Mechanistic Implications for Linseed Oil Drying
For each of the samples studied, identical values of k1and k2 were found for the A B C model. In addition, the quality of fit and residual spectra improved when the values of k1 and k2 were fixed to be equal. This strongly suggests that the air drying of linseed oil is better modeled as two sequential reactions with the same rate constant, rather than a single reaction obeying pseudo first-order kinetics as commonly implemented in the literature.(van Gorkum and Bouwman 2005) While only subtle differences are seen in the single wavelength fittings between these two models, the interpretation of the reaction mechanism and rate determining steps involved in linseed oil drying is changed dramatically.
The one-step model has frequently been interpreted as indicating the rate determining step in the drying process is an H-atom abstraction by the drier, with subsequent steps being too rapid to observe experimentally. This mechanism leads to the rate law: Rate = k[Co][A ]. In contrast, a two-step model with identical rate constants indicates two identical rate determining steps in the mechanism, with the only difference between the rate laws being the presence of [A ] or [B ].
Two hypothetical mechanisms that would lead to this type of rate law present themselves. In the first, H-atom abstraction by the drier is the rate determining step in both the conversion of A to Band B to C . This is equivalent to the rate determining step being initiation and leads to the rate laws: Rate1= k[Co][A ] and Rate2 = k[Co][B ]. This would require similar activation energies for H-atom abstraction from both A and B . The second possibility is that the rate determining step is the reaction ofA or B with a propagating radical. This is equivalent to the rate determining step being propagation and leads to the rate laws: Rate1 = [R•][A ] and Rate2 = [R•][B ]. This mechanism requires the activation energies for radical attack on olefin groups in both A and B to be similar.
We currently favor the latter hypothesis as an explanation for the observed kinetic data for three reasons. First, it can explain the induction periods seen in the drying of linseed oil as the time needed not only to consume natural antioxidants (Orlova et al. 2021), but also build up a steady-state concentration of propagating radicals. Secondly, a rate dependence on steady-state radical concentration is consistent with the observed rate dependence on drier concentration. Specifically, in this mechanism the drier affects the drying rate indirectly through the steady-state concentration of propagating radicals by affecting initiation and termination reactions. Previous studies have suggested the driers can catalyze both initiation and termination reactions, consistent with this hypothesis (van Gorkum and Bouwman 2005; Charamzová et al. 2018). Finally, it makes logical sense that a radical attack on an alkene group in either A or B would have comparable activation energies, and therefore rate constants, while different activation energies would be expected for H-atom abstraction fromA or B .