Masterarbeit Robin Kolvenbach Mit Anhang

Technische Universität München

Department Chemie Lehrstuhl für Technische Chemie II

Prof. Johannes A. Lercher

Diffusion and Separation Characteristics of Binary

Hydrocarbon-Mixtures in MFI

Diffusions- und Trenneigenschaften von

Kohlenwasserstoffmischungen in MFI

Master Thesis

-----------------------------------------------------------------

Vorgelegt von Bsc. (TUM) Robin Kolvenbach

Betreuer: Prof. Dr. J. A. Lercher

Garching, April 2010

„Wer die erhabene Weisheit der Mathematik tadelt, nährt sich von Verwirrung“

Leonardo da Vinci

A Acknowledgement

Acknowledgement

There are a lot of people without whom this thesis had not been written and

whom I owe my deepest gratitude.

First of all Prof. Lercher for giving me the opportunity to work in his group and

trusting me with the most challenging issue for my work.

Then I would like to thank PD Dr. Jentys for guiding me through this thesis and

also over the last years during my study at Technische Universität München.

I would like to address my deepest gratitude to Oliver Gobin who is an

archetype for every scientist. I owe my gratitude to him for his guidance and

excellent advice throughout this thesis. The intense discussions we had

showed me how to perform scientific work in a proper way.

I would like to thank the whole group for their support during this thesis. I have

to address my special thanks to Xaver Hecht and the whole technical team

without whom this thesis would have been impossible.

Of course I would like to thank my wonderful parents and my family, brothers

and my sister for supporting me my whole live.

B Abstract

Abstract

The diffusion and separation characteristic of binary hydrocarbon mixtures

through zeolitic wafers were studied with a Wicke Kallenbach cell. Therefore,

the transport of a benzene/p-xylene mixture and a p-xylene/m-xylene mixture

was examined in ZSM5 powder pressed to wafers of 50, 100 and 150 mg. This

report analyzes the transport mechanism and tries to falsify two models, the

statistically dense membrane and the classical bed adsorber. Therefore several

parameters were varied: different measurement and activation temperatures as

well as compacting pressures were examined. It was found that the model of

the classical bed adsorber suits the experimental results. These were mainly an

equilibrium separation factor of 1 and the form of the transmission curves

which were both independent on the change of experimental conditions.

Considering the transport mechanism the diffusion through the mesopores was

found to be the rate determining step once the system was under stationary

conditions. The time until stationary conditions were reached as well as the

transmission time were clearly influenced by the capacity of the adsorber. The

capacity was determined by the temperature during the experiment and

activation as well as the weight of the wafer.

The steady state diffusion coefficients were 10-6 m2/g obtained by the Wicke

Kallenbach measurements, which are much faster than the diffusion

coefficients of 10-15 m2/g of the parent MFI as measured by pressure

modulation frequency response experiments and uptake rate measurements.

As a consequence the transport mechanism in the Wicke Kallenbach wafer can

be assumed to be Knudsen diffusion through the mesopores.

The pore size of the mesopores was confirmed either by calculations from the

Wicke Kallenbach experiments applying the theory of Knudsen diffusion or

nitrogen physisorption isotherms using DFT analysis. A pore size of 6 to 15 nm

was found in which the transport through the 6 nm pores seem to be the

determining step of the rate of diffusion.

C Zusammenfassung

Zusammenfassung

Die Diffusion und die Trennung einer Mischung bestehend aus zwei

Kohlenwasserstoffen wurde in einer Wicke Kallenbach Zelle untersucht. Hierbei

wurden Gemische aus Benzol/p-Xylol und m-Xylon/p-Xylol an einem Wafer aus

ZSM5 untersucht. Es wurden Pellets zu 50, 100, 150 mg durch Pressen des

Pulvers hergestellt. Dieser Bericht analysiert die Transportmechanismen

innerhalb des Wafers und falsifiziert zwei Modelle, zum einen die Idee einer

statistisch dichten Membran und den klassischen Bettadsorber. Hierbei

wurden verschiedene Parameter variiert, unter anderem die Experiment- und

Aktivierungstemperatur als auch den Pressdruck während der Herstellung des

Pellets. Es wurde festgestellt, dass das Modell des Bettadsorbers in der Lage

ist, die experimentellen Ergebnisse hinreichend gut zu beschreiben. Diese

waren vornehmlich ein Trennfaktor von 1 und die Form der Durchbruchskurve,

welche charakteristisch für Adsorber ist.

Der Transport durch den Wafer unter stationären Bedingungen wurde durch

die Diffusion in den Mesoporen determiniert. Hierbei hängt die Zeit bis zum

Erreichen des Gleichgewichts genauso wie die Durchbruchzeit von der

Kapazität des Adsorbers ab. Diese wiederum wurde beeinflusst von der

Experiment- und Aktivierungstemperatur als auch von der Dicke des Wafers.

Es wurden Diffusionskoeffizienten von 10-6 m2/g in den Wicke Kallenbach

Messungen gefunden welche im Vergleich zu 10-15 m2/g für das

korrespondierende Pulver deutlich größer waren. Die Diffusionskoeffizienten

des Pulvers wurden mittels pressure modulation Frequenz Antwort Methode

und Uptake Rate Messungen bestimmt. Anhand der gemessenen

Diffusionskoeffizienten kann angenommen werden, dass die Diffusion in den

Poren einer Knudsen Diffusion in den Mesoporen entspricht.

Die Porengröße wurde daraufhin durch zwei Methoden bestimmt. Zum einen

durch eine DFT Analyse einer Stickstoffphysisorptionsisotherme und zum

anderen durch Berechnung aus den experimentellen Wicke Kallenbach Daten

unter Benutzung der Theorie der Knudsen Diffusion. Es wurde eine Porengröße

von 6 bis 15 nm gefunden wobei der Transport in den 6 nm Poren den

gesamten Diffusionstransport determiniert.

D Abbreviations

Abbreviations

A amplitude of FR experiment

Aper poke surface area needed statiscally for one poke [m2]

Aper successful poke surface area needed statiscally for a poke leading to

sorption of the adsorbent into the pore system [m2]

AS surface species

Aw Cross section of the wafer [m2]

a parameter corresponding to the amount of adsorbate in the

pores cB and on the surface cA

B amount of gas present in the sheet

BP adsorbate inside the channel system

b parameter corresponding to the amount of adsorbate in the

pores cB and on the surface cA

C normalized gas phase concentration

Ct time dependent concentration [mol/l]

C∞ concentration at infinite time [mol/l]

c concentration of diffusing component [mol/m3]

c0 initial adsorbed phase concentration [mol/m3]

co equilibrium adsorbed phase concentration [mol/m3]

c∞ steady state adsorbed phase concentration [mol/m3]

cA concentration in the adsorbed phase [mol/m3]

ce equilibrium concentration inside the particle [mol/m3]

c(1,2), feed adsorbate concentration in the feed [mol/m3]

E Abbreviations

c(1,2), measurement adsorbate concentration in the permeate during the

measurement [mol/m3]

cp effective heat capacity of the adsorbent sample [J/kgK]

cs surface concentration [mol/m2]

D(c) concentration dependent diffusion coefficient

D0 pre exponential factor of the Arrhenius ansatz

Deff diffusion coefficient in the pore system [m2/s]

DK,eff effective Knudsen diffusion coefficient [m2/s]

DLS dynamic light scattering

dp pore diameter [m]

EA,D activation energy of diffusion [kJ/mol]

F volumetric flow rate [m3/s]

FHe volumetric flow rate of the sweep gas [m3/s]

Fmolecules Number of molecules transmitting through wafer per

second [molecules/s]

∆H heat of adsorption [J]

h external heat transfer coefficient [W/m2K]

J diffusive molar flow rate [mol/m2s]

K parameter proportional the slope of the adsorption

isotherm

KH Henry constant

k Boltzmann constant [J/mol]

ka rate constant of Adsorption [1/s]

L characteristic length of diffusion [m]

F Abbreviations

mean value of characteristic length of diffusion [m]

M molar weight [kg/mol]

MFC mass flow controller

m(t) mass dependent on the time

m0 starting mass

m∞ end mass

N statiscal number of successful pokes during the

transmission of the adsorbate through the wafer

NA Avogadro constant [1/mol]

n number of parallel transport processes

P partial pressure [Pa]

P0 standard pressure (1 bar)

Pe partial pressure of the diffusion component in the gas

phase at equilibrium condition [Pa]

p pressure amplitude of FR experiment

pB pressure amplitude of blak of FR experiment

Q dimensionless concentration in the adsorbed phase

Q0 equilibrium value of the average dimensionless adsorbed

phase concentration

R gas constant [J/molK]

r radius of the Wicke Kallenbach pellet [m]

ra rate of adsorption [mol/s]

S separation factor

SAd adsorption cross section [m2/mol]

G Abbreviations

Sw cross section of the adsorbent bed

SBET BET surface area [m2/g]

Sext external surface area [m2/g]

SEM Scanning electron microscopy

T temperature [K]

T0 experimental temperature (FR) [K]

TI initial and final steady state temperature [K]

TEM transmission electron microscopy

t time [s]

tHasley thickness of a monolayer of physisorbed nitrogen

according to the theory of Halsey [nm]

UHV ultra high vacuum

VFR volume of the FR system [m3]

Ve,FR equilibrium volume (FR) [m3]

Vma macropore volume [cm3/g]

Vme mesopore volume [cm3/g]

Vmi micropore volume [cm3/g]

vmicro,max maximum micropore volume [cm3/g]

Vmol molar volume [m3/mol]

Wsat maximum amount of adsorbed gas = W0 [mol/m2]

X adsorbate in the gas phase

XRD X-Ray diffraction

x space coordinate

H Abbreviations

xAdsorbate molar ratio of the adsorbate either in the feed or the

permeate

y length coordinate [m]

Zw Number of hits of a molecule with the wall [1/m2s]

I Abbreviations

Greek Symbols

α the dimensionless parameter describing the heat transport

β the dimensionless parameter describing the heat transport

δ characteristic function of FR experiment

mean value of the characteristic function of FR experiments

εp porosity factor

χ phase lag of the concentration inside the sheet

γ relative amplitude

κ rate constant of the surface barrier

η dimensionless radial coordinate

φ phase of the FR experiment

φB phase of the blank FR experiment

ρ effective density of the adsorbent sample [kg/m3]

ρB density of adsorbent bed

θ surface coverage

τ dimensionless time

τF tortuosity factor

υ amplitude of the perturbation

ω frequency of perturbation [1/s]

J Table of Contents

Table of Contents

Acknowledgement ............................................................................................. A

Abstract ............................................................................................................. B

Zusammenfassung ............................................................................................. C

Abbreviations ..................................................................................................... D

Greek Symbols.....................................................................................................I

1. Introduction ................................................................................................. 1

2. Theoretical Section ..................................................................................... 4

2.1 Zeolites ..................................................................................................... 4

2.2 Wicke Kallenbach Experiments ................................................................ 8

2.3. Frequency Response experiments ........................................................ 10

2.4. Uptake rate measurements ................................................................... 14

3. Experimental ............................................................................................. 19

3.1. Material .................................................................................................. 19

3.2. Wicke Kallenbach experiments ............................................................. 21

3.3.1 Sample preparation ......................................................................... 21

3.2.2 Experimental setup .......................................................................... 22

3.3. Frequency response experiments ......................................................... 25

3.3.1. Sample preparation ........................................................................ 25

3.3.2. Experimental Setup ......................................................................... 26

3.4. Uptake rate measurements ................................................................... 27

3.4.1 Sample preparation ......................................................................... 27

3.4.2. Experimental Setup ......................................................................... 27

4. Results ...................................................................................................... 29

4.1 Wicke-Kallenbach experiments .............................................................. 29

K Table of Contents

4.2. Frequency Response experiments ........................................................ 41

4.3. Uptake Rate measurements .................................................................. 43

4.4. Nitrogen physisorption isotherms.......................................................... 47

5. Discussion ................................................................................................ 49

6. Conclusion ................................................................................................ 69

Literature .......................................................................................................... 71

Appendix

1 Introduction

1. Introduction

The understanding of diffusion processes in porous media is crucial for the

development of new and more effective catalysts and molecular sieves.

Especially the diffusion in micropores became a very important field as this is

often the rate controlling step in a complex reaction network. Moreover it is

possible to increase the selectivity of a process by shape selective catalysts

[1,2]. Most of the time these are zeolites or related materials because the pore

structure can be tuned to favor the desired product. The difference in the

diffusivity of two components due to the pore diameter of a porous substrate

can also be used for separation by size exclusion. Sakai et al. showed the

separation of p-xylene from a ternary mixture of the xylene isomers with the

help of a MFI-type zeolite membrane [3].

Another approach to enhance the separation of hydrocarbons by zeolites was

recently published by our group. The enhanced separation is caused by a

surface modification with a silica layer of 3 nm thickness [4,5]. This over-layer

leads to a variation of the sticking probability on the modified surface which

speeds up selectively the sorption rate in the porous over-layer and has in

combination with the intrinsic size exclusion of the MFI micropores the

consequence of an enhancement of the sorption rate.

To be able to determine the intracrystalline diffusivity many different methods

were developed in the last decades among these uptake rate measurements

[6,7,8,9] as for instance zero length column [10,11], different NMR techniques

for example the widely applied pulsed field gradient method [12,13,14,15],

frequency response experiments [16,17,18,19] and rapid scan IR-

spectroscopy[4,5,19]. Furthermore microscopic IR techniques offer the

possibility to monitor the diffusion process in a sample [20,21].

Another widely used method is the measurement in a Wicke Kallenbach cell.

This experiment offers the possibility to determine the diffusive flow through a

micro-, meso- or macroporous wafer. Originally Wicke and Kallenbach

invented the method for monitoring the diffusivity of CO2 in active coal [22].

Since then the method was used for several different types of experiments

either in the classical form or modified to fit the requirements.

2 Introduction

Sun et al. applied the method to measure intracrystalline diffusivity of fast

transport processes such as methane in Silicalite 1 [23]: they mounted large

silicalite crystals (100x100x300 μm) at the center of an aluminum disk where

both sides of the crystals were exposed by using an epoxy resin. They

preformed the measurement with methane, ethane, propane and butane. The

experiments showed excellent results, which were in agreement with

previously reported intracrystalline diffusivities determined by frequency

response techniques.

Many other authors used zeolite membranes grown on a support, most of the

time alumina to investigate intrapore transport processes. Keizer et al.

demonstrated for example the possibility to separate mixtures of molecules

with small and large kinetic diameters [24]. N-hexane was chosen as small and

2,2-dimethylbutane as large molecule. Separation factors larger than 600 were

obtained in a temperature range between 298 and 473 K.

Tuchlenski et al. quantified the amount of surface diffusion of non adsorbing

gases in porous glass with a pore radius of 3.5 nm by applying a modified

Wicke-Kallenbach cell [25]. They obtained excellent results in describing the

diffusion of a non-adsorbing gas through the membrane by applying the dusty

gas model (DGM). Similar experiments were carried out by Arnóst et al. [26].

They examined the transport of ternary mixtures made of hydrogen, helium,

nitrogen or argon in mesoporous alumina wafers. They also tried to model the

transport processe with the DGM and in addition with the mean pore transport

mode model. Unfortunately they found out that it is impossible to model this

process as the molecules influence each other in the gas during the

transmission through the wafer.

The aim of this report is the examination and understanding of transport

phenomena of binary mixtures consisting of strong adsorbing substances

during the transmission through a pressed wafer of ZSM5 in a Wicke

Kallenbach cell.

The experiments should also give more insight in the separation behavior of

hydrocarbons of such wafers. They should answer the question if these wafers

act like a membrane or analogue to a bed adsorber. The experimental part

consists of Wicke Kallenbach experiments applying pressed wafers of ZSM5

3 Introduction

and binary mixtures of benzene and p-xylene as well as p-xylene and m-xylene

as adsorbates to see whether it is possible to separate these compounds.

