Cahn-type theory

Cahn plot 206-209, 259 Cahn-type theory 258, 259 Carbocation 1... 

In conclusion, the Cahn-Hilliard theory is a modernization of van der Waals, confirming cmd extending the latter. With these theories and their many variants and extensions the framework is basically available for computing interfacial tensions from molecular interactions. Carrying out the computations is no easy matter, especially if the molecules are not spherical and if their interactions contain contributions other than those of the Lennard-Jones type. Then the quality of the results is determined by the quality of the choice of the parameters, analytical approximations, truncations, etc. A promising alternative is to invoke computer solutions, which will be treated in the next section. 

The Kinetics of Spinodal Decomposition. Cahn s kinetic theory of spinodal decomposition (2) was based on the diffuse interface theory of Cahn and Hilliard (13). By considering the local free energy a function of both composition and composition gradients, Cahn arrived at the following modified linearized diffusion equation (Equation 3) to describe the early stages of phase separation within the unstable region. In this equation, 2 is an Onsager-type... 

Involving the time dependence AFm t) (Equation 1) is close to the thermodynamics of systems with fading memory (Day, 1972) and the TTT type (time-temperature-transformation) diagram, a so-called nose diagram in the spinodal dccompasition theory (Huston et ah, 1966 Cahn, 1968). 

In case that all gradients being not too large, we may neglect higher orders of smallness in interplanar spacings at the Taylor expansion. Otherwise, we will arrive at a nonlocal theory of Cahn-Hilliard type. Then elementary mathematics leads to the following expression for the flux... 

A homogeneous mixture quenched from a stable phase into a thermodynamically unstable state within a phase diagram develops into an inhomogeneous system. Spinodal decomposition (SD) is induced by the instability of an order parameter, which is usually concentration [101]. In the early stages, the SD is interpreted within the framework of the Cahn theory for an isotropic SD [102,103]. In contrast, in the late stages, the SD is governed by diffusion or hydrodynamic processes and exhibits slow coarsening [104]. There are two types of order parameters that describe a system. One is a conserved order parameter such as concentration of binary mixtures. The other is a non-conserved order parameter such as the polarization of a ferroelectric... 

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