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Laboratory Course
Functional Materials
Membranes M202
Aim: It is the aim of this experiment to determine the sorption-
and desorption-behaviour of atechnical relevant material (Kapton)
by thermogravimetry (TGA).
Table of Contents
1
Introduction......................................................................................................2
2
Basics.................................................................................................................22.1
Aim of this
experiment.......................................................................................................22.2
Polymers and
Polyimides....................................................................................................22.3
Transport
variables.............................................................................................................32.4
Rate limiting
steps...............................................................................................................5
3 Proceeding
steps................................................................................................63.1
Clean
Furnace.....................................................................................................................63.2
Calibration
..........................................................................................................................63.3
Preparing the samples
.......................................................................................................63.4
Measurements......................................................................................................................63.5
Export
Data.........................................................................................................................7
4 Evaluation of
results.........................................................................................74.1
Converting
Data..................................................................................................................74.2
Plotting
Data........................................................................................................................74.3
Calculating the diffusion
coefficient..................................................................................74.4
Comparing the
samples......................................................................................................75
Bibliography......................................................................................................86
Appendix............................................................................................................96.1
Operating instructions for the
software............................................................................96.2
Diffusion coefficients for
Kapton.....................................................................................13
File: /home/hg/Praktikum/Membranes/membranes.sxw, Stand
17/03/2004
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M202: Membranes
1 IntroductionPolymer membranes are of great technical interest.
They play an important role for gasseparation, especially for
oxygen enrichment in combustion processes or for medical use,
e.g.artificial lung, for nitrogen enrichment in petrochemical
processing and in food packing. Themost important physical
constants for gas separation are the permeability P, which is
theproduct of gas flux and membrane thickness divided by pressure
difference across themembrane and permselectivity α=PA /PB, where A
is the more permeable gas and B is the lesspermeable gas. These
properties are mostly dependent on the polymer structure. Normally
apolymer with high permeability has low selectivity. To improve the
possibilities of polymermembranes polymers with high permeability
and high selectivity are needed. Thereforeseveral researches on gas
separation membranes were done in the last years.
Permeability is a function of diffusion and solubility: SDP ⋅= .
Hence, diffusion is animportant physical quantity for the
functionality of membranes. Therefore in this labcoursethe
diffusion coefficient of water in the polyimide Kapton has to be
determined in adesorption experiment. The desorption will be
measured by the change in weight by TGA(Thermogravimetric
Analysis). Kapton will be used, because it is of great technical
relevanceand suitable for a labcourse due to a large measurable
effect and short time constants.
2 Basics
2.1 Aim of this experimentIn this labcourse the water sorption
of a membrane will be determined. Kapton will be used,because it is
well known, it absorbs remarkable amounts of water and the
experiment takesonly a few minutes at room temperature.
2.2 Polymers and PolyimidesA polymer is defined as a substance,
which is build up of repeating units of one or more kindsof atoms
or atom groups. Small molecules can be connected by chemical bonds
to a longmolecule chain (macromolecule). Many monomer molecules are
connected to a polymer.Polymers can be completely unordered
(amorphous), partly ordered (semicrystalline) oralmost ordered
(crystalline). Polymers can be classified in thermoplastics,
elastomers andthermosets.Most of the properties are determined by
interactions between the chains, where theinteraction energies are
relatively low.Most polyimides are polycondensates of tetra
carboxylic acids and diamines. Furthersynthesis methods are
polymerization of maleate acid anhydride and diamine
andpolyaddition by agglomeration of an additional diamine on bis
maleate imide. They can bethermoplastics or thermosets. A
distinction is difficult, because often polyimides decomposebefore
they reach their glasstransition temperature. Typical properties
are high glass transitiontemperature, chemical resistance and high
burn resistance.The polyimide Kapton is typically used in the
electro technology e.g. for isolating andpackaging ICs.As these
materials are used in technical surrounding, humidity changes and
consequently, thewater contents in the polymer is changing. Because
many properties are strongly dependent
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M202: Membranes
on solvent content, it is of major importance to study the
sorption- and desorption-behaviourof water in
Kapton.Thermogravimetry is a technique which measures the mass
change of a sample with a balanceas a function of temperature in a
well defined atmosphere in the scanning mode at constantheating
rate or as a function of time in the isothermal mode. Thermal
changes accompanyingmass change, such as decomposition,
sublimation, reduction, oxidation, desorption,absorption and
vaporization, can be detected and quantified by TGA.
