(489d) Modeling Transient Diffusion of Gases In Glassy Polymers by the Dual Mode Model: Is the Local Equilibrium Hypothesis Necessary?

The
description of the mass transfer of gaseous species in glassy
polymers is of major interest for numerous

industrial
applications (packaging, adhesives, controlled release, membrane
processes..). A quantitative

description
of penetrant solution diffusion in glassy polymers has been developed
during 60s and 70s, known

as
the Dual Mode Model. This theory decomposes the sorbed molecules into
two species. The molecules

obeying
Henry law are considered as mobile and the molecules following
Langmuir law are considered as

immobile
in a first approach. Later, this theory has been extended to consider
the immobilization as

partial
for molecules following Langmuir law order to obtain a closer
approach to the experimental results.

The
partial immobilization model achieves an acceptable time lag
prediction (i.e. transient diffusion data)

by
assuming a local equilibrium everywhere in the membrane. Thus the
partial immobilization model is

considered
nowadays as the most appreciate and relevant transport model for the
gas diffusion in glassy

polymers.

A
common feature of the total and partial immobilization models is to
make use of the so-called local

equilibrium
hypothesis. This assumption was initially applied in the total
Immobilization Model as a neces-

sary
and sufficient condition for its mathematical description. Although
the Immobilization Model was later

shown
not be able to quantitatively represent the transport data, the
hypothesis has been maintained in

the
Partial Immobilization Model. This assumption is of interest because
it offers the possibility to largely

decrease
the complexity of the mathematical framework: it enables indeed the
ratio of the Langmuir and

Henry
population to be calculated throughout the polymer matrix thickness,
leading to one partial differ-

ential
equation to be solved in place of two. Surprisingly, to our
knowledge, no research has addressed the

analysis
of the incidence of the local equilibrium hypothesis on the
prediction performances of the Dual

Mode
Model. This question has been addressed through a systematic
simulation study and the main results

will
be reported in this communication.

The
experimental time-lag data previously reported for a series of ten
different systems (one glassy

polymer
/ one gaseous penetrant) by different authors have been compared to
the predictions of three

different
models: the total immobilization model (TIM), the partial
immobilization model (PIM) and the

dual
mode model without the local equilibrium hypothesis (named hereafter
the Dual Diffusion Model,

DDM).
Remarkably, based on exactly the same set of dual mode parameters
(sorption and diffusion data),

the
latter one (DDM) offers the best global fit when compared to the two
classical dual mode approaches.

Two
examples of comparative curve fits are shown in figure 1, for the N2
/Polycarbonate and CO2
/PET

systems.
It has to be stressed that the DDM model leads to the same
permeability expression as the

partial
immobilization model under steady state conditions. Additionally, the
general framework of the dual

mode
model is maintained for the DDM, except the need to make use of a
local equilibrium relationship

within
the polymer matrix. The predictions obtained by the three different
approaches on the different set

of
experimental data will be shown and discussed. The implications
offered by the DDM, especially with

regard
to the no more required local equilibrium assumption will be more
specifically analyzed.