To investigate the differences between the powder and the pressed wafer,

pressure modulation frequency response and uptake rate measurements were

performed. These techniques allow the determination of the time constant of

the diffusion and the examination of the transport mechanism by fitting the

experimental data to theoretical models.

The combination of all these different techniques should answer the question

which diffusion mechanism occurs in a pressed Wicke Kallenbach wafer and

shows if it is possible to separate hydrocarbons with a pressed zeolitic wafer.

4 Theoretical Section

2. Theoretical Section

2.1 Zeolites

Zeolites are microporous tecto-silicates which are nowadays widely used in

industrial processes [27]. Because every zeolite is a potential catalyst, adsorber

or cation exchanger they are applied in several processes [28] e.g. methanol to

gasoline [29] or selective catalytic reduction of nitric oxide by ammonia [30].

One of the most important operation areas is the petrochemical industry, in

particular fluid catalytic cracking [31], isomerization [32,33] and alkylation

[34,35].

The name Zeolite was used for the first time in 1756 by the mineralogist A.F.

Cronsted who observed bubbles while heating the mineral Stilbite. The origin

of the name zeolite are the two greek words “zeon”(to boil) and

“lithos”(stone) [36]. Nowadays over 180 different zeolite structures are

known among them 40 natural and 140 synthetic topologies. They are

identified by a three letter code defined by the IUPAC (International Union of

Pure and Applied Chemistry) [37] and the IZA (International Zeolite Association)

[38] e.g. FAU = Faujasite.

Figure 1:Primary and secondary building units (PBU, SBU) of zeolitic frameworks.

Zeolites consist of SiO44- and AlO4

5- tetrahedrons as primary constitution which

built up a three dimensional secondary structure by linking through the oxygen

atoms (Figure 1). These secondary building units (SBU) can be separated in 20


different unique polyhedrons. The combination of the primary and secondary

units leads to huge and complex structural diversity with three dimensional

channel- and pore - systems, cages and super – cages [38].

Due to the regular structure of the material the pore size distribution is very

sharp. Figure 2 shows the pore size distribution of several different adsorbents

in comparism. The pores have a diameter below 1.3 nm which means they are

in the range of kinetic diameters of molecules. This property gives the

opportunity to perform size exclusive as well as shape selective reactions.

Additionally selective adsorption of a molecule from a reaction mixture

becomes possible because molecules larger than the pore openings cannot

enter in contrast to smaller ones.

Figure 2: Pore size distribution of zeolites in comparism to the standard adsorbents silica gel and active cole [39].

The isomorphous exchange of Si4+ by Al3+ opens out into a negative charge

which has to be compensated either by an inorganic or organic cation

consequently an alkali, earth alkali cation, quaternary ammonium ion or proton

[40] (Figure 3).

The general elemental formal for zeolites is Mx/m[(AlO2)x(SiO2)y]•wH2O where m

is the charge of the cation and w the number of water atoms is the cage.


Thereby the Si/Al ratio is defined by the ratio of y/x and has to be greater than

1 due to the Löwenstein rule [41]. This rule indicates that Al-O-Al linkages are

forbidden in zeolite frameworks. Si/Al ratios from 1 to infinity which describes

pure silica zeolites are common.

Figure 3: Structural formulas showing the effect of isomorphic exchange of silicon by aluminum

and the compensation by either an inorganic or organic cation M+ (a) or proton (b) [42].

The aluminum content is one of the characteristics determining the reactivity of

a zeolite by the density of negative charge in the framework. This has

enormous consequence for the density and strength of the Brønstedt acid

sites, the ion exchange capability, the thermal stability and hydrophilic

properties [43]. This dependence provides the opportunity to tune the reaction

properties of a zeolite by altering the degree of aluminum in the framework.

Summarizing the physical and chemical properties [44] of zeolites it may be

adhered that they have a high surface area, a molecular dimension of the

pores, a high adsorption capacity, high ion-exchange capability, high thermal

and hydrothermal stability, the possibility of modulation the electric properties

of the active sites and the possibility for pre-activating the molecules in the

pores by strong electric fields and molecular confinement.

Although the microporousity is one of the main advantages of zeolites it is a

disadvantage at the same time. The reason for this is the slow diffusion in the

micropores which leads to limitations of the rate of chemical reactions. To

solve this problem intense activities are ongoing over the last years.


There are mainly two ways to overcome this problem. One is to make nano

sized particles [45] and the other one is to synthesize mesoporous materials

like MCM-41 [46].

The synthesis of zeolites is usually performed under hydrothermal conditions

using reactive gels in alkaline media at 80 – 200 °C. These reactive gels are

produced from hydrated aluminum and silicon species e.g. hydroxides. Metal-

powder or salts dissolved in sodium hydroxide solution usually serve as

aluminum source. The silicon source which is normally the colloidal dioxide is

combined with the aluminum containing solutions under hydrothermal

conditions [47].

Figure 4: Two different method of ZSM5 synthesis [48].

A structure directing agent (SDA) is added to the reaction mixture to control

zeolite growth in means of pore size and network dimensions. Usually tertiary

amines serve as SDA e.g. a tertiary-propyl-ammonium salts in the case of

ZSM5. The pH of the reaction mixture is adjusted between 9 and 13. In this

high temperature and pressure conditions a reactive gel is formed. Inside this

gel zeolitic nuclei occurs which then starts the crystal growing. Depending on

the synthesis method zeolite crystals or polycrystalline zeolite material is

formed. These two different methods are described in Figure 4.


During the last 50 years many other preparation methods were developed.

They were extensively reviewed before [49,50,51,52] and will not be discussed

here.

2.2 Wicke Kallenbach Experiments

This method for investigating the diffusivity in porous media was developed by

Wicke and Kallenbach in 1941 [22]. In principle two countercurrent gas flows

graze the sample wafer in a 90° angle. One of the flows is loaded with probe

substances and the other one contains of pure sweep gas (Figure 5). The

sample is placed into the cell as a wafer which is either produced by

compacting of powder or as a grown membrane.

The diffusion through the wafer is driven by the concentration difference

between both flows. The pressure on both sides of the cell has to be the same

to avoid pressure driven transport through the sample. Therefore, the

volumetric flow rate of the loaded and the unloaded stream has to be the

same.

Figure 5: Flow scheme of the Wicke Kallenbach cell showing the fluxes going in and out of the cell and indication where the diffusive transport takes place.

If the experiment is performed with two or more substances it is possible to

determine the ability of the sample to separate the adsorbates by comparing

the feed concentration to the concentration in the permeate. Hence it is

possible to calculate a separation factor by:

(2.2.1)

If a separation is observed during the experiment the separation factor has to

differ from 1. Furthermore it is possible to calculate the diffusion coefficient of


the adsorbates inside the pellet from the steady state molar ratios of these

experiments by (2.2.2)

(2.2.2)

In this equation L is the characteristic length of diffusion, r is the radius of the

pellet, FHe is the volumetric flow rate of the sweep gas and xAdsorbate is the molar

ratio in the feed and in the permeate at steady state conditions, respectively.

In principle three different kinds of diffusion have to be considered in porous

media. In the case of molecular diffusion the mean free path of a molecule is

shorter than the pore diameter. As a result the diffusion process can be

described analogue to the free vacuity by the first fickian law by substituting

the diffusion coefficient by an effective diffusion coefficient (Deff). The latter

consists of an additional porosity factor (εp) which describes the ratio of pore

openings compared to the total surface area as well as a tortuosity-factor (τF)

specifying the differences of the pore geometry from the ideally assumed

cylinder [53].

(2.2.3)

If the pore size is small or the gas pressure is low the mean free path is longer

than the pore diameter. Consequently the molecules hit the pore walls much

more often than other molecules. In this case the so called Knudsen diffusion

is observed. The conditions for this kind of diffusion are summarized in the

following table [53]:

Table 1: Depence of the occurring of Knudsen diffusion on the partial pressure of the adsorbate and the pore size

dp [nm] <1000 <100 <1 <2

p [105 Pa] 0.1 1 10 50

The diffusive flow in the Knudsen theory can mathematically be expressed by

equation (2.2.4) [53].

(2.2.4)


In here dp is the pore diameter, R is the gas constant, T is the temperature, M is

the molar mass and c the concentration of the diffusing component. Analogue

to the fickian law the effective diffusion coefficient can be described by

equation (2.2.5) [53].

(2.2.5)

The third kind diffusive transport is the diffusion in pores with a diameter below

1 nm ocurring in zeolites. In this case the pore radius is in the range of the

minimum kinetic diameter of the diffusing molecule. Therefore the diffusion

coefficients found in zeolites are much lower than the molecular or Knudsen

coefficients.

The mathematical description is the first fickian law for a system in a steady

state as shown in (2.2.3). For non steady state situations the second fickian law

is used and calculated separately for each specific case. The solutions for all of

these constraints can be found in Crank et al. [54].

The dependence of the effective diffusion coefficient on the pore diameter is

shown in Figure 6.

Figure 6: Dependence of the effective diffusion coefficient on the pore size of porous adsorbents.

2.3. Frequency Response experiments

The frequency response method offers the opportunity to determine transport

pathways and their kinetics in a batch adsorber [60]. In this method the volume

of the reaction vessel is altered periodically by ±1 % while tracking the

pressure simultaneously. By changing the volume the adsorption/desorption


equilibrium is disturbed and tries to equilibrate again. This equilibration can be

followed by tracking the pressure (Figure 7).

Figure 7: Simulated data of a frequency response experiment with a square wave volume perturbation showing the signal of the magnet which describes the volume (blue) and the

corresponding pressure trend (red) against the time.

The experimental data is then compared to the solution of theoretical models in

order to find the best match. By matching the experimental data to the models

the mechanism of the transport process and its kinetic parameters can be

obtained.

The model equations used for the curve fitting can be found by solving the

mass balance in a closed volume as described previously by Yasuda et al. [16].

They obtained two characteristic functions characterizing the system:

(2.3.1)

(2.3.2)

(2.3.3)

Where p is the pressure amplitude of the experiment, pB is the corresponding

pressure amplitude in a blank experiment, φ is the phase of the experiment, φB

is the phase of the blank measurement and δ is the characteristic function.

Herein n is the number of parallel transport processes. Furthermore K is a

parameter proportional the slope of the adsorption isotherm, the temperature

(T), the volume of the system (VFR) and the gas constant (R).

Blank experiments are needed to exclude the non-idealities of the apparatus

itself from the outcome of the experiment [60]. The characteristic functions (δ)

are solutions of the second fickian law using the right boundary conditions. In

this work two different transport mechanisms are examined: the diffusion in an


infinite sheet and an infinite sheet with surface resistance. The mass balance of

an infinite sheet without surface barrier is defined as [17]:

(2.3.4)

where P is the pressure in the system, V is volume, R is the gas constant, T0 is

the experimental temperature and B is the amount of gas present in the sheet.

Assuming the volume is changed sinusoidal we can formulate the volume as:

(2.3.5)

herein Ve,FR is the equilibrium volume, υ is the amplitude of the perturbation, ω

is the frequency of perturbation and t is the time. The vapor pressure of the

diffusing substance and the concentration in the pores can generally be

described by:

(2.3.6)

(2.3.7)

where Pe is the partial pressure of the diffusion component in the gas phase at

equilibrium condition, ce is the equilibrium concentration inside the particle, p

(∆p/2) and γ are the relative amplitudes, φ and χ are the phase lags both

depending on the frequency ω.

The diffusion inside the pores is described by the second fickian law:

(2.3.8)

Herein c is the concentration in the pores, D(c) is the concentration dependent

diffusion coefficient and x is the space coordinate. Since the perturbations are

defined to be small fick´s law eases to:

(2.3.9)

In this work we consider the case of one dimensional diffusion in sheet with

plane boundaries at x=0 and x=L. The boundary conditions define the

concentration at the boundaries to be proportional to the sinusoidal changing

vapor pressure in the gas phase [55], [56]:

(2.3.10)

(2.3.11)

As a consequence the integral of the amount of gas present inside the sheet,

B, is given by:

(2.3.12)


Where Be is the equilibrium amount if gas present inside the sheet. The

amplitude A is expressed by [56]:

(2.3.13)

(2.3.14)

where KH is Henry´s law constant, p is the relative amplitude of the pressure, ω

is the frequency, L is the length of the sheet and D is the diffusion coefficient.

Furthermore the coefficient ψ in equation (2.3.12) is defined by:

(2.3.15)

Substituting (2.3.12) into the material balance (2.3.4) leads to the two equations

(2.3.1) and (2.3.2) where the in and out-of-phase functions are given by:

(2.3.16)

(2.3.17)

The other mechanism we want consider is surface controlled diffusion.

Therefore we have to add another equilibrium upstream to the one we

considered before describing the surface adsorption. This leads to the

following reaction network [57]:

X ↔ AS ↔ BP

where X is the adsorbate in the gas phase, AS is the surface species and BP is

the adsorbate inside the channel system. The corresponding material balance

is defined by:

(2.3.18)

The solution using the previously described terms for P, V and B result in these

in- and out of phase functions [16]:

(2.3.19)

(2.3.20)

where κ is the rate constant of the surface barrier and a and b are parameters

corresponding to the amount of adsorbate in the pores cB and on the surface cA

[60]:


(2.3.21)

(2.3.22)

Additionally the definition of the parameter K of the characteristic functions

(2.3.1) and (2.3.2) changed. In the case of a surface barrier it is defined by [57]:

(2.3.23)

Because most of the zeolites do not have a uniform particle size a normal

distribution is introduced which modifies the characteristic functions [60]:

(2.3.24)

Herein and describing the mean values of the characteristic function and

the thickness of the sheet, respectively.

2.4. Uptake rate measurements

To determine the kinetics of adsorption processes in porous materials a step

change of the adsorbate pressure is performed and the change in mass of the

sample is tracked. The altering of the pressure surroundings causes a shift in

the surface concentration of the adsorbate species which can be described by

the diffusional time constant (D/r2) [7].

The time constant and thereby the diffusivity can be obtained by matching the

experimental data to an appropriate model describing the diffusion process.

The method can be used for either macro-, meso- or microporous diffusion. A

general mathematical model is applied developed by Ruthven et al. [58] for

systems controlled by intracrystalline diffusion. It has the following

assumptions:

1) The sample consists of a ensemble of spherical particles

2) Intracrystalline diffusion is the only significant resistance to mass

transfer. Therefore the sorbate concentration at the surface of the

particles is always in equilibrium with the adsorbate in the

surrounding fluid phase.

3) The diffusivity is constant and the equilibrium relationships are linear.

4) The experiment is performed under isothermal conditions.


According to these approximations the system can be described by the

following differential equations. Based on the first fickian law the first one

defines the behavior of the dimensionless adsorbed phase concentration (Q)

dependent on the dimensionless time (τ):

(2.4.1)

(2.4.2)

(2.4.3)

in here η is the dimensionless radial coordinate, cA is the concentration in the

adsorbed phase, c0 is the initial adsorbed phase concentration and c∞ is the

steady state adsorbed phase concentration.

The second and third equation describe the average of the adsorbed phase

concentration over the particle (2.4.5) and its time dependence (2.4.6):

(2.4.5)

(2.4.6)

where Q is the dimensionless concentration in the adsorbed phase, η is the

dimensionless radial coordinate, ∆H is the heat of adsorption, τ is the

dimensionless time as defined in (2.4.3), ρ is the effective density of the

adsorbent sample, cp is the effective heat capacity of the adsorbent sample, c0

is the initial adsorbed phase concentration, c∞ is the final steady state

adsorbed phase concentration, T is the temperature, h is the external heat

transfer coefficient, TI is the initial and final steady state temperature, D is the

Diffusion coefficient and L is the radius of the particles

(= characteristic length of diffusion). Obviously the heat transfer has to be

taken into account even if it is disregarded later due to the isothermal

conditions. As a result the concentration of the adsorbed phase at the particle

surface can be defined by (2.4.7):

(2.4.7)

where cs is the surface concentration and co the equilibrium adsorbed phase

concentration.

