Gibbs Energy of Polymerization

Monomers can only be polymerized when the Gibbs energy of polymerization is zero or negative. The entropy of polymerization of monomers with olefinic double bonds is of the order of (AS2p)ic —105 kJK mol according to Table 16-11. The entropy component T(A5 jp), consequently, can take values of between —19 and —52 kJ/mol at temperatures between —100 and - -200°C. Therefore the enthalpy of polymerization must have at least the same values in order that AG Jp can be zero or negative. In the polymerization of rings, similar principles can be derived, except that here the entropy of polymerization, contrary to what is found for ethylene derivatives, is not independent of constitution. 

If both the enthalpy and entropy of polymerization are negative (most frequent case), then it is also appropriate to work at as low a temperature as possible when trying to polymerize an unknown monomer. Admittedly, activation may then become difficult, and it may be necessary to look for better initiators. Since the temperature 7 decreases with increasing dilution, it is advantageous to work in the melt or in very concentrated solution. The ceiling temperature is raised by working under pressure or preorienting the monomer by the formation of complexes with suitable additives. The formation of complexes will make the entropy of polymerization more positive. 

In systems with temperature 7, AG p becomes more positive as the temperature increases. Since AG p is related to the equilibrium constant K , and this, in turn, from Table 16-5, is related to the degree of polymeriza-don. Y must become lower as the temperature increases. The exact function Y =f T) depends on the type of equilibrium. 

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Thus, the monomer concentration at equilibrium, [Af], is equal to the reciprocal of the equilibrium constant. The following, on the other hand, holds for the standard Gibbs energy of polymerization ... 

The molar standard Gibbs energy of polymerization can be calculated from the equilibrium constants K of the polymerization- iepolymerization equilibrium ... 

If the equilibrium constant K is determined from the molar concentrations, then the molar Gibbs energy of polymerization AG p calculated in this way is not generally identical with the molar Gibbs energy AG of the complete process, since the interactions of monomer and polymer remain to be considered. These interactions differ in extent according to the state of aggregation (Table 16-6). 

This statement requires further consideration. When the equilibrium constant for the polymerization is smaller than unity, then, according to equation (16-43), the Gibbs energy of polymerization is positive. For 1 > > 0, however, the polymer concentration Mf+i]g is, according... 

The Gibbs energy of polymerization can be ejqrressed as a ftmction of two other thermodynamic functions enthalpy and entropy of polymerization. For equilibrium conditions, we have... 

There is the following relationship between Gibbs energy of polymerization and equilibrium constant K ... 

Gibbs energy of polymerization is strongly negative for the polymerization of strained three- and four-membered cyclic ethers therefore, polymerization is practically irreversible, which means that there are no thermodynamic barriers for reaching quantitative conversions even at low [M]o and higher temperamres. It should be remembered, however, that kinetic factors may prevent quantitative conversion if a termination reaction occurs. 

Gibbs energy of polymerization (AGp) may be expressed as a sum of standard enthalpy of polymerization (AG ) and a term related to instantaneous concentrations of monomer ([M]) and growing polymer ([...-m ]) ... 

The formal thermodynamic criterion of a given monomer polymerizability is related to a sign of the Gibbs energy of polymerization (cf. eqn [3]) ... 

The concentration of this species in liquid sulfur was estimated from the calculated Gibbs energy of formation as ca. 1% of all Ss species at the boihng point [35]. In this context it is interesting to note that the structurally related homocyclic sulfur oxide Sy=0 is known as a pure compound and has been characterized by X-ray crystallography and vibrational spectroscopy [48, 49]. Similarly, branched long chains of the type -S-S-S(=S)-S-S- must be components of the polymeric S o present in liquid sulfur at higher temperatures since the model compound H-S-S-S(=S)-S-S-H was calculated to be by only 53 kJ mol less stable at the G3X(MP2) level than the unbranched helical isomer of HySs [35]. 

The occurrence of these reactions is always determined by thermodynamic factors. Oxirane has a large ring strain. Its polymerization around room temperature exhibits AGp<0. For 1,4-dioxane under the same conditions, AGp > 0. In other words, polyoxirane will split off 1,4-dioxane because the Gibbs energy of its depolymerization is negative. Actually the polymer should depolymerize completely. That this is not the case, is caused by kinetic factors. Termination of depolymerization need not coincide with termination of polymerization. 

Therefore, over the temperature range of 0 to 50°C glucagon is almost completely trimerized.B Polymers are formed by the polymerization of monomers, and proteins can aggregate (or associate) as in the illustration.above. It is sometimes of use to know the relationship between the partial molar Gibbs energies of the polymer and the monomer or protein from which it is formed. To be completely general, suppose species A (whether it be a protein or polymer) polymerizes according to the reaction... 

Figure 6-5. Reduced molar Gibbs energy of mixing AG "IRT as a function of the volume fraction 02, of solute monomeric unit with different interaction parameters xo and degrees of polymerization Xi of the solute in low-molecular-weight solvents (Xi = 1). Calculations according to Equation (6-32) with a = 0.

The monomer concentration can remain constant for two reasons. First, a steady state can exist in which consumption of monomer by polymerization is directly compensated by subsequent diffusion of free monomer into the latex particle. The monomer concentration is then always lower than the saturation concentration at equilibrium. Second, the monomer concentration in the latex particles will be constant when the Gibbs interfacial energy A Gy and swelling A Gq cancel, so that the Gibbs energy of the monomer in equilibrium will be zero ... 

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