Equilibrium of Radical Polymerization

As for step-growth polymerization, the presentation of the kinetics of radical polymerization must be followed by a description of its equilibrium. The Gibbs free energy, G, for any system at temperature T is defined as H — TS, where H and S are the enthalpy and entropy of the system, respectively. The change in Gibbs free energy, AGp, for the formation of a polymer 

From thermodynamies, we know that a proeess oceurs spontaneously only when AGp is negative and, at equilibrium, AGp is zero. In ease 1, AGp would be negative below a eertain temperature and positive above it. This implies that the reaction would occur only below this temperature, which is called the ceiling temperature. In case 2, AGp is always negative and, therefore, the polymerization occurs at all temperatures. In case 3, AGp is always positive and therefore the reaction does not go in the forward direction. In case 4, the reaction would occur only when the temperature of the reaction is above a certain value, called the floor temperature. 

It may be pointed out that, in general, ASp is a function of the monomer concentration in the system, so the ceiling temperature (or the equilibrium temperature) also depends on the monomer concentration. This dependence is 

Equation (5.6.8) represents a very important result in that it has an extra, non-negligible term, ASp/R, which is not present in the corresponding reaction of small molecules. From this equation, we can find the equilibrium monomer concentration at the temperature at which the polymerization is being carried out. It turns out that the equilibrium concentration of monomer is very low at normal temperatures of polymerization that are far below T. For example, for styrene at 60° C, [M]g is obtained using values of AHp and ASp foxmd in Ref. 4 (for hquid styrene and solid amorphous polystyrene) as 

It has aheady been observed that there is considerable change in physical properties of the reaction mass as the hquid (or gaseous) monomer is polymerized to the sohd polymer. If the temperature of polymerization, T, is greater than the glass transition temperature of the sohd polymer (T ), the terminal conversion is the same as that given by Eq. (5.6.8) [22]. If the temperature of polymerization is 

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