RESEARCH ACTIVITY
Research activity has been devoted mainly to the following
areas:
1.
membrane separations.
1.1. membrane distillation.
1.2. development of affinity
membranes; analysis of affinity membrane apparatus.
1.3. membrane gas separations.
1.4. metal membranes for hydrogen
separation.
1.5. reverse osmosis.
1.6. pervaporation.
2.
diffusionin polymers.
2.1. Fickian diffusion and
chemical post-treatment.
2.2. non-Fickian diffusion.
2.2.1. localized swelling and viscoelastic
diffusion.
2.2.2. stress and deformation effects in non-Fickian
diffusion.
3.
thermodynamics and thermomechanical properties of polymeric
fluids.
3.1.
solubility, diffusivity and permeability in solid polymers.
3.2.
model predictions and correlations for the solubility in glassy
polymers.
3.3.
thermo-rheological constitutive equations.
3.2. foundations of rational
thermodynamics.
4
Separation and purification of proteins and
immunoglobulins
4.1. development of affinity
membranes and affinity membrane modules.
4.2. experimental characterization
of affinity membranes and affinity membrane modules.
4.3. modelling of affinity
membrane behavior.
5
chemical processes in microelectronics.
5.1 CVD reactions.
5.2 growth of silicon oxide
and silicon nitride.
The research activity lead to over 200 scientific publications,
two patents and numerous presentations to scientific international
meetings.
Brief overview of research achievements
The research activity performed has been developed in a period
of over 33 years. The main focus of this description is on
the more recent research interests which have been active at
least in the last decade; they involve different membrane
separation processes and the related topic concerning the
diffusion in solid polymers. The general approach is
essentially based on continuum theories.
1. Membrane
separation processes.
The topic has been studied in particular with the main aim to
develop new membrane processes and to inspect their potential
applicability as separation techniques; more common membrane
separation techniques have also been studied with the aim to
inspect their feasibility to non traditional applications.
1.1. Membrane distillation
(MD). The process is based on the use of microporous
hydrophobic membranes, in contact with an aqueous stream,
containing either salts or dissolved organics (VOC's) or gases: the
hydrophobicity of the membrane material prevents the liquid from
entering into the membrane pores, as long as the pressure
prevailing over the aqueous solution is lower than the minimum
entry pressure of the membrane material. Typical values of the
minimum entry pressure for microporous membranes in polypropylene
or in PTFE are in the order of 210 bar. When the pressure over the
liquid inlet stream is kept below the minimum entry pressure,
the entrance of the membrane pores separates the liquid phase from
a vapour phase trapped inside the pores; the membrane thus acts as
a physical support for a meniscus through which a liquid vapour
equilibrium is established giving rise to a separation process. The
transport through the membrane takes place in the vapour phase
supported inside the pores and may be due to molecular diffusion
(as it occurs in most of the cases), to Knudsen diffusion (as it
occurs at low pressures), or to convection (Poiseuille flow). Most
frequently the actual driving force for mass transport inside the
pores is a partial pressure gradient along the pore itself, but a
total pressure gradient may also be obtained.
The research studies performed have shown that the operation may
be conducted through set-ups which may appear rather
different even if they are all ultimately interpreted based on the
same physical phenomena; I have considered direct contact
membrane distillation (DCMD), gas gap membrane distillation (GGMD),
sweeping gas membrane distillation (SGMD), vacuum membrane
distillation (VMD).
Indeed the permeate side of the membrane can be in contact with
another aqueous liquid; this configuration is referred to as
DCMD. The driving force for separation
may be sustained in different ways: i) by keeping a temperature
difference across the membrane, so that there are
different liquid vapor conditions at the menisci existing at
the entrance and at the exit of the pores, respectively; the water
flux thus will be directed from the warm side solution to the cold
side, if the temperature difference is sufficiently
large; ii) by keeping a concentration difference across
the membrane, e.g. by using in the permeate side an
extractant which is not volatile and depresses the activity
of water (e.g. salts, glycols, polyglycols).
The process has been studied both experimentally and
theoretically and a careful model description has been also
developed which accounts for the following transport resistances:
mass transport from the bulk liquid to the membranes (responsible
for the so called concentration polarization), heat transfer from
the bulk liquids to the membranes surfaces (responsible for the so
called temperature polarization), heat and mass transfer across the
membrane. It has been shown that in several cases of interest the
process is controlled by heat transfer within the liquid phases,
while in other situations it may be controlled by mass transfer
within the liquids and seldom by mass transfer within the membrane.