2.3 Transport variablesThe simplest approach to diffusion is
according to Fick’s law, where diffusion, in particular adiffusion
current J, occurs in order to reduce a given concentration
gradient:
∂∂−=xcDJ . (1)
(See also M 304 (precipitation and diffusion) and M 603
(Multiple phase diffusion)). In thepresent experiment we have to
take into account that diffusion might be concentrationdependent
and that chemical interaction between the diffusing element and the
matrix mightoccur. The latter is generally taken into account in
the thermodynamic factor.First, we will briefly repeat some basic
thermodynamic quantities.Activity a, being the ratio of the
pressure above a material pi to a given reference pressure pi0
0i
i
ppa = (2)
The chemical potential is given by aRT ln0 += µµ , with a as the
activity.
The simplest case for a binary system is that no interaction
occurs and thus the activity isequal to the concentration. Next,
the activity can be at least proportional to the
concentration(Henry’s law). See Fig. 1
Fig. 1: Henry’s and Raoult’s law as extreme cases of the
relationbetween activity and concentration of one component in a
binarysystem.
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For penetration of solvents into polymers several cases have to
be distinguished depending onthe concentration and temperature (see
Fig. 2).
Fig. 2: Temperature penetrant activity diagram of
non-Fickiantransport phenomena in polymers.
Here we consider only concentration independent diffusion.The
transport of a homogenous polymer membrane follows a
solution-diffusion-mechanism.
The rate v of the diffusing molecule is the product of the
chemical potential
∂∂
xµ and the
mobility m :
∂∂⋅−=
xmv µ . (3)
The number of particles which diffuse per time unit through the
plane unit is termed currentdensity J. It is the product of rate v
and concentration c of the particles:
∂∂−==
xcmvcJ µ . (4)
The thermodynamic diffusion coefficient is given by RTmDT = ,
with R as the gas constantand T as the temperature. The chemical
potential is given by aRT ln0 += µµ , with a as theactivity. This
modifies equation (4) to:
∂∂
∂∂−=
xc
caDJ T ln
ln. (5)
Comparing this equation with the first Fick law results in a
relation between the empiricaldiffusion coefficient given by eq.
(1) and the tracer diffusion coefficient times thethermodynamic
factor.
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∂∂=
caDD T ln
ln(6)
Ideal systems show no interactions with the polymer matrix,
hence the thermodynamic factoris unity. For ideal systems the
activity is equal to the concentration. Water in Kapton does
notbehave ideal (see Fig. 3a)-c) in the Appendix), but often it is
frequently approximated asideal. Organic vapors and fluids are
strongly interacting non-ideal systems. For non-idealsystems the
dependence on concentration has to be taken into account. This is
formallydescribed by the dual-sorption-model. The
dual-sorption-model assumes additionally asolution mechanism, which
adsorbs solved molecules on inner surfaces of pores. Within
smallpressure intervals linearity in c(p) with an effective
solubility S can be assumed ( pSc ⋅= ).With this condition the
first Fick law modifies to:
Mdpp
PxpDSJ 21
−≡
∂∂−= . (7)
In this equation the diffusion coefficient was replaced by the
quotient of pressure decreaseand membrane thickness dM. SDP ⋅= is
the permeability. The permeability P is the masswhich diffuses
through the membrane at standard temperature and pressure (STP)
multipliedwith the membrane thickness. In the literature often the
unit Barrer (Ba) is used. As the pressure dependence of the
sorption was not taken into account, the here definedpermeability
is an effective variable.
