Diffusion and adsorption of linear and branched alkanes in zeolites

Diffusion and Adsorption of Linear and Branched Alkanes in Zeolites

Proefschrift

Ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 10 september 2007 om 12:30 uur

door

Alexandre Filipe PORFÍRIO FERREIRA licenciado em engenharia química

Dit proefschrift is goedgekeurd door de promotors: prof. dr. J. A. Moulijn

prof. dr. ir. A. Bliek

Samenstelling promotiecommissie: Rector Magnificus

Prof. dr. J. A. Moulijn Prof. dr. ir. A. Bliek Prof. dr. F. Kapteijn Prof. dr. J.C. Jansen Prof. dr. J. Kärger Dr. J. Rouquerol Dr. G. Rothenberg Voorzitter Technische Universiteit Delft, promotor Universiteit Twente, promotor Technische Universiteit Delft Universiteit Stellenbosch Universität Leipzig Université de Provence - CNRS Universiteit van Amsterdam

The research reported in this thesis was carried out at the Van‘t Hoff Institute for Molecular Sciences, Faculty of Science, University of Amsterdam (Nieuwe Achtergracht 166, 1018 WV, Amsterdam, The Netherlands) with financial support of Stichting Technische Wetenschappen – Chemische Wetenschappen (STW-CW).

ISBN 978-90-9022147-2

Copyright  2007 by A.F.P. Ferreira

i

Content

Introduction 1 1.1 Adsorption 3 1.2 Diffusion 6 1.3 NIR Spectroscopy 11 References 16

Inline Monitoring of Adsorption 19

2.1 Introduction 21 2.2 Theory 22 2.3 Experimental 25 2.4 Results 27 2.5 Conclusions 38 References 39

Adsorption and Differential Heats of Adsorption of Normal- and Iso-Butane 41

3.1 Introduction 43

3.2 Experimental Section 44

3.3 Theory: Adsorption Equilibrium 46

3.4 Results and Discussion 48

3.5 Conclusions 53

References 54

Multicomponent Adsorption and Diffusion of Butane Isomers 57

4.1 Introduction 59

4.2 Experimental Section 60

4.3 Diffusion Model 63

4.4 Results and Discussion 64

4.5 Conclusions 73

ii

5.1 Introduction 79

5.2 Experimental Section 80

5.3 Theory 83

5.4 Results and Discussion 86

5.5 Conclusions 95

References 97

Influence of Si/Al Ratio on Hexane Isomers Adsorption Equilibria 101

6.1 Introduction 103

6.2 Experimental Section 104

6.3 Isotherm models 105

6.3 Results and Discussion 106

6.4 Conclusions 114

References 115

Summary and Evaluation 119

Samenvatting 125

List of Publications 131

Acknowledgements 135

1

“Unless the molecules of a gas which may strike a solid surface all rebound elastically there will necessarily be a higher concentration of molecules of the gas in the surface layer of the solid than in the body of the gas. If any molecules impinging on the surface are condensed, a certain time interval must elapse before they can evaporate. This time lag will bring about the accumulation of molecules in the surface layer, and may thus be looked upon as the cause of adsorption.”

Irving Langmuir Irving Langmuir Irving Langmuir Irving Langmuir 1

MOTIVATION. Branched hydrocarbons are preferred to linear hydrocarbons as ingredients in petrol, as they enhance the fuel octane number. By catalytic isomerisation linear hydrocarbons are converted into branched hydrocarbons, then it becomes necessary to separate the mixture. A variety of zeolites may be used for this purpose, either on thermodynamics or kinetics basis. Therefore, adsorption and diffusion data are essential to the development of sorption based separation methods, but also they provide key information regarding the catalytic isomerisation over zeolites. However, the experimental assessment of multi-component adsorption data is not straightforward and is highly time-consuming.

1.1

Adsorption

Several definitions of adsorption have appeared in the literature such as Coulson et al.2,

Ruthven3,4, and Yang5. All such definitions express a similar concept:

Adsorption is a phenomenon in which one or more components of a fluid (adsorbate) are extracted via selective bonding to a solid (adsorbent) medium.

The surface of a solid represents a discontinuity of its structure. Hence, when the solid is exposed to a gas, the gas molecules will form bonds with it and become attached. Adsorption phenomena are classified by the nature of those interactions between gas molecules and the solid phase. If the solid and gas molecules are bonded by relatively weak forces such as the van der Waals force, then it is classified as physical adsorption. On the other hand, chemisorption involves much stronger forces, arising from electron transfer

between the gas and solid phase molecules. As pointed out by Ruthven3, physical adsorption

is more useful for developing practical periodic adsorption processes, as it is easier to reverse the adsorption (regenerate the original solid phase) by manipulating the external operating conditions.

One of the requirements for solid adsorbents is to offer a large surface area per unit volume, so as to be able to adsorb the maximum amount of the adsorbate. As a consequence, commercial adsorbents are usually produced from microporous materials, which allow the gas molecules to diffuse through their pores. The gas molecules are adsorbed onto the solid surface until their concentration in the gas phase is equal to the equilibrium value corresponding to the adsorbed phase concentration.

adsorbed onto the solid surface is directly related to the concentration in the micropores and the availability of the free sites.

Figure 1.1: A representation of a solid particle in an adsorption bed3.

Adsorption isotherms describe the equilibrium conditions for the adsorbate onto the surface of the adsorbent. Usually the amount of material adsorbed is some complex function of the concentration of the adsorbate. Generally, adsorption is an exothermic process while desorption is an endothermic process. Isotherms can be expressed in the general mathematical form:

nai

,

T

=

nai

*.f(P

i

)

(1.1)

where nai is the amount of species i adsorbed at equilibrium at a fixed temperature, T, and

Pi the corresponding gas-phase partial pressure, nai* is the saturation loading of species i.

Many models have been proposed to match the isotherm curves obtaining from experimental data. One of the most commonly used is the Langmuir model. For adsorption of pure gas adsorbate, the Langmuir isotherms can be expressed as:

Kp

Kp

n

n

a asat

+

=

1

(1.2)

Ideal model

spherical crystallites

External fluid film

Micropore

where na is loading (adsorbate concentration in the particles) and p is pressure (adsorbate

concentration in the gas phase), nasat is saturation loading,

K

is the adsorption equilibrium

constant.

At low pressure where K•p may be neglected in comparison with unity, and Langmuir isotherms reduce to Henry’s Law:

p

K

n

a

=

_{H (1.3)}

where

K

_H is the Henry’s Law constant.

Adsorption Experimental Methods

Accurate equilibrium data is necessary for proper design of adsorption-based separation or purification processes, the isotherm data have to be correlated before their use in a design model for an easier handling. Therefore, experimental systems have to measure accurately over a wide range of pressures and temperatures are being object of a strong emphasis. Gravimetric or volumetric techniques have usually been used for isotherm data measurements of gas adsorption. Both techniques present problems, volumetric equipment has an accumulation of the error, effects associated with flow patterns, by passing, and aerodynamic factors such as buoyancy, influence data obtained by the gravimetric method, this results in extensive data corrections.

