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Abstract

Temperature programmed desorption (TPD) with reaction is a useful technique for characterising catalysts.

A general model that simulates TPD with reaction experiments was developed and successfully validated.

The generality of the model means multiple catalytic sites may be specified, each having a distribution of

activation energy. Additionally, any reactant/catalyst system may be modelled by specifying the reactions

involved in the system. Three case studies were performed where the model was fit to experimental TPD

data from the literature. Some experiments were performed on one of the systems studied

(isopropylamine/ZSM-5) in order to better understand critical underlying processes. Quantitative

information such as distribution of activation energies for each catalytic site, pre-exponential factors and

relative site populations were extracted from the cases studied. The values obtained compare well with

those reported in the literature and with values determined using other quantitative techniques.

Temperature Programmed Desorption with Reaction

Developing a general model for quantitative analysis

Karim Al Shebani Al Nehlawi Homerton College Partner: Qing (Chely) Miao Supervisor: Dr. Patrick Barrie 40 pages + Preface + Title Page + Safety Appendix

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Contents 1. Introduction and aims ............................................................................................................................................... 2

1.1 What is temperature programmed desorption? .............................................................................................. 2

1.2 What are the benefits of TPD with reaction? ................................................................................................... 3

1.3 Aims of this research project ............................................................................................................................ 3

2. Literature review ....................................................................................................................................................... 4

2.1 Qualitative analysis ........................................................................................................................................... 4

2.2 Simple quantitative analysis ............................................................................................................................. 7

2.3 Quantitative analysis for determining kinetic parameters ............................................................................... 8

2.4 Brief description of isopropylamine/ZSM-5 system ....................................................................................... 11

3. Experiments ............................................................................................................................................................ 12

3.1 Experimental procedure ................................................................................................................................. 13

3.2 Thermal decomposition of propene ............................................................................................................... 14

3.3 Desorption of propene from ZSM-5 ................................................................................................................ 15

4. Model description ................................................................................................................................................... 16

4.1 Background knowledge ................................................................................................................................... 16

4.2 Generating a TPD curve .................................................................................................................................. 19

5. Model validation and discussion of results ............................................................................................................. 23

5.1 Comparison with specific model ..................................................................................................................... 24

5.2 Case Study: CO on nickel ................................................................................................................................. 25

5.3 Case Study: formic acid on copper .................................................................................................................. 30

5.4 Case Study: Isopropylamine on ZSM-5 ........................................................................................................... 34

6. Conclusion ............................................................................................................................................................... 37

7. Further work ........................................................................................................................................................... 37

8. Nomenclature ......................................................................................................................................................... 37

9. Works cited ............................................................................................................................................................. 38

10. Safety appendix ................................................................................................................................................... 41

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1. Introduction and aims

Catalysts play a vital role in a wide variety of industries and understanding how they perform their function

can help in designing superior catalysts. Many financial, environmental and social benefits have arisen

from the study of catalysts, such as catalytic converters in car exhausts and catalytic crackers in oil

refineries. Characterising catalysts in order to extract functional information is a key step in developing a

thorough understanding of catalyst performance and can enable process improvements to be made.

1.1 What is temperature programmed desorption?

Temperature programmed desorption (TPD) is an experimental technique used to characterise catalysts

(King, 1975). It provides a wealth of information and is exclusive to the investigation of solid catalysts with

gaseous species. Typically, a catalyst sample is placed in a reactor with a heating element such that the

temperature can be programmed accordingly. The flow rate of gaseous species into the reactor can be

controlled and a mass spectrometer is usually used to detect the species leaving the reactor. The catalyst

may be subjected to pre-treatment as necessary, such as heating with an inert carrier gas to eliminate

adsorbed water vapour or bombarding with argon ions to clean a metal crystal surface. A gaseous probe

molecule is then injected into the reactor (usually in pulses of known volume) until the required coverage

has been attained on the catalyst. The remainder of the experiment can either be conducted with

continuous flow of a carrier gas in vacuum conditions. The temperature is then ramped linearly with time

so that:o)( TttT where is the heating rate (K/s) and

oT is the initial temperature (K).