This set of equations is solved with the initial boundary conditions (2.4.8) and

(2.4.9):


(2.4.8)

(2.4.9)

in here the first initial boundary condition indicates that the starting adsorbate

of the experiment is zero. The second one defines that the concentration of the

adsorbed phase does not change in the center of the particles.

The solution taking the boundary conditions into account can be obtained by

Laplace transformation and is shown in (2.4.10) and (2.4.11):

(2.4.10)

(2.4.11)

where qn is given by the roots of:

(2.4.12)

thereby Q0 is defines the equilibrium value of the average dimensionless

adsorbed phase concentration, α and β are the dimensionless parameters

describing the heat transport and are formulated by (2.4.13) and (2.4.14)

(2.4.13)

(2.4.14)

Considering the assumption of isothermic conditions (α ∞ and β 0) the

solution for the average dimensionless adsorbate concentration reduces to

(2.4.15):

(2.4.15)

This equation is then used to perform curve fitting with the fit parameter τ. By

knowing the length of diffusion the diffusion coefficient can be obtained.

2.5. Analysis of physisorption isotherms

The mostly applied method to analyze nitrogen physisorption isotherms was

developed by Brunauer, Emmett and Teller in 1938 [59]. It offers the possibility

to determine the surface area of a solid sample. In principle it is an extension of

the classical Langmuir isotherm, which is only valid for monolayer adsorption,

to multilayer adsorption.


The following assumption corresponds to this theory:

1) gas molecules adsorb in an infinite number of layers

2) each layer is treated independently which means that it has no

interaction with other layers

3) each layer can be treated with the theory of Langmuir adsorption

This leads to the BET equation:

(2.5.1)

with VAd equals the total amount of adsorbate adsorbed on the sample, P is the

partial pressure of the adsorbate, P0 is the standard pressure and Vm is the

volume of a monolayer.

2.5.1 is the linearized form of this equation. Based on this the monolayer

coverage can be obtained from the slope and the intercept of the resulting

graph shown in 2.5.2:

(2.5.2)

Furthermore it is possible to determine the surface area (2.5.3) if the adsorption

cross section of the adsorbing molecule is known.

(2.5.3)

In here Vm is the volume of a monolayer, Vmol is the molar volume of the

adsorbing gas, NA is the Avogadro constant, SAd is the adsorption cross section

of the adsorbing molecule and M is the molecular weight of the adsorbing

molecule.

Additionally it is possible to analyze the isotherm concerning the micro- and

mesopore volume. A the possible way is the t-plot method: the experimentally

obtained isotherm is compared to a standard isotherm by plotting them against

each other at the same P/P0 points.

The standard isotherm is thereby represented by the thickness of adsorbed

layers. In this thesis the method of Halsey [70] is used to produce the standard

isotherm. The corresponding equation is:

(2.5.4)


The obtained values are then plotted against the experimentally observed data.

Linear regions of the resulting plot correspond to regions where the standard

and the experimental isotherm have the same physical properties. These

regions can be described mathematically to determine the micro- and

mesopore volume.

The first linear region with a positive slope is defined as the point closely after

the micropores are completely filled and before the mesopore condensation

begins. It can be described by:

(2.5.5)

In here vmicro,max defines the volume of the micropores, kt is a coefficient

depending on the layer thickness, the units of vads and Sext. For standard units k

is defined by 1/(4.3532xtHasley) with tHasley representing the thickness of a

monolayer in the case of nitrogen 0.354 nm.

According to equation 2.5.5 the intercept of the first linear region defines the

micropore volume whereas the external surface area can be obtained from the

slope of the graph.

The second linear region with a positive slope describes the region shortly after

the mesopore condensation. Consequently the intercept of the second linear

region identifies the addition of the micro- and the mesopores. The last step is

to determine the mesopore volume. To do so the value of the combination

micro- and mesopore volume is subtracted by the previously obtained

micropore volume.

19 Experimental

3. Experimental

3.1. Material

Polycrystalline H-ZSM5 samples with a particle size < 100 nm and a Si/Al

ration of 45 [60] were provided by Südchemie AG. The nitrogen physisorption

isotherms were obtained using a PMI automated sorptometer at liquid nitrogen

temperature (77 K) after outgassing under vacuum for at least 6 hours. The

specific and the external surface area, the macro-, meso- and micropore

volume as well as the total pore volume (Table 2) were determined by nitrogen

physisorption (Figure 8) and applying the Brunauer-Emmett-Teller (BET) theory

in the range from 0.03 to 0.10. Between 0.1 and 0.3 mbar the plot was not

linear with a negative intercept (BET C constant).

1E-5 1E-4 1E-3 0.01 0.1 1

0

20

40

60

80

100

120

140

160

180

200

(b)

Am

ou

nt A

dso

rbe

d (

cm

3 S

TP

g-1)

Relative Pressure (-)

(a)

Figure 8: Nitrogen physisorption isotherms of the parent H-ZSM5 material (a) [5].

0.0 0.5 1.0 1.5 2.0

50

75

100

125

150

(b)

Vmi

Am

ou

nt A

dso

rbe

d (

cm

3 S

TP

g-1)

s

Vmi

+ Vme

(a)

Figure 9: αs plot of the parent (a) material. Two linear regions can be found at αs=0.5 corresponding to the micropore volume and at αs= 1.2 belonging to the sum of micro- and mesopore volume [4].

SBET

[m2/g]

Vmi

[cm3/g]

Vme

[cm3/g]

Vma

[cm3/g]

Sext

[m2/g]

Vtot

[cm3/g]

Parent 423 0.12 0.04 0.22 65 0.38

Table 2: [60,5]: Results of the nitrogen physisorption experiment for the parent ZSM5 sample. SBET is the total surface area determined by applying the BET theory, Sext is the external surface area and Vmi, Vme, Vma and Vtot are the micro-, meso and micropore volume obtained by using the αs comparative plot

Additionally the Langmuir surface area was determined by performing a

Langmuir plot in the relative pressure range up to 0.10 mbar. The macro-,

20 Experimental

meso- and micropore volumes were obtained by using a αs comparative plot

(Figure 9) [61] with nonporous hydroxylated silica [62] as reference adsorbent.

The particle size distribution was determined by dynamic light scattering (DLS)

and scanning electron microscopy (SEM). DLS measurements were performed

on a Malvern Zetasizer Nano ZS. Prior to the measurement the sample was

dispersed in water with help of an ultrasonic bath where it was kept for several

hours. The measurements were repeated at different concentrations several

times. SEM images were produced on a REM JEOL5900 LV microscope

operating at 25 kV with a resolution of 5 nm and a nominal magnification of 3.0

x 106. The samples were used without further purification. As shown in Figure

10 the particles contain of larger agglomerates of smaller particles with a

diameter of 0.36 ± 0.17 µm.

Figure 10: Scanning electron microscopy of the H-ZSM5 parent material [60].

The size of the primary particles was obtained by transmission electron

microscopy (TEM) and X – Ray diffraction (XRD) methods. The TEM images

were recorded on a JEOL-2011. The powdered samples were suspended in an

ethanol solution and dried on a copper-carbon grid prior to the measurement.

The powder diffraction patterns were measured on a Phillips X`pert Pro XRD

instrument operating at the Cu-Kα radiation at 40 kV with a Nickel filter to

remove the Cu-Kβ. The samples were used without pretreatment. Powder

patterns were produced using a spinner system with a ¼ inch divergence slit

between two angles of 5 an 70°. Step size was 0.017° with a scan time of 115s

per step. Both methods show that the primary particle size is below 100 nm

(Figure 11, Figure 12).

21 Experimental

Figure 11: TEM images of the parent H-ZSM5 sample[4].

Figure 12: XRD of the parent H-ZSM5 material showing the characteristic reflexes of ZSM5 [60].

The XRD of the parent material shows sharp reflexes at the characteristic

positions of ZSM5 (Figure 12).

Benzene and p-xylene (> 99.5 % GC standard) were supplied by Sigma Aldrich

and were used without further purification.

3.2. Wicke Kallenbach experiments

3.3.1 Sample preparation

All powdered samples were compacted into a stainless steel (b) ring at 20 kN

for 2 minutes using the pressing instruments shown in Figure 13.

The sample was then subsequently built into the Wicke Kallenbach cell and

was flushed with helium for 30 minutes. Afterwards the sample was activated

at 723 K for 1 hour in a helium flow of 50 ml/min for each of the two flows and

an incremental heating rate of 10 K/min.

The experiments were performed at a constant gas flow of 50 ml/min for each

of the two countercurrent flows. Thereby the loading with benzene was

22 Experimental

performed with a volumetric flow rate of 2 ml/min and p-xylene was saturated

with 18 ml/min. Assuming 100% saturation of the streams this leads to a ratio

of 1.33/1 bezene/p-xylene in the feed.

Figure 13: CAD model of the pressing instruments used to produce wafers for the Wicke Kallenbach cell containing of a plunger (a), the ring inserted in the cell (b) and the stamp pad

(c). The whole instrument consists of stainless steel.

To determine the temperature dependence of the separation, measurements at

130°C (403.15 K), 100°C (373.15 K) and 70°C (343.15 K) were executed. In

addition the sensitivity of the wafer thickness was examined in testing wafers

of 150, 100 and 50 mg. Also the influence of the compacting pressure and the

activation temperature was tested.

3.2.2 Experimental setup

The cell shown in Figure 14 is made of 6 pieces, two endplates (a,f) and two

rings, one holding the sample wafer (d) and the other holding the screws (c)

and two 2 mm thick graphite sealings (b,e). The flow rate is controlled by 4

mass flow controllers (MFC) Bronkhorst EL-flow select, two of them with a

range of 200 ml/min used for the sweep gas and the other two with a range of

20 ml/min leading to the saturators. These MFCs are computer controlled by

Flow DDE V4.41 and Flow View V1.09 (Bronkhorst).

The temperature of the cell is regulated via an Eurotherm 2404 PID controller.

The loading of the gas stream with benzene and p - xylene is performed via

two saturators, cooled down to 15°C in a thermostat (Huber K12-cc-NR) with a

1:1 glycol/water mixture as cooling agent to avoid condensation of the

adsorbate inside the system. Figure 15 shows a CAD Model of the saturators

23 Experimental

used. These saturators consist of two nearly identical parts which are

connected.

Figure 14: CAD Model of the Wicke Kallenbach cell containing two end plates (a,f), two sealings made out of graphite (b,e), an aluminum ring holding the screws (c) and the inner

stainless steel ring clamping the sample (d).

Figure 15: CAD Model of the saturator used to load the gas stream with adsorbates benzene and p – Xylene.

24 Experimental

The base body comprises a half inch t - piece and tube which is welded up

(a,b) and serves as a flask for the adsorbate. The gas flow enters the saturator

at point (c). The following 2 way valve controls the direction of the flow. It can

either enter the tube filled with adsorbate (a) or go through the bypass (e) back

into the system. The bypass is needed to clean the system before and after the

measurement.

To save the system from floating with adsorbate in the case of low-pressure

inside the system an empty second tube (b) is connected to the first flask. After

passing this station the stream gets back into the system through another 2

way valve (d) which connects the bypass (b) and the saturator.

An image of the total setup is shown in Figure 16.

Figure 16: Setup for the Wicke Kallenbach experiments containing the Wicke Kallenbach cell, the mass flow controllers (MFC) the saturators and the electronic for controlling the

temperature and the flows.

The permeate stream is connected to a vacuum system via a heated capillary

and differential pumped inlet system. The UHV is produced by a turbo-

25 Experimental

molecular pump TMH 071-003 (Pfeiffer Vacuum). This allows pressures down

to 10-9 mbar. During the measurements the vacuum is 10-5 mbar.

The permeate is analyzed by a mass-spectrometer (WR 13302, Hiden

Analytical) in the MID mode controlled by MASSoft Professional (Hiden

Analytical) computer software.

3.3. Frequency response experiments

3.3.1. Sample preparation

Two different kinds of samples, specifically powdered and pressed samples,

were used in this experiment. In the case of the powdered samples 35 mg

were carefully dispersed on glass-wool at the bottom of a quartz tube to have

isolated particles and thereby avoid bed effects.

Furthermore two types of pressed wafers were studied: Wicke Kallenbach-

wafers of 100 mg and IR wafers 6 mg weight. Both were carefully broken into

smaller pieces to fit in the quartz tube sample holder. Glass-wool was placed

at the bottom of the sample holder to have the same conditions as in the

experiments with powdered samples.

In both cases the glass-tube was connected to a UHV setup, placed into an

oven and pumped to 10-7 mbar. The samples were activated at 723K for 1 hour

with a temperature ramp of 10 K/min at ultra high vacuum conditions to

remove the adsorbed water.

The adsorbate was added with a partial pressure of 0.31 mbar at a

temperature of 373 K until the adsorption equilibrium was fully established.

During the experiment the volume of the setup was changed periodically in a

frequency range of 5 to 10-3 Hz and a square waved volume perturbation ±1%

in amplitude.

The pressure response was fourier transformed by obtaining the amplitude and

the phase lag. The resulting characteristic functions were fitted with the model

equations described in 2.3. by a nonlinear parameter fitting using a CMA

evolutional strategy in matlab [63]. The objective minimized to find the best

consistency was the root mean square error normalized to the variance of the

data. To be sure that the best parameters were found which is equal to the

26 Experimental

global minimum the calculation was performed three times with different

starting parameters.

3.3.2. Experimental Setup

An overview of the setup for the frequency response experiments is given in

Figure 17. The setup is basically a UHV unit equipped with volume perturbation

part which consists of two magnetically driven plates sealed with UHV bellows.

The UHV is produced by a turbo-molecular pump TMH 071-003 (Pfeiffer

Vacuum). This allows pressures down to 10-8 mbar. To enable the turbo pump

to start a zeolite trap is build into the system to produce vacuum of about 10-2

mbar.

Figure 17: Image of the frequency response setup showing the modulation unit, the vacuum chamber, the sample cell and the dosing system.

The pressure is recorded online via a Baratron pressure transducer (MKS

16A11TCC). The system is controlled via HP VEE based software. The

27 Experimental

adsorbing substrate is added by a separately pumped dosing system with an

all metal regulating valve UDV 040 (Pfeiffer Vacuum) to put the gas phase

corresponding to the liquid adsorbate into the system.

3.4. Uptake rate measurements

3.4.1 Sample preparation

A Wicke Kallenbach wafer of 100 mg was pressed as described in 2.1. and

broken afterwards into small pieces of 6 to 10 mg. One of these pieces was

subsequently filled into the quartz crucible which was then placed into the

balance.

The balance was connected to an UHV system and pumped 10-7 mbar. The

sample was activated at 723 K in UHV conditions to remove the adsorbed

water and cooled down to the experiment temperature of 373 K. The

adsorbate was added in a pressure jump with partial pressures of 0.1, 1, 2 and

10 mbar and was kept constant during the whole experiment while the sample

mass was monitored by a Seteram TG-DSC 111.

The mass of the sample was normalized afterwards by:

(3.4.1)

where m0 is the mass at the beginning of the experiment and m∞ is the mass at

the end. This normalized data was then fitted with theoretical models

described in 2.4. by nonlinear parameter fitting using a CMA evolutional

strategy in matlab [63]. The procedure was identical to the one described in

section 3.3.

3.4.2. Experimental Setup

The main item of the setup is a Seteram TG-DSC 111 microbalance (Figure 18)

equipped with quartz insertions and crucibles being heat insensitive. The

balance is connected to a UHV unit with a turbo-pump TMH 071-003 (Pfeiffer

Vacuum) which is able to produce a vacuum of 10-8 mbar. Additionally an oil

pump is connected to the system to produce on the one hand the fore-vacuum

of 10-3 mbar crucial for a turbo-pump system and on the other hand pumping

the inlet system for the adsorbates.

28 Experimental

The inlet system contains of a ¼ inch connection to fit the round bottomed

flask filled with adsorbate to the system. This fitting is linked to an all metal

regulating valve UDV 040 (Pfeiffer Vacuum) connecting the inlet part to the

vacuum system.

