step. Internal coordination of the chain-end s carbonyl group of the intermediate Pd-alkyl species, together with CO/olefin competition, prevents double olefin insertion, and thermodynamics prevent double CO insertions. The architecture of the copolymer thus assists in its own formation, achieving a perfect chemoselectivity to alternating polyketone. 

The requirement of the presence of the polymerization catalyst in the depolymerization process stems from the principle of microscopic reversibility. If, for example, all free radicals are removed from the system by simply endcapping the polymer, the thermodynamic equilibrium dictates that depolymerization state cannot be reached and the system will be stable. This was the approach employed by Ito and Willson in stabilizing polyphthaldehyde resists. [See for example, C.G. Willson, H. Ito, J.M.J. Frechet, T.G. Tessier, F.M. Houlihan, Approaches toward the design of radiation sensitive polymeric imaging systems with improved sensitivity and resolution, J. Electro chem. Soc. 133, 181 (1986)]. 

In case the reverse of the polymerization, the depolymerization, is significant, a more complicated kinetics describes the chain reactions. Figure 3.30 shows the scheme. If rates of the forward and reverse reactions become the same, equilibrium is reached. The equilibrium temperature is called the ceiling temperature, T (at a given concentration or vapor pressure [A]). Standard thermodynamics applies to this equilibrium (see Chap. 2). On depolymerization, the entropy of the system, S, increases because the number of molecules increases. With a positive AS, a T must exist at sufficiently high temperature, since one can write AG = AH - TAS, where AG is the Gibbs function or free enthalpy and AH, the enthalpy of the reaction. 

The second classification has been recently used in a later review article by Meijer and co-workers. This classification is mainly concerned with the mechanism of supramoiecuiar polymerization, which has been defined as the evolution of Gibbs free energy as a function of monomer conversion to polymer (p) from zero to one (p = 0 1) as the concentration, temperature, or some other environmental parameter is altered. This classification has been extremely effective in describing the vast array of examples of SPs, correlating mechanistic similarities with their covalent counterparts, which are widely understood to be classified mechanistically. In this scheme, the authors clearly identify the most fundamental difference between covalent and SPs as the difference in kinetic versus thermodynamic control. The authors argue that it is from this dramatic difference between covalent polymers and SPs, due to the reversibility of the noncovalent interactions, that SPs derive their special properties. This review did not include, however, SPs made from large macromolecular building blocks. 

A few brief comments are merited about the thermodynamics of polymerization reactions [42,43]. In principle, all polymerization reactions are reversible. However, the reversibility of the propagation step is very dependent on there being a reaction mechanism available for the reverse process. In the majority of polymerization reactions, the depropagation step is either not possible or other side reactions occur which dominate under conditions where reversibility might be expected. Thus, the ability to study thermodynamic equilibria in a polymerization process is restricted to relatively few polymerization systems even though thermodynamic behaviour is not a function of the precise nature of the propagating species in, say, chain polymerization processes. 

But suppose that we wanted to convert the polymer back into monomer. In that case, the necessary reaction is the reverse of the polymerization, and it is not a thermodynamically spontaneous process at ordinary temperatures. We could still drive the reaction backward to produce methyl methacrylate monomer. But we would need to maintain a high temperature, providing enough energy to allow the molecules to go against nature s preferred direction. So what is the role of energy in the directionality of nature ... 

The single most important property of a polymeric interpheise is its interfacial tension. This property describes the energy required to create the interphase and can be readily defined through classical thermodynamics. The interfacial tension Y for a polymer-air interface (ie, the surface tension) is generally defined in terms of the work required to reversibly divide and separate a material into two parts, as depicted in Figure 1. The work required to perform the separation is called the work of cohesion, Wc, and provides an operational definition for the surface tension ... 

Anionic surfactants are the most commonly used type in the emulsion polymerization. These include sulfates (sodium lauryl sulfate), sulfonates (sodium dodecylbenzene sulfonate), fatty acid soaps (sodium or potassium stearate, laurate, palmitate), and the Aerosol series (sodium dialkyl sulphosuccinates) such as Aerosol OT (AOT, sodium bis(2-ethylhexyl) sulfosuccinate) and Aerosol MA (AMA, sodium dihexyl sulphosuccinates). The sulfates and sulfonates are useful for polymerization in acidic medium where fatty acid soaps are unstable or where the final product must be stable toward either acid or heavy-metal ions. The AOT is usually dissolved in organic solvents to form the thermodynamically stable reverse micelles. [22] Nonionic surfactants usually include the Brij type, Span-Tween 80 (a commercial mixture of sorbitol monooleate and polysorbate 80), TritonX-100[polyoxyethylene(9)4-(l,l,3,3-tetramethylbutyl)-phenyl... 

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