Flory-Huggins model volume-fraction relation

For more strongly sorbing penetrants, such as C02 and Cj and Cj hydrocarbons, BET III isotherms indicative of Floiy-Huggins swelling behavior are common. The Flory-Huggins model, shown below, relates the penetrant activity (O/) to the sorbed volume fraction v of the component. Typically, the activity is replaced by the ratio of the penetrant partial pressure p and the component vapor pressure po ... 

A modified Cahn-Hilliard (CH) model [114] is used for the theoretical analysis of the impact of thermal diffusion on phase separation by taking into account an inhomogeneous temperature distribution, which couples to a concentration variation via the Soret effect. The Flory-Huggins model is used for the free energy of binary polymer-mixtures. The composition is naturally measured in terms of volume fraction 0 of a component A, which can be related to the weight fraction c by... 

Taking into account the modes in which the water can be sorbed in the resin, different models should be considered to describe the overall process. First, the ordinary dissolution of a substance in the polymer may be described by the Flory-Huggins theory which treats the random mixing of an unoriented polymer and a solvent by using the liquid lattice approach. If as is the penetrant external activity, vp the polymer volume fraction and the solvent-polymer interaction parameter, the relationship relating these variables in the case of polymer of infinite molecular weight is as follows ... 

The Flory-Huggins theory uses the lattice model to arrange the polymer chains and solvents. We have looked at the lattice chain model in Section 1.4 for an excluded-volume chain. Figure 2.1 shows a two-dimensional version of the lattice model. The system consists of si,e sites. Each site can be occupied by either a monomer of the polymer or a solvent molecule (the monomer and the solvent molecule occupies the same volume). Double occupancy and vacancy are not allowed. A hnear polymer chain occupies N sites on a string of N-l bonds. There is no preference in the direction the next bond takes when a polymer chain is laid onto the lattice sites (flexible). Polymer chains consisting of N monomers are laid onto empty sites one by one until there are a total tip chains. Then, the unoccupied sites are filled with solvent molecules. The volume fraction of the polymer is related to rip by... 

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