Diffusion coefficient thermodynamic

One of the simplest early free-volume diffusion models was formulated in (51,52,60). The concept of this model was considered an advance, because some of the parameters required to describe the concentration dependence of the diffusion coefficient could be obtained from the physico-chemical properties of the polymer and penetrant. The relation proposed for the calculation of the thermodynamic diffusion coefficient, DT, was (51,60) ... 

Fujita (ljD related the thermodynamic diffusion coefficient, D, to the fractional free volume, v, by... 

Dj - thermodynamic diffusion coefficient (also equal to the intrinsic diffusion coefficient (Eq. 1.2.29)... 

The thermodynamic diffusion coefficient I>j- is related to the mobility by the relation < ... 

The thermodynamic diffusion coefficient is equal to the observed diffusion coefficient only for ideal svstems and at low volume fractions tpj —> 0 giving dlnaj/db j —> 1 and D =... 

The driving force is given by the gradientdp/dx. The frictional coefficient can be related to the thermodynamic diffusion coefficient Dj-. If ideal conditions ate assumed, i.e. if the thermodynamic diffusion coefficiraitis equal to the observed diffusion coefficient, eq. V -140 then becomes... 

It has already been shown in chapter V that the thermodynamic diffusion coefficient can be expressed as ... 

Substituting Equation (2) into (1), and recognizing kT/r as the thermodynamic diffusion coefficient and c/P as the solubility coefficient S, gives ... 

Perluorosulfonated ionomer membranes have high water permeabilities and excellent selectivities for water over most gases and organic liquids. These membranes have been shown to be useful for dehydration applications. Water transport in these membranes is non-Fickian. Water permeability and solubility coefficient vary with water vapor pressure. Concentration dependent thermodynamic diffusion coefficients have been obtained by combining the steady state water permeability data and the equilibrium sorption data. These diffusion coefficients correspond to what would be obtained from an experiment with infinitismal partial pressure drop across the membrane. 

The concept of free volume in a polymer is an extension of the ideas of Cohen and Turnbull [141], first used to describe the self-diffusion in a liquid of hard spheres. Such theories suggest that the permeant diffuses by a cooperative movement between the permeant and the polymer segments, from one hole to the other within the polymer. The creation of a hole is caused by fluctuations of local density due to thermal motion. Based on the concept of the redistribution of free volume to represent the thermodynamic diffusion coefficient [142], and the standard reference state for free volume [143], Stem and Fang [144] interpreted their permeability data for nonporous membranes, and Fang, Stem, and Frisch [ 145] extended the theory to include the case of permeation of gas and liquid mixtures. 

The theory is based on the assumption that a diffusing molecule can only move from one place to another when the local free volume around that molecule exceeds a certain critical value. The probability of finding such sufficient free volume is proportional to exp( —Ff), where is a parameter describing the amount of free volume needed and is proportional to d, the Lennard-Jones size parameter, 0 is the volume fraction of permeant and is the fractional free volume of the system. The thermodynamic diffusion coefficient Dj may be related to this probability by... 

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