A proper non trivial criterion based on dimensionless numbers has
also been developed to compare the effects on the process rate of
resistances different in nature and in physical dimensions, as heat
and mass transfer resistances.
The energy efficiency of the process was also studied and
related to the process conditions and membrane properties
(thickness and porosity). The economical study indicated
that the process is attractive to produce pure water from
salt solutions when low temperature heat sources are available,
and/or when low potentiality is required. The process is
interesting for the low temperature concentration of fruit juices
either by using temperature differences or by using extractants in
the permeate side; the juices thus obtained may be very
concentrated (up to 60 ° Brix) and still retain most of the
original aroma compounds. When applied to fermentation broths, the
process shows also interesting potential applications in the
achievement of continuous fermentation through the removal of
ethanol.
The results are reported in the publications N. 31, 39, 41, 43,
44, 48, 49, 50, 52, 57, 58, 60, 61, 66.
When the permeate side of the membrane is in contact with a
stagnant layer of inert gas which is then in contact with the
liquid condensed on a refrigerated surface, we have the GGMD
configuration. The physical resistances controlling the process are
the same entering DCMC, with the addition of heat and mass transfer
in the gas gap. Also for the present configuration studies have
been performed similar to the ones outlined for the DCMD case. The
main advantage of this configuration is associated to a more
efficient use of energy since virtually only the latent heat is
provided by the liquid and the energy losses across the
membrane are rather minor. This is beneficial in comparison to DCMD
when no energy recovery is possible. A further advantage of the
GGMD configuration is represented by the possibility to control the
pressure of the gas gap to values below the atmospheric pressure,
thus enhancing significantly the process rate.
The results are reported in the publications N. 48, 50, 52, 60,
66.
When the permeate side of the membrane is in contact with a
stream of sweeping gas the configuration is referred to as
SGMD . In this case another process variable is
introduced due to the possibility of varying the gas flow rate and
thus the transfer resistances (for mass and heat transport) in the
gas phase. The process has been modelled both for flat and for
tubular membranes; the model simulations well represent the results
obtained in the experimental study performed. The process has
been developed also in co-operation with Snamprogetti S.p.A.,
Milan, and a patent has been obtained (N. 53). The feasibility of
the process to extract volatile contaminants from aqueous streams
was also established; the results are reported in the publications
N. 51, 53 (patent), 89, 91.
Finally, when the permeate side of the membrane is kept at
pressures below the condensation pressure of the permeating gases
the configuration is referred to as vacuum membrane distillation
(VMD) and this was first studied and introduced in the
literature by my group. This process has been thoroughly studied
since it appears interesting for its technical and
economical features. The main resistances are encountered by heat
and mass transfer in the liquid feed and by mass transfer in the
membrane. By using permeable membranes one usually operates at
conditions in which the membrane does not offer any significant
resistance and the process is controlled by the transport phenomena
in the liquid phase. First theoretically, by extending the
criterion to compare the effects of resistances of different
dimensions already used for DCMD, and then experimentally it was
demonstrated in particular that for streams containing VOC's, the
flux of water is essentially controlled by heat transfer only,
while the flux of the organic components are determined by both
heat and mass transfer in the liquid. The use of capillary
membranes is thus not recommended, in spite of the larger area per
unit volume, due to the high resistances encountered in the laminar
flow inside; the use of tubular membranes thus improves
significantly (by a factor 5 at least) the process performance,
as model calculations indicate and experiments confirm.
The mathematical model developed indicates also the
particular role of the downstream pressure in the case of aqueous
streams containing VOC's. At low pressures high fluxes are
observed, as expected, with permeating vapours essentially
containing water with little percent of VOC. With increasing the
downstream pressure, the total flux decreases essentially due
to a decrease in the water flux while the flux of organic remains
practically unaltered; this is so until the pressure value exceeds
the water vapour pressure at the operating temperature. Therefore
it is convenient to operate at sufficiently high pressures and not
at a high vacuum; we can thus obtain a vapour phase which exceeds
70-80% wt in the organic, from a liquid feed containing 2% of VOC.
