Helfand-Tagami model

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 ... 

Helfand and Tagami model is based on self-consistent field that determines the configurational statistics of macromolecules in the interfacial region. At the interface, the interactions between statistic segments of polymers A and B are determined by the thermodynamic binary interaction parameter, Since the polymers are immiscible, there are repulsive enthalpic effects that must be balanced by the entropic ones that cause chains A and B to intermingle. 

Helfand and Tagami [75,76] introduced a model which considered the probability that a chain of polymer 1 has diffused a given distance into polymer 2 when the interactions are characterised by the Flory-Huggins interaction parameter x They predicted that at equilibrium the thickness , d c, of the interface would depend upon the interaction parameter and the mean statistical segment length, b, as follows ... 

K. W. Foreman and K. F. Freed (1998) Lattice cluster theory of multicomponent polymer systems Chain semiflexibility and speciflc interactions. Advances in Chemical Physics 103, pp. 335-390 K. F. Freed and J. Dudowicz (1998) Lattice cluster theory for pedestrians The incompressible limit and the miscibility of polyolefin blends. Macromolecules 31, pp. 6681-6690 E. Helfand and Y. Tagami (1972) Theory of interface between immiscible polymers. 2. J. Chem. Phys. 56, p. 3592 E. Helfand (1975) Theory of inhomogeneous polymers - fundamentals of Gaussian random-walk model. J. Chem. Phys. 62, pp. 999-1005... 

Roe (1975) developed a quasicrystalline lattice model for conditions where Xi2 Xcr (where Xcr is the critical value of the interaction parameter at the phase separation) and for Xn Xcr Xcr- Under the first conditions (high immiscibility), the theory predicted a proportionality between Vj2 and Xn whereas under the secmid (near the phase separation), a proportionality between Vi2 and xn was predicted. By contrast with the previously summarized Helfand and Tagami predictions. Roe s theory indicates that the product V12A/ should be proportional to... 

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