To obtain experimental data of the adsorptive characteristics of an adsorbent for a given mixture is the first step in the design of an adsorptive separation process. However, measurement of multi-component adsorption equilibria represents an inordinate amount of work. As a result, a number of theories have been developed to predict adsorption

There are different methods to measure multi-component gas adsorption equilibrium, the most known are:

• volumetric-gravimetric method 7,

• volumetric-chromatographic method 8,

• gravimetric-chromatographic method 8,

• and oscillometric-chromatographic method 8.

None of these methods is suitable for measuring kinetics properties9. The

volumetric-gravimetric method is limited to binary mixtures, and the mass of the two components must be significantly different. Therefore, this method cannot measure equilibrium properties of

isomeric mixtures9. The methods that use gas chromatography for analysis disturb the

overall adsorbed phase by taking samples of the gas phase, giving origin to some uncertainty. Although, when accessing only adsorption equilibrium properties the uncertainty might be low, accessing adsorption kinetic properties will be impossible due to the high number of samples necessary.

1.2

Diffusion

Diffusion is the process of irregular particle movement generated by the particles thermal

energy10. It occurs in any type of matter, even if on different scales of length and time. It is

a fundamental phenomenon in nature10. Consider two containers of gas A and B separated

Figure 1.2: A general representation of molecular diffusion.

Since the average kinetic energy of different types of molecules (different masses), which are at thermal equilibrium, is the same, then their average velocities are different. Their average diffusion rate is expected to depend upon that average velocity, which gives a relative diffusion rate:

T

diffusion rate

K

m

=

(1.4)

where the constant K depends upon geometric factors including the area across which the diffusion is occurring. The relative diffusion rate (Knudsen separation factor) for two different molecular species is then given by:

A B

m

diffusion rate of A

diffusion rate of B

=

m

(1.5)

Transport mechanisms in small pores

There are different types of mass transport in small pores; the most important ones are presented on figure 1.3.

Viscous flow Capillary condensation Surface diffusion

Molecular (Fickian) diffusion Knudsen diffusion Activated diffusion (zeolites)

Figure 1.3: A general representation of different transport mechanisms in pores.

Viscous Flow:

Viscous flow is the flow of a gas through a channel under conditions where the mean free path is small in comparison with the transverse section of the channel, so the flow characteristics are determined mainly by collisions between the gas molecules.

Capillary Condensation:

Capillary condensation is known to occur when multilayer adsorption from adsorbate molecules proceeds to the point where pore spaces are filled with condensed liquid and separated from the gas phase by menisci.

Surface Diffusion:

Surface diffusion is also used to explain a type of pore diffusion in which solutes adsorb on the surface of the pore and hop from one site to another through interactions between the surface and molecules.

Molecular (or Fickian) Diffusion:

Molecular, or transport, diffusion occurs when the mean free path is relatively short

compared to the pore size, and is described by Fick's law as follows11:

C

J

D

t

∂

=

∂

(1.6)

where J is the mass flux, D is the transport diffusion coefficient (or Fickian diffusion

coefficient), and ∂C/∂t is the concentration gradient. The transport diffusivity relates

Knudsen Diffusion:

The Einstein relation describes Knudsen diffusion as follows10,12:

2

_{( )}

₆

s

r t

=

D t

(1.7)

where Ds is the self-diffusivity and

r t

2

( )

denotes the mean squared distance

covered by the molecules under study during the observation time t. Knudsen diffusion occurs when the mean free path is relatively long compared to the pore size, so the molecules collide frequently with the pore wall. Knudsen diffusion is dominant for pores that range in diameter between 2 and 50 nm.

Activated diffusion (zeolites):

Single-file mode diffusion is characterized by the fact molecules are unable to pass each other in pores or channels and it is proportional to the square route of time, and

expressed as10,13,14:

2

( )

2

r t

=

F t

(1.8)

where F is the diffusion mobility.

Methods of investigation

Molecular diffusion under the confinement of nanoporous materials is of double interest. From the point of view of fundamental research, studying molecular diffusion in nanoporous materials provides unique insights into their host-guest relation. On the other hand, the rate of molecular propagation is one of the decisive quantities affecting some nanoporous materials based processes.

experimental techniques have been developed to measure the diffusivity of molecules in zeolites. However, each method has its limitations and the results from these different methods are not always consistent. Recently, theoretical simulations of adsorbed molecules in zeolites and modeling of diffusion processes became a very popular method of

investigation due to the fast development of computers15.

Experimental techniques of diffusion measurement

Traditionally, molecular diffusion studies in zeolites have been performed by subjecting the sample to a step in the surrounding pressure and by recording the sample response. This is a macroscopic / non-equilibrium approach. The existing experimental methods can be divided in two types, so called, micro- and macroscopic techniques. The experimental procedure determines the type of diffusion coefficients measured: transport or self-diffusivity. Generally, macroscopic methods determine transport self-diffusivity. From microscopic methods, usually, the self-diffusivity is obtained, which is a diffusion coefficient under equilibrium conditions. Below, the most commonly applied methods are resumed:

Microscopic techniques:

Pulsed Field Gradient NMR (PFG-NMR) / Equilibrium Quasi-Elastic Neutron Scattering (QENS) / Equilibrium Interference microscopy / Non-equilibrium

Macroscopic techniques:

Wicke-Kallenbach (membrane) permeation / Equilibrium Single crystal membrane technique (SCM) / Equilibrium Uptake methods (gravimetric, volumetric) / Non-equilibrium Frequency response (FR) / Non-equilibrium

Zero-length column (ZLC) –/ Non-equilibrium

Chromatographic, such as frequency / Non-equilibrium Membrane permeation / Non-equilibrium

Karger10 and some other authors (e.g. Koriabkina16) present (extensive) reviews on the

1.3

NIR Spectroscopy

Historically, spectroscopy referred to a branch of science in which visible light was used for theoretical studies on the structure of matter and for qualitative and quantitative analyses. Recently, however, the definition has broadened as new techniques have been developed that utilize not only visible light, but many other forms of electromagnetic and non-electromagnetic radiation: microwaves, radio waves, x-rays, electrons, phonons (sound waves) and others. NIR spectroscopy is the measurement of the wavelength and intensity of the absorption of near-infrared light by a sample. It is an absorption spectroscopy technique, which uses the range of electromagnetic spectra in which a substance absorbs.

Near-infrared light spans the 800 nm - 2.5 µm (12,500 – 4,000 cm-1) range, between infrared

and the visible light regions. It is energetic enough to excite overtones and combinations of molecular vibrations to higher energy levels.

Figure 1.4: General representation of the electromagnetic spectrum.

It is non-destructive method of molecular analysis, and is typically used for quantitative

measurement of organic functional groups, especially O-H, N-H, C-H and C=O17. This is due

to overtones and combinations of fundamental vibrations of mainly hydrogen bonds e.g.

ΒOH, ΒNH and ΒCH (figure 1.5). NIR is used in several applications, which include

Instrumentation

Spectroscopy is often used in physical and analytical chemistry for the identification of substances through the spectrum emitted from them or absorbed in them. The components and design of NIR instrumentation are similar to uv-vis absorption spectrometers. The light source is usually a tungsten lamp and the detector is usually a PbS solid-state detector.

Sample holders can be glass or quartz and typical solvents are CCl4 and CS2. The convenient

instrumentation of NIR spectroscopy compared to IR spectroscopy makes it much more suitable for online monitoring and process control.

Another option is to use Fourier transform near-infrared (FT-NIR) spectroscopy; it is also a measurement technique for collecting near-infrared spectra. Instead of recording the amount of energy absorbed when the frequency of the near-infrared light is varied (monochromator), the IR light is guided through an interferometer. After passing the sample the measured signal is the interferogram. Performing a mathematical Fourier Transform on this signal results in a spectrum identical to that from conventional (dispersive) near-infrared spectroscopy. FT-NIR spectrometers are cheaper than conventional spectrometers because building of interferometers is easier than the fabrication of a monochromator. In addition, measurement of a single spectrum is faster for the FT-NIR technique because the information at all frequencies is collected simultaneously. This allows multiple samples to be collected and averaged together resulting in an improvement in sensitivity. Because of its various advantages, virtually all of the modern near-infrared spectrometers are FT-NIR instruments.

Calibration models

Calibration allows relating instrumental measurements (in our case the NIR absorbance spectra) to the (concentration / partial pressure of the) sample of interest. This is a two-step procedure where 1) data is calibrated and 2) predictions based on the calibration are made.

analyte levels, comprise a group known as the calibration set. This set is used to develop a model that relates the amount of sample to the measurements by the instrument. In some cases, the construction of the model is simple due to a certain relationship, such as Beer's Law in the application of UV or NIR spectroscopy. Unlike spectroscopy, other cases can be much more complex, and it is in these cases where construction of the model is the time-consuming step. Once the model is constructed, it can predict analyte levels based on measurements of new samples.

Beer-Lambert law

Beer-Lambert's law was independently discovered (in various forms) by Pierre Bouguer in

1729, Johann Heinrich Lambert in 1760 and August Beer in 185218-20.

The fractional reduction of the beam intensity, −∂I/I, is proportional to the attenuation

coefficient

α

c

, and to the layer thickness, ∂x, i.e.20,

- / = c

∂

I I

α

∂

x

(1.9)

Integrating this equation, one obtains the intensity I transmitted through the slab/medium, which is for a homogeneous medium given by the well-established Beer– Lambert’s exponential attenuation law:

1 1 10 0 0

,

I

10

lc

,

log

I

a

lc

a

I

I

α

α

−

=

=

= −

(1.10) where

α

4

π

k

λ

=

, a is absorbance, I0 is the intensity of the incident light, I1 is the

intensity after passing through the medium, l is the distance that the light travels through

is the absorption coefficient or the molar absorptivity of the medium, λ is the wavelength of the light, k is the extinction coefficient.

I

0

I

1

l

c

a

Figure 1.6: Diagram of Beer-Lambert absorption law - a light beam travels through a medium of length l.

Multi component analyses

To perform multi component analyses the Net Analyte Signal (NAS) theory was employed. This theory was originally derived from classical least squares in spectral calibration where

the responses of all pure analytes and interferents are assumed to be known21. The net

analyte vector is a convenient diagnostic that enables figures of merit (sensitivity, limit of detection, etc.) to be calculated in a manner similar to univariate regression. The net

analyte signal vector was originally defined by Lober22,23 as the part of a measured signal

References

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Langmuir, I., J. Am. Chem. Soc. 1916, 38, 2221.

Coulson, J.M.; Richardson, J.F.; and Peacock, D.G., Chemical Engineering, volume 3.

Pergamon Press, Oxford 2nd. Edition, 1975.

Ruthven, D.M., Principle of Adsorption and Adsorption Processes. John Willey & Sons, New York, 1984.

Ruthven, D.M.; Farooq, S.; and Knaebel, K.S., Pressure Swing Adsorption. VCH, New York, 1994.

Yang, R.T., Gas Separation by Adsorption Processes. Butterworths, Boston, 1987.

Sun, M.S.; Talu, O.; and Shah, D.B., J. Phys Chem. 1996, 100, 17276.

Calleja, G.; Pau, J.; Calles, J.A., J. Chem. Eng. Data 1998, 43, 994.

Keller, J.U.; Dreisbach, F.; Rave, H.; Staudt, R.; Tomalla, M., Adsorption 1999, 5, 199.

Keller, J.U.; Staudt, R., Gas adsorption equilibria: experimental methods and Adsorption Isotherms, Sringer, New York, 2005.

Karger, J., Adsorption 2003, 9, 29.

Chen, N.; Degman, T.; Smith, C., Molecular transport and reaction in zeolites: design and application of shape selective catalysts, VCH Publishers, New York, 1994.

Malek, K.; Coppens M.-O., J. Chem. Phys. 2003, 119, 2801.

14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

Fedders, D.E., Phys. Rev. B 1978, 17, 40-46.

Keil, F.J.; Krishna, R.; Coppens, M.-O., Rev. Chem. Engng. 2000, 16, 71.

Koriabkina, A.O., Diffusion of alkanes in MFI-type zeolites. Ph.D Thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands: 2003

Ozaki, Y.; Amari,T., Near-infrared spectroscopy in chemical process analysis, John M. Chalmers (eds), Cleveland, 2000.

Lambert, J.H., Photometria sive de mensura et gradibus luminis, colorum et umbrae, Augustae Vindelicorum, Basel, 1760.

Beer, A., Annalen der Physik 1852, 86, 78.

Hubbell, J.H., Phys Med. Biol. 2006, 51, R245.

Bro, R., Andersen, C.M., J. Chemom. 2003, 17, 646.

Lober, A., Anal. Chem. 1986, 58, 1167.

2

Isaac Newton Isaac Newton Isaac Newton Isaac Newton 1

Inline Monitoring of Adsorption

∗

2.1

Introduction

New gasoline specifications demand a lower amount of olefins and aromatics in gasoline. Consequently, there is a greater need in the petroleum industry for catalytic isomerization

to convert straight chain hydrocarbons to branched hydrocarbons2. Branched hydrocarbons

are preferred as ingredients in petrol because they enhance the fuel octane number. Then the separation of linear and branched hydrocarbons becomes necessary. Improving and optimizing such a separation is a problem with growing industrial importance. A variety of zeolites may be used for the separation process. These zeolites can be selected either on

the basis of their sorption thermodynamics3 or of their sorption kinetics4. Equilibrium and

kinetic data are therefore essential for the development of sorption based separation methods. These data provide also key information regarding the catalytic isomerization on zeolites themselves.

The objective of this project is to measure adsorption properties of mixtures of isomers. We are interested in equilibrium data as well as in kinetics. For that we need a fast in-line analytical technique that allows us to quantify the isomers in the mixture. An in-line technique is necessary because our system operates in gas phase. Off-line techniques (like Gas Chromatography) are not suitable, since they require that samples be “taken out” and such procedure would change the adsorption process and disturb the equilibrium results. We need a fast technique due to the fact that adsorption can be a very fast process for some adsorptive/adsorbent systems. Spectroscopy is the most suitable tool to get the desired information. Therefore, we use a manometric set-up coupled with a near infrared (NIR) spectrometer. NIR spectroscopy is a fast, non-intrusive technique that allows us to measure the gas phase composition without interfering with the adsorption.

region and one for the high-pressure region. The influence of the different preprocessing methods on the calibration model is expected to be small due to the fact that background spectrum and the calibration spectra are collected within a short period from each other. In contrast the influence on the time based experiments results is expected to be larger, and is expected to increase proportionally with the difference between the environmental conditions of background and measurement.

