Activation energy chains

Though ionic polymerization resembles free-radical polymerization in terms of initiation, propagation, transfer, and termination reactions, the kinetics of ionic polymerizations are significantly diflFerent from free-radical polymerizations. In sharp contrast to free-radical polymerizations, the initiation reactions in ionic polymerizations have very low activation energies, chain termination by mutual destruction of growing species is nonexistent, and solvent effects are much more pronounced, as the nature of solvent determines whether the chain centers are ion pairs, free ions, or both. No such solvent role is encountered in free-radical polymerization. The overall result of these features is to make the kinetics of ionic polymerization much more complex than the kinetics of free-radical polymerization. 

Because the chemiluminescence intensity can be used to monitor the concentration of peroxyl radicals, factors that influence the rate of autooxidation can easily be measured. Included are the rate and activation energy of initiation, rates of chain transfer in cooxidations, the activities of catalysts such as cobalt salts, and the activities of inhibitors (128). 

The unsaturation present at the end of the polyether chain acts as a chain terminator ia the polyurethane reaction and reduces some of the desired physical properties. Much work has been done ia iadustry to reduce unsaturation while continuing to use the same reactors and hoi ding down the cost. In a study (102) usiag 18-crown-6 ether with potassium hydroxide to polymerise PO, a rate enhancement of approximately 10 was found at 110°C and slightly higher at lower temperature. The activation energy for this process was found to be 65 kj/mol (mol ratio, r = 1.5 crown ether/KOH) compared to 78 kj/mol for the KOH-catalysed polymerisation of PO. It was also feasible to prepare a PPO with 10, 000 having narrow distribution at 40°C with added crown ether (r = 1.5) (103). The polymerisation rate under these conditions is about the same as that without crown ether at 80°C. 

Chlorination of Methane. Methane can be chlorinated thermally, photochemicaHy, or catalyticaHy. Thermal chlorination, the most difficult method, may be carried out in the absence of light or catalysts. It is a free-radical chain reaction limited by the presence of oxygen and other free-radical inhibitors. The first step in the reaction is the thermal dissociation of the chlorine molecules for which the activation energy is about 84 kj/mol (20 kcal/mol), which is 33 kJ (8 kcal) higher than for catalytic chlorination. This dissociation occurs sufficiendy rapidly in the 400 to 500°C temperature range. The chlorine atoms react with methane to form hydrogen chloride and a methyl radical. The methyl radical in turn reacts with a chlorine molecule to form methyl chloride and another chlorine atom that can continue the reaction. The methane raw material may be natural gas, coke oven gas, or gas from petroleum refining. 

The individual steps in chain reactions involving radicals are characteristically of small activation energy, between about 10 and 50kJmol and so these reactions should occur at an immeasurably high rate at temperatures above 500 K (see Table 2.1), which is a low temperature for a useful combustion process. The overall rate of the process will tlrerefore depend mainly on the concentrations of tire radicals. 

Important differences are seen when the reactions of the other halogens are compared to bromination. In the case of chlorination, although the same chain mechanism is operative as for bromination, there is a key difference in the greatly diminished selectivity of the chlorination. For example, the pri sec selectivity in 2,3-dimethylbutane for chlorination is 1 3.6 in typical solvents. Because of the greater reactivity of the chlorine atom, abstractions of primary, secondary, and tertiary hydrogens are all exothermic. As a result of this exothermicity, the stability of the product radical has less influence on the activation energy. In terms of Hammond s postulate (Section 4.4.2), the transition state would be expected to be more reactant-like. As an example of the low selectivity, ethylbenzene is chlorinated at both the methyl and the methylene positions, despite the much greater stability of the benzyl radical ... 

FIG. 14 Semi-log plot of mean chain length L vs width of the open slit D at various temperatures in 3d. Full symbols denote flexible chains and empty symbols semirigid chains with activation energy a = 0.5 [61]. 

In general, the activation energies for both cationic and anionic polymerization are small. For this reason, low-temperature conditions are normally used to reduce side reactions. Low temperatures also minimize chain transfer reactions. These reactions produce low-molecular weight polymers by disproportionation of the propagating polymer ... 

Ea = Arrhenius activation energy Es = excess stress energy AEr = potential barrier for bond rotation Eel = molecular elastic energy F = mean force potential f = average force on the chain fb = bond breaking force H0 = Hookean spring constant kB = Boltzmann constant... 

Fig. 20. Bond scission activation energy and lifetime (Tt) plotted as a function of applied force. The solid curve is derived from Eq. (65) based on the Morse potential, the other data are redrawn from Ref. [101]. The upper abscissa gives the overall elastic strain before failure. The numbers indicate the minimum chain lengths which will fail at a particular force...

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

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