This has been observed for a variety of aqueous mixtures containing
various VOC's as MTBE, ethanol, n-propyl alcohol, acetone, methyl
acetate. The economical analysis of the process indicates that in
comparison to pervaporation VMD is more convenient when
operated in turbulent flow and is also more convenient than air or
vapour stripping followed by adsorption on active carbon. The
theoretical and experimental analysis has been performed to find
out under what conditions the process is controlled either by heat
transfer resistances or by mass transfer resistance, developing
suitable dimensionless parameter to compare such different
resistances. The feasibility of the process to concentrate fruit
juices and musts has also been inspected.
The results are reported in the publications N. 56, 70, 78, 79,
83, 85, 89, 98, 99, 111, 115, 126, 130, 151.
1.2. Affinity membrane
separations.
This relatively recent separation technique has been studied in
my lab through an initial co-operation with Professor G. Belfort
(Rensslear Polytechnic Institute, Troy, NY), for the
selective separation of proteins from a protein solution. The
process is an alternative to the affinity chromatography procedure
typically followed. My studies started simply by considering the
purification from cell lysates of a class of fusion
proteins i.e. proteins which contain the protein of
interest linked (through a linker as factor Xa or an intein) to
another protein which can be easily recognised and adsorbed onto
the membrane surface. For the latter the maltose binding
protein (MBP) was considered. The desired fusion proteins can
be produced as endocellular proteins, by DNA modified E.
coli strains. The same affinity membrane, selective for MBP,
can be applied to all the different fusion proteins containing MBP
as one domain. The study proved first the process feasibility by
considering the following steps: i) cell growth and
harvesting; different strains codify for MBP fused with
-galactosidase or with rubredoxin or with intein-CBD; ii)
recovery of the protein from the cell lysate by using
traditional techniques or also the affinity membranes produced;
iii) surface modification of commercial membranes in order to
obtain membranes which selectively bind to the MBP domain; iv)
determination of the adsorption and desorption kinetics of the
fusion proteins over the modified membranes; v) determination
of the sorption isotherm of the protein over the membrane; vi)
obtain the protein desorption and study the efficiency; vii) model
simulation for the process rate.
The study pointed out that cellulose membranes, modified by
amylose chemically bound onto the surface, are selectively binding
the fusion protein considered even from the direct centrifuged cell
lysate. After a mild wash with water to detach proteins subject to
nonspecific week bonds only, the elution step revealed the presence
on the membrane of the fusion protein in rather pure conditions,
with an extremely high selectivity. The same membranes apply
equally well for all the three MBP fusion proteins inspected. A
simple but effective model simulation has been proposed, which
indicates that the sorption process is highly non linear.
The affinity membranes obtained have been used for several
fusion proteins containing the MBP domain, studying the sorption
isotherms, sorption and desorption kinetics and capacity.
The work has been extended to affinity membranes containing
selective ligands for lectins and immunoglobulins as IgG and IgM.
Affinity membranes for lectins obtained from Momordica
charantia seeds, and for peanuts agglutinin and Ricinus
communis agglutinin were prepared and studied following the
same lines indicated above.
Most recently this topic has been developed by considering
affinity membranes suitable for the purification of monoclonal
antibodies from the supernatant of industrial cell coltures. The
different affinity membranes considered have been obtained from
different preactivated supports made of regenerated cellulose or
polyethersulfone. Also different ligands have been used, beyond
Protein A, namely protein A mimetic synthetic ligands as A2P,
provided by Prometics ltd., and D-PAM, provided by Xeptagen SpS.,
sequences of 6 peptides provided by professor. R.G. Carbonell of
NCSU-Raleigh, NC. Different spacers between membrane surface and
ligand have also been inspected, considering among others thyole
and azido compound. The main target proteins considered are h-IgG
and h-IgM. The membranes prepared have been characterized with pure
protein solutions both in batch and dynamic mode, studying also the
variation of adsorption capacity, sorption and elution kinetics
versus feed flow rate and membrane lifetime. The membranes have
then been used with complex mixtures as industrial supernatants of
cell coltures as well as different sera. In parallel to the
experimental analysis performed, the monoclonal antibody separation
through affinity membranes has been simulated through a model
implemented in ASPEN ustom Modeller and the model developed is
appropriate to describe more than satisfactorily the breackthrough
curves experimentally observed at various feed flow rates and
concentrations, both for pure protein solutions as well as for
supernatant of cell coltures. In general, the use of affinity
membranes shows advantages since they are much faster than
processes based on traditional beads, and do not show any problems
associated to column packing or high pressure drops.
