Mesoscopic phase separation dynamics of compressible copolymer melts

In this paper we extend the dynamic mean-field density functional method, derived from the generalized time-dependent Ginzburg-Landau theory, to the mesoscopic dynamics of compressible polymer liquids. We discuss and compare different classes of compressibility models: exactly incompressible, the Helfand’s harmonic penalty model, and a cell model. We present numerical results and show that the penalty model is a very practical and easy to use solution. In the current $\mathrm{nVT}$ ensemble dynamics algorithms application of the cell model leads to a variation of the pressure and, depending on conditions, the system develops liquid-gas transitions. We show that the morphology of a phase separated diblock copolymer melt around a gas bubble has intruiging structures, with lamellar phases oriented towards the gas-liquid interface.