2.2

Theory

The NIR region (15 000 cm-1 – 4 000 cm-1) is the region between infrared and the visible

light region. NIR absorption spectra correspond to overtone and combinatorial modes of

fundamental vibrations5. Therefore, in the NIR region absorption is weak, which allows

measuring gas composition at high pressures. The vibrational overtone and combination bands that give rise to absorption in the near infrared range can be ascribed mainly to

functional groups that contain a hydrogen atom (e.g., OH, CH, NH)6. The broad complex

bands present in the NIR region are the result of overlapping bands. Therefore, a multivariate analysis is required.

Many economic factors are directly affected by the hydrocarbon composition. There are several applications of NIR spectroscopy related with hydrocarbon processes such as monitoring of the composition and BTU content of natural gas online, analyses of the monocyclic aromatic components in gasoline, octane rating of gasoline and determination

of gas-oil ratio for crude oil5,7. Boelens et al.8 showed that it is possible to perform fast and

accurate analysis of n-alkanes in gaseous mixtures of linear, branched and cyclic alkanes with use of NIR spectroscopy.

Calibration models

Model 1- linear model:

y = α P + β (2.1);

This model represents a linear relation between pressure (P) and the univariate spectral

quantity (y). The model has only 2 parameters α and β that are determined by linear

regression.

Model 2 – 2nd order polynomial model:

y = α P2 + β P + γ (2.2);

This model represents a parabolic relation between pressure (P) and the spectral quantity

(y). This model has 3 different parameters α, β, and γ.

Model 3a - bi-linear model / non-continuous:

To assure that the model represents an injective function, a transition pressure

parameter (PC) is introduced to indicate where transition occurs of one region to the other

region of the model. The model equations are:

If P < PC (Low Pressures region, LP)

y = αL P + βL (2.3);

if P ≥ PC (High Pressures region, HP)

y = αH P + βH (2.4);

The model has 4 parameters αL, βL, αH and βH that are determined by independent linear

Model 3b -bi-linear model / continuous:

This model follows the equations given for model 3a with one extra border condition:

If P = PC, then

αH PC + βH = αL PC + βL⇔

⇔βH = (αL - αH) PC + βL

(2.5);

Consequently, the model has only 3 parameters αL, βL, and αH that are determined by

minimum square route error method.

In the multicomponent case y is a corrected spectral quantity, as it is presented in the next section.

Net Analyte Signal Theory (NAS)

With the variation of environment humidity during a time based experiment, water bands can appear that might cause problems in the analysis of the spectra. NAS theory can be used to perform the correction for the presence of such water bands in the spectra.

As presented by Lorber9 the net analyte signal of a certain analyte may be computed as

the part of its spectrum orthogonal to the contribution of other coexisting constituents. The

analyte spectrum s (n×1) can always be decomposed into s⊥ and s=,

s = s⊥ + s= (2.6);

where s= is the part of the analyte spectrum that is not orthogonal to the interferent, and is

a linear combination of pure interferent spectra. Only the orthogonal part, s⊥ is unique for

the sought for analyte and can be computed by 9:

Where I (n×n) is the identity matrix, and W is the interferents matrix, with spectra of

interferents on its columns and W+ is a generalized inverse of W. In the present case, W is a

vector representing the water band spectrum of dimension (n×1). Further information about

NAS theory can be found in the literature9,10,11.

For the calibration model in multi component cases is used the vector s⊥ to compute the

spectral quantity y.

2.3

Experimental

Experimental apparatus

Netherlands) monitors the gas cell pressure. The volume of the gas cell chamber is 204 cm3,

and the sample holder chamber has a volume of 24.4 cm3.

Materials

Commercially available MFI from Zeolyst (Zeolyst International, A partnership of PQ Corporation and CRI Zeolites, Inc., 1700 Kansas Avenue, Kansas City, KS 66105-1198, USA) was used as adsorbent material, with a silica alumina ratio (Si/Al) of 100, and the crystals do not have a regular shape. The sample was calcined for 6 h at 873 K in air. The mass of the used sample was of 4.05 g, and was cleaned at 573 K during a minimum of 3 hours

under a vacuum lower than 8x10-6 mbar. The adsorptive gases used were n-butane with a

99.5% purity, and i-butane with 99.95% purity from Praxair (Praxair N.V., Nijverheidsstraat 4, B-2260 Oevel, Belgium). These gases were used without any further pre-treatment.

Experimental Procedure

For single and multi component calibration models, NIR spectra (average of 10 scans with

2 cm-1, 4 cm-1, 8 cm-1, 16 cm-1, 32 cm-1 and 64 cm-1 of resolution) of pure gases are recorded

at 373 K for several pressures. The data is treated as explained in the Results section. All sorption experiments were done at 373 K. To perform an adsorption experiment gas (or vapor) is fed into the gas cell while closing valve 2 in order to isolate the sample. After introduction, valves 1 and 2 are kept closed during the initial period, keeping the pressure constant at its initial value. Spectral data acquisition is started during this initial period. When valve 2 is opened, the adsorption process starts, at this moment a pressure drop is observed. Spectra are recorded in time, so the adsorption uptake can be computed as a function of time. This procedure is repeated to obtain a full adsorption isotherm. Desorption is performed in a similar way. The zeolite is preloaded (by an adsorption step) and then valve 2 is closed to keep the sample isolated. Valve 1 is open to evacuate the system, when maximum vacuum is achieved valve 1 is closed. While the pressure is kept constant at 0 kPa, the recording of spectra is started. Valve 2 is opened after a few minutes and desorption starts until pressure achieves its equilibrium value.

2.4

Results

The information of n-butane and i-butane is only located in a small part of the spectral range. Therefore, the performance of the spectroscopic method highly depends on wavenumber selection. After a preliminary study two spectral ranges are selected. The first

range is from 6700 cm-1 to 7350 cm-1 and also includes some water bands. The second range

is between 8000 cm-1 to 8700 cm-1. These ranges correspond to CH2 stretch + bend and CH3

stretch vibrations respectively. The intensity in the selected spectral regions appeared to be linearly dependent of gas pressure, although a small non-linearity is still visible when y (spectral quantity) is plotted versus P (pressure). Different spectral preprocessing treatments were tried in this work and compared to no preprocessing (see table 2.1).

Table 2.1: Preprocessing methods.

Method Description

None: no preprocessing of spectra

OffSet: Offset preprocessing, the offset value is calculated using the

interval of [6400; 6475] cm-1 for the first region, and [7600; 7750]

cm-1 for the second region.

Drift: Correction of base line with a 1st order polynomial, the intervals

selected to compute the baseline are [6400; 6475] and [7600; 7750] for the first region; [7600; 7750] and [9000; 9200] for the second region.

Drift-WB: Correction of base line followed by a water-band correction using

Calibration Results

Calibration models

The purpose of this sub-section is to give an overview of spectral measurements (resolution influence – precision of model vs. scanning velocity), and to draw some preliminary conclusions on the calibration models (model 1, 2 and 3a). The spectral quantity y in this sub-section is defined as the area of the spectral bands on the selected ranges. Figure 2.2 presents the calibration results for i-butane, using the 6 different resolutions and its residual standard deviation (RSD), using OffSet correction. The n-butane results are not shown due to their similar behaviour.

y (a .u .) 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 R S D (a .u .) 0 50 100 150 200 250 -8 -6 -4 -2 0 2 4 6 p (kPa) p (kPa)

Figure 2.2: Calibration lines (a, c, e) and residual standard deviation (RSD) vs. pressure (b, d, f) for i-butane at 373 K using OffSet correction. Models: model 1 (a, b), model 2 (c,

d) and model 3a (e, f). Resolution: (_{) 2 cm}-1_{, (}_{) 4 cm}-1_{, (}_{) 8 cm}-1_{, (}_{) 16 cm}-1_{, (}_{) 32}

cm-1 and () 64 cm-1.

It can be observed that resolution has hardly any influence in the calibration model “quality”, since the values of RSD are in the same order of magnitude for the different

resolutions, in the three types of models. Therefore, resolution 4 cm-1 was chosen to use in

the calibration models. This option is based on the trade-off between spectral information – scanning velocity. The chosen resolution allows 1 scan in less than one second and the obtained spectral bands are very similar to the ones obtained using the highest resolution

allowed by the spectrometer (2 cm-1).

The bi-linear model presents the lowest RSD values. Consequently, it was opted to use it as calibration model in the future work.

Bi-linear models: continuous vs. non-continuous

In the previous sub-section it was concluded that the bi-linear model in its discontinuous form presents the best fit to the experimental data. However, this model has an inherent disadvantage. For a narrow range of y values there might exist no solution, or two different solutions in P. With objective of improving the calibration model both forms were

compared. Only the 4 cm-1 scanning resolution was used for this evaluation. If each

calibration spectrum is represented by a vector s, then y is the Euclidean norm of the vector. An offset correction of the spectra was used as preprocessing method.

y (a .u .) 0 10 20 30 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1 p (kPa) R S D (a .u .)

300

0 50 100 150 200 250 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 R S D (a .u .) 0 50 100 150 200 250 -0.03 -0.02 -0.01 0 0.01 0.02 p (kPa) p (kPa)

Figure 2.3: Calibration lines (a) and residual standard deviation (RSD) vs. pressure for

model 3a (b) and model 3b (c), for i-butane, at 373 K and OffSet correction. (₎

Experimental values, () model 3a and () model 3b.

Figure 2.3 presents the obtained results for the two calibration models. Although, the continuous model is numerically more robust it presents lower sensitivity in the pressures

between 0 and Pc. Additionally, the non-continuous model is simpler to implement and in

our case the discontinuity in the y values seems to be rather small. Therefore, numerical complications are not expected in its implementation. As conclusion, it was decided to use the non-continuous model for calibration of the spectral data, using a scanning resolution of

4 cm-1.

a)

Preprocessing methods

It is important to check whether the different treatments affect the performance of our calibration model. Using the raw data without preprocessing (option “None”) is not

considered for calibration. For PC the value of 60 kPa is selected. Figure 2.4 presents the

calibration lines for a) n-butane and b) i-butane at 373 K using Drift correction; the calibration lines for OffSet and Drift-WB are similar and therefore not presented. The solid lines are the linear regression models and the open symbols are the experimental results.

y (a .u .) 0 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 y (a .u .) 0 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 p (kPa) p (kPa)

Figure 2.4: Calibration lines for a) n-butane and b) i-butane at 373K using Drift correction.

Table 2.2 (for the Low Pressures region, LP) and table 2.3 (for the High Pressures region, HP) present the residual standard deviation (RSD) of the calibration models with offset, drift and drift + water bands preprocessing techniques. These RSDs are in absorbance units.

Table 2.2: – Residual standard deviation for i- and n-butane calibration for P < PC.

RSD in LP (a.u.) i-butane n-butane

OffSet 2.8 x10-3 4.8x10-3

Drift 1.7 x10-3 9.6x10-4

Drift – WB 1.1 x10-3 6.2x10-4

Table 2.3: – Residual standard deviation for i- and n-butane calibration for P ≥ PC.

RSD in HP (a.u.) i-butane n-butane

OffSet 2.1 x10-2 1.5 x10-2

Drift 2.2 x10-2 1.4 x10-2

Drift – WB 1.5 x10-2 9.8 x10-3

The RSD value is directly related with the precision of the methods. Low values of RSD mean better prediction of P (pressure). From a close look into the tables one can observe that all methods present RSD values with the same order of magnitude. Though a small improvement is observed when Drift-WB preprocessing is used.

Time based results

In the time based experiments, performed to measure the kinetics of adsorption / desorption, a spectral baseline drift was observed as a function of time. A representative example is presented in figure 2.5. When the gas cell is empty (P = 0 kPa), the absorbance spectra do not show band like features, this is the initial step of desorption (0-2 min.). When valve 2 is open, the pressure in the gas cell increases due to the n-butane desorption, giving the appearance of spectral bands. (2-100 min).

A b s o rb a n c e ( a .u .) 3000 4000 5000 6000 7000 8000 9000 10000 -0.1 0 0.1 0.2 0.3 0.4 0.5 6800 7000 7200 -0.04 -0.02 0 0.02 0.04 8200 8400 8600 P = Pdesorption P = 0kPa Wavenumber (cm-1₎

In order to study the effect of the different preprocessing methods, 3 different quantities are derived from the each spectrum. They are listed in 2.4.

Table 2.4: List of the quantities that are calculated from the time based experiments.

Quantity Description

Intensity in range [6700,7350] cm-1 – I1 Euclidean norm of the vector that corresponds

to the spectrum in the [6700,7350] cm-1 range.

Intensity in range [8000,8700] cm-1 – I2 Euclidean norm of the vector that corresponds

to the spectrum in the [8000,8700] cm-1 range.

Total Intensity – Itot Euclidean norm of the vector that corresponds

to the spectrum when the absorbances are merged in one single vector.

The ranges [6700,7350] cm-1 and [8000,8700] cm-1 are indicated in figure 2.5. During the

initial step of desorption (0-2 min) these 3 intensities should be zero absorbance. When the desorption starts the spectral quantities should sharply rise during the first few seconds, after which a plateau should be observed when the equilibrium pressure is reached. Spectral disturbance, such as drift, can mask desired analytical information about the adsorption process.

The time-based spectra were preprocessed by three methods: None, OffSet and Drift.

Figure 2.6 shows the norms of Itot, I1 and I2 as a function of time. Figure 2.6a shows that

without preprocessing Itot, I1 and I2 curves have high noise levels and do not present the

expected plateau behavior. The instability masks the start of the desorption process completely. Secondly, OffSet preprocessing was performed (figure 2.6b), and the norms of

the resultant spectra were calculated and plotted in function of time. Though the Itot curve

behaviour seem to represent a valid desorption experiment, one can observe that I1 and I2

correct the spectra. When two absorbance regions are used for analysis it is not sufficient

to evaluate the total intensity, Itot. The “partial” quantities (I1 and I2) must present also the

expected plateau behaviour, since both regions are independent from each other. Figure

2.6c shows Itot, I1 and I2 curves for the drift preprocessing. These curves represent normal

behaviour, which indicates that drift correction eliminates all baseline problems.