The ratio αxy=PX /PY of two different substances in one membrane
is termed permselectivity.The higher the value of α the more
selective the membrane is for the substance X. Thepermselectivity
can be split into diffusion selectivity and solution
selectivity
Y
X
Y
Xxy S
SDDa ⋅= . (8)
In ideal systems the solubilities are very small. Then α is
mainly determined by the diffusionselectivity. The most important
point in “engineering” membranes is to obtain high permeabilities
and (!)high selectivities at the same time. Normally high values of
P exclude high values of α. Thisproblem can be solved with well
tailored ‘chain stiffness’. This is the main point in recentpolymer
membrane research.
2.4 Rate limiting stepsFor the reaction of a solvent with the
polymer, e.g. the in- or out-diffusion, there must be arate
limiting step. This can either be the transfer through the
interface air / membrane or thetransport in the membrane via
diffusion of the molecules. If the interface reaction is the
ratelimiting step, usually the concentration in the polymer
increases linearly with time. On theother hand, if diffusion is
rate limiting, the concentration increases according to the
parabolicgrowth law, i.e. with the square root of time. Details can
be found in the book of Crank,keyword “outgassing of a thin plate”.
Concerning the temperature dependence of concentration changes,
they are usually Arrhenian–like. However, depending on the rate
limiting process, the corresponding activation energycan be either
attributed to the activation energy of diffusion or to reaction
processes at theinterface.
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3 Proceeding stepsSeveral samples should be saturated with H2O
vapor. These samples should be desorbed inthe TGA. The desorption
will be measured by a change in weight. For the saturation there
are given sample holders, small petri dishes, large petri dishes
andheating plates for each sample and the Kapton foil samples.
3.1 Clean FurnaceFirst the furnace has to be cleaned by heating
it to above 600 °C.
3.2 Calibration Before the measurements the TGA has to be
calibrated with respect to weight and temperaturescale. Weight
calibration is usually done by setting the empty sample pan to zero
and thenputting a known mass onto the sample pan and giving weight
into to the software. Here theweight calibration has to be done for
each sample holder and should be saved with
differentnames.Temperature calibration is done by putting a
magnetic sample onto the sample pan, putting apermanent magnet
around and heating the magnetic sample up to the Curie temperature,
i.e.measuring the magnetic phase transition. (Detailed steps for
software in the Appendix).
3.3 Preparing the samples After the calibration steps the
samples should be prepared as follows:
• Measure the weight of the samples with a balance. Masses
around 1 mg are desirable.• Put the samples in the small petri
dishes. Fold the samples, if they are too large. • Put the small
petri dishes in the large petri dishes.• Fill the large bottom of
the large petri dish with H2O.• Heat the petri dishes on the plates
at given temperatures measured with a thermocouple.• On the basis
of the temperature there will be defined water gas pressure. So the
sampleswill be saturated with a defined H2O concentration.
3.4 Measurements
3.4.1 Baseline The first measurement is the baseline, where the
weight change should be measured atconstant temperature for a given
time. The baseline shows the behaviour of the empty sampleholder.
(Detailed steps in the Appendix)
3.4.2 SamplesAll the samples should be measured for the same
time with automatic baseline subtractionunder the same conditions
in vacuum. This is easier than correcting the data after
theexperiment for baseline influences. (Detailed steps for software
in the Appendix).
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3.5 Export DataIn order to facilitate evaluation of the date,
these should be converted to ASCII-Format andstored on a disk.
(Detailed steps for software in the Appendix).
4 Evaluation of results
4.1 Converting DataConvert the Data in mass lost versus t .
4.2 Plotting Data
Replot all the data in mass lost
∞mmt versus t in one diagram.
4.3 Calculating the diffusion coefficientCalculate the diffusion
coefficient from the above data/plot. Give reasons for the
selection ofdata, i.e. why did you use only part of the data for
fitting?
4.4 Comparing the samplesCompare the results of the different
measurements and discuss these with respect topreparation
conditions.
