Uphill diffusion in binary systems and spinodal decomposition

9 Uphill diffusion in binary systems and spinodal decomposition 

Uphill diffusion occurs in binary systems because, strictly speaking, diffusion brings mass from high chemical potential to low chemical potential (De Groot and Mazur, 1962), or from high activity to low activity. Hence, in a binary system, a more rigorous flux law is (Zhang, 1993)  

If the composition of a phase falls inside the spinode, the phase would undergo spontaneous decomposition into two phases. That is, heterogeneity would arise from homogeneity. From an energetic point of view, the homogeneous phase is at an unstable equilibrium state, meaning that without disturbance at all, the equilibrium could persist, but the tiniest microscopic perturbation (there would always be perturbation due to thermal motion) would grow to produce hetero- 

the fluctuation would change with time with the same periodicity of Lin, but the amplitude would change as 

From the above analysis, it can be seen that D in Pick s first law J = -DVC (Equation 3-6) may be either positive or negative (accounting for uphill diffusion), and it can vary from positive to negative along a spinodal decomposition diffusion profile. If, on the other hand. Pick s law is modified as J = -(T /y)Va (Equation 3-61), then V is always positive in a binary system. 

---