Donatelli equation

For IPN s, Donatelli et al. earlier derived an equation especially for semi-IPN s of the first kind (polymer I crosslinked, polymer II linear) and extended this to full IPN s by assuming that the molecular weight of polymer II is infinite. Michel et al. solved the Donatelli equation considering several boundary cases, and reinterpreted the constants involved. However, because of the semi-empirical nature of the Donatelli equation, its intrinsic shortcomings limit its applicability. 

Basic equations were derived by Donatelli et al. and Yeo et al. [Donatelli et. al, 1977 Yeo et ah, 1983]. Both assumed spheres of polymer 2 dispersed in polymer 1, although the spinodal decomposition model and much electron microscopy suggests that interconnected cylinders may be more prevalent, as discussed above. The Yeo et al., equation is the more general ... 

Figure 8.31. Modulus-composition data for SBR/PS full IPN s and semi-1 materials compared with theory (O) series 3 (semi-1) (A) series 4 (full) ( ) series 5 (full), (a) Kerner s equation (upper bound) (b) Davies equation (c) Kerner s equation (lower bound). (Donatelli et ai, 1975.)...

Donatelli et also applied the Kerner and Davies theories to their sequential IPNs and found that the Davies equation fits best (see Figure 6.33). Two of these compositions, shown in the lower part of Figure 2.3, suggest dual-phase continuity in a qualitative way. Semi-II IPNs, illustrated in the center of Figure 2.3, fell below the Davies line, suggesting one continuous and one discontinuous phase. While the Dickie et al latex materials would not be expected to exhibit dual-phase continuity, it is interesting that both the Allen et al and the Donatelli et al. materials do. 

A. A. Donatelli, L. H. Sperling, and D. A. Thomas, A Semiempirical Derivation of Phase Domain Size in Interpenetrating Polymer Networks, /. Appl Polym. Sci. 21(5), 1189 (1977). Equations for phase domain size in IPNs and semi-I IPNs. Effect of crosslink density, composition, interfacial tension. 

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