The results are partially reported in the publications N. 92,
93, 101, 112, 119, 122, 123 (patent), 124, 127, 129, 136, 145, 150,
152, 153, 157, 164, 166, 170, 172.
1.3. Gas separations.
Gas separations can be obtained through polymeric membranes
often in the glassy phase. The separation factor is determined by
the combined effect of solubility and of diffusivity in the
membrane. Both properties are usually measured from pure gases and
very seldom directly from mixtures of gases, which are in fact used
in practical applications. Most often the separation factor
expected from given mixtures is simply estimated from pure gas
data. It is vice versa known that in some cases the expectations
based on pure gas data definitely fail even qualitatively, as it is
the case of CH 4 / n-C 4H 10 in
poly(1-trimethylsilyl-1-propyne) (PTMSP). Such
unexpected behaviours are largely due to the effects of the
solubility of different components into the solid polymer. The
problem of the determination of the solubility of gases and vapours
in glassy polymers has been considered, both experimentally and
theoretically; it must be noticed that in a glassy phase the
traditional true thermodynamic equilibrium conditions
do not apply since the glass is a nonequilibrium phase.
Experimental results have been obtained for the solubility, or
rather pseudo-solubility, in glassy PTMSP of different alcohols and
n-alkanes, under different conditions. It has been shown that the
classical dual mode model does not apply even qualitatively in
order to describe the solubility of alcohols since the isotherm is
s-shaped with a very small solubility coefficient at low pressures.
It has been shown, however, that when the isotherms are represented
in terms of penetrant chemical potential, in place of
penetrant pressure, versus penetrants mass fraction, the behaviour
observed for the n-alkanes is qualitatively similar to that
observed for the alcohols. Based on this hint, and on a lattice
fluid theory, a model has been developed for the Gibbs free energy
of a nonequilibrium glassy mixture (NELF model). That model
rests upon the use of the polymer partial density as a proper
measure of the out-of-equilibrium frozen into the glass; that value
is governed by the bulk rheology of the glassy membrane. The
thermodynamic model developed in publications N. 96 and 102, proves
to be entirely predictive; it is simply based on the
volumetric properties of the pure polymers and the pure penetrants,
and is in excellent good agreement with the
experimental data available for binary mixtures.
The model has been also extended to the case of mixtures of
penetrants and of polymers and is able to
quantitatively explain the observed behaviour for the case
of CO 2/C 2H 4 mixtures in glassy PMMA (publ. N. 104). The
model is also able to account for the different isotherms observed
in PTMSP by alcohols and n-alkanes. The success of this tool
motivated the invitation received to deliver the
lecture presented at the 1997 Gordon Research Conference on
Membranes (Andover, NH, Aug 3-8, 1997).
The approach has also been extended to swelling penetrants for
which a simple correlation method has been developed based
virtually on a single solubility data point.
The model represents an important and promising tool to predict
the expected separation behaviour from mixtures of gases and, on
the other side, to select the best glassy polymer for given gas
separations. It was also shown that the general non-equilibrium
thermodynamic analysis allows to extend this approach for the
solubility in glassy polymers to different models other than the
lattice fluid model initially considered. Indeed application of the
method also to SAFT and PHSC models, suitably modified for the
non-equilibrium approach, proved equally satisfactory. A rather
broad series of polymer penetrants pairs and of polymeric
blends has been used for the comparison with model
calculations.
Most recently it has been shown that the model accounts also for
the experimentally known, but as yet unexplained, dependence of the
infinite dilution solubility coefficient in glassy polymers on
penetrant critical temperature. In addition, application of the
model to composite matrices formed by a high free volume
glassy polymer and solid nanoparticles has shown that the model can
be used to predictin a very reliable way the solubility isotherms
of several different solutes once the solubility isotherm of one
single test vapor is known. The fractional free volume of the
polymer matrix, which is calculated from the model also allows to
calculate the proper dependence of penetrant diffusivity on the
filler loading in the mixed matrix, and to describe the unexpected
increase of solubility, diffusivity and permeability which is
experimentally in polymers loaded with fumed silica
nanoparticles.
The permeability of gaseous penetrants in glassy polymeric membranes is presently under investigation, by developing a rigorous theoretical model able to represent well the permeability dependence on upstream pressure, including also the non-monotonous trend commonly known as "plasticization effect". The model proves also suitable for the development of a predictive procedure for the premeability of gases in glassy matrices. Particularly interesting is also the possibility to describe well the permeability of gas mixtures in glassy polymeric membranes.
1.4. Metal membranes for
hydrogen separation.
In recent years, thanks also to a relevant financial support, I
have started a project focused on the study of membranes and
membrane modules for the separation of hydrogen from the streams
obtained from reforming reactors, at operating conditions around
400 °C to 600 °C, at pressures below 15 bars. The experimental
equipment was designed anew, setup and thoroughly tested for
safety. Different metal membranes have been tested based on Pd/Ag
alloys, which were made available by collaborating institutions and
also produced in my lab via electroless plating. The membrane
properties were tested by varying the pretreatments, temperature of
operation and feed gas composition. Remarkably, for some membranes
which are endowed with very interesting selectivity, a relevant
effect of concentration polarization in the gas phase was observed
and documented in detail. The CFD simulation of the membrane
module, which has been performed in parallel, helped obtaining
proper modifications of the membrane module with better
fluid-dynamics and overall membrane behavior. At the same time the
same simulation also confirmed the presence of gradients of
hydrogen concentration in the gas phase when the membrane
permeability used is that of the membrane for which the experiments
indicated hydrogen fluxes sensitive to the feed flow rate. The
activity so far lasted less than three years and publication of
data was possible only for a part of the results obtained (see ref.
173)
1.5. Reverse osmosis.
Reverse osmosis is a rather well established operation for
desalination purposes. However its potentials in the treatment of
process streams deriving from chemical processes have not yet been
investigated in sufficient detail. The increasing concern for water
reuse and the stringent requirements for water discharge make this
application interesting. The problem has been studied at the pilot
plant level, by considering two different process waters, one
deriving from a Montedipe plant in Mantua (IT), the other deriving
from a process stream from a Ciba-Geigy plant in Pontecchio
(Bologna, IT). In both cases the aqueous streams contained also a
complex mixture of organic components with a broad molecular weight
spectrum. The feasibility of the process has been established and
the design variables optimised. The work has lead to the plant
design and economical evaluations. The results have been partially
published in ref. N. 67 and partially are held as proprietary
results.
1.6. Pervaporation.
The pervaporation (PV) process has been studied by considering
water/ethanol mixtures and also by examining the separation of
organic/organic mixtures. In the first case the applicability of
PTMSP membranes was considered, in view of the high permeability of
that membrane versus the alcohol. The main reference application is
the set-up of a continuous fermentation with a continuous
removal of ethanol from the broth. The effects of ethanol
concentration were inspected, as well as the ageing effects
observes in the membrane when contacted with liquid feeds. The
experimental result indicated that there is an appreciable
influence of the membrane thickness, which cannot be scaled
according to the rules governing Fickian diffusion (ref. 69,
80).
The potential application of PV to the separation of
organic/organic mixtures has been examined by using a
modified PPO membrane containing hydrohyl groups, (Eniricerche), in
order to render it suitable for the separation of MTBE from
methanol. The process gave rise to interesting separation factors
ranging from about 7 to over 20 depending upon the concentration
range of the feed mixture. It has been observed that the flux of
MBTE is non monotonous with increasing the MTBE content of the
mixture but undergoes a minimum. The flux of methanol, vice-versa,
was found to be monotonous and linearly decreasing with
increasing the MTBE mass fraction in the feed. The permeability of
either component was calculated by extending to the case of PV the
permeability concept introduced for gas separations, based on the
thermodynamic properties of MTBE/methanol mixtures. The values and
the trends observed were consistent with the fact that methanol is
a swelling agent for the modified PPO membrane (ref. 88).
2. Diffusion
in polymers.
This subject is partially related to the previous one, for the
cases in which the determination of the diffusion coefficient is
important to calculate the permeability and/or the separation
factors. In several other cases the main motivation is
different and resides in specific applications as packaging,
coating, desolventisation of polymers, stress cracking of polymer
products, drug delivery systems.
2.1. Fickian diffusion and
chemical post-treatment.