The whole system is operated by a Seteram controller which is connected to a

computer. A HP VEE based software is used to control the system and to track

all relevant data which is the mass, the pressure and the heat signal.

Figure 18: System used for uptake rate measurements consisting of a microbalance, vacuum system with a mass spectrometer, a dosing system and a controller.

29 Results

4. Results

4.1 Wicke-Kallenbach experiments

The diffusion and separation of benzene and p-xylene in H-ZSM5 have been

studied using the Wicke-Kallenbach method. In general the shape of the

benzene concentration curve was exponential with a clear overshooting. The

concentration gradient of p-xylene showed also an exponential form but

without the over-swinging behavior. Thereby the maximum of the over-

swinging of the benzene curve occured at the time the p-xylene uptake started.

This behavior was independent on the temperature during experiment and

activation, the thickness of the wafer and the compacting pressure.

The ratio between the equilibrium concentration of benzene and p-xylene had

a constant value around 1.43 for every performed experiment and hence

similar to the feed. This equals a separation factor of 1 valid for each

experiment. The uptake time of benzene and p-xylene differed by more than an

hour. An example of the concentration graph is shown in Figure 19 for 100 °C,

a wafer of 100 mg and 50 ml/min volume flow. In here the p-xylene

concentration was multiplied by the ratio of benzene and p-xylene (1.43).

Figure 19: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer

weight and 50 ml/min volume flow.

0 10 20 30 40 50 60 70 80 90 10010

-10

10-9

10-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

Benzene

p-Xylene

30 Results

Because the uptake time for benzene and p-xylene differed as shown in Figure

19 the separation factor was clearly depending on the time. Figure 20 shows

this time dependence. It points out that the separation factor was 1 in the

beginning, started increasing very fast after 5 minutes and reached a sharp

maximum of 104 after 20 minutes corresponding to the maximum of the

benzene breakthrough curve. After 100 minutes the graph had a constant value

of 1 due to the equilibrium concentration of benzene and p-xylene.

Figure 20: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 100mg wafer weight, a mixture of benzene/p-xylene

and 50 ml/min volume flow.

To study whether the uptake and thus the separation factor was influenced by

the temperature, experiments at 130, 100 and 70°C were carried out. Figure 21

displays the trend of the concentration of benzene at these three temperatures.

It points out that the time to the breakthrough of benzene varied between 7

minutes for 130 °C and 18 minutes for 70 °C. It shows as well that the benzene

uptake curve kept its exponential form thus the over swinging got stronger with

increasing temperature.

The breakthrough time of p-xylene was also temperature dependent changing

from 15 minutes for 130°C to 37 minutes in the case of 70°C as shown in

Figure 22.

0 50 100 150 200 250 300 35010

-2

100

102

104

106

time [min]

Sepe

ratio

n Fa

ctor

[-]

31 Results

Figure 21:Concnetration vs. time diagram of benzene breakthrough curves at 130°C (black), 100°C (red) and 70°C (blue) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer

of 100mg, a mixture of benzene/p-xylene and a volume flow of 50ml/min.

Figure 22: Concentration vs. time diagram of p-xylene breakthrough curves at 130°C (black), 100°C (red) and 70°C (blue) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer

of 100mg, a mixture of benzene/p-xylene and a volume flow of 50ml/min.

The breakthrough time as well as the time to the equilibrium concentration

decreased with increasing temperature. As in the case of benzene the overall

form of the uptake curve stayed exponential but the graph got steeper the

higher the temperature was.

Similar time dependence was found in the separation factors. Figure 23 shows

that the maximum shifted from 15 minutes towards 37 minutes with decreasing

0 10 20 30 40 50 60 70 80 90

10-7

10-6

10-5

time [min]

c [m

ol/l

]

130 °C

100 °C

70 °C

0 50 100 15010

-9

10-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

130 °C

100 °C

70 °C

32 Results

temperature. But independent of the temperature the constant value 1 was

reached.

Figure 23: Seperation factor vs. time diagram at different temperatures of 130 (blue), 100 (red) and 70°C (black) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer, a mixture of

benzene/p-xylene, a weight of 100 mg and a volume flow of 50ml/min.

To examine whether the amount of adsorbent or the thickness of the wafer had

an influence on the uptake or the separation factor pellets with weights of 50,

100 and 150 mg were used at constant temperature of 100°C keeping the

other experimental conditions untouched.

The obtained graph for benzene is shown in Figure 24. It can be seen that the

transmission time got longer the more material was used for the wafer and

hence with increasing thickness of the wafer. Considering the form of the

graphs it can be seen that curves were stretched increasing the thickness of

the wafer keeping the overall exponential form with an over-swinging before

reaching the equilibrium concentration. Consequently the chart got less steep

in exponential region and had a longer over-swinging period the higher the

weight of the wafer was. Furthermore the equilibrium concentration got smaller

with increasing thickness of the wafer.

20 40 60 80 100 12010

-2

100

102

104

time [min]

Sepe

ratio

n Fa

ctor

[-]

130°C

100°C

70°C

33 Results

Figure 24: Concentration vs. time diagram of benzene breakthrough curves with a wafer weight of 50mg (black), 100mg (red) and 150mg (blue) in a Wicke Kallenbach experiment with a

pressed H-ZSM5-wafer, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min

Figure 25: Concentration vs. time diagram of p-xylene breakthrough curves with a wafer weight of 50mg (black), 100mg (red) and 150mg (blue) in a Wicke Kallenbach experiment with a

pressed H-ZSM5-wafer, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min

Similar to the benzene curves the graph of p-xylene (Figure 25) got less steep

with increasing weight of the wafer. As in all other measurements before an

over-swinging is not observed.

As in the case of benzene the uptake time got longer with more material used

for making the wafer. Looking at the form of the breakthrough curves it is

0 50 100 150 200 250 300 35010

-8

10-7

10-6

10-5

time [min]

c [m

ol/l

]

50mg

100mg

150 mg

0 50 100 150 200 250 300 35010

-8

10-7

10-6

10-5

time [min]

c [m

ol/l

]

50 mg

100 mg

150 mg

34 Results

obviously exponential for all of the three weights but was also stretched for

thicker wafers.

The equilibrium concentration was smaller by the same percentage than in the

case of benzene. As a result the separation factor stayed 1 independent on the

thickness of the wafer. Remarkable is the time dependence of the separation

factors: similar to the uptake curves of benzene and p-xylene the maximum

separation factor shifted to longer time periods with increasing thickness of the

wafer (Figure 26).

Figure 26: Seperation factor vs. time diagram of wafers with weights of 150 (blue), 100 (red) and 50 mg (black) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer, a mixture

of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min

In another experiment the influence of the activation temperature on the

separation was examined. In order to do so the activation was performed at

150 °C instead of 450 °C as in the previous experiments. As shown in Figure

27 and Figure 28 the overall form of the transmission curves was independent

on activation temperature. Differences could be observed in the breakthrough

time and the total uptake time.

The breakthrough time was shortened by 6 minutes from 12 to 6 minutes for

benzene and by 9 minutes from 26 to 17 minutes in the case of p-xylene. The

breakthrough curves got more flat in both cases which results in a less over-

shooting in the case of benzene and longer uptake times in both cases.

0 50 100 150

10-2

100

102

104

time [min]

Sepe

ratio

n Fa

ctor

[-]

150mg

100mg

50mg

35 Results

Figure 27: Concentration vs. time diagram of benzene breakthrough curves with a activation temperature of 150 (black), 450°C (red) in a Wicke Kallenbach experiment with a pressed H-

ZSM5-wafer of 100 mg, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.

Figure 28: Concentration vs. time diagram of p-xylene breakthrough curves with a activation temperature of 150 (black), 450°C (red) in a Wicke Kallenbach experiment with a pressed H-


But even if the uptake time got longer a constant separation factor is reached

earlier specifically after 80 instead of 120 minutes (Figure 29). The constant

separation factor equals the previous experimental results with a value of 1.

0 50 100 150 200 250 300 350 40010

-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

150°C

450°C

0 50 100 150 200 250 300 350 40010

-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

150°C

450°C

36 Results

Figure 29: Seperation factor vs. time diagram with a activation temperature of 150 (black), 450°C (red) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer of 100 mg, a

mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.

To check, whether the pressure of the compacting had an influence on the

result of the experiment a wafer of 100 mg were pressed with minimum force

of 10 kN. The curves shown in Figure 30 and Figure 31 revealed the same

behavior as the previously described with the over- swinging in the benzene

transmission curve but in a less extend as previously observed and the pure

exponential curve of the p-xylene graph.

Figure 30: Concentration vs. time diagram of benzene breakthrough curves with a compacting pressure of 10kN (black), 20kN (red) in a Wicke Kallenbach experiment with a pressed H-


0 20 40 60 80 100 120 140 160 180 20010

-4

10-2

100

102

104

time [min]

Sepe

ratio

n Fa

ctor

[-]

150°C

450°C

0 50 100 150 20010

-8

10-7

10-6

10-5

time [min]

c [m

ol/l

]

10 kN

20 kN

37 Results

Figure 31: Concentration vs. time diagram of p-xylene breakthrough curves with a compacting pressure of 10kN (black), 20kN (red) in a Wicke Kallenbach experiment with a pressed H-


Differences were seen in the breakthrough times. They were 7 instead of 12

and 19 instead of 26 minutes for benzene and p-xylene, respectively. Even if

the breakthrough time differed the overall uptake times stayed the same which

were 200 for benzene and 240 minutes in the case of p-xylene.

The separation factor was identical to the former experiments 1. The time

dependence of the separation factor is shown in Figure 32.

Figure 32: Seperation vs. time diagrams with a compacting pressure of 10kN (black), 20kN (red) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer of 100 mg, a mixture of

benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.

0 50 100 150 200 250 30010

-8

10-7

10-6

10-5

time [min]

c [m

ol/l

]

10 kN

20 kN

0 20 40 60 80 100 120 140 160 180 20010

-1

100

101

102

103

time [min]

Sepe

ratio

n Fa

ctor

[-]

10kN

20kN

38 Results

The form stayed untouched of the compacting even the height of the maximum

is precisely the same with values around 700. The point of the maximum is

shifted from 20 to 15 minutes for 10 kN corresponding to the faster uptake for

the less compacted sample.

In addition the desorption (Figure 33) of benzene and p-xylene from the Wicke-

Kallenbach-wafer of 100 mg was evaluated at 100°C. Therefore, a normal

uptake procedure was performed as described before. After the concentrations

of the adsorbates reached a constant level the adsorbed species were

desorbed with unloaded sweep gas streams of 50 ml/min each until both

concentrations equaled zero.

Figure 33: Desorption-curve of benzene (blue) and p-xylene (red) at 100°C until 3090 min then the desorption was performed with a heating of 1°C per minute until 450°C and afterwards

cooled down stepwise to 100 °C again.

At that point an activation program with a heating rate of 1°C per minute was

started with a final temperature of 450°C. This temperature was then hold for 1

hour and subsequently cooled down stepwise to 100°C.

In here the desorption-curve of benzene was much steeper than the one of p-

xylene. It reached zero after 37 minutes and showed no more desorption even

if the temperature was raised. In contrast to that the p-xylene desorption curve

equals zero after 177 minutes and showed a clear maximum in desorption after

the temperature was increased corresponding to a temperature of 176°C.

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.5

1

1.5

2

2.5

3

3.5

4x 10

-5

time [minutes]

c [m

ol/l

]

Benzene

p-Xylene

39 Results

An identical Wicke Kallenbach experiment using a standard 100 mg wafer as

described previously was also performed with m-xylene and p-xylene as single

components due to experimental constraints. The result is shown in Figure 34.

Figure 34: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and consecutively p-xylene (black) and m-xylene (red), 100°C, 100mg wafer


As m- and p-xylene have the same mass distribution in a mass spectrometer it

was not possible to determine the separation in one experiment. Hence the

transmission of the single components was examined.

The form of both curves was identically exponential with a large slope in the

starting region. Differences could be found in transmission and the uptake

times. Thereby m-xylene showed a breakthrough time of 10 minutes whereas

p-xylene needed 40 minutes to transmit. In contrast the uptake time was much

longer for m-xylene than for p-xylene specifically 350 and 100 minutes for m-

xylene and p-xylene , respectively.

0 50 100 150 200 250 300 35010

-7

10-6

10-5

time [min]

c [m

ol/l

]

p-Xylene

m-Xylene

40 Results

Table 3: Experimental results of the Wicke-Kallenbach experiments

Sample Experiment

Number

Wafer

Weight

[mg]

Compacting

pressure

[kN]

Experimental

Temperature

[K]

Activation

Temperature

[K]

Breakthrough

Time

Benzene

[min]

Breakthrough

Time

m-xylene

[min]

Breakthrough

Time

pXylene

[min]

H-ZSM5 1 100 20 373 723 12 27

H-ZSM5 2 100 20 353 723 19 41

H-ZSM5 3 100 20 403 723 7 17

H-ZSM5 4 150 20 373 723 23 47

H-ZSM5 5 50 20 373 723 3 9

H-ZSM5 6 100 20 373 423 7 16

H-ZSM5 7 100 10 373 723 7 17

H-ZSM5 8 100 20 373 723 10 40

Experiment

Number

Uptake

Time

Benzene,

[min]

Uptake

Time

m-Xylene

[min]

Uptake

Time

p-Xylene

[min]

Equilibrium

Concentration

Benzene

[mmol/l]x102

Equilibrium

Concentration

m-Benzene

[mmol/l]x102

Equilibrium

Concentration

p-xylene

[mmol/l]x102

Separation factor

1 270 185 3.6 2.49 1.01

2 290 210 3.7 2.76 0.94

3 270 250 3.55 2.4 1.03

4 295 240 2.51 1.6 1.14

5 250 450 5.4 2.96 1.28

6 350 300 3.53 2.22 1.11

7 400 370 3.75 2.73 0.91

8 350 100 0.81 1.66 1.23

41 Results

The most important factor, the separation factor, was 1.23 in this experiment

taking the ratio of feed concentration into account which was 2.52 p-xylene/m-

xylene. All experiments are summarized in Table 3.

4.2. Frequency Response experiments

To understand which transport mechanism is rate determining in the Wicke

Kallenbach experiment three different frequency response experiments were

carried out. The first measurement was performed with a powdered sample,

the next with very thin wafers which were of a weight between 6 and 10 mg

and lastly with a wafer of the same type as used in the Wicke Kallenbach cell

with a weight of 100 mg. The wafers were broken into smaller pieces before

starting the measurement to fit into the quartz sample holder.

The characteristic functionns obtained from the measurements of the powder

and the thin wafer are compared in Figure 35 and Figure 36. The functions of

the Wicke Kallenbach wafer are not shown here because the time constant

(L2/D) was too large and therefore no suitable data was obtained.

The out of phase function (Figure 35) was nearly identical for both samples

showing a maximum at 0.02 Hz. This maximum corresponds to a time constant

of 50.25s using the method described by Gobin et al. [60] which defines the

reciprocal value of the maximum of the out-of-phase function to be the time

constant. In addition the diffusion coefficients were calculated by simply

dividing L2 by the time constant. Assuming a particle size of 0.4μm obtained by

SEM the diffusion coefficients were 2.15x10-15 and 2.36x10-15 m2/s for the thin

wafer and the powdered sample, respectively.

Curve fitting was applied employing the model equations described in 2.3.

using on the one hand a simple pore diffusion model in an infinite plane sheet

and on the other a more sophisticated model assuming a surface resistance

control. Both models were used with and without a particle size distribution to

see the impact of a non-uniform size distribution. The fits for the surface

resistance model are also shown in Figure 35 and Figure 36. The obtained

transport parameters for all theoretical models and both samples are

summarized in Table 4 and Table 5.

42 Results

Figure 35: Out of phase function of the ZSM5 sample in powdered state (black) and pressed to a thin wafer (red) including the fit (lines) with a surface resistance model in a non-uniform sheet.

Figure 36: In of phase function of the ZSM5 sample in powdered state (black) and pressed to a thin wafer (red) including the fit (lines) with a surface resistance model in a non-uniform sheet.

