In our previous study, we proposed a modified double lattice model, which is capable of describing and predicting the phase equilibria of binary polymer solutions. The model successfully describes the liquid-liquid equilibria having an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST), but cannot predict the closed miscibility loop phase behavior. The closed miscibility loop phase behavior may be mainly due to highly specific interactions such as hydrogen bonding. The purpose of this study is to extend our previous model to describe closed miscibility loop phase behavior by employing a new specific interaction term to account for highly specific interactions. According to the proposed model, quantitative description is in good agreement with experimental data and gives improved results when compared with those of other methods. (c) 2008 Elsevier Ltd. All rights reserved.