Polymerization-Depolymerization Equilibria

The predicted variation of Tc with [M]g can be found by inserting the Arrhenius expressions into Eq. (6.161), whence 

Equation (6.164) shows that there is a series of ceiling temperatures corresponding to different equilibrium monomer concentrations. For a monomer solution of any concentration taken as [M]e, there is a temperature at which polymerization will not occur. In fact, for each concentration taken as [M]g there will be a plot analogous to Fig. 6.13 showing kdp = p[M]e at its Tc. Thus there is an upper temperature limit above which a polymer cannot be produced even from pure monomer at equilibrium. The designation of a singular Tc value, often referred to in the literature as the ceiling temperature, usually refers to the Tc for the pure monomer or in some cases for the monomer at unit molarity taken as [M]e. 

An alternative approach to the problem of determining ceiling temperature is based on the recognition of Tc as the temperature at which LGp = 0, and hence ffomEq. (6.158), 

This equation implies that at the ceiling temperature (Tc) the monomer concentration in equilibrium with long chain polymer is [M]e. Equation (6.167) can be rewritten as 

The equations derived above can be used to calculate how much monomer will be in equilibrium with high-molecular weight polymer at any temperature (see Problems 6.33 and 6.34). 

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In an attempt to avoid the polymerization/depolymerization equilibrium that occurs during melt polycondensation, Albertsson and Lundmark (1988) also studied the irreversible reaction of adipic anhydride with ketene. However, they reported very little difference in molecular weights when two ketene syntheses were compared to melt polycondensation and ringopening polymerization using a zinc catalyst (Albertsson and Lundmark, 1988). 

Equation 5 is valid only for irreversible reactions. For a copolymerization reaction that contains a polymerization-depolymerization equilibrium, Equation 5 is oversimplified. Depolymerization (Equation 2) is not considered in Equation 5. The following derivation of a generally valid equation for a copolymerization will include this retroreaction. 

One can describe the copolymerization of a-methylstyrene and methyl methacrylate with Equations 5 and 33. Equation 5 reflects only a mathematical approach, whereas Equation 33 takes into account the polymerization-depolymerization equilibrium investigated in the homopolymerization of a-methylstyrene. 

In Figure 6 Equation 37 combined with Equation 38 was used to evaluate the copolymerization behavior. It is now assumed that the sequence with two monomer units Mi cannot depolymerize, but that longer sequences are subject to the polymerization-depolymerization equilibrium. 

Cleavage of formaldehyde from the active centers and polymerization of formaldehyde at the same cationic chain ends (polymerization-depolymerization equilibrium of formaldehyde) (9). 

The molecular weight of the resulting polymer is comparatively small (of the order of dozens of thousands), and at temperatures above 100°C. the monomer does not polymerize completely owing to the establishment of polymerization-depolymerization equilibrium. These features are typical of the radical polymerization of methacrylates. 

Problem 6.39 To study the polymerization-depolymerization equilibrium of a-methylstyrene, solutions of this monomer in tetrahydrofuran were polymerized [61] at several temperatures using a sodium-naphthalene complex as initiator. The polymerization reaction was allowed to proceed for as long as 2.5 to 65 hours, after which the reaction was terminated with water and the polymer precipitated in methanol, dried, and weighed. The concentration of monomer remaining at equilibrium was obtained from the difference in the original monomer and the polymer formed. The equilibrium concentration values obtained at several temperatures are given below ... 

Problem 6.41 If a free-radical polymerization of 1.0 M solution of methyl methacrylate was being carried out at 100°C, what would be the maximum possible conversion of the monomer to polymer, that is, till the polymerization-depolymerization equilibrium is reached (Take relevant data from Table 6.13.)... 

Type of Cation and Cation Ratio. The polymerization-depolymerization equilibrium conceivably can be influenced by the stabilizing effect of certain cations on certain precursors. The cations present also may determine the way in which these building blocks are joined to give a framework structure. Reaction mixtures, identical except for the cation introduced with the phosphate, yield different products at the same pH. 

Temperature. Temperature influences the polymerization-depolymerization equilibrium. Higher temperatures cause denser materials to crystallize. Selbin and Mason (23) reported that they had to use a lower temperature to obtain the gallosilicate analog of zeolite X. Temperatures above 70 °C caused a gallosilicate of sodalite structure to crystallize. Countless examples for the temperature effect are given in the literature (see, e.g., Ref. 2). 

The glass-transition temperature depends on the mobility of the chain segments and can therefore be raised by stiffening the chain (see Section 10.5.3). Thus, a-methyl styrene forms a polymer that, in contrast to poly-(styrene), does not deform at lOC C, because of a glass-transition temperature of 170°C. However, since the thermodynamic ceiling temperature for for the polymerization/depolymerization equilibrium is also simultaneously lowered (see Section 16.3), poly(a-methyl styrene) degrades more easily than poly(styrene), so that it is not so easy to work by injection molding. 

The polymerization-depolymerization equilibrium is not between the growing chain and the originally propagating monomer, trioxane, but to formaldehyde [Eq. (60)] [241, 242]. Thus formaldehyde should be considered as a comonomer [236, 243], which will be accumulated until its equilibrium concentration and pressure is reached. 

Heterocycles often exhibit low ceiling temperature, which has an incidence on the kinetics of polymerization. Assuming a first-order kinetic law with respect to each reactive entity and a polymerization-depolymerization equilibrium occurring... 

Fig. 1. Change in energy of a polymerization/depolymerization equilibrium along the reaction coordinate, showing the relation of the activation energies of propagation and depropagation and the heat of polymerization.

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