Helfand-Tagami

The Helfand-Tagami lattice theory predicts that there is reciprocity between the interfacial tension coefficient and the interfacial thickness, and the product, Al , is independent of the thermodynamic binary interaction parameter, Furthermore, the theory led to the conclusions that (i) the surface free energy is proportional to... 

Figure 4.3. Verification of the molecular weight dependence of the interfacial tension coefficient, as predicted by the Helfand-Tagami theory (see Eq 4.6)...

Interphase theories Immiscible blends density profile compatibilized compatibilized - semi experimental, p vs. ((). Helfand Tagami, 1971, 1972 Helfand Sapse, 1975 Noolandi, 1984 Utracki, 1991 1992... 

The Helfand-Tagami lattice theory predicts that there is reciprocity between the interfacial tension coefficient and the interfacial thickness, and the product, Vqo A/oq, is independent of the thermodynamic binary interaction parameter, Xii- Furthermore, the theory led to the conclusions that (i) the surface free energy is proportional to Xif (ii) the chain ends of both polymers concentrate at the interface (iii) any low molecular weight third component is repulsed to the interface (iv) the interfacial tension coefficient is a linear function of temperature (see Eq. 4.5 and Fig. 4.2) and (v) the interfacial tension coefficient increases with molecular weight to an asymptotic value, Vqo, as illustrated in Fig. 4.3 ... 

The Helfand-Tagami lattice theory predicts that 1. Product, Al Vi2 = const. 2. Surface free energy is proportional to 3. Polymeric chain-ends concentrate at the interface ... 

In the Helfand-Tagami mean field formulation, the effective mean field on a segment of polymer A, which is the reversible work of adding the segment at position r, where the densities are pA(r) and Pb(>") less the work of adding the segment to bulk A, is given by ... 

From the above equations it is clear that, with decreasing interaction parameter Xui the density profile becomes flatter and the interfacial thickness increases with the square-root of Xi2- When Xu approaches zero, AI goes to infinit) that is, the interface can no longer be distinguished and a single-phase system is formed. The basic Helfand-Tagami model was then extended by Broseta et al. [44] for the interface of polymers with defined chain lengths ... 

Comparing Eqs (3.23) and (3.25), it can be shown that the interface becomes broader in systems with low-molecular-weight components [45]. The experimentally estimated interfacial thicknesses [45-48] were found to be in reasonable agreement with the Helfand-Tagami and Broseta predictions. The distribution of the chain segments for systems containing at the interface a block copolymer as a compatibilizer, was derived by Noolandi [49]. Typical values of the interfacial thickness in different polymer blends are summarized in Table 3.1. 

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