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5 BibliographyHatakeyama, T. and Zhenhai, L.: Handbook of
Thermal Analysis, John Wiley & Sons Ltd.,New York, 1998.Atkins,
P.W.: Physical Chemistry, 6. Ed., Oxford University Press,
1998.Neogi, P.: Diffusion in Polymers, Dekker, New York,
1996.Crank, J.: The mathematics of diffusion, Oxford University
Press, Oxford, 1975.Martienssen, W., Beke, D.L.: Diffusion in
Semiconductors and Non-Metallic Solids,Landolt-Börnstein, New
Series Bd. IIIB; Kap. 9 Faupel, F. and Kroll, G.: Diffusion in
glassyand semicrystalline polymers, Springer, Berlin, 1999.Mulder,
M.: Basic Principles of Membrane Technology, Kluwer, Dordrecht,
1996.Paul, D.R. and Yampolskii, Y.P.: Polymeric Gas Separation
Membranes, CRC Press BocaRaton, 1994.Ghosh, M.K. and Mittal, M.K.,
Polyimides: Fundamentals and Applications, Dekker, NewYork,
1996.Lecture “Polymers” of Prof. Faupel, University of KielLecture
“Solid State Physics” of Prof. Faupel, University of Kiel
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6 Appendix
6.1 Operating instructions for the software
6.1.1 Clean furnace
Click the button in order to start the cleaning of the furnace.
You have to wait until
it is finished.
6.1.2 CalibrationWith “View-Calibrate” the last calibration has
to be invoiced?. (The subwindow “MethodEditor” has to be
active.)
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With “Restore-All” the last calibration has to be restored:
After restoring, the calibration has to be saved with “Safe and
Apply”.Now the calibration could be started. In this lab course
only room temperature experimentsare done, so only the “Weight” has
to be calibrated. The hole steps are explained by thesoftware. The
weight calibration has to be done for each sample holder and saved
withdifferent names.
6.1.3 MeasurementsThe subwindow “Method Editor” has to be
active.
6.1.3.1 Basel ineOpen the baseline method with “File-Open
Method”. It could be found in the
file“Pyris\Praktikum\Baseline”.Fill in the “Method Editor” the
missing data.
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Close the furnace with and calibrate zero weight with clicking
.
Open furnace with and put the baseline reference sample in the
sample holder.
Close furnace and calibrate sample weight with clicking .
Start the measurement with .
6. 1.3.2 SamplesFor each sample:Calibrate zero weight before
inserting the sample.Insert the sample prepared under the
conditions described in the previous chapters. Use thesame
measurement parameters as for the baseline measurement.Calibrate
sample weight.Mark in “Initial State” “Use Baseline Substraction”
with a cross.
Turn on the pump.Slightly open the valve after 1 min. Pumping
should remove moisture from the furnace whilekeeping (not much less
than) atmospheric pressure.Turn off the pump.
Stop the measurement with .
(The running measurement can be seen in the subwindow ”Data
analysis”.)
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6.1.4 Export DataThe subwindow, from which the data should be
exported has to be active.Open with “View-Method Used” the “Method
Properties”.
Create the data file with “Create” and mark “Include Data
Points” with a cross. The ASCII-File has the filename of the
measurement with the ending .txt.
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6.2 Diffusion coefficients for Kapton
Fig. 3a: Unmodified and hygrothermally aged Kapton
polyimide(PMDA-ODA). Average H2O diffusion coefficient
fromsorption/desorption measurements vs. H2O concentration at 30°C.
1:unmodified 0.3 mm film (birefringence 0.0972), long-time method,
2:hygrothermally aged 2 mm film, 3: unmodified 2 mm
film(birefringence 0.0177), half-time method, see [86Yan].
Fig 3b: Kapton polyimide (PMDA-ODA, film thickness: 0.3
mm).Average H2O diffusion coefficient from
sorption/desorptionmeasurements (long-time approximation) vs. H2O
concentration at30°C, 45°C and 60°C see [85Yan].
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Fig. 3c: Kapton polyimide (PMDA-ODA). Average H2O
diffusioncoefficient from sorption/desorption measurement vs.
H2Oconcentration at 30°C. 1: 0.3 mm film (birefringence 0.0972),
long-time method, 2: 2mm film (birefringence 0.0177), half-time
method,3: 2 mm film, long-time method.
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