Synthesis, Characterization, and Gas Permeation Properties

General Introduction
A simplified transport model is valid for all the porous membranes irrespective of
their actual microporous structure. The gas permeance, Q, through a porous
membrane can be described as:
where M is the molecular weight of the gas, R the gas constant, T the temperature, and
Vc and Tc are the critical volume and critical temperature of the gas, respectively. 34 α
is the Knudsen diffusion factor and β is the surface diffusion factor, both of which are
independent of the real geometric pore structures.
On the other hand, the mechanism of gas separation by non-porous
membranes is quite different from that of the porous integuments and is best explained
by the solution-diffusion model, 35 attributing the diffusion and solubility of gases in
the membranes to the molecular properties of diameter, shape, or volume and
condensability or polarity, respectively. 22c,33b,33c,36 According to this mechanism, the
gas molecules first dissolve in the surface of a dense membrane, and then the dissolved
entities diffuse through the transient gaps between the polymer chains, hence, the
permeation (P) of gas A through a polymer membrane is described as the product of
gas solubility (S) in the upstream face of the membrane and effective average gas
diffusion (D) through the membrane.
Q MRT � �e
In other words, permeability, the pressure- and thickness-normalized gas flux
through the polymer film, depends upon two factors: a thermodynamic term, S,
characterizing the number of gas molecules sorbed into and onto the polymer and a
kinetic term, D, characterizing the mobility of gas molecules as they diffuse through
the polymer. 37 The solubility coefficient, S, is determined by the condensability of
the penetrants, the polymer-penetrant interactions, and the amount of free volume in
10
β
P �
S � D
A
A
�Vc Tc�
A
(1)
(2)