Laboratory Course
Functional Materials
Membranes
M202
Aim: It is the aim of this experiment to determine the sorption- and desorption-behaviour of a
technical relevant material (Kapton ) by thermogravimetry (TGA).
Table of Contents
1 Introduction......................................................................................................2
2 Basics.................................................................................................................2
2.1 Aim of this experiment.......................................................................................................2
2.2 Polymers and Polyimides....................................................................................................2
2.3 Transport variables.............................................................................................................3
2.4 Rate limiting steps...............................................................................................................5
3 Proceeding steps................................................................................................6
3.1 Clean Furnace.....................................................................................................................6
3.2 Calibration ..........................................................................................................................6
3.3 Preparing the samples .......................................................................................................6
3.4 Measurements......................................................................................................................6
3.5 Export Data.........................................................................................................................7
4 Evaluation of results.........................................................................................7
4.1 Converting Data..................................................................................................................7
4.2 Plotting Data........................................................................................................................7
4.3 Calculating the diffusion coefficient..................................................................................7
4.4 Comparing the samples......................................................................................................7
5 Bibliography......................................................................................................8
6 Appendix............................................................................................................9
6.1 Operating instructions for the software............................................................................9
6.2 Diffusion coefficients for Kapton.....................................................................................13
File: /home/hg/Praktikum/Membranes/membranes.sxw, Stand 17/03/2004
M202: Membranes
1 Introduction
Polymer membranes are of great technical interest. They play an important role for gas
separation, 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. The
most important physical constants for gas separation are the permeability P, which is the
product of gas flux and membrane thickness divided by pressure difference across the
membrane and permselectivity α =PA /PB, where A is the more permeable gas and B is the less
permeable gas. These properties are mostly dependent on the polymer structure. Normally a
polymer with high permeability has low selectivity. To improve the possibilities of polymer
membranes polymers with high permeability and high selectivity are needed. Therefore
several researches on gas separation membranes were done in the last years.
Permeability is a function of diffusion and solubility: P = D ⋅ S . Hence, diffusion is an
important physical quantity for the functionality of membranes. Therefore in this labcourse
the diffusion coefficient of water in the polyimide Kapton has to be determined in a
desorption 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 relevance
and suitable for a labcourse due to a large measurable effect and short time constants.
2 Basics
2.1 Aim of this experiment
In 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 takes
only a few minutes at room temperature.
2.2 Polymers and Polyimides
A polymer is defined as a substance, which is build up of repeating units of one or more kinds
of atoms or atom groups. Small molecules can be connected by chemical bonds to a long
molecule chain (macromolecule). Many monomer molecules are connected to a polymer.
Polymers can be completely unordered (amorphous), partly ordered (semicrystalline) or
almost ordered (crystalline). Polymers can be classified in thermoplastics, elastomers and
thermosets.
Most of the properties are determined by interactions between the chains, where the
interaction energies are relatively low.
Most polyimides are polycondensates of tetra carboxylic acids and diamines. Further
synthesis methods are polymerization of maleate acid anhydride and diamine and
polyaddition by agglomeration of an additional diamine on bis maleate imide. They can be
thermoplastics or thermosets. A distinction is difficult, because often polyimides decompose
before they reach their glasstransition temperature. Typical properties are high glass transition
temperature, chemical resistance and high burn resistance.
The polyimide Kapton is typically used in the electro technology e.g. for isolating and
packaging ICs.
As these materials are used in technical surrounding, humidity changes and consequently, the
water 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-behaviour
of water in Kapton .
Thermogravimetry is a technique which measures the mass change of a sample with a balance
as a function of temperature in a well defined atmosphere in the scanning mode at constant
heating rate or as a function of time in the isothermal mode. Thermal changes accompanying
mass change, such as decomposition, sublimation, reduction, oxidation, desorption,
absorption and vaporization, can be detected and quantified by TGA.
2.3 Transport variables
The simplest approach to diffusion is according to Fick’s law, where diffusion, in particular a
diffusion current J, occurs in order to reduce a given concentration gradient:
 ∂c 
J = − D  .
(1)
 ∂x 
(See also M 304 (precipitation and diffusion) and M 603 (Multiple phase diffusion)). In the
present experiment we have to take into account that diffusion might be concentration
dependent and that chemical interaction between the diffusing element and the matrix might
occur. 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
a=
pi
pi 0
(2)
The chemical potential is given by µ = µ 0 + RT ln a , with a as the activity.
The simplest case for a binary system is that no interaction occurs and thus the activity is
equal 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 relation
between activity and concentration of one component in a binary
system.
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For penetration of solvents into polymers several cases have to be distinguished depending on
the concentration and temperature (see Fig. 2).
Fig. 2: Temperature penetrant activity diagram of non-Fickian
transport phenomena in polymers.
Here we consider only concentration independent diffusion.
The transport of a homogenous polymer membrane follows a solution-diffusion-mechanism.
 ∂µ 

 ∂x 
The rate v of the diffusing molecule is the product of the chemical potential 
and the
mobility m :
 ∂µ 
v = −m ⋅ 
(3)
.
 ∂x 
The number of particles which diffuse per time unit through the plane unit is termed current
density J. It is the product of rate v and concentration c of the particles:
 ∂µ 
J = vc = −mc  .
(4)
 ∂x 
The thermodynamic diffusion coefficient is given by DT = mRT , with R as the gas constant
and T as the temperature. The chemical potential is given by µ = µ 0 + RT ln a , with a as the
activity. This modifies equation (4) to:
 ∂ ln a  ∂c 
J = − DT 
  .
(5)
 ∂ ln c  ∂x 
Comparing this equation with the first Fick law results in a relation between the empirical
diffusion coefficient given by eq. (1) and the tracer diffusion coefficient times the
thermodynamic factor.
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 ∂ ln a 
D = DT 
(6)

 ∂ ln c 
Ideal systems show no interactions with the polymer matrix, hence the thermodynamic factor
is unity. For ideal systems the activity is equal to the concentration. Water in Kapton does not
behave ideal (see Fig. 3a)-c) in the Appendix), but often it is frequently approximated as
ideal. Organic vapors and fluids are strongly interacting non-ideal systems. For non-ideal
systems the dependence on concentration has to be taken into account. This is formally
described by the dual-sorption-model. The dual-sorption-model assumes additionally a
solution mechanism, which adsorbs solved molecules on inner surfaces of pores. Within small
pressure intervals linearity in c(p) with an effective solubility S can be assumed ( c = S ⋅ p ).
With this condition the first Fick law modifies to:
p − p2
 ∂p 
J = − DS   ≡ P 1
.
(7)
dM
 ∂x 
In this equation the diffusion coefficient was replaced by the quotient of pressure decrease
and membrane thickness dM. P = D ⋅ S is the permeability. The permeability P is the mass
which diffuses through the membrane at standard temperature and pressure (STP) multiplied
with 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 defined
permeability is an effective variable.
The ratio α xy=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. The
permselectivity can be split into diffusion selectivity and solution selectivity
DX SX
⋅
.
(8)
DY SY
In ideal systems the solubilities are very small. Then α is mainly determined by the diffusion
selectivity.
a xy =
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 . This
problem can be solved with well tailored ‘chain stiffness’. This is the main point in recent
polymer membrane research.
2.4 Rate limiting steps
For the reaction of a solvent with the polymer, e.g. the in- or out-diffusion, there must be a
rate limiting step. This can either be the transfer through the interface air / membrane or the
transport in the membrane via diffusion of the molecules. If the interface reaction is the rate
limiting step, usually the concentration in the polymer increases linearly with time. On the
other hand, if diffusion is rate limiting, the concentration increases according to the parabolic
growth 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 energy
can be either attributed to the activation energy of diffusion or to reaction processes at the
interface.
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3 Proceeding steps
Several samples should be saturated with H2O vapor. These samples should be desorbed in
the 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 and
heating plates for each sample and the Kapton foil samples.
3.1 Clean Furnace
First 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 temperature
scale. Weight calibration is usually done by setting the empty sample pan to zero and then
putting a known mass onto the sample pan and giving weight into to the software. Here the
weight calibration has to be done for each sample holder and should be saved with different
names.
Temperature calibration is done by putting a magnetic sample onto the sample pan, putting a
permanent 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 samples
will 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 at
constant temperature for a given time. The baseline shows the behaviour of the empty sample
holder. (Detailed steps in the Appendix)
3.4.2 Samples
All the samples should be measured for the same time with automatic baseline subtraction
under the same conditions in vacuum. This is easier than correcting the data after the
experiment for baseline influences. (Detailed steps for software in the Appendix).
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M202: Membranes
3.5 Export Data
In order to facilitate evaluation of the date, these should be converted to ASCII-Format and
stored on a disk. (Detailed steps for software in the Appendix).
4 Evaluation of results
4.1 Converting Data
Convert the Data in mass lost versus
t.
4.2 Plotting Data
m 
Replot all the data in mass lost  t  versus
 m∞ 
t in one diagram.
4.3 Calculating the diffusion coefficient
Calculate the diffusion coefficient from the above data/plot. Give reasons for the selection of
data, i.e. why did you use only part of the data for fitting?
4.4 Comparing the samples
Compare the results of the different measurements and discuss these with respect to
preparation conditions.
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5 Bibliography
Hatakeyama, 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 glassy
and 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 Boca
Raton, 1994.
Ghosh, M.K. and Mittal, M.K., Polyimides: Fundamentals and Applications, Dekker, New
York, 1996.
Lecture “Polymers” of Prof. Faupel, University of Kiel
Lecture “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 Calibration
With “View-Calibrate” the last calibration has to be invoiced?. (The subwindow “Method
Editor” has to be active.)
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M202: Membranes
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 experiments
are done, so only the “Weight” has to be calibrated. The hole steps are explained by the
software. The weight calibration has to be done for each sample holder and saved with
different names.
6.1.3 Measurements
The subwindow “Method Editor” has to be active.
6.1.3.1 Basel ine
Open 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
Open furnace with
and calibrate zero weight with clicking
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 Samples
For each sample:
Calibrate zero weight before inserting the sample.
Insert the sample prepared under the conditions described in the previous chapters. Use the
same 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 while
keeping (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 Data
The 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 ASCIIFile 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 from
sorption/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/desorption
measurements (long-time approximation) vs. H2O concentration at
30°C, 45°C and 60°C see [85Yan].
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Fig. 3c: Kapton polyimide (PMDA-ODA). Average H2O diffusion
coefficient from sorption/desorption measurement vs. H2O
concentration at 30°C. 1: 0.3 mm film (birefringence 0.0972), longtime method, 2: 2mm film (birefringence 0.0177), half-time method,
3: 2 mm film, long-time method.
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