As the temperature increases, the rate of desorption from the catalyst initially increases and the coverage

on the catalyst decreases. However at some point in the experiment the coverage becomes small enough

that the rate of desorption decreases with temperature. There is therefore a maximum in the rate of

desorption at a particular temperature. A peak shape is thus characteristic of TPD results when plotted as

the desorption rate of species versus temperature. Figure 1 below depicts the set-up of a TPD experiment.

The catalyst sample could be a packed bed, a differential packed bed (very thin layer of catalyst) or an

exposed flat surface. Note that the concentration of adsorbed species is usually defined using a

dimensionless value of coverage, namely the ratio of occupied sites to total sites on a catalyst.

Figure 1: Typical set-up for a TPD experiment

Figure 2: TPD of ammonia on H-mordenite and ZSM-5 zeolites. The mordenite curve has been vertically shifted to make it easier

to see (Niwa & Katada, 1997).

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For illustration, Figure 2 above shows a TPD experiment using ammonia to probe the sites of H-mordenite

and ZSM-5 zeolites; note that ammonia desorbs without reaction in this case. The vertical axis is

proportional to the rate of desorption, and the horizontal axis could be interchanged between time and

temperature since they vary linearly with respect to each other. Peaks that occur at higher temperatures

indicate stronger binding energies to the sites on the catalyst; additionally, the area under the TPD curve is

proportional to the population of sites on the catalyst. In this case, the catalysts show two peaks, indicating

that there are two types of sites on which ammonia adsorbs, one strong and one weak. It is also clear that

mordenite contains more sites of higher binding strength than ZSM-5. This simple example shows how

useful TPD could be as a tool to characterise catalysts.

1.2 What are the benefits of TPD with reaction?

For the most part, species which do not undergo reaction on the catalyst are chosen for TPD studies so as

to simplify analysis. However, under certain circumstances, it may be beneficial to select a molecule that

does undergo reaction, resulting in different species desorbing from the catalyst; this is termed TPD with

reaction. TPD with reaction allows one to probe specific sites on a catalyst and can provide information on

reaction mechanisms and the activation energies for reaction. For instance (with reference to Figure 2

above), more information may be gained on ZSM-5 by using a reactive species such isopropylamine that is

believed to decompose only on strong Brønsted sites, rather than using ammonia. The products of the

reaction are ammonia and propene, which can be detected using the mass spectrometer, providing data

specific for characterising the Brønsted acid sites of a zeolite. However, detailed interpretation of results

becomes much more complicated when reaction occurs on the catalyst. There are many unknown

variables that make accurate quantitative data analysis difficult, to the extent that Falconer & Schwarz

(1983) remarked that a complete theoretical description of TPD with reaction (TPDR) is not likely. Despite

this, it might be possible to extract important information from TPDR with well designed experiments and

carefully chosen reactive molecules. However, thus far, the conclusions derived in the literature from TPD

with reaction studies have been predominantly qualitative.

1.3 Aims of this research project

The key aim of this research project is to develop a general model that can be used to extract quantitative

information from TPD with reaction experiments. The flexibility of a general model means that it could be

used on various reactant/catalyst systems with different reaction mechanisms at work. Consequently, the

next aim of this project is to validate the model by applying it to several case studies found in the literature

and comparing the results attained with those available in the literature. The final aim is to conduct TPD

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with reaction experiments on the isopropylamine/ZSM-5 system and attempt to extract quantitative

parameters using the general model developed.

2. Literature review

This section reviews the types of analysis currently performed on TPD data and the information that can be

extracted as a result. The power and versatility of TPD experiments as a tool for characterising catalysts is

demonstrated and the difficulties associated with accurately determining quantitative parameters are

discussed, especially with reference to reactive systems. Furthermore, a brief description of the

isopropylamine on ZSM-5 system is given.

2.1 Qualitative analysis

The qualitative analysis that can be performed on TPD data is best illustrated by giving specific examples.