Both samples showed nearly the same parameters independent on the

assumed model. The time constant was in the range of 67 to 75 seconds, the

corresponding diffusion coefficient was between 2.16 and 2.59 x 10-15 m2/s. K

showed values between 0.24 and 0.27. All of the models had a apparently

good fitting probability confirmed by the normalized root mean square errors

which were in an acceptable range of 0.40 to 0.52. Thereby the model with

10-3

10-2

10-1

100

101

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

frequency [Hz]

out-

of-p

hase

cha

ract

eris

tic fu

nctio

n [-

]

NormRMS-Error = 0.44666

D = 2.5916e-015

K = 0.25392

powder

fit powder

fit thin Wafer

thin Wafer

10-3

10-2

10-1

100

101

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

frequency [Hz]

in-o

f-ph

ase

char

acte

rist

ic fu

nctio

n [-

]

powder

fit powder

thin wafer

fit thin wafer

43 Results

non-uniform particle sizes and a surface resistance had the best correlation

with the experimental data.

Table 4: Transport parameters for a powdered sample of ZSM5 obtained by curve fitting assuming theoretical models describing a uniform infinite sheet, a uniform infinite sheet with surface resistance control a non-uniform infinite sheet and a non-uniform infinite sheet with surface resistance control

Model L2/D [s] D x 1015

[m2/s]

K NRMS-error

Uniform infinite sheet 70.48 2.27 0.24 0.52

Uniform infinite sheet with surface

resistance

70.36 2.27 0.24 0.52

Non-uniform infinite sheet 61.74 2.59 0.25 0.45

Non-uniform infinite sheet with

surface resistance

67.24 2.38 0.25 0.44

Table 5: Transport parameters for a thin wafer of ZSM5 obtained by curve fitting assuming theoretical models describing a uniform infinite sheet, a uniform infinite sheet with surface resistance control a non-uniform infinite sheet and a non-uniform infinite sheet with surface resistance control

Model L2/D [s] D x 1015

[m2/s]

K NRMS-error

Uniform infinite sheet 68.40 2.34 0.26 0.43

Uniform infinite sheet with surface

resistance

68.32 2.34 0.26 0.44

Non-uniform infinite sheet 73.20 2.19 0.27 0.40

Non-uniform infinite sheet with

surface resistance

74.18 2.16 0.27 0.40

4.3. Uptake Rate measurements

The gravimetric uptake curves of an 8 mg piece of a 100 mg Wicke Kallenbach

wafer having a thickness of 1 mm were obtained at adsorbate partial pressures

of 0.1, 1, 2 and 10 mbar and 373 K. All of the curves showed an exponential

uptake with a large time constant (L2/D) between 3.58x102 and 5.77x103

seconds obtained by curve fitting with the theoretical model described in 2.4.

44 Results

Figure 37: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 1 mbar and 373K. The figure shows the experimental data (black) and the

result of the curve fitting (red) applying an infinite plane sheet model of 1mm thickness.

Figure 38: Fitted uptake curves of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at 373K at partial pressures of 0.1mbar (black), 1mbar (red), 2mbar (blue) and 10 mbar (green).

Figure 37 shows an example of such an uptake curve for the case of 1 mbar

having a clear exponential behavior. It also shows the good quality of the fit

and therefore of the applied model. Figure 38 summarizes the uptake

measurements by showing the results of the curve fitting. Thereby the graphs

got steeper with increasing partial pressure of the adsorbate which is equal to

a decreasing time constant with the loading. This indicates a clear dependence

of the diffusion coefficient on the concentration which can be calculated by

0 500 1000 15000

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed c

once

ntra

tion

[-]

0 200 400 600 800 1000 1200 1400 16000

0.2

0.4

0.6

0.8

1

time [s]

norm

aliz

ed m

ass

[-]

0.1 mbar

1 mbar

2 mbar

10 mbar

45 Results

dividing L2 by the time constant. Thereby half of wafer thickness which is

0.5 mm equals L. The obtained parameters are summarized in Table 6.

Table 6: Summary of the parameters obtained curve fitting of the experimental data of a H-ZSM5 Wicke – Kallenbach wafer of 100mg applying a theoretical model describing an isothermal infinite plane sheet of the thickness 1mm

Partial pressure [mbar] L2/D x 102 [s] D x 1010 [m2/s] NRMS-error

0.1 57.7 0.43 0.30

1 18.3 1.37 0.26

2 7.75 3.23 0.73

10 3.58 6.98 0.64

To see how the diffusion coefficients of benzene in a ZSM5 Wicke Kallenbach

wafer depend on the partial pressure they were plotted with the partial

pressure on the x-axes and the diffusion coefficient on the y-axes. The

outcome is shown in Figure 39. A linear dependence is obtained.

Figure 39: Dependence of the diffusion coefficient on the partial pressure of Benzene in a Wicke Kallenbach wafer of 100mg.

To determine differences between the Wicke Kallenbach wafer and the

powdered sample the uptake rate of a powdered sample was also measured.

In order to do so 4.3 mg of the powder was dispersed on glass wool analogue

to the pressure frequency response experiments to avoid bed effects. The

adsorbate benzene was dosed into the system in steps of 0.1, 1, 2 and 10

mbar by simultaneously tracking the mass.

0,00E+00

1,00E+01

2,00E+01

3,00E+01

4,00E+01

5,00E+01

6,00E+01

7,00E+01

8,00E+01

0 2 4 6 8 10 12Dif

fusi

on

co

eff

icie

nt

x 1

01

1 [m

2 /s]

partial pressure [mbar]

46 Results

Figure 40:: Fitted uptake curves of benzene in H-ZSM5 powder at 373K at partial pressures of 0.1mbar (black), 1mbar (red), 2mbar (blue) and 10 mbar (green).

Data processing was performed identical to the other experiment by non-linear

parameter fitting using a CMA evolutional strategy in matlab which resulted the

fitting shown Figure 40 and Table 7.

Table 7: Summary of the parameters obtained curve fitting of the experimental data of a powdered H-ZSM5 applying a theoretical model describing isothermal infinite plane sheet of the thickness 0.4 μm

Partial pressure [mbar] L2/D x 102 [s] D x 1016 [m2/s] NRMS-error

0.1 2.22 7.21 0.29

1 2.7 5.93 0.25

2 3.4 4.71 0.36

10 6.14 2.61 0.28

The characteristic length of diffusion is defined here as the particle size of

0.4 μm. In contrast to the wafer the diffusion coefficient decreased with

increasing partial pressure which can also be seen in Figure 41. A linear

decrease of the diffusion coefficient with the pressure was obtained. This is

most likely due to non idealities of the experiment. Especially it is impossible to

perform the uptake of partial in a step function. Consequently the bigger the

change of partial pressure is the longer the uptake takes which means that it is

further away from the ideal step function. This means that the adsorption

0 50 100 150 2000

0.2

0.4

0.6

0.8

1

time [s]

norm

aliz

ed m

ass

[-]

0.1 mbar

1 mbar

2 mbar

10 mbar

47 Results

process of benzene in this MFI powder sample is too fast to get a reliable

result from the gravimetric uptake.

Figure 41: Trend of the diffusion coefficient of H-ZSM5 powder obtained by uptake rate measurements.

4.4. Nitrogen physisorption isotherms

The procedure of the nitrogen physisorption measurement of the Wicke

Kallenbach wafer was identical to the one described in the experimental

section (3.1). The outcome compared to the isotherm of the parent material is

shown in Figure 42 and Figure 43.

Figure 42:Nitrogen physisorption isotherms of H-ZSM5 parent powder material (black) and the same material pressed to a wafer of 100 mg (red).

0,00E+00

1,00E+00

2,00E+00

3,00E+00

4,00E+00

5,00E+00

6,00E+00

7,00E+00

8,00E+00

0 2 4 6 8 10 12Dif

fusi

on

co

eff

icie

nt

x 1

016 [

m2 /

s]

partial pressure [mbar]

0

50

100

150

200

250

300

350

0,00E+00 2,00E-01 4,00E-01 6,00E-01 8,00E-01 1,00E+00 1,20E+00

Vad

s[cm

3/g

]

P/P0 [-]

48 Results

Figure 43: Nitrogen physisorption isotherms of H-ZSM5 parent powder material (black) and the same material pressed to a wafer of 100 mg (red) in the range of 0.2 to 0.9 p/p0.

Both curves are typical type 4 isotherms. A remarkable change was observed

after pressing the powder to a wafer. The pressure region from the starting

point until 0.2 was nearly identical for either the powder or the wafer. At 0.2 the

hysteresis starts to open in the case of the wafer which occurred at 0.8 in the

case of the powder. Moreover the total size of the loop obtained was much

bigger in the case of wafer than for the powder. The data was then analyzed

applying the BET formula resulting in a BET surface area of 4 46 m2/g.

0

50

100

150

200

250

300

350

2,00E-01 3,00E-01 4,00E-01 5,00E-01 6,00E-01 7,00E-01 8,00E-01 9,00E-01

Vad

s[cm

3/g

]

P/P0 [-]

49 Discussion

5. Discussion

In order to understand how the ZSM5 wafer behaves during a Wicke

Kallenbach experiment two theories were postulated describing the wafer. On

the one hand a statistically dense membrane and on the other hand the

classical bed adsorber. Statistically dense membrane represents in this context

a mesoporous layered wafer in which the diffusing molecule has to pass at

least one particle during the diffusion process (Figure 44).

Figure 44: Principle of a statistically dense membrane.

This means the whole transport mechanism is controlled by the diffusion

through the particle which defines the kinetic of the pore diffusion as rate

determining. This model assumes a steady state during the diffusion; hence

the system is not in equilibrium at any time.

The other possible model is a flow adsorber showing transmissions curves as

described extensively before [53]. This model assumes an adsorption front

going through the particle bed until the adsorbent is saturated.

Figure 45: Principle of a classical bed adsorber [72].

In contrast to the dense membrane this model is based on the assumption of

thermodynamic control. Consequently it has an adsorption region (Figure 45)

50 Discussion

where the system is not in equilibrium but the overall rate is controlled by the

strength of adsorption. It assumes an established adsorption/desorption

equilibrium in the wafer after the breakthrough of the adsorbates is finished.

The first remarkable aspects in the obtained data were the breakthrough times.

The overall trend was that the breakthrough of benzene was faster than the

one of p-xylene. This behavior can be explained with both models. In the case

of the dense membrane the faster diffusing component would penetrate faster.

This assumption would be in good accordance with Gobin et al. [60] who found

intra crystalline diffusion coefficients of 5.28x10-13 and 2.46x10-13 m2/s for

benzene and p-xylene, respectively.

But on the other hand this breakthrough time distribution is also typical for flow

adsorbers. Based on the theory the weaker adsorbing substance penetrates

first. This matches the found breakthrough times which are in good agreement

with Mukti et al. who determined adsorption enthalpies of benzene and p-

xylene of -51 kJ/mol and 94 kJ/mol, respectively [64].

The next interesting result was the temperature dependence. A clear decrease

of the transmission time with increasing temperature was found which would

also be typical for both models. This can be explained for the membrane with

an increase of the diffusion coefficient with increasing temperature as

described in the literature [60]. The higher diffusion coefficient leads to a faster

transport through the pore system resulting in a decreased breakthrough time

at higher temperatures.

The explanation for the adsorber model is the decreasing capacity with the

increasing temperature as indicated by the isotherms. They show a decrease

of loading at increasing temperature. As a result less substance can be

adsorbed at the adsorbent which have to lead also to a decreased

transmission time.

Furthermore an influence on the wafer thickness was found. An increase of the

breakthrough time with increasing thickness was observed. This is in

agreement with both models. The explanation for the model of a statistically

dense membrane is simple, the thicker the wafer is the more particles have to

be passed statistically.

51 Discussion

On the other hand this observation agrees with the adsorber model. Increasing

the wafer thickness has the same effect as decreasing the temperature: it

results in a higher adsorption capacity. Based on this theory a higher capacity

leads to a longer breakthrough time [65].

The transmission times clearly decreased when the activation temperature was

decreased to 423K because the water was not removed completely from the

zeolite. This is inconsistent with the membrane model because a higher loading

makes it harder to diffuse through a particle. As a result the breakthrough time

should had been increased or at least stayed constant and not decreased as it

is shown in Figure 27 and Figure 28.

Considering the adsorber model a higher water loading lowers the capacity

because less adsorption places are reachable for the diffusing substance. As a

consequence shorter transmission times are expected. Thus, the experimental

data also agreed with the postulate of a bed adsorber analogue.

After discussing the breakthrough times the form of the transmission curve has

to be considered. In the experiments an overshooting in the benzene graph

and a pure exponential uptake of p-xylene was observed in every experiment

with H-ZSM5 as adsorbent independent on the temperature, wafer thickness,

activation temperature or compacting pressure. This type of breakthrough

curves is typical for bed adsorbers [53].

The overshooting arises due to the competitive adsorption of benzene and p-

xylene. In this case benzene adsorbs faster than p-xylene but the adsorption is

weaker. Consequently benzene is displaced by p-xylene which then occupies

the adsorption centers and by this leads to an accumulation of benzene in the

non-equilibrium zone. Once the equilibrium in the adsorber is established the

concentrations of benzene and p-xylene are constant. It follows that the

concentration of benzene shortly after the breakthrough is higher than the

steady state concentration which can be seen as an overshooting of the graph.

As discussed before the weaker adsorbing substance broke through first and

showed an overshooting. In contrast to this the adsorbate with the higher

adsorption enthalpy, in this case p-xylene [64], had a longer breakthrough time

and showed no overshooting at all. Therefore, the form of the transmission

curve can be explained by the model of a classical adsorber.

52 Discussion

To allow the comparison of the experimental data with the postulate of the

dense membrane the experimental data was tried to fit numerically. A solution

of the second fickian law derived by Crank et al. [54] for the diffusion through a

membrane was used:

(5.1)

where Cω is the concentration at infinite time, D is the diffusion coefficient

which was previously determined by Gobin et al. [60] and L is the characteristic

length of diffusion

Unfortunately it was impossible to fit the experimental data with a sufficient

goodness of fit. This means that it is not possible to describe the

experimentally obtained data with the model of a membrane. This strongly

suggests that the model of a statistically dense membrane is not describing

this particular Wicke Kallenbach experiments in a proper way.

The most important parameter for this process is the separation factor

because the aim of these wafers was the separation of benzene and p-xylene.

Unfortunately the separation factor in the experiments equaled independent on

any changes 1. This result can`t be explained with the dense membrane model.

If the transport process would had been controlled by pore diffusion a

separation factor higher than 1 had to be found because according to Gobin et

al. [60] the diffusion of benzene is by an order of 2 faster than the diffusion of

p-xylene inside the ZSM5 pore system. As the model assumes a kinetic control

the permeation flows of benzene and p-xylene must had been different from

each other which would had led to a separation.

According to Sun et al. [23] it is possible to calculate the concentration in the

permeate at steady state conditions by:

(5.2)

where AW is the cross section of the wafer, D is the intracrystalline diffusion

coefficient, KH is the Henry constant and L is the thickness of the wafer. The

concentration of p-xylene in steady can be calculated from the ratio of the p-

xylene/benzene concentration. This equals taking V>> AxDxK/L into account:

(5.3)

53 Discussion

According to 5.3 the separation factor can be mathematically described by

Dp-xylene/Dbenzene for the model of a membrane. Assuming this model it is possible

to calculate the theoretically expected separation factors according to the

previously reported diffusion coefficients [60]. The results are shown in Table 8.

Table 8: Theoretically expected separation factors of the Wicke Kallenbach experiment assuming a statiscally dense membrane applying the diffusion coefficients reported by Gobin et al. [60]

T [°C] Diffusion coefficient

Benzene x 10-15

[m2/s]

Diffusion coefficient

p-xylene x 10-15

[m2/s]

Seperation factor

[-]

70 3.96 0.97 4.08

100 7.34 2.48 2.96

130 12.9 6.02 2.14

Also a temperature dependence on the permeation flux [3,66,67] is expected

as the diffusion coefficient varies with the temperature which would had

influenced separation factor as well. But the results show that neither the

expected temperature dependence nor a separation factor at all was observed

in the experiments.

