Entropy depolymerization

On the other hand, labile metal ions, for which 98% plus reactions should be easily obtained, often undergo side reactions and depolymerizations (the reverse reactions) are favored from entropy considerations. 

There is one further remarkable interconversion. The four polymers (RBNR) (mentioned in Section IV,A) are thermally stable, except for (EtBNEt) , which can be transformed into the borazine (EtBNEt)3 at 150°C (18). Such a depolymerization will proceed without considerable change of energy but with a substantial gain in entropy. For kinetic reasons, it cannot proceed with alkyl groups larger than ethyl. 

The entropy term is negative so that it is the enthalpy or energy term that drives the polymerization. At low temperatures, the enthalpy term is larger than the TASp term so that polymer growth occurs. At some temperature, called the ceiling temperature, the enthalpy and the entropy terms are the same and AGp = 0. Above this temperature depolymerization occurs more rapidly than polymer formation so that polymer formation does not occur. At the ceiling temperature depolymerization and polymerization rates are equal. The ceiling temperature is then defined as... 

Equation 3 shows that for a given monomer concentration [M]eq at temperatures above a critical value Tc the rate of the depolymerization step becomes greater than the rate of the polymerization step and dominates the reaction. The critical temperature Tc is called ceiling temperature (22, 23). (AH is the enthalpy of polymerization, and AS° is the entropy of polymerization at the monomer concentration [M] = 1 mole/liter.) The concentration of the monomer at equilibrium [M]eq is identical to the equilibrium constant K, which is defined by the rate constants kp and kd. 

Figure 9.10 presents the mechanism of the polymerization of formaldehyde starting from anhydrous formaldehyde and formaldehyde hydrate. In addition, a reaction path is shown that also connects trimeric formaldehyde ( trioxane, F) with paraformaldehyde (H). In practice, though, this reaction path is only taken in the reverse direction, upon heating (entropy gain ) of paraformaldehyde in aqueous acid as a depolymerization of H —> F. 

Spiro orthoesters (92, R = Me, Ph, and H) show typical equilibrium polymerization behavior at or below ambient temperature. [92] The poly(cyclic orthoester)s derived from 92 depolymerize to the monomers, although they have sufficient strains to be able to undergo ring-opening polymerization. The polymerization enthalpies and entropies for these three monomers were evaluated from the temperature dependence of equilibrium monomer concentrations (Table 5). The enthalpy became less negative as the size of the substituent at the 2-position in 92 was increased H < Me < Ph. This behavior can be explained in terms of the polymer state being made less stable by steric repulsion between the bulky substituents and/or between the substituent and the polymer main chain. The entropy also changed in a similar manner with the size of the substituents. 

This idea becomes even more pointed when we look at polymerization. Polyvinyl chloride is the familiar plastic PVC and is made by reaction of large numbers of monomeric vinyl chloride molecules. There is, of course, an enormous decrease in entropy in this reaction and any polymerization will not occur above a certain temperature. Some polymers can be depolymerized at high temperatures and this can be the basis for recycling, low... 

Using the enthalpy and entropy of polymerization data for methyl methacrylate from Table 6.13, calculate the depolymerization rate constant of poly(methyl... 

Polymerization entropies can be determined in several ways via the temperature dependence of the equilibrium concentrations of the monomer, via the heat capacity, via the activation constants for polymerization and depolymerization, or via an incremental calculation method. The heat capacity serves to determine the entropy of polymerization because the quotient of specific entropy and specific heat capacity, (A5 /c ) is about unity at 298 K for polymers irrespective of their constitution. False results occur if, for example, monomer association in the vapor phase occurs, or if, with polymers, there is a physical transition in the temperature range between calorimetric measurement and equilibrium measurement. 

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. 

In certain cases, the entropy of polymerization can also be calculated using an increment method. A direct determination, for example, of from the heat capacity is possible, but this method can give incorrect values in some circumstances. Incorrect values are observed when a monomer associates in the vapor phase, or when physical transitions occur in polymers in the range of temperatures between calorimetric measurements and equilibrium measurements. If such effects are excluded, then the quotient S%s/Cp 298 is remarkably constant for the most dissimilar monomer-polymer systems (Table 16-10). Determination of the entropy of polymerization from the temperature dependence of the equilibrium concentrations of the monomer is relatively unambiguous. Alternatively, it can be determined from the Arrhenius parameters Ap of polymerization and A p of depolymerization [of equation (16-52)]. 

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