Peak Temperature & Area under TPD Curve

In general, a peak on a TPD curve represents desorption from a type of site on the catalyst surface.

However, bear in mind that peaks may overlap and it can become difficult to separate individual sites from

each other. The temperature at which the maximum rate is observed for a peak is called the peak

temperature, Tp. Sites with stronger binding energies to the adsorbate will have higher values of Tp and the

peaks will be shifted to higher temperatures. The area under a TPD curve is proportional to the amount of

adsorbate that has desorbed i.e. the area is proportional to the change in coverage of an adsorbate during

the TPD experiment. Accordingly, the area under a peak is proportional to the population of the site it

corresponds to, such that a more populous site would have a larger peak area. This information can be

used to compare and contrast different catalysts. Moreover, it can be used to evaluate how a catalyst

changes as a result of different preparation methods, composition, stages of deactivation or other

properties. The TPD curve is also a unique identifier for a catalyst and can be used for quality control

purposes when manufacturing large quantities of catalyst or indeed when preparing small batches in the

laboratory.

Varying Initial Coverage

TPD curves are also used extensively for determining catalytic reaction mechanisms and orders of reaction.

Take for example, the reaction of an adsorbate to produce a species that desorbs instantly, such that the

TPD peak observed for the product is indicative of the reaction and not the desorption of the product. If

the reaction is first order, then the value of the peak temperature Tp does not change with initial coverage

of the adsorbed reactant; however, if the reaction is second order or higher, then Tp will shift to lower

values as the initial coverage is increased. Therefore, one may perform several TPD experiments with

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different initial coverages of the reactant to determine whether or not the reaction is first order.

Additionally, quantitative analysis can be performed to determine the order of the reaction; this is

discussed later. One problem is that the product species may readsorb onto catalyst downstream in the

reactor, particularly when porous catalysts are used. The effect this has is to ‘delay’ the TPD curve and shift

it to higher temperatures (Gorte, 1982), which adds another degree of complexity that can hamper data

analysis. Another problem that arises is that the product does not desorb instantly and, as initial surface

coverage is increased, binding strength of the product usually decreases as a result of unfavourable

adsorbate-adsorbate interactions. This causes Tp to shift to lower temperatures, potentially resulting in an

incorrect conclusion that the reaction is of order higher than one. Figure 3 below shows the TPD curves for

hydrogen desorption from a supported nickel catalyst at varying initial coverages. Molecular hydrogen

adsorbs dissociatively into two H(ads) atoms; therefore, the desorption process is second order because the

two atoms need to recombine and the effect this has on decreasing the peak temperature can be clearly

seen.

Figure 3: TPD of adsorbed hydrogen on a supported Ni catalyst. Initial overage increases from (a) to (e) (Lee & Schwarz, 1982).

Figure 4: TPD of adsorbed CO on Ru(001) with varying initial

coverages. Note that the curves have been shifted vertically to make it easier to see and the Langmuir L is a unit of coverage

(Brown & Vickerman, 1981).

Varying initial coverage can sometimes reveal more information. For example, Figure 4 shows the TPD of

CO on a surface crystal of Ru(001). As the initial coverage increases, a new peak labelled β2 appears. This

shows how adsorbed CO molecules preferentially adsorb onto the β3 site before the β2 site, suggesting the

β3 site has higher binding strength. Moreover, this shows that the CO molecule is mobile on the surface of

Ru(001) since it can move to a β3 site if it were to first adsorb on a β2 site.

Varying Adsorption Temperature

The temperature at which molecules are adsorbed onto the catalyst can be varied in order to gain further

insight. If lower adsorption temperatures are used, this may reveal any weakly bound species. Higher

adsorption temperatures can eliminate weakly bound species from the TPD curve or promote reactions

that produce desired adsorbed species. For example, in order to determine whether surface carbon

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species are involved in the mechanism of hydrogenation of CO on metal surfaces, CO can be adsorbed at

high temperatures on a metallic catalyst. This promotes the dissociation reaction that produces C(ads) and

O(ads). A TPD experiment with hydrogen flowing as a carrier gas can then be performed at low

temperatures, with CO(ads), C(ads) and O(ads) all present, which gives information on how adsorbed carbon

species take part in the reaction. For instance, this has been performed on a supported ruthenium catalyst

by Low & Bell (1979).