A b s o rb a n c e ( a .u .) 0 20 40 60 80 100 0 0.02 0.04 0.06 0.08 0.1 A b s o rb a n c e ( a .u .) 0 20 40 60 80 100 0 0.02 0.04 0.06 0.08 0.1

Time (min) Time (min)

A b s o rb a n c e ( a .u .) 0 20 40 60 80 100 0 0.02 0.04 0.06 0.08 0.1 Time (min) 0 00 0Itot 0000I1 0000I2

Figure 2.6: Norm of spectral ranges I1, I2 and Itot as a function of time after preprocessing

method: a) None b) OffSet and c) Drift.

Time based Control Experiment

Some checks were performed to find possible causes for this observed drift. Lamp intensity and voltage intensity were checked as a possible cause. A temperature effect in

a) b)

the detector and in the room humidity could cause such a problem. We recorded blank spectra and the temperature of the detector for 48 hours in which the temperature would change from 15 to 20°C. Blank spectra are spectra of the background conditions, and are representative also for a real experiment. The results are shown in figure 2.7.

A b s o rb a n c e ( a .u .) 4000 6000 8000 10000 -0.15 -0.1 -0.05 0 0.05 0.1 6800 7000 7200 -0.03 0 0.03 0 0.06 0.09 8200 8400 8600 Wavenumber (cm-1₎

Figure 2.7: Blank raw spectra as a function of time. The two subplots have the same scale in ordinates.

A clear baseline drift is observed in figure 2.7. Water bands appear at 3900 cm-1, 5700

cm-1, 7200 cm-1 and 8800 cm-1. Both, baseline drift and water bands, are time dependent.

The blank spectra were treated in the same way as the spectra collected during a

desorption experiments. Without treatment, the 1st region [6700, 7400] cm-1 contains

intense water-bands, in the 2nd region [8000, 8700] cm-1 a baseline drift can be observed

(subplots of figure 2.7). OffSet correction reduces the baseline problem but waterbands are still present. With Drift preprocessing the baseline is almost corrected however,

water-bands are still visible (figure 2.8), mainly in the [6700, 7400] cm-1 region. The [8000, 8700]

cm-1 region where the water bands were weaker is almost totally corrected by Drift

A b s o rb a n c e ( a .u .) 6700 6900 7100 7300 -0.04 -0.03 -0.02 -0.01 0 A b s o rb a n c e ( a .u .) 8000 8200 8400 8600 -3 -2 -1 0 x 10 -3 Wavenumber (cm-1_{) Wavenumber (cm}-1₎

Figure 2.8: Drift corrected spectra for the 2 selected regions.

Figure 2.8 shows clearly that Drift is insufficient to correct for water bands, which disturb the data analysis. Therefore, also water-band correction is included in the preprocessing step. One of the final spectra of figure 2.8 is selected, to represent the water band spectrum. All spectra are corrected for water bands using the NAS approach (see figure 2.9). Although some spectral drift still remains, this is not significant, and the corrected spectra present mainly instrumental noise.

A b s o rb a n c e ( a .u .) 6700 6900 7100 7300 -4 0 4 8x 10 -3 A b s o rb a n c e ( a .u .) 8000 8200 8400 8600 -4 0 4 8x 10 -4 Wavenumber (cm-1_{) Wavenumber (cm}-1₎

Figure 2.9: NAS spectra corrected for water band.

with the results without any treatment (None), although the temperature effect (on the baseline drift or room humidity) is still visible after drift correction. The norm of the NAS vector was calculated, the resulting NAS signal was plotted as a function of time in figure 2.11. In this case the NAS signal should have a similar magnitude as the other spectral norms used. A major improvement is observed after Drift-WB correction. The results of figure 2.11 can be compared “directly” with ones presented on figure 2.10b. Therefore, one must pay attention that the scale of figure 2.11 is 100 times smaller than the one in figure 2.10b. The NAS signal is almost reduced to the noise level, which is in agreement with the fact that the data are from a control experiment, where only blank spectra were recorded.

T ( °C ) 0 10 20 30 40 50 60 17 19 21 23 A b s o rb a n c e ( a .u .) 0 25 50 75 0 0.4 0.8 1.2 1.6 2 Time (h)

Time (h)

Figure 2.10: Temperature profile and Itot in function of time for the 3 different

preprocesses. —— None, — — OffSet, - - - - Drift.

N A S v a lu e ( a .u .) 0 10 20 30 40 50 60 70 0 0.01 0.02 Time (h)

Figure 2.11: NAS vector norm (corrected for water-bands) in function of time. —— Total,

— — Partial [8000, 8700] cm-1, - - - - Partial [6700, 7350] cm-1.

The most robust method to preprocess time base data is drift correction, which can be improved when combined with correction of water bands. This treatment will be adopted as the tool for data treatment on monitoring the adsorption/desorption time base experiments.

2.5

Conclusions

References

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Newton, I., Philos. Trans. R. Soc. London 1671/72, 80, 3075.

Schenk, M.; Vidal, S.L.; Vlugt, T.J.H.; Smit, B.; Krishna, R., Langmuir 2001, 17, 1558.

Tondeur, D.; Wankat, P.C., Sep. Purif. Methods 1985, 14(2), 157.

Karger, J.; Ruthven, D.M., Diffusion in zeolites and other microporous solids, John Wiley and Sons (eds), New York, 1992.

Fujisawa, G.; Agthoven, M.A.; Jenet, F.; Rabbito, P.A.; Mullins, O.C., Appl. Spectrosc. 2002, 56(12), 1615.

Ozaki, Y.; Amari,T., Near-infrared spectroscopy in chemical process analysis, John M. Chalmers (eds), Cleveland, 2000.

Mullins, O.C.; Joshi, N.B.; Groenzin, H.; Daigle, T.; Crowell, C.; Joseph, M.T.; Jamaluddin, A., Appl. Spectrosc. 2000, 54(4), 624.

Boelens, H.F.M.; Kok, W.Th.; Noord, O.E.; Smilde, A.K., Appl. Spectrosc. 2000, 54(3), 406.

Lorber, A.; Faber, K.; Kowalski, B.R., Anal. Chem. 1997, 69(8), 1620.

Boelens, H.F.M.; Kok, W.Th.; Noord, O.E.; Smilde, A.K., Anal. Chem. 2004, 76, 2656.

3

Axel Fr. Cronstedt Axel Fr. Cronstedt Axel Fr. Cronstedt Axel Fr. Cronstedt 1

Adsorption and Differential Heats of

Adsorption of Normal- and Iso-Butane

∗

3.1

Introduction

Adsorption phenomena were known in ancient civilisations. The adsorbent properties of clay, sand and wood charcoal were utilised in a wide range of applications, such as

desalination of water, the clarification of fat and oil and the treatment of many diseases2.

