Polymerization Gibbs energy

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]. 

Tanaka [198] made an attempt to determine the contribution of ring strain and basicity to the reactivity of cyclic ethers in copolymerization by means of Gibbs polymerization energy. He derived a relation between the relative reactivities of an m-membered ring with i substituents to that of an n-membered cyclic ether with j substituents. He included a linear combination of their basicity differences, A(pKb)m and of Gibbs energy, A(AG)m., in his relation (a, b, and c are constants)... 

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. 

The presence of a carbon-halogen bond is not absolutely essential for the occurrence of tranfer to monomer. Moore et al. [37] studied styrene polymerization with y-irradiation. They measured thermodynamic quantities, particularly the Gibbs energy, enthalpy, entropy and volume changes by the method of rotating sectors and found that transfer to monomer is negli-... 

A chemical reaction proceeds spontaneously when the corresponding Gibbs energy is negative, AG = AH — TAS < 0. Under normal conditions, ethylene and other monomers can exist only because the relevant chemical reactions (including polymerization) cannot occur unless the monomer mole-... 

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.

From a thermodynamic viewpoint, the Gibbs energy change for the polymerization must be negative. Consequently, polymerizations are generally only thermodynamically permitted within a certain temperature range (see Section 16). 

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 ... 

The equilibrium constant will equal unity and the molar Gibbs energy will consequently be zero at a certain temperature. This temperature is called the transition temperature of the polymerization, and is given as... 

In the majority of cases, one is concerned with the polymerization of a liquid monomer to a condensed polymer, that is, in A This represents the Gibbs energy for the conversion of 1 mol of liquid monomer into 1 mol of monomeric units of amorphous polymer above the glass transition... 

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