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

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

2

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.

3

M202: Membranes

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.

4

M202: Membranes

∂∂=

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.

5

M202: Membranes

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).

6

M202: Membranes

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.

7

M202: Membranes

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

8

M202: Membranes

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.)

9

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 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.

10

M202: Membranes

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”.)

11

M202: Membranes

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.

12

M202: Membranes

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].

13

M202: Membranes

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.

14