화학공학소재연구정보센터
홈 로그인 로그아웃 연락처 사이트맵
Macromolecular Research, Vol.29, No.10, 681-693, October, 2021
DOI10.1007/s13233-021-2083-7  Export Citation
Classical Critical Behaviors and Ginzburg Criteria for Polymer Mixtures
Junhan Cho†
  • Department of Polymer Science & Engineering, Dankook University, 152 Jukjeon-ro, Suji-gu, Yongin, Gyeonggi-do 16890, Korea
E-mail:
We provide a pedagogical argument on classical critical behaviors of polymer mixtures, which include an ordinary critical point and several multicritical points such as tricritical, isotropic Lifshitz, and isotropic Lifshitz tricritical points. Various scaling exponents and singularities near those critical points are first derived through analyzing Landau free energies in general but suitable forms. A simple binary blend of A and B homopolymers in the mean-field picture is taken as an example of the ordinary critical point to verify its critical exponents and scaling laws by formulating its Landau free energy with the explicit vertex coefficients. A ternary blend consisting of A and B homopolymers of the same sizes and also symmetric A-B diblock copolymer is then employed to get the classical critical exponents and scaling laws for the multicritical points through directly evaluating phase equilibria and scattering functions with varying chain length ratios. In addition, the validity of the mean-field description in the vicinity of those critical points is discussed based on Ginzburg criteria and upper critical dimensions.
Keywords:classical critical behaviors;ordinary critical point;Lifshitz point;tricritical point;Lifshitz tricritical point;critical exponent;Landau free energy;Ginzburg criteria;upper critical dimension;polymer blends
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