Diffusion coefficients in amorphous solids

In a second step, a molar activation energy, EA, of the motion of the methylene groups in the polymethylene chain is introduced. This activation energy EA = wRTc = 10.089 8.31451 1036.2 = 86.923 kJ mol 1 is defined as a magnitude proportional to 

Finally, analogous to the gas phase an equation for the diffusion coefficient, DP of a n-alkane with i carbon atoms in an amorphous polymethylene is obtained (Brandsch et al., 1998)  

Equation (6-20) can be used as a reference equation for all polymers. It represents a theoretical construction resulting from an asymptotic correlation and the assumption of an infinite chain composed of methylene groups representing the amorphous polymer matrix. 

The factor 0.1351 in the exponent of Eq. (6-21) can be used as an acceptable approximation for most hydrocarbons and other solutes with low polarity. 

The diffusion coefficients of n-paraffins with 12 to 22 carbon atoms in high density (HDPE) and low density polyethylene (LDPE) have been measured by a permeation method (Koszinowski, 1986). Methanol (MeOH) and ethanol (EtOH) were used as contacting liquid phases which minimized interaction between these polar solvents and the nonpolar polymers. No interaction was observed over the investigated temperature range of 6 to 40 °C for both solvents. 

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Diffusion coefficients in amorphous solids such as oxide glasses and glasslike amorphous metals can be measured using any of the methods applicable to crystals. In this way it is possible to obtain the diffusion coefficients of, say, alkah and alkaline earth metals in silicate glasses or the diffusion of metal impurities in amorphous alloys. Unlike diffusion in crystals, diffusion coefficients in amorphous solids tend to alter over time, due to relaxation of the amorphous state at the temperature of the diffusion experiment. 

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