Dynamics versus energetics in phase separation

Phase separation may be driven by the minimization of a suitable free energy $F$. This is the case, e.g., for diblock copolymer melts, where $F$ is minimized by a steady periodic pattern whose wavelength λ_GS depends on the segregation strength α⁻¹. It has long been known that in one spatial dimension λ_GS ≃ α^−1/3. Here we study in detail the dynamics of the system in 1D for different initial conditions and by varying α by five orders of magnitude. We find that, depending on the initial state, the final configuration may have a wavelength λ_D with λ_min(α)<λ_D < λ_max(α), where λ_min ≈ ln(1/α) and λ_max ≈ α^−1/2. In particular, if the initial state is homogeneous, the system exhibits a logarithmic coarsening process which is arrested whenever λ_D ≈ λ_min.