Thermal Initiation in Absence of Initiator

The mechanism of self-initiation in therm polymerization of styrene has been shown (Barr et al., 1978) to involve the formation of a Diels-Alder dimer (I) of styrene [Eq. (6.74)] followed by the transfer of a hydrogen atom from the dimer to a styrene molecule [Eq. (6.75)]. The existence of the dimer has been confirmed by UV spectroscopy. 

Problem 6.10 There is evidence (Barr et al., 1978) that thermal self-initiated polymerization of styrene may be of about five-halves order. Show that this is in agreement with the established initiation mechanism involving a Diels-Alder dimer formation [Eqs. (6.74) and (6.75)]. 

The higher than second-order rate observed for thermal conversion of monomer indicates that Eq. (6.74) is the slow step. Representing the concentration of Diels-Alder dimer (I) by [D] and that of styrene by [M], 

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