The thermodynamics of polymer phase separation constitutes a crucial topic in polymer physics,and the associated parameters pertaining to the critical point of the phase diagram,namely,xc and φc,present a challenge and a pivotal aspect in this area of study.This paper aims to address the inadequacies and insufficiencies of conventional derivative methods employed in teaching,based on the mathematical properties of the free energy-composition curve itself.We present a new approach to derive xc and φc using two fundamental mathematical tools,derivatives,and elementary inequalities,which not only simplifies the process but also offers a fresh perspective,thereby enhancing students'comprehension and knowledge of the theory associated with the critical point of phase separation.
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