Using Isotopes

Mass spectrometers can differentiate between molecules containing different isotopes. Therefore, one

may mark specific atoms on a reactant using isotopes as a way of gaining more information on reaction

mechanisms. The mechanism for the Fischer-Tropsch reaction, which catalytically converts CO + H2 into a

mixture of hydrocarbons and water, has been debated in the literature for many years. A popular

mechanism suggests CO(ads) dissociates into adsorbed C(ads) and O(ads) atoms, H(ads) atoms then combine with

C(ads) and O(ads) to form hydrocarbons and water. A key step in validating this mechanism is to prove that

CO(ads) actually dissociates on the catalyst and that it does so at a temperature similar to that at which the

Fischer-Tropsch reaction takes place. McCarty & Wise (1979) used isotope TPD methods that confirm the

dissociation of CO on a supported ruthenium catalyst. 12C18O and 13C16O were co-adsorbed in equimolar

amounts and a TPD experiment was performed, the results of which are shown in Figure 5 below.

Figure 5: TPD of

12C

18O and

13C

16O adsorbed on a alumina-supported Ru catalyst, indicating that reversible dissociation occurs.

The species 12C16O and 13C18O were desorbing in significant amounts at temperatures above 375 K,

indicating that reversible dissociation must be occurring. McCarty & Wise (1979) also quantitatively

determined that the exchange rate between isotopes peaked at 427 K, whereas the production of

methane during hydrogenation of adsorbed CO on the same catalyst peaked at 470 K. This shows that CO

dissociation occurs at lower temperatures than the Fischer-Tropsch reaction, supporting the reaction

mechanism discussed above.

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2.2 Simple quantitative analysis

Quantitative data normally extracted from TPD data include (Falconer & Schwarz, 1983):

Active surface area of catalyst

Coverage of adsorbates

Relative population of different sites

Order of reaction

Activation energy of desorption or reaction

Pre-exponential factor for the rate constant

Active Surface Area of Catalyst

The area under a TPD curve is proportional to the number of molecules that have desorbed from the

catalyst. If an adsorbate achieved full coverage on a catalyst, then by calculating the number of molecules

that desorbed after a TPD experiment (assuming all molecules desorb) and by knowing the surface area

occupied by each molecule, the active surface area of the catalyst can be determined. Choosing an

adsorbate that does that not adsorb into multiple layers on the catalyst can simplify the analysis

significantly. The rate of desorption measured by the mass spectrometer is normally in arbitrary units;

therefore, a calibration experiment must be performed whereby a known amount of adsorbate is loaded

onto the catalyst and a TPD experiment is performed. The area under the resulting TPD curve is calculated,

which allows us to relate the arbitrary units of the mass spectrometer to known units of desorption, such

as μmol/s. Attention must be paid to the fact that the sensitivity of some mass spectrometers varies with

different molecules such that it is often preferred to conduct this calibration for each molecule detected.

Coverage

Equation 1 below may be used to calculate the coverage as a function of temperature T if the catalyst

was initially loaded with coverage of one monolayer (i.e. o = 1). Note that this may not apply when

reactions are present that can produce other adsorbed species. Equation 2 may be used when the initial

coverage is not unity, but it requires the area for desorption of a monolayer to be known. The rate of

desorption is r.

f

ooT

T

T

T

dTr

dTr

T

1 (1)

f

o ooT

f

o

T

T

TT

T

dTr

dTr

dTr

T1

(2)

Note dTddtdr .

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Relative population of Sites

The area beneath a peak is also proportional to the population of its corresponding site. Therefore, if peaks

can be separated from each other, then the relative population of different types of site can be

determined; however, this becomes difficult when peaks overlap

2.3 Quantitative analysis for determining kinetic parameters

The kinetic parameters that are usually determined are the order of desorption/reