Effect of Deuterium Substitution on Compatibility Conditions

In the next step the variation of the solubility parameter 8 is considered due to the change in the microstructure. All three descriptions agree that the parameter 8 of the random copolymer E EEx should decrease monotonically with increasing ethyl ethylene fraction x (see the inset to Fig. 10a). The original Bates formulation are extended beyond isotopic mixture by [136, 143] (but still for nonpolar substance and similar volumes of interacting species (VE-Vee)/V 1.4% 1) emphasizing the role of AV/V alone [136] or correlated Aa/a 

The change of the solubility parameter 8eixi maybe assumed to be linear with deuterium fraction e and composition Xj (0 ej l, 0 xj 1)  

Finally the effective interaction parameter (hxj/dxj.ej) in a mixture of a pro-tonated random copolymer hx- and a partly deuterated (to extent ej) random copolymer dxj is written using Eqs. (16a) and (18b) for Xj value close to Xj one  

The effective interaction parameter (hXj/dXj.ej) in Eq. (19) is a function of two unknown parameters, %E/EE and %h/d, so these can be extracted [143] from two experimentally determined values of the overall interaction parameter for each pair of structurally identical mixtures with a swapped isotope labeled component, i.e., for dXj/hXj and hxj/dxj. In order to fit to the specific form AT-1 of the interaction parameter used in the approach described above we re-express all effective interaction parameters as [91] x(hXj/dxi,e1)=xcTc/T, where %c= (N1l/2+Njl/2)2/(2N1Nj) and Tc is given by experiment. It turns out [145] that this is a good approximation for studied random polyolefins (see Fig. 9) as the entro-pic term B of Eq. (17a,b) is small (it contributes less than 6% for most of the blends) and the weak ( -dependence of % may be neglected as it is not directly involved here. 

The isotope swapping effect may be also used to infer the order of solubility parameters [139] for protonated blend components 8xi and 8xj since their interaction parameter %(hXj/hXj) (see Eq. 16a) yields only the magnitude of the difference 8xi-8xj. We have  

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