In modern times new applications did appear; the separation of linear and branched hydrocarbons is a problem with growing industrial importance, because of its potential for

the octane number enhancement3. Branched alkanes have higher octane number than linear

alkanes, thus the formers are preferred as ingredients in the gasoline. Separation by distillation is difficult and energy consuming because the linear and branched alkanes have close boiling points. Therefore, the separation can be performed by selective adsorption using a Pressure Swing Adsorption (PSA) unit. Materials, like zeolites, may be used for this separation process. Therefore, their sorption properties have received an increasing

attention in the past years4-16. Adsorption equilibrium data are essential to the development

of adsorption based separation methods. These data are also relevant to the catalytic isomerization in the zeolite itself.

The selectivity of an adsorbent for a particular separation is determined by differences in the free energy of adsorption of the mixture molecules, in the zeolite. Differences in free

energy of adsorption arise from energy or entropic effects, or a combination of both7.

Although PSA processes are usually operated at ambient temperature, the adsorption and desorption steps in a cycle operates under approximately adiabatic conditions. The magnitude of the temperature change inside of a PSA column is induced by adsorption or desorption heats, and can be determined by an energy balance using the individual heats of adsorption of the mixture’s components. As the adsorption loading is highly sensitive to the adsorbent temperature, the selectivity is closely related to the magnitudes of the individual heats of adsorption. Therefore, an accurate design requires precise values for the heats of adsorption.

3.2

Experimental Section

In the present work the adsorption properties of n-butane and i-butane on MFI are being studied. Adsorption isotherms and differential heats of adsorption are accessed directly by a manometric set-up combined with a micro-calorimeter.

Experimental Set-up

The experiments were performed in a micro-calorimeter (Calvet C80, Setaram) connected to a house built manometric apparatus. Figure 3.1 shows a scheme of the experimental setup.

The calorimeter used for these experiments is of the Calvet type, which measures the heat flux in and/or out of the sample cell, and can be operated isothermally at a fixed temperature. Gas or vapour can be fed into the system by a piston, that can introduce a full, ½ or ¼ stroke. The introduction pressure can not be higher than 100 kPA. Two pressure transducers with different sensitivities allow an accurate measurement of pressure, of the gas phase in contact with the sample, from 0 kPa to 10 kPa and from 0 kPa to 1000 kPa.

Vacuum better than 5×10-7 mbar is achieved when cleaning the sample. The manometric set

up is operated automatically by a Visual Basic in-house programmed software.

The isotherm calculations are performed by this programme. The setup has two independent data acquisition systems, one for the manometric (isotherm) data, the other for the calorimetric data. All valves in the manometric part are type SS-4BK-V51-1C (from Swagelok), the pressure transducers are Baratron of type 121AA in the range 100 mbar, 1000 mbar and 10000 mbar.

Materials and pretreatments

Commercially available MFI from Zeolyst (Zeolyst International) was used as adsorbent material, with a silica alumina ratio (Si/Al) of 100. The sample was calcined for 6 h at 873 K in air. The mass of the used sample was 1.89 g, and cleaned at 573 K during a

minimum of 6 hours under a vacuum better than 5×10-7 mbar. The adsorptive gases used

were n-butane with a 99.5% purity, and i-butane with 99.95% purity from Praxair (Praxair N.V). These gasses were used without any further pre-treatment.

Experimental

Blank measurements have been performed for n- and i-butane at 373 K, 398 K and 423 K. The zeolite sample was outgassed at 573 K during 6 hours under a vacuum better than

5×10-7 mbar. Isotherms and heat fluxes have been measured in a continuous way for the 2

gases at the 3 different temperatures. For pressures up to 1 kPa a small amount of gas was introduced (piston in the ¼ of a stroke position, admission pressure of 5 kPa), this allows measuring several adsorption equilibrium points in the low pressure region - the Henry region. Then, the introduction pressure and volume are increased; the piston introduces ½ of stroke, with a pressure of 50 kPa, until an equilibrium pressure of 9.8 kPa. The final equilibrium points (equilibrium pressure between 9.8 kPa and 200 kPa) were performed with the piston on the full stroke position and an introduction pressure of 100 kPa.

3.3

Theory:

Adsorption Equilibrium

Isotherms models

MFI type zeolites have two types of channels that are connected via intersections. One channel type is straight, and has an elliptical cross section with diameters equal to 0.52 nm and 0.58 nm. The other type, zigzag type, has nearly circular shape, with a diameter of

0.54 nm16. The intersections have a diameter of roughly 0.9 nm17. Molecules have the

tendency to adsorb in the smaller channels to maximize the attractive interactions with the MFI walls. Geometric constrain can appear if the molecular diameter is too large, this leads to preferential adsorption on the larger intersections. Simulations of sorbate spatial distribution show that the side groups in the branched alkanes force these to sit in the

channel intersections, while the linear alkanes prefer to reside in the channels18. This

means that there are two different sites in MFI structure, where adsorption can take place. A double Langmuir model would be necessary to describe the adsorption in these different sites.

p

K

p

K

n

p

K

p

K

n

n

I I I sat a C C C sat a a

+

+

+

=

1

1

, , (3.1)

Where na is loading (adsorbate concentration in the particles) and p is pressure

(adsorbate concentration in the gas phase). The two adsorption sites give rise to two

different saturation amounts. They are indicated by nasat,C and nasat,I (C – channels, I –

intersections).

K

_C and

K

_I are the adsorption equilibrium constants for the two sites.

When one of the sites is inaccessible to the adsorbate molecules, the double Langmuir

model simplifies to the well-known Langmuir model. Where

n

asat represents the saturation

loading and

K

the adsorption equilibrium constant.

Kp

Kp

n

n

a asat

+

=

1

(3.2)

Henry’s Law region

Equation 3.2 is the Langmuir isotherm; its mathematical nature is able to reproduce the general shape of a Type I isotherm. At low pressure K•p may be neglected in comparison with unity, and the equation simplifies to:

p

K

n

a

=

_H (3.3)

In the Henry’s Law region, adsorption is proportional to the pressure, and the isotherm is

reduced to a straight line through the origin.

K

_H is the Henry’s Law constant. However, in

this region the Langmuir model must still be observed, thus the right side of equations 3.2 and 3.3 must be equal, obtaining in this way equation 3.4.

K

n

K

_H

=

asat (3.4)

The

K

_H values can be obtained directly by fitting the linear part of the isotherm to

equation 3.3 and forcing it to pass by the origin.

The derived values of

K

_H , at different temperatures, can be described with the

integrated form of the van ‘t Hoff equation17.

)

exp(

0 0

RT

U

K

K

_H

=

_H

−

∆

(3.5)

where

∆

U

0is the internal energy of adsorption at zero coverage. The adsorption

enthalpy,

∆

H

0 at zero coverage can be calculated from the following equation2.

