Spinodal decomposition without diffuse interface theory-I. Theory

It has been shown that when higher derivative tenns of the diffuse interface expansion are included in the theory of spinodal decomposition, exceptional results are obtained. Within a mean field pair interaction (MFPI) interpretation, the coefficients of terms ▽²ⁿc in the extended diffuse interface expansion eventually become infinite in magnitude. These anomalies are discussed and circumvented in a new analysis of spinodal decomposition. Within the MFPI interpretation a Fourier analysis of the composition is made at an earlier stage in the analysis. The result is a diffusion equation which can be related to the usual diffusion equation of spinodal decomposition. In the early stages, the only change encountered is that the factor κβ² in the amplification factor is replaced by a function K(β). When κ is defined, K(β) approaches κβ² in the limit of small β. When, because of long-range intermolecular potentials, the standard definition of κ does not converge, K(β) remains well defined but no longer increases as β² in the small β limit. This can result in amplification factors which are qualitatively different from those predicted by the standard theory.