In this paper

the free energy-composition curves and phase diagrams in polymer physics are discussed and interpreted. The free energy-composition curve is presented in 3D illustration

and the phase diagram is displayed and discussed intuitively. The factors influencing the trend of the free energy-composition curve are discussed from the point of view of mathematics. It is further clarified that the common tangent point is different from the binodal point. It is proven that the composition of separated states after phase separation is the abscissa of the common tangent points of the free energy curve. The proof method is easy enlightening and acceptable for students to understand

and it can be a useful supplement to the knowledge system and teaching ideas of phase separation thermodynamics in polymer physics.