The Self-diffusion Coefficient of Xe in Elastomers

As discussed in Section 12.4 the PFGE experiment allows the measurement of the Xe self-diffusion coefficient in arbitrary materials. 

It is important to know for which A the transition from the time dependent Deff to the constant Dtort occurs. Using the relationship r2 = 6D0A with D0 10 n m2/s, which is a typical value for polymers, and A between 10 2 and 1 second, the range accessible for most PFGE experiments, one finds ( r2 )1/2= 0.8-8 pm. Consequently, the PFGE experiment is able to detect in a material diffusion barriers if the space between these barriers has dimensions in this range. 

In Section 12.3 it was described how, with the help of a two-dimensional exchange spectrum, domain sizes in the iPP/EP blend are estimated. There an estimated value for the Xe diffusion coefficient was used. Now with experimental data from Table 12.2 the average EPDM domain size for the iPP/EPDM blend can be calculated. It was assumed that the structure of the EPDM in the blend is the same as in the pure material, (i.e., the Xe diffusion coefficient in the EPDM domains in the blend is equal to the measured D for pure EPDM and likewise for iPP), then r2 for Xe in the EPDM domain during A = 1.2 seconds is 20 grn. In the same time r2 for Xe in the iPP matrix is approximately 5 grn. These distances for a diffusion time of 1.3 milliseconds, the inverse of the frequency difference 770 Hz of the two lines in the Xe NMR spectrum of the blend, are 0.6 and 0.2 grn, respectively. The average size of the EPDM domains in the iPP/EPDM blend is 

The above treatment also suggests that most Xe in the iPP matrix is absorbed in a shell around the EPDM domain with thickness d, where d must be larger than 0.2 pm and significantly smaller than 5 pm. 

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