Study of phase-diagram domains

We propose a novel approach to calculate the thermodynamic phase diagrams. Differing from the conventional method in which the boundaries of the coexisting phases are the ultimate goal, the present work crosshatches the domains of the homogeneous phase and also the phases in coexistence. This was done by treating the separated phases as a composite system whose Helmholtz free energy density is expressed as the sum average of the constituent free energy densities which are weighed by their respective volume proportions. As a result, both the domains of the coexisting phases and the homogeneous single phase can be determined in addition to locating the phase boundaries, customarily obtained by imposing the thermodynamic equilibrium conditions of equal pressure and equal chemical potential. We illustrate the elegance of the theory by studying a thermally responsive microgel system.