On the Diffusivity of Vitamin E in UHMWPE

Since vitamin E (or any other sort of antioxidants) are in low concentration for economic and technical reasons (not lowering the mechanical properties of polymer), it is not expected to change the free volume fraction of the polymer. The diffusion is thus expected to obey Pick s law, with the diffusion coefficient D supposed independent of the antioxidant concentration  

This equation was analytically solved by Crank [81] in the case a plate having a 2h thickness such as  

In the field of research on food packaging, some authors from the have investigated the structure dilfusivity relationships of antioxidants and have proposed models relating the dilfusivity with the molar mass of penetrant and a matrix dependent parameter [82], Among those models, there are  

Where D is expressed in cm s, and M in g mol k Those equations generally fit rather well the dilfusivity of linear molecules [84, 85], but 

For example, the A coefficient expresses the tortuosity linked to the barrier role of crystallites. It is thus not surprising that this parameter is higher in HDPE than in LDPE. 

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