Polymer sorption isotherm Flory-Huggins

Type III is the sorption isotherm of Flory-Huggins. Here the solubility coefficient increases continuously with pressure. It represents a preference for formation of penetrant pairs and clusters it is observed when the penetrant acts as a swelling agent for the polymer without being a real solvent. An example is water in relatively hydrophobic polymers containing also some polar groups. 

For ideal systems (usually as in elastomers), the solubility wiU be independent of concentration and the sorption curve will follow Henry s law (Equation 4.6), i.e., gas concentration within the polymer is proportional to the applied pressure. For nonideal systems (usually as in glassy polymers), the sorption isotherm is generally curved and highly nonlinear. Such behavior can be described by free-volume models and Flory-Huggins thermodynamics—comprehensive discussions on this may be found elsewhere [1,25,26]. 

Mathematically, the sorption data for the amorphous acrylic pol)nners which will be considered here cannot be correlated by a single parameter sorption Isotherm. In the Flory-Huggins theory, the parameter is the Interaction parameter, which for the simplest possible case characterizes the enthalpy of mixing which results from the Intermolecular bonding mismatch between polymer and water. A two parameter sorption Isotherm provides an excellent vehicle for data treatment. The two parameters can be identified as the interaction parameter and a clustering parameter. 

Vapor sorption isotherms in a polymer as computed from Flory-Huggins theory by using interaction parameters shown. 

The model appears to describe accurately sorption isotherms when the equation of state parameters of both polymer and penetrant are determined. Like the Flory-Huggins modef, the Sanchez-Lacombe model assumes that the different components mix randomly in a lattice. Unlike the Flory-Huggins model, the Sanchez-Lacombe model permits some lattice sites to be empty, which allows holes or free volmne in the fluid. The addition of free volume to the lattice permits volume changes upon mixing components. The amount of absorbed penetrant in the polymer is determined by equating the chemical potential of the penetrant and the chemical potential of the penetrant in the mixture and by satisfying the equation of state of the pure penetrant phase and of the polymer-penetrant mixture. At fixed temperature and pressure, these conditions are met by equations 5-7. 

This type of sorption isotherm arises when the interactions between permeant molecules are strong relative to permeant/polymer interactions, and the solubility coefficient increases continuously with increasing pressure. This sorption can be described for non-polar systems by the Flory-Huggins relationship... 

Sorption and diffusion of water vapour in polymers have been studied mainly for development of water vapour barriers. Some of these studies date back to 1944 [41]. Many attempts have been made in order to describe the sorption behavior of water vapor onto solid surfaces of the membrane and its pores. As described by Vieth [41], a deviation from Henry s law was observed in 1944, in the sorption of water by hydrated cellulose membranes. It was postulated that two competing phenomena are responsible for this observation dissolution, which obeys Henry s law, and adsorption, which follows the Langmuir isotherm. With other polymer systems the ability of water molecules and/or polar groups in the polymer matrix to interact with each other has given rise to sorption isotherms which may follow Henry s law, Flory-Huggins or BET types [41]. 

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