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 lambda(GS) depends on the segregation strength alpha(-1). It has long been known that in one spatial dimension lambda(GS) similar or equal to alpha(-1/3). Here we study in detail the dynamics of the system in 1D for different initial conditions and by varying alpha by five orders of magnitude. We find that, depending on the initial state, the final configuration may have a wavelength lambda(D) with lambda(min)(alpha) < lambda(D) < lambda(max)(alpha), where lambda(min) approximate to ln(1/alpha) and lambda(max) approximate to alpha(-1/2). In particular, if the initial state is homogeneous, the system exhibits a logarithmic coarsening process which is arrested whenever lambda(D) approximate to lambda(min).