Furthermore the separation factor showed a clear dependence on the time

which means that it reached a maximum after 10 to 50 minutes depending on

the temperature, the wafer thickness, the compacting pressure and the

activation temperature. The observed behavior fits perfectly the model of an

adsorber. As expected the position of the maximum corresponded to the

capacity of the adsorber. The time until the maximum was reached increased

with increasing capacity produced by a lower temperature during experiment

and activation and a higher thickness of the wafer. The maximum of the

separation factor occurred at the same time as the maximum of the over

swinging of the benzene concentration curve. It was identical with the

breakthrough time of p-xylene.

To determine the amount of adsorbed species on the pellet a desorption

experiment was carried out. In order to do so adsorption until equilibrium

conditions was achieved, afterwards the adsorbate stream was stopped and

the adsorbate was desorbed with the help of sweep gas (50 ml/min). The

amount of adsorbed species was then determined by integration with respect

54 Discussion

to t of the resulted data. The obtained values were then multiplied by 2

because the desorption occurred in both directions of the cell but the amount

was only tracked at one of the streams. Hence, the concentration of adsorbed

species inside the wafer equals the integration with respect to t of the tracked

concentration signal multiplied by 2.

The integration resulted in a concentration of 5.86 x 10-4 and 1.33 x 10-3 mol/l

for benzene and p-xylene. This led to a ratio of benzene/p-xylene of 0.44 which

means that the concentration of p-xylene was more than two times higher than

the concentration of benzene. This result is in good accordance with the

adsorption enthalpies measured by Mukti et al. [64]. It is another hint for the

adsorber theory because this model predicts that the process is

thermodynamically controlled. By this means the concentration ratio inside the

sheet must be equal to the ratio calculated from the isotherms which depend

on the adsorption enthalpies.

To confirm the theory of the adsorber the number of hits was calculated which

the molecules have with the pore wall during one transmission through the

wafer. This is important because it has to be shown that it is possible to

establish an adsorption/desorption equilibrium during the transmission time. If

it is impossible to build up an equilibrated state the whole adsorber theory is

no longer supportable.

The base of the calculation were the sticking probabilities obtained by

Reitmeier et al. [4] having values of 2.10x10-7 and 2.18x10-7 for benzene and p-

xylene. This parameter describes the probability that a poke between the

adsorbate and the outer surface of a porous material leads to a pore entering.

The starting point of the calculation is the overall number of wall collisions

depending on the partial pressure of adsorbate and the temperature derived

from the kinetical gas theory [68]:

(5.4)

where P is the partial pressure of the adsorbate in the feed, m is the mass of

one molecule, k is the Boltzmann constant and T is the temperature [K]. To be

able to calculate how many hits a molecule has with the walls of the

mesopores during the transmission through the wafer, the flow of molecules

per second entering the sample has to be calculated:

55 Discussion

(5.5)

In here p defines the partial pressure of the adsorbate in the feed, R in the gas

constant, T is the temperature, F(He) is the flow of the sweep gas and NA is the

Avogadro constant. With this data it is possible to determine the surface area

of the adsorbent needed for one poke of the adsorbate:

(5.6)

In the next step the surface area needed for poke leading to the sorption of the

adsorbate is identified by taking the sticking coefficient into account:

(5.7)

As the external surface area of the wafer is known the successful hits during

the transmission of the adsorbate through the wafer could be obtained by:

(5.8)

The results for temperatures of 343, 373 and 403 K and the adsorbates

benzene and p-xylene are summarized in Table 9.

Table 9: Results of the calculation considering the number of pokes leading to a pore entering during the transmission of benzene and p-xylene through the Wicke Kallenbach wafer

Adsorbate T

[K]

PFeed

[Pa]

Zw x 10-24

[1/(m2s)]

Fmolec.x10-16

[Molec./s]

Aper poke

x109

[m2]

Aper suc. poke

x102

[m2]

Nx102

[-]

Benzene 343 313,2 5.04 1.86 3.68 1.75 3.71

Benzene 373 313,2 4.84 1.81 3.75 1.78 3.64

Benzene 403 313,2 4.65 1.78 3.82 1.82 3.57

p-Xylene 343 234 3.23 1.32 4.10 1.88 3.46

p-Xylene 373 234 3.10 1.24 4.00 1.83 3.54

p-Xylene 403 234 2.98 1.21 4.06 1.86 3.49

The number of successful pokes is in the range of 350 per molecule during the

transmission through the wafer. This means that the establishing of an

adsorption/desorption equilibrium as postulated in the adsorber theory is in

good accordance with the previous determined sticking coefficients.

Consequently the theory of an adsorption zone is also valid.

Furthermore it is possible to estimate the length of the zone which is not in

equilibrium known as adsorption zone because it equals the length between

56 Discussion

two successful pokes. This value can simply be evaluated by taking the

reciprocal value of N and multiplying it with the total length of diffusion. This

leads to a length of the adsorption zone of 2.9x10-3 mm.

The final evidence for the assumed bed adsorber analogue gave the

comparison of the uptake curves of m-xylene and p-xylene which had to be

measured in two consecutive experiments due to experimental constraints.

The result is shown in Figure 34. Obviously m-xylene transmitted after 10

minutes where as breakthrough of p-xylene took 40 minutes. The form did not

change compared to the experiments of benzene and p–xylene and showed

both the same exponential form as p–xylene in the previous measurements.

This is due to the consecutive measurement: the overshooting as previously

seen in benzene is only observed if two adsorbates are present and the

adsorption enthalpies differ clearly [53].

The separation factor calculated as described in 2.2.1 had a value of 1.23

which equals 1 taking the error of the experiment into account. This is a totally

different behavior compared to the previously reported separation of p-xylene

from a mixture of o-, m- and p-xylene with the help of an MFI membrane [3].

Sakai et al. demonstrated that the differences in permeability due to the larger

minimum kinetic diameters of m-xylene in comparism to p-xylene lead to a

separation factor of 10 p-xylene/m-xylene at 373 K. This is significantly

different to our experiment. This experiment shows that the pressed Wicke

Kallenbach wafer did not act similar to a membrane and by this means the

theory of a statically dense membrane is not valid for this system.

In contrast to the theory a bed adsorber describes the experimental data very

good. The transmission times can be understood by the accessible adsorption

centers. M-xylene can only reach the outer surface having a BET surface area

of 65 m2/g. The sorption into the pores of the zeolite to adsorb at the

adsorption places inside the pore system is very slow due to the minimum

kinetic diameter. This process could be seen in the slow uptake in the late time

region of the uptake curve.

The other adsorbate p-xylene was able to access the pore system to adsorb

there which led to a transmission time of 40 minutes. Comparing this to the

observed BET total surface area of 446 m2/g of the wafer it can be concluded

57 Discussion

that the uptake time has a clear dependence on the accessible adsorbtion

centers. This is in good agreement with the postulated bed adsorber.

The fact that no separation occurred was due to the rate determining step

which was the Knudsen diffusion through the mesopores after the

adsorption/desorption equilibrium is established. As m-xylene and p-xylene

have the same mass the Knudsen diffusion coefficients have to be identical

(2.2.5) as the speed of this transport type is independent on the kinetic

diameter.

All these facts summarized in Table 10 show that the model of an adsorber

describes the wafer of the Wicke Kallenbach experiment bes

Table 10: Summary of the experimental facts and check of consistency to the adsorber and the statistically dense membrane model

Experimental Fact/Model Adsorber Membrane

breakthrough time consistent consistent

temperature dependence on breakthrough time of

benzene/p-xylene

consistent consistent

influence of wafer thickness on breakthrough time of

benzene/p-xylene

consistent inconsistent

dependence of the activation temperature on the

breakthrough time of benzene/p-xylene


form of the uptake curves consistent -

equilibrium/ steady state separation factor = 1 benzene/p-

xylene


equilibrium/ steady state separation factor = 1 p-xylene/m-

xylene


missing temperature dependence on the separation factor

of benzene/p-xylene


time dependence of the separation factor of benzene/p-

xylene

consistent -

sticking probalities consistent consistent

no activation energy of the diffusion consistent inconsistent

58 Discussion

Table 11: Summary of the results of the calculatng the diffusion coefficients of benzene and p-xylene in a Wicke Kallenbach wafer consisting of H-ZSM5. Furthermore the pore diameters calculated from these diffusion coefficients assuming Knudsen diffusion are reviewed

Sample Wafer

Weight

[mg]

Compacting

pressure

[kN]

Experimental

Temperature

[K]

Activation

Temperature

[K]

Diffusion

coefficient

Benzene x 10-7

[m2/s]

Diffusion

coefficient

p-xylene x 10-7

[m2/s]

pore diameter

calculated from

DBenzene x 10-9

[m]

pore diameter

calculated from

Dp-xylene x 10-9

[m]

H-ZSM5 100 20 373 723 6.51 6.39 6.14 7.02

H-ZSM5 100 20 343 723 6.74 7.20 6.53 8.14

H-ZSM5 100 20 403 723 6.39 6.18 6.11 6.54

H-ZSM5 150 20 373 723 6.56 5.77 6.18 6.35

H-ZSM5 50 20 373 723 4.88 3.60 4.61 3.96

H-ZSM5 100 20 373 423 6.32 5.62 5.96 6.18

H-ZSM5 100 10 373 723 6.61 7.16 6.24 7.88

59 Discussion

This fact leads to a characteristic length of diffusion equally to the thickness of

the wafer, in contrast to the radius of on particle as in the case of the

statistically dense membrane model. Consequently it was the possible to

calculate the diffusion coefficients by equation (2.2.2) from the equilibrium

molar ratios:

(5.10)

where L is characteristic length, r is the radius of the wafer, FHe is the flow rate

of the sweep gas helium and xAdsorbate is the molar ratio of the adsorbate in the

feed and the permeate at equilibrium conditions, respectively.

From the observed diffusion coefficients which were in the range of 10-6 m2/s

we could assume Knudsen diffusion. As a consequence it was possible to

calculate the radius of the pores by transposing (2.2.5). The transposed

equation is expressed by:

(5.11)

where R is the gas constant, T is the temperature, M is the molar mass. The

results of the calculation are shown in Table 11. The assumed Knudsen

diffusion is confirmed by the calculated pore diameters which are in the range

of 6 to 8 nm. Pores of this size were defined as mesopores [69] by the IUPAC

(International Union of Pure and Applied Chemistry). This means that the

diffusion in pressed wafers was limited by the transport in mesopores of 6 to 8

nm size.

Figure 46: SEM image of the surface of a Wicke Kallenbach wafer.

60 Discussion

This result fits to the impression of the SEM image which shows separated

particles (Figure 46)

It indicates as well that the wafer had pores of larger diameters than the

calculated ones of 6 to 8 nm but these pores were obviously not rate

determining. Thus, we can assume that the calculated pore diameters are the

smallest which occurred in the Wicke Kallenbach pellets as they determined

the transport rate.

The assumption of Knudsen diffusion determining the transport through the

wafer is also in good agreement with the physisorption isotherm of nitrogen.

Figure 47: t-plot produced with the method of Hasley for the H-ZSM5 Wicke Kallenbach wafer.

As previously described the isotherm had a much larger loop even at low

pressures of 0.2 P/P0 which corresponds to mesopores formed during the

pressing procedure. The BET surface area did not change from the powder to

the pressed disk and stayed at 420 to 450 m2/g.

The total volume of the micro- and mesopores was determined using a t-plot

(Figure 47) produced with the method of Halsey [70]. The results are

summarized in Table 12. It resulted in a total micropore volume of 0.147 cm3/g

and a mesopore volume of 0.232 cm3/g. A clear enhancement of the mesopore

volume was obtained compared to the pore volume of the parent material [5]

which was 0.147 cm3/g and 0.132 cm3/g micro– and mesopore volume. The

y = 0,048x + 0,147

y = 0,0095x + 0,3789

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 1 2 3 4 5 6 7 8 9

v ad

s[c

m3/g

STP

]

tHasley [nm]

61 Discussion

micropore volume stayed untouched which is the expected characteristic as

the micropores built up by the zeolite framework. This is not influenced by the

pressing of the powder and consequently the micropore volume had to stay

the same.

To have a closer look on the mesopores a DFT analysis of the physisorption

isotherm was performed to obtain the pore diameter of mesopores shown in

Figure 48.

Table 12: Results of the analysis if physisorption isotherms of H-ZSM5 in the powdered and the pressed form applying the BET equation [59] and the t-plot method [70]

Material SBET [m2/g] VMicro [cm3/g] VMeso [cm3/g]

powder 420 0.147 0.132

100 mg Wafer 446 0.147 0.232

The DFT analysis (Figure 48) showed an increase of mesopores with a

maximum of the distribution at a pore diameter of 17 nm. This is in good

agreement with the pore diameters calculated from the diffusion

measurements which were 6 to 8 nm. The huge pores indicated by the SEM

image are not found in the physisorption isotherm as they are larger than 65

nm.

Figure 48: pore size distribution of the parent H-ZSM5 material (black) and the Wicke Kallenbach wafer (red) obtained by DFT calculation.

0,00E+00

5,00E-04

1,00E-03

1,50E-03

2,00E-03

2,50E-03

50 150 250 350 450 550 650

dV

[cm

3/Å

/g]

pore size [Å]

62 Discussion

The assumption of Knudsen diffusion could also be confirmed by looking at the

activation energy which was determined by an Arrhenius ansatz describing the

diffusion coefficient by [66]:

(5.12)

(5.13)

In here D is the diffusion coefficient, EA,D is the activation energy of diffusion, R

is the gas constant and T is the temperature.

According to 5.13 it was possible to obtain the activation energy of the

diffusion of benzene and p-xylene for the rate determining step inside the sheet

by plotting 1/T against ln (D) (Figure 49).

Figure 49: Determination of the activation energy of benzene (black) and p-xylene (red) by an Arrhenius ansatz.

The calculation resulted in activation energies of -1.03 and -2.96 kJ/mol for

benzene and p-xylene, respectively. Taking the error of the system including

the inlet system and the mass spectrometer into account the activation energy

of diffusion was in the range of zero. Afterwards the ideal activation energy of

the Knudsen diffusion in the examined system was determined by calculation

the diffusion coefficients with:

(5.14)

The mean value of the obtained pore diameters from Table 11 was used for the

calculation. The results are shown in Table 13, Table 14 and Figure 50.

-14,4

-14,3

-14,2

-14,1

0,0024 0,0029

ln(D) [-]

1/T [1/K]

benzene

p-xylene

63 Discussion

Table 13: Calculated ideal Knudsen diffusion coefficients of benzene

T [K] D x 10-7 [m2/s]

343 6.38

373 6.65

403 6.91

Table 14: Calculated ideal Knudsen diffusion coefficients of p-xylene

T [K] D x 10-7 [m2/s]

343 5.47

373 5.70

403 5.93

Figure 50: Theoretical evaluation of the activation energy of benzene (black) and p-xylene (red) from the calculated Knudsen diffusion coefficients by a Arrhenius ansatz.

The results imply activation energies of 1.54 kJ/mol for both substances which

shows that the Knudsen diffusion has nearly no activation energy in this

system. Thus, the obtained activation energies of the measurements are in

good agreement with the theory and are consequently another hint for the

existence of Knudsen diffusion. This fact is also inconsistent with the

previously described theory of a dense membrane because the apparent

diffusion of benzene and p-xylene in the used ZSM5 sample has activation

energies according to Gobin et al. [60] of 23 and 35 kJ/mol, respectively.

Additionally curve fitting was preformed with the transmission curves of the

Wicke Kallenbach experiment. The aim of this method is to fit kinetic

-14,5

-14,4

-14,3

-14,2

-14,1

0,0023 0,0028

ln(D) [-]

1/T [1/K]

benzene

p-xylene

64 Discussion

parameters from the transmission curves of the Wicke Kallenbach

experiments. In order to do so a kinetic model was assumed and tried to fit the

experimental data. The data was fitted with a set of differential equations

describing an adsorber with an irreversible Langmuir adsorption.