The experimental determination of the diffusion coefficient of
various penetrants in PTMSP films was obtained through a specific
transient gravimetric technique especially designed to be
compatible also with the fast sorption rates observed for some
penetrants in that matrix. A series of alkyl alcohols and of
alkanes was considered which show a very interesting unusual
behaviour. The n-alkanes presented a concentration dependance
for the diffusion coefficient endowed with a rather flat maximum;
vice versa, with increasing the penetrant concentration, the
diffusivity of alcohols showed initially a rather pronounced
minimum followed by a subsequent maximum. It has been shown that
such different behaviours in the same matrix are associated to the
thermodynamic factor for diffusion (i.e. the partial derivative of
the penetrant chemical potential with respect to the log of the
penetrant mass fraction). The latter quantity was experimentally
determined through the solubility isotherm which has a rather
different trend for alkanes and for alcohols. The mobility
coefficient, i.e. the proportionality constant between the
mass flux and the chemical potential gradient, can thus be
calculated as the ratio between diffusivity and the
thermodynamic factor. Remarkably, the mobility coefficient shows
indeed exactly the same monotonous and parallel trend in all the
cases inspected, thus indicating that the major differences
observed for the diffusion coefficients are due to the
thermodynamic factor alone. The above behaviour was also shown to
be consistent with the high free volume present in the PTMSP matrix
and, in addition, indicated a simple way to correlate if not to
predict the diffusion coefficient of different penetrants in PTMSP.
The results have been partially published in refs. N. 95, 97,103,
105.
The effects of diffusion processes in the thermal post-treatment
of poly(butylen terephthalate) (post polycondensation) were also
studied both experimentally and theoretically. The major chemical
reactions in thermal post-polycondensation were considered and the
effect of the diffusion towards the external surfaces of the low
molecular species involved (1,4-butanediol, terephthalic acid and
water) were studied. In comparison with the experimental data
obtained, the model was thus able to account for the increase in
the polymer molecular weight versus post-treatment time at any
position inside the polymer matrix. Thus it gave a correct guidance
for the post-polycondensation treatment of PBT products. The
results have been published in ref. N. 32, 35, 46.
2.2. Non-Fickian
diffusion.
The different non-Fickian mass transport behaviours observed in
solid polymers have been extensively studied in the past by G.C.
Sarti, both theoretically and experimentally. From an experimental
point of view the mass transport kinetics of liquid n-alkanes in
glassy polystyrene has been studied at different temperatures; the
mechanical properties of the samples were well characterised with
regard to the critical stress for craze growth and propagation. In
all the cases inspected the presence of a discontinuity front was
always observed, marking the separation between penetrated and
unpenetrated glassy matrix. The front position changes in time
according to a power law (t n) with an exponent n varying between
0.5 (Fickian like ) to unity (Case II) behaviour. In the high
temperature range, still below the glass transition temperature, an
anomalous behaviour was observed very close to Fickian like
behaviour; as the temperature decreases the exponent n increases
towards the Case II behaviour. The mass transport process results
from the combined effects of the diffusion resistance encountered
across the penetrated region, and the swelling resistance offered
by the matrix around the swelling front. The latter factor would
give rise to a constant penetration rate per se (i.e. n=1),
while the diffusive resistance per se would give rise to an
exponent equal to 0.5. The kinetics of the advancing front was
shown to be nicely correlated to the craze propagation kinetics.
Analogous studies have been performed in PMMA by using methanol,
ethanol and propanol as the penetrants. By considering planar
geometries, both weight uptake and swelling measurements were
performed, monitoring the position of the internal swelling front
(separating the penetrated from the unpenetrated region) as well as
of the external sample surfaces. The fast swelling agent, methanol,
gives rise to an anomalous diffusion behaviour very close to a
Fickian like response; in this case the process is controlled
almost completely by the diffusion resistance. For ethanol
and propanol, viceversa, the swelling resistance is controlling,
for the usual sample thickness considered (around 1mm), thus giving
rise to a CaseII kinetics i.e. to a constant sorption rate.
In all cases the existance of an internal moving front indicates
the presence of a shock concentration wave travelling towards the
sample midplane, at a velocity decreasing in time for the case of
methanol and at constant velocity for the higher alcohols.
The effect of the pre-elongation treatments was also studied by
prestretching the samples to different elongation values and then
freezing in the elongation prior to the sorption process. Higher
pre-elongations result in higher sorption rates, as otherwise
expected; moreover, with increasing the elongation frozen in the
glassy matrix, a higher importance of the swelling resistance was
also observed giving rise to behaviors closer to CaseII the higher
the elongation ratio considered.
These results have been discussed in publications N. 18, 22, 26,
34, 40, 87.
The mentioned different non-Fickian behaviours have been
modelled according to different model approximations which are
hereafter schematically listed and discussed.
