Theoretical studies of colloidal phase diagrams

• Main Authors: Chien-Cheng Huang, 黃建程
• Other Authors: 賴山強
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/54920750706328807828

碩士 === 國立中央大學 === 物理研究所 === 95 === We draw attention to a theoretical means to calculate the colloidal phase diagrams. The proposed method has the salient feature of following closely the experimental spirit since the crystalline structures of the solid phase is assumed unknown given the initial physical conditions. With this theoretical model, the phase-diagram domains which comprise of pure phases, two coexisting phases, three or multiple separated phases can all be crosshatched in addition to yielding their respective volume proportions. The methodology proceeds with treating the coexisting phases as a combined system whose composite free energy density is written as the sum average of the free energy density values which are weighed by their re-spective volume proportions. Under this scheme, the thermodynamic phase transition has reduced to an optimization problem searching the lowest value of the composite free energy for all possible combination of phases, including pure liquid, pure solid, gas-liquid, gas-solid, liquid-solid, etc. For the calculation of the solid free energy in any structure which is needed in the thermodynamic perturbation theory, we applied the fundamental measure theory to obtain the solid hard sphere free energy, and used the Rascon et al.''s [C. Rascon, L. Mederos, and G. Navascues, Phys. Rev. E 54, 1261 (1996)] theoretical approach to calculate the pair distribution function. The genetic algorithm was finally employed to integrate all these in-gredients. As illustrations to demonstrate the usefulness of the present theory, we first tested the idea by studying the charged colloidal system and confirmed that our calculations reproduced satisfactorily our previous results [G.F. Wang and S.K. Lai, Phys. Rev. E 70, 051402-1 (2004)]. Then, we extend the calculation to the colloid-polymer mixtures. In the latter study, we unveiled the mystery of gas-liquid-solid triangular region previously advo-cated by Lekkerkerker et al. [H.N.W. Lekkerkerker, W.C.K. Poon, P.N. Pusey, A. Stroobants, and P.B. Warren, Europhys. Lett. 20, 559 (1992) ].