The breakthrough curve was in this case specified by two differential

equations, one for the gaseous and one for the solid phase. These formulas

define the concentration dependent on time of the adsorbate where the solid

phase concentration is replaced by the surface coverage (Θ). Hence, the rate

of adsorption can be formulated by (6) [53].

(5.15)

In here Θ is the normalized surface coverage [71], ka is the reaction rate

coefficient and c is the concentration of the adsorbate in the gas phase.

The mass balance of the fluid phase describes the concentration of the

adsorbate dependent on the time [72]

(5.16)

These set of differential equations can be solved analytically according to

Bohart et. al [73]. The solution is shown in (5.17):

(5.17)

where C is the normalized concentration in the gas phase calculated by c/c0, ka

denotes the reaction rate coefficient, c0 is the concentration in the feed, t is the

reaction time, WSat is maximum amount of adsorbed gas, ρB is the density of

the bed, S is the section of the adsorbent bed and F is the gas flow rate.

Nonlinear parameter fitting was performed using a genetic algorithm

implemented in matlab. The fitting parameters were F and ka. The objective

minimized was the normalized root mean square error divided by t3 to get a

better fit in initial region of the curves. One example of the obtained fits is

shown in Figure 51.

65 Discussion

Figure 51: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer

weight and 50 ml/min volume flow and the corresponding fit for benzene (black) and p-xylene (blue).

…

Figure 52: Trend of the parameter k with the temperature.

Due to the very primitive model and the in comparison to that very complex

adsorption behavior of the system the fits were poor. Nevertheless it was

possible to find trends for the strength of adsorption and the diffusion

coefficient. Hereby ka served as the parameter describing the limiting factor of

the adsorption on particle level which is according to Gobin et al. [60] the pore

entering step and F is proportional to the diffusion coefficient as the transport

through the pellet is a fully diffusive.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

t [s]

norm

aliz

ed c

once

ntra

tion

[-]

fit Benzene

measurement Benzene

fit p-Xylene

measurement p-xylene

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

60 70 80 90 100 110 120 130 140

k a [1

/s]

T [°C]

66 Discussion

The only trend observed was the dependence on the temperature. This can be

seen in the benzene fits. In here both parameters, k and F increased with

increasing temperature which was the expected behavior as activated

transport process getting faster with increasing temperature.

These trends are shown in Figure 52 and Figure 53. But even if these

parameters show a trend in the temperature it is very difficult to interpret the

outcome with respect to the experiment.

In conclusion the curve fitting shows that the used model is much too trivial to

be able to describe the complex behavior of the Wicke Kallenbach system we

looked at. Nevertheless it was shown that the fitting gave the same information

as the experiment itself.

This can be a good starting point for applying a more sophisticated model and

try to understand the mechanism inside the pellet by mathematical modeling.

Figure 53: Trend of the parameter k with the temperature.

Looking at the frequency response experiments is as well interesting. It was

found that the diffusion coefficient of the powdered sample was about

2.5x10-15 m2/s for benzene in H-ZSM5 which is much slower than the measured

diffusion coefficients in particles with a larger diameter. As intensely discussed

by Gobin et al. [60] the rate determining step is in the case of such small

particles no longer the intracrystalline diffusion but the surface adsorption and

the pore entering step.

Interestingly the time constant did not change after pressing the particles to

thin wafers of 6 to 10 mg and diameters of 20 mm. It proves that the

0,00E+00

5,00E-12

1,00E-11

1,50E-11

2,00E-11

2,50E-11

3,00E-11

3,50E-11

4,00E-11

4,50E-11

5,00E-11

60 70 80 90 100 110 120 130 140

F [m

3 /s]

T [°C]

67 Discussion

characteristic length of diffusion equals the one for a powder and a thin wafer

which means that the rate controlling transport step is in both cases the same.

This denotes that the diffusion in a thin wafer can be described in the same

way as for a powdered sample.

The behavior changed dramatically if the powder was pressed to Wicke

Kallenbach pellets of 1 mm thickness. The characteristic functions for this

experiment were not interpretable due to a very large time constants as can be

seen in Figure 54. The maximum of the out-of-phase function was below 10-3

Hz which means that they are not in the range of the frequency response

experiment. Therefore, the uptake rate measurements were performed

because this method is able to determine large time constants.

Figure 54: In of phase (blue) and out of phase (red) functions obtained by a pressure frequency response experiment with a Wicke Kallenbach wafer of 100mg and benzene as adsorbate.

With this method time constants of 350 to 5700 s were found which are

impossible to obtain with the frequency response method. The characteristic

length of diffusion differed for the Wicke Kallenbach wafer as discussed before

which was half of the wafer thickness (0.5 mm), in contrast to the particles

(0.4 μm). This led to diffusion coefficients of 10-10 m2/s.

Taking into account the values obtained by the Wicke Kallenbach experiments

(10-6 m2/s ) valid for the mesopores and the diffusivities for the powdered

sample (10-15 m2/s) it can be assume that the adsorption in a Wicke Kallenbach

wafer is controlled by a mixture of both processes. But it can be seen from the

10-3

10-2

10-1

100

101

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Frequency [Hz]

char

acte

rist

ic fu

nctio

ns [-

]

fit-v1 in

fit-v1 out

68 Discussion

Wicke Kallenbach experiment that the flow through the wafer once the

adsorption desorption equilibrium is reached is only controlled by the transport

through the mesopores.

Applying the powder to the uptake rate measurement of benzene time

constants of 220 to 614 s were found. Surprisingly the time constant increased

with increasing benzene partial pressure which means that the diffusion

became slower with increasing vapor pressure. This behavior showed clearly

the non idealities of the system. It can be concluded that the dosing of

adsorbate into the system had the biggest influence on the result. This means

that it is impossible to perform a step change of the adsorbate concentration

with the used setup. Therefore, the diffusion of benzene in H-ZSM5 powder is

too rapid for uptake rate measurements. This is in good agreement with the

pressure modulation experiments and thereby with the previously reported

diffusivities [60].

69 Conclusion

6. Conclusion

The transport processes of strong adsorbing substances on pressed wafers in

a Wicke Kallenbach cell were investigated. In order to do so the system H-

ZSM5 with adsorbates benzene and p-xylene was examined. Experimental

results confirmed that the wafer could be described as a bed adsorber

analogue. The results leading to this conclusion were in particular the clear

dependences of the transmission time, the uptake time and the form of the

breakthrough curve on the temperature, the wafer thickness, the activation

temperature and the compacting pressure.

The wafer was a mesoporous accumulation of ZSM5 powder with the same

BET surface area as the non-compacted sample of 430 m2/g. During the

pressing procedure mesopores of 6 to 15 nm diameter were formed which was

confirmed by DFT calculations of the nitrogen physisorption isotherm and

calculations from the Wicke Kallenbach experiment.

At equilibrium conditions, which means after saturation of the wafer the

transport process was limited to the rate of diffusion through the mesopores.

Thus the separation factor is 1 independent of external parameters like

temperature, activation temperature, wafer thickness and compacting pressure

for molecules having a similar molar mass. This could be seen in the

experiments applying either p-xylene benzene mixtures or a blend of p-xylene

and m-xylene. Especially the measurement with m-xylene and p-xylene varified

that the wafer acted like a bed adsorber. The previously reported assumption,

that the pressed wafer acts like a grown membrane and could separate p-

xylene from a mixture of xylenes as described in the literature applying a MFI

membrane [3], proved to be wrong. So unfortunately it is impossible to

separate hydrocarbons with a pressed membrane of MFI particles.

The change in rate determining transport steps from the powder to the wafer

was also approved by the combination of pressure modulation frequency

response and uptake rate measurements. They show an increase of time

constants of two orders of magnitude by compacting the powder to a wafer

which is due to a increase of the charactistic length of diffusion from 0.4 μm to

1 mm. The diffusion coefficient previously reported by Gobin et al. [60] for the

70 Conclusion

parent wafer was confirmed whereas the uptake rate measurements showed

an increase in the diffusion coefficient by 5 orders of magnitude approving that

the uptake in the wafer is determined by a combination of Knudsen diffusion

and the pore entrance step. Nevertheless the Wicke Kallenbach experiments

showed that once the adsorption desorption equilibrium is established the

Knudsen diffusion controls the transmission rate.

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I Appendix A: Results

A. Results

A.1 Wicke Kallenbach experiments

A.1.1Variation of the temperature

Figure I: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 70°C, 100mg wafer weight

and 50 ml/min volume flow.

Figure II: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer


0 50 100 150 200 250 300 35010

-10

10-9

10-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

Benzene

p-Xylene

0 50 100 150 200 250 300 35010

-10

10-9

10-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

Benzene

p-Xylene

II Appendix A: Results

Figure III: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 130°C, 100mg wafer


Figure IV: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 70°C, 100mg wafer weight, a mixture of benzene/p-xylene and 50

ml/min volume flow.

0 50 100 150 200 250 30010

-9

10-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

Benzene

p-Xylene

0 50 100 150 200 250 300 350

10-1

100

101

102

103

time [min]

Sepe

ratio

n Fa

ctor

[-]

III Appendix A: Results

Figure V: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 100mg wafer weight, a mixture of benzene/p-xylene and

50 ml/min volume flow.

Figure VI: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 130°C, 100mg wafer weight, a mixture of benzene/p-xylene and


0 50 100 150 200 250 300 35010

-2

100

102

104

106

time [min]

Sepe

ratio

n Fa

ctor

[-]

0 50 100 150 200 250 300 35010

-2

10-1

100

101

102

103

time [min]

Sepe

ratio

n Fa

ctor

130

°C H

-ZSM

5

IV Appendix A: Results

A.1.2 Variation of the wafer thickness

Figure VII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 50mg

wafer weight and 50 ml/min volume flow.

Figure VIII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 150mg

wafer weight and 50 ml/min volume flow.

0 100 200 300 400 500 600 700 80010

-8

10-7

10-6

10-5

time [min]

c [m

ol/l

]

Benzene

p-Xylene

0 100 200 300 400 500 600 70010

-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

Benzene

p-Xylene

V Appendix A: Results

Figure IX: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 50mg wafer weight, a mixture of benzene/p-xylene and 50

ml/min volume flow.

Figure X: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 150mg wafer weight, a mixture of benzene/p-xylene and


0 100 200 300 400 500 600 700 80010

-2

10-1

100

101

102

103

104

time [min]

Sepe

ratio

n Fa

ctor

[-]

0 100 200 300 400 500 60010

-2

10-1

100

101

102

103

104

time [min]

Sepe

ratio

n Fa

ctor

[-]

VI Appendix A: Results

A.1.3 Variation of the activation temperature

Figure XI: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer

weight and 50 ml/min volume flow, activated at 423 K.

Figure XII: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 100mg wafer weight, a mixture of benzene/p-xylene

and 50 ml/min volume flow, activated at 423 K (black) and 723 K (red).

0 50 100 150 200 250 300 350 40010

-8

10-7

10-6

10-5

10-4

time [min]

c [m

ol/l

]

Benzene

p-Xylene

0 20 40 60 80 100 120 140 160 180 20010

-4

10-2

100

102

104

time [min]

Sepe

ratio

n Fa

ctor

[-]

150°C

450°C

VII Appendix A: Results

A.1.4 Influence of the compacting pressure

Figure XIII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer

weight and 50 ml/min volume flow, compacted with a pressure of 10 kN.

Figure XIV: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 100mg wafer weight, a mixture of benzene/p-xylene and

50 ml/min volume flow, compacted with pressure of 10 kN (black) and 20 kN (red)

0 50 100 150 200 250 30010

-8

10-7

10-6

10-5

time [min]

c [m

ol/l

]

Benzene

p-Xylene

0 20 40 60 80 100 120 140 160 180 20010

-1

100

101

102

103

time [min]

Sepe

ratio

n Fa

ctor

[-]

10kN

20kN

VIII Appendix A: Results

A.2 Frequency Response experiments

A.2.1 H-ZSM5 powder

Figure XV: In- (black) and out-of-phase (red) functions of the batch FR experiment of H-ZSM5 powder. The fit was produced by applying a non-uniform infinite sheet model.

Figure XVI: In- (black) and out-of-phase (red) functions of the batch FR experiment of H-ZSM5 powder. The fit was produced by applying a non-uniform infinite sheet model with surface

resistance.

10-3

10-2

10-1

100

101

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Frequency [Hz]

char

acte

rist

ic fu

nctio

ns [-

]

in-of-phase

out-of-phase

fit in-of-phase

fit out-of-phase

10-3

10-2

10-1

100

101

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Frequency [Hz]

char

acte

rist

ic fu

nctio

ns [-

]

in-of-phase

out-of-phase

fit in-of-phase

fit out-of-phase

IX Appendix A: Results

A.2.2 H-ZSM5 thin wafer

Figure XVII: In- (black) and out-of-phase (red) functions of the batch FR experiment of an H-ZSM5 Wicke Kallenbach wafer. The fit was produced by applying a non-uniform infinite sheet

model.

Figure XVIII: In- (black) and out-of-phase (red) functions of the batch FR experiment of an H-ZSM5 Wicke Kallenbach wafer. The fit was produced by applying a non-uniform infinite sheet

model with surface resistance.

10-3

10-2

10-1

100

101

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Frequency [Hz]

char

acte

rist

ic fu

nctio

ns [-

]

in-of-phase

out-of-phase

fit in-of-phase

fit out-of-phase

10-3

10-2

10-1

100

101

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Frequency [Hz]

char

acte

rist

ic fu

nctio

ns [-

]

in-of-phase

out-of-phase

fit in-of-phase

fit out-of-phase

X Appendix A: Results

A.3 Uptake Rate measurements

A.3.1 H-ZSM5 powder

Figure XIX: Uptake curve of benzene in H-ZSM5 powder at a partial pressure of 0.1 mbar and 373K. The figure shows the experimental data (black) and the result of the curve fitting (red)

applying an infinite plane sheet model of 1mm thickness.

Figure XX: Uptake curve of benzene in H-ZSM5 powder at a partial pressure of 1 mbar and 373K. The figure shows the experimental data (black) and the result of the curve fitting (red)


0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed m

ass

[-]

experiment

fit

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed m

ass

[-]

experiment

fit

XI Appendix A: Results

Figure XXI: Uptake curve of benzene in H-ZSM5 powder at a partial pressure of 2 mbar and 373K. The figure shows the experimental data (black) and the result of the curve fitting (red)


Figure XXII: Uptake curve of benzene in H-ZSM5 powder at a partial pressure of 10 mbar and 373K. The figure shows the experimental data (black) and the result of the curve fitting (red)


0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed m

ass

[-]

experiment

fit

0 100 200 300 400 500 600 700 800 9000

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed m

ass

[-]

experiment

fit

XII Appendix A: Results

A.3.2 H-ZSM5 Wicke Kallenbach wafer

Figure XXIII: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 0.1 mbar and 373K. The figure shows the experimental data (black) and the


Figure XXIV: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 1 mbar and 373K. The figure shows the experimental data (black) and the


0 200 400 600 800 1000 1200 1400 1600 18000

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed m

ass

[-]

experiment

fit

0 200 400 600 800 1000 12000

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed m

ass

[-]

experiment

fit

XIII Appendix A: Results

Figure XXV: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 2 mbar and 373K. The figure shows the experimental data (black) and the


Figure XXVI: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 10 mbar and 373K. The figure shows the experimental data (black) and the


0 200 400 600 800 1000 1200 14000

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed m

ass

[-]

experiment

fit

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s]

norm

aliz

ed m

ass

[-]

experiment

fit

XIV Appendix A: Results

A.4 Nitrogen physisorption isotherms

A.4.1 H-ZSM5 powder

Figure XXVII: Nitrogen physisorption isotherm of ZSM-5 parent powder material.

Figure XXVIII: t-plot produced with the method of Hasley for H-ZSM5 powder.

0

50

100

150

200

250

300

0,00E+00 2,00E-01 4,00E-01 6,00E-01 8,00E-01 1,00E+00 1,20E+00

Vad

s[cm

3/g

]

p/p0

y = 0,0304x + 0,2787R² = 0,9908

y = 0,0542x + 0,1471R² = 0,9979

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0 1 2 3 4 5

v ad

s[c

m3/g

STP

]

tHasley [nm]

XV Appendix A: Results

Figure XXIX: Linearization of the nitrogen physisorption isotherm in the low pressure range according to the BET theory of an H-ZSM5 powder sample.

A.4.2 H-ZSM5 Wicke Kallenbach wafer

Figure XXX: Nitrogen physisorption isotherm of a H-ZSM5 Wicke Kallenbach wafer.

y = 0,0104x + 3E-06R² = 0,9999

0,00E+00

1,00E-04

2,00E-04

3,00E-04

4,00E-04

5,00E-04

6,00E-04

7,00E-04

8,00E-04

9,00E-04

0,00E+001,00E-022,00E-023,00E-024,00E-025,00E-026,00E-027,00E-028,00E-029,00E-02

(p/p

0)/

Vad

s*(1

-p/p

0) [

g/cm

3]

p/p0 [-]

0

50

100

150

200

250

300

350

0,00E+00 2,00E-01 4,00E-01 6,00E-01 8,00E-01 1,00E+00 1,20E+00

Vad

s[cm

3/g

]

p/p0 [-]

XVI Appendix A: Results

Figure XXXI: t-plot produced with the method of Hasley for a H-ZSM5 Wicke Kallenbach wafer.

Figure XXXII: Linearization of the nitrogen physisorption isotherm in the low pressure range according to the BET theory of an H-ZSM5 Wicke Kallenbach wafer.

y = 0,048x + 0,147R² = 0,9966

y = 0,0095x + 0,3789R² = 0,5502

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 1 2 3 4 5 6 7 8 9

v ad

s[c

m3/g

STP

]

tHasley [nm]

y = 0,0098x + 5E-08R² = 1

0

0,0001

0,0002

0,0003

0,0004

0,0005

0,0006

0,0007

0,0008

0,0009

0,00E+001,00E-022,00E-023,00E-024,00E-025,00E-026,00E-027,00E-028,00E-029,00E-02

(p/p

0)/

Vad

s*(1

-p/p

0) [

g/cm

3]

p/p0 [-]

XVII Appendix A: Results

A.5 Matlab source code

A.5.1 Processing of Wicke Kallenbach experimental data

function f_Trennfaktor_gegen_Zeit_und_TAbhaengigkeit [ filename dirpath ] = uigetfile ( '130'); [ MZ1 ] = textread ([ dirpath filename ]); t_MZ1 = MZ1 ( :, 1 ); Start1 = 2.17 .* ( 10 ^ 6 ); m1 = find ( t_MZ1 == Start1 ); t_MZ1 = MZ1 ( m1 : end, 1 ); I_MZB1 = MZ1 ( m1 : end, 3 ); I_MZX1 = MZ1 ( m1 : end, 4 ); c_MZB1 = 6936.1 .* I_MZB1; c_MZX1 = 10173 .* I_MZX1; c_MZX1 = c_MZX1 .* 1.44; S1 = c_MZB1 ./ ( c_MZX1 ); t_MZ1 = t_MZ1 - t_MZ1 ( 1 ); t_MZ1 = t_MZ1 ./ 60000; figure( 1 ) plot ( t_MZ1, S1, 'r+' ) xlabel ( 'time [min]' ), ylabel ( 'Seperation Factor 130 °C H-ZSM5' ),

title ( 'Trend of Seperation Factor' ) figure( 2 ) semilogy ( t_MZ1, c_MZB1, 'ks', t_MZ1, c_MZX1, 'r+') xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-

ZSM5 130 °C' ),legend ( 'Benzene', 'p-Xylene' ) [ filename dirpath ] = uigetfile ( '100'); [ MZ2 ] = textread ([ dirpath filename ]); t_MZ2 = MZ2 ( :, 1 ); Start2 = 2.93 .* ( 10 ^ 6 ); m2 = find ( t_MZ2 == Start2 ); t_MZ2 = MZ2 ( m2 : end, 1 ); I_MZB2 = MZ2 ( m2 : end, 3 ); I_MZX2 = MZ2 ( m2 : end, 4 ); c_MZB2 = 6936.1 .* I_MZB2; c_MZX2 = 10173 .* I_MZX2; c_MZX2 = c_MZX2 .* 1.44; S2 = c_MZB2 ./ ( c_MZX2 ); t_MZ2 = t_MZ2 - t_MZ2 ( 1 ); t_MZ2 = t_MZ2 ./ 60000; figure( 3 ) plot ( t_MZ2, S2, 'r+' ) xlabel ( 'time [min]' ), ylabel ( 'Seperation Factor 100 °C HZSM-5' ),

title ( 'Trend of Seperation Factor' ) figure( 4 ) semilogy ( t_MZ2, c_MZB2, 'ks', t_MZ2, c_MZX2, 'r+') xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-

ZSM5 100 °C' ),legend ( 'Benzene', 'p-Xylene' ) [ filename dirpath ] = uigetfile ( '70'); [ MZ3 ] = textread ([ dirpath filename ]); t_MZ3 = MZ3 ( :, 1 ); Start3 = 2.26 .* ( 10 ^ 6 ); m3 = find ( t_MZ3 == Start3 ); t_MZ3 = MZ3 ( m3 : end, 1 ); I_MZB3 = MZ3 ( m3 : end, 3 ); I_MZX3 = MZ3 ( m3 : end, 4 ); c_MZB3 = 6936.1 .* I_MZB3; c_MZX3 = 10173 .* I_MZX3; c_MZX3 = c_MZX3 .* 1.44; S3 = c_MZB3 ./ ( c_MZX3 );

XVIII Appendix A: Results

t_MZ3 = t_MZ3 - t_MZ3 ( 1 ); t_MZ3 = t_MZ3 ./ 60000; figure( 5 ) plot ( t_MZ3, S3, 'r+' ) xlabel ( 'time [min]' ), ylabel ( 'Seperation Factor 70 °C HZSM-5' ),

title ( 'Trend of Seperation Factor' ) figure( 6 ) semilogy ( t_MZ3, c_MZB3, 'ks', t_MZ3, c_MZX3, 'r+') figure( 7 ) xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-

ZSM5 70 °C' ),legend ( 'Benzene', 'p-Xylene' ) semilogy ( t_MZ1, c_MZB1, 'kx', t_MZ2, c_MZB2, 'ko',t_MZ3, c_MZB3,

'ks' ) xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-

ZSM5 T - Äbhängigkeit Benzol' ), legend ( '130 °C', '100 °C', '70 °C'

) figure( 8 ) semilogy ( t_MZ1, c_MZX1, 'rx', t_MZ2, c_MZX2, 'ro',t_MZ3, c_MZX3,

'rs' ) xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-

ZSM5 T - Äbhängigkeit p-Xylol' ), legend ( '130 °C', '100 °C', '70 °C'

)

XIX Appendix B: Simulation

B. Simulation

B.1 Curve fitting of Wicke Kallenbach experiments

Figure XXXIII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 70°C, 100mg

wafer weight and 50 ml/min volume flow and the corresponding fit for benzene (black) and p-xylene (blue).

Figure XXXIV: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg


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XX Appendix B: Simulation

Figure XXXV: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 130°C, 100mg


Figure XXXVI: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 50mg


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XXI Appendix B: Simulation

Figure XXXVII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 150mg


Table I: Parameters obtained by non-linear curve fitting of the transmission curves of the Wicke Kallenbach experiments

Benzene p-Xylene

T [K] Weight [g] k [1/s] F [m3/s] k [1/s] F [m3/s]

343 100 0.029 2.14x10-11 0.013 1.1x10-11

373 100 0.053 3.08x10-11 0.012 9.94x10-12

403 100 0.082 4.50x10-11 0.014 2.00x10-11

373 50 0.047 3.00x10-11 0.014 2.45x10-11

373 150 0.300 1.71x10-11 0.010 7.54x10-12

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XXII Appendix B: Simulation

B.2 Matlab source code of Wicke Kallenbach curve fitting

B.2.1 Main program

function [] = f_Wicke_Kallenbach_curve_fitting ( start )

% In the first part the data is read and converted [ filename dirpath ] = uigetfile ( 'Xylol' ); [ Xylol ] = textread ([ dirpath filename ]); t = Xylol ( : , 1 );

% Then the normalized concentration vs. time diagram is calculated

from the % experimental data Start1 = start; n = find ( t == Start1 ); t = Xylol ( n : end, 1 ); I_Xylol = Xylol ( n : end, 3 ); I_Benzol = Xylol ( n : end, 4 ); C_Xylol = I_Xylol ./ max ( I_Xylol ); C_Benzol = I_Benzol ./ max ( I_Benzol ); t = t - t ( 1 ); t = t ./ 1000;

% Afterwards the curve fitting is performed applying a genetic

algorithm [ kB FB ] = f_Wicke_Kallenbach_ga_fit_breakthrough_curve_Benzene( t,

C_Benzol ) [ kX FX ] = f_Wicke_Kallenbach_ga_fit_breakthrough_curve_xylene( t,

C_Xylol )

%In the last step the solutions are plotted together with the

experimental %data Wsat = 0.0744; rhoB = 1.44 * 10 .^ 3; S = 4.18 * ( 10 .^ -8 ); x = 10 ^ -3; c0B = 0.13; c0X = 9.77 .* ( 10 .^ -2 );

for n = 1 : 1 : length ( kB )

XB = (kB ( n ) .* Wsat .* rhoB .* S ./ ( FB ( n ))) .* x;

TB = kB ( n ) .* c0B .* t;

CB ( :, n ) = exp ( TB - (0.9999 .* TB )) ./ ( exp ( TB - (0.9999 .*

TB )) + exp ( XB - (0.9999 .* TB )) - exp ( - 0.9999 .* TB ));

end

for m = 1 : 1 : length ( kX )

XX = (kX ( m ) .* Wsat .* rhoB .* S ./ ( FX ( m ))) .* x;

TX = kX ( m ) .* c0X .* t;

XXIII Appendix B: Simulation

CX ( :, m ) = exp ( TX - (0.9999 .* TX )) ./ ( exp ( TX - (0.9999 .*

TX )) + exp ( XX - (0.9999 .* TX )) - exp ( - 0.9999 .* TX ));

end

for n = 1 : 1 : length ( kB ) for m = 1 : 1 : length ( kX )

x = kB ( n ); y = FB ( n ); z = kX ( m ); u = FX ( m ); i = 3 + ( n - 1 ) .* length ( kX ) + m; figure ( i ) plot ( t, CB ( :, n ), 'k+', t, C_Benzol, 'r-', t, CX ( :, m ), 'b*',

t, C_Xylol, 'go' ) legend ( 'fit Benzene', 'measurement Benzene', 'fit p-Xylene',

'measurement p-xylene' ) text( 20000, 1,... ['kB = ',num2str(x)],... 'HorizontalAlignment','center') text( 20000, 0.75,... ['FB = ',num2str(y)],... 'HorizontalAlignment','center') text( 20000, 0.5,... ['kX = ',num2str(z)],... 'HorizontalAlignment','center') text( 20000, 1,... ['FX = ',num2str(u)],... 'HorizontalAlignment','center') end end

B.2.2 Genetic algorithm

% This script implements the Simple Genetic Algorithm described % in the examples section of the GA Toolbox manual. % % Author: Andrew Chipperfield % History: 23-Mar-94 file created % % tested under MATLAB v6 by Alex Shenfield (22-Jan-03) function [ kB FB ] =

f_Wicke_Kallenbach_ga_fit_breakthrough_curve_Benzene( t, CB_fit ) %imax = 3;

GGAP = .9; % Generation gap, how many new individuals are

created NVAR1 = 1; % Number of variables NVAR2 = 1; NIND = 40; % Number of individuals MAXGEN = 3000; % Number of generations PRECI = 20; % Precision of binary representation

% Build field descriptor FieldD1 = [rep([PRECI],[1, NVAR1]); rep([10^-5;1],[1, NVAR1]);... rep([1; 0; 1 ;1], [1, NVAR1])];

XXIV Appendix B: Simulation

FieldD2 = [rep([PRECI],[1, NVAR2]); rep([0.1 * 10^-10; 10^-5],[1,

NVAR2]);... rep([1; 0; 1 ;1], [1, NVAR2])];

% Initialise population Chrom1 = crtbp(NIND, NVAR1*PRECI); Chrom2 = crtbp(NIND, NVAR2*PRECI); % Reset counters Best = NaN*ones(MAXGEN,1); % best in current population gen = 0; % generational counter

% Evaluate initial population x = [bs2rv(Chrom1,FieldD1) bs2rv(Chrom2,FieldD2)]; [ObjV] = f_Wicke_Kallenbach_simulate_breakthrough_curve_Benzene_fit

( x, t, CB_fit ); ObjV = ObjV';

% Track best individual and display convergence Best(gen+1) = min(ObjV); figure(2) plot(log10(Best),'ro');xlabel('generation'); ylabel('log10(f(x))'); text(0.5,0.95,['Best = ',

num2str(Best(gen+1))],'Units','normalized'); drawnow;

% Generational loop while gen < MAXGEN,

% Assign fitness-value to entire population FitnV = ranking(ObjV);

% Select individuals for breeding SelCh1 = select('sus', Chrom1, FitnV, GGAP); SelCh2 = select('sus', Chrom2, FitnV, GGAP);

% Recombine selected individuals (crossover) SelCh1 = recombin('xovsp',SelCh1,0.7); SelCh2 = recombin('xovsp',SelCh2,0.7);

% Perform mutation on offspring SelCh1 = mut(SelCh1); SelCh2 = mut(SelCh2);

% Evaluate offspring, call objective function x = [bs2rv(SelCh1,FieldD1) bs2rv(SelCh2,FieldD2)]; [ObjVSel] =

f_Wicke_Kallenbach_simulate_breakthrough_curve_Benzene_fit ( x, t,

CB_fit ); ObjVSel = ObjVSel';

% Reinsert offspring into current population [Chrom1 ObjV]=reins(Chrom1,SelCh1,1,1,ObjV,ObjVSel); [Chrom2 ObjV]=reins(Chrom2,SelCh2,1,1,ObjV,ObjVSel);

% Increment generational counter gen = gen+1;

% Update display and record current best individual Best(gen+1) = min(ObjV); figure(2)

XXV Appendix B: Simulation

plot(log10(Best),'ro'); xlabel('generation');

ylabel('log10(f(x))'); text(0.5,0.95,['Best = ',

num2str(Best(gen+1))],'Units','normalized'); drawnow; end I = find(ObjV == (min(ObjV))); P1 = bs2rv(Chrom1,FieldD1); kB = P1 ( I ); P2 = bs2rv(Chrom2,FieldD2); FB = P2 ( I ); % End of GA

B.2.3 Fitness function

function [ObjV] =

f_Wicke_Kallenbach_simulate_breakthrough_curve_Benzene_fit ( x, t,

CB_fit )

ka = x ( : , 1 ); Wsat = 0.0744; rhoB = 1.44 * 10 .^ 3; S = 4.18 * ( 10 .^ -8 ); FB = x ( : , 2 ); x = 10 ^ -3; c0B = 0.13;

for n = 1 : 1 : length (ka)

XB = (ka ( n ) .* Wsat .* rhoB .* S ./ ( FB ( n ))) .* x;

TB = ka ( n ) .* c0B .* t;

CB = exp ( TB - ( TB .* 0.9999 )) ./ ( exp ( TB - ( TB .* 0.9999 )) +

exp ( XB - ( TB .* 0.9999 )) - exp( - TB .* 0.9999 ));

x = (( CB - CB_fit ) .^ 2 ); y = ( x ( 2 : end ) .* t ( 2 : end ) .^ 3 ) ./ ( 2 ); FitnV ( n ) = sum( y );

end

ObjV = FitnV;

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