RT

U

H

=

∆

−

3.4

Results and Discussion

Equilibrium Adsorption data

Experimental data on single component adsorption isotherms and differential heats of adsorption, of n-butane and i-butane, on MFI zeolite, at 373 K, 398 K and 423 K, for a pressure range from 0.01 kPa to 200kPa, were obtained.

n a(m m o l g -1) 0 0.4 0.8 1.2 1.6 2 0.01 0.1 1 10 100 1000 0 0.1 0.2 0.01 0.1 1 0 0.4 0.8 1.2 1.6 2 0.01 0.1 1 10 100 1000 0 0.1 0.2 0.01 0.1 1 n a(m m o l g -1) 0 0.2 0.4 0.6 0.8 1 0.01 0.1 1 10 100 1000 0 0.1 0.2 0.01 0.1 1 0 0.2 0.4 0.6 0.8 1 0.01 0.1 1 10 100 1000 0 0.1 0.2 0.01 0.1 1 p (kPa)

Figure 3.2: a) n-Butane and b) i-Butane isotherms on MFI at (
) 373 K, () 398 K, (
)

423 K. Full lines are the isotherm model fits by eqn. (3.2). Dashed line is literature6 data

at 373 K.

The isotherms of the C4 isomers are shown in figure 3.2. They are found to have a Type I

shape2. Therefore, isotherm data were fitted with the classical Langmuir model given by

equation 3.2. The data are in agreement with the literature data6, especially for the low

a)

pressures region. The differential heats of adsorption as function of coverage for the two isomers at 373 K, 398 K and 423 K are plotted on figure 3.3. The continuous rise of the differential heat of adsorption of n-butane presented on figure 3.3 shows that the sample behaves energetically homogenous in the adsorption process, and the rise is due to the adsorbate-adsorbate interactions. When these sites are fully occupied, the heat of adsorption presents an abrupt decrease pointing to adsorption on the external surface, and not in a second energetically different site. On the other hand, i-butane heats of adsorption present only plateau behaviour, keeping the heats of adsorption constant until a certain loading, characteristic of only one energetic site. Therefore, the use of Langmuir model to fit the equilibrium data for both components is supported by the information extracted from the heats of adsorption. For both cases it can be said that the heats of adsorption have a “plateau” like behaviour, and it depends on the nature of the adsorbate and temperature. The final abrupt decrease of the differential heat of adsorption essentially corresponds to the adsorption on the external surface. This can explain the plateau length dependence with temperature and molecular structure. The maximum loading is inversely proportional to the temperature. Therefore, at higher temperatures the micropores are totally filled at lower loading, so the “plateau” length is shorter. In the case of i-butane a sharp peak is also observed, this is due to the fact that i-butane molecules sit preferentially

on the intersections18, so adsorbate-adsorbate interactions become noticeable only when

the loading is near the maximum capacity of the adsorption sites. Gener et al.3 presents

similar behaviour for C6 isomers.

H e a t o f A d s o rp ti o n ( k J m o l -1) 0 20 40 60 80 0 0.5 1 1.5 2 0 20 40 60 80 0 _0.2 0.4 0.6 0.8 1 na_{(mmol g}-1₎

na(mmol g-1)

Figure 3.3: a) n-Butane and b) i-Butane heats of adsorption on MFI, at (
) 373 K, ()

398 K, and (
) 423 K. (×) Zhu et al. isosteric enthalpy of adsorption17.

The range of the experimental heats of adsorption presented by Vlugt19 for n-butane is 48

kJ•mol-1 to 56.1 kJ•mol-1, and for i-butane is between 46.7 kJ•mol-1 and 56 kJ•mol-1. These

data are in agreement with the values presented in this study. Eder20 measured a heat of

adsorption of 58 kJ•mol-1 for n-butane, and 52 kJ•mol-1 for i-butane. Thamm21 has reported

the sharp peak in the heats of adsorption observed in the i-butane case also. Zhu et al.17

reports isosteric enthalpies of adsorption for n-butane and i-butane that are in agreement with ones presented by this study (figure 3.3).

The equilibrium points at high loadings (heats of adsorption inferior to 40 kJ•mol-1),

represent mainly adsorption on external surface. Therefore, they were not used in the

fitting of equation 3.2 to derive

K

and

n

asat parameters. The parameters

K

and

n

asat are

reported on table 3.1.

In the literature it is reported that n-butane adsorbs first on the channels. Therefore,

from values presented on table 3.1 for

n

asat and the heats of adsorption (figure 3.3), one

can conclude that n-butane molecules adsorb only on the zeolite channels. On the other hand, for i-butane the preferential adsorption site reported in the literature is the intersections (4 intersections per unit cell).

Table 3.1: Langmuir

K

and

q

_sat parameters on MFI.

The saturation loadings present on table 3.1 for i-butane are lower than 4 m.u.c. In addition, figure 3.3 provides the extra information that the zeolite behaves energetically homogenous for the case of i-butane until the maximum loading. Therefore, one can conclude that i-butane adsorbs on the intersections only. Adsorption on external surface starts when the intersections are totally occupied. As expected, the saturation loading decreases with temperature, as well as the adsorption equilibrium constant.

Henry’s Law constants

Henry constants for the different temperatures were calculated by using equation 3.3.

The method used was to plot of ln(na)/ln(p) versus 1/ln(p) for the Henry’s Law region

points, and to fit a straight line with intercept equal to 1, the slope of this line is ln(

K

_H).

The values derived in this way are compared on the table 3.2 with ones obtained by the equation 3.4 and literature values.

Table 3.2: Henry’s Constant for n-butane and i-butane on MFI.

Sorbate Temp. (K) a KH (10-2 _{mmol g}-1 _kPa-1₎ b K nasat (10-2 _{mmol g}-1 _kPa-1₎ c KH (10-2 _{mmol g}-1 _kPa-1₎ K nasat (10-2 _{mmol g}-1 _kPa-1₎ n-butane 373 45.36 44.47 34.56 46.04 d 398 16.95 16.61 12.80 408 09.75 d 423 6.80 6.88 5.33 i-butane 373 26.07 27.64 20.55 31.83 e 398 10.36 10.74 7.94 408 08.88 e 423 4.55 4.95 3.44 a

equation (3.3), b equation (3.4), c Zhu et al.17, d KC and nasat,C6, e KI and nasat,I6

estimation can be obtained using the parameters from the isotherm fit (equation 3.4). The values presented in this study are in good agreement with ones of the literature.

Figure 3.4 is the plot of ln(KH) versus 1/T. Equation 3.5 can be represented as a line with

intercept equal to ln(KH0) and slope equal to -∆U0/R. The computed values for KH0 and -∆U0

are shown on table 3.3 and compared with literature values. From equation 3.6 the values

for -∆H0 can be derived, the values are presented also in table 3.3.

KH (m m o l g -1 k P a -1) 0.01 0.1 1 0.0023 0.0025 0.0027 1/T (K-1₎

Figure 3.4: ln(KH) as function of 1/T for adsorption of () n-butane and () i-butane on

MFI. Full lines are the models fit by eqn. (3.5).

Table 3.3: Thermodynamic Adsorption parameters for n-butane and i-butane on MFI.

KH0

(10-8 mmol g-1 kPa-1)

-∆U0

(kJ mol-1) -∆H0

Sorbate This study Lit.a This Study Lit.a (kJ mol-1)

n-butane 05.12 4.88 49.52 48.8 52.62

i-butane 10.46 5.72 45.58 46.7 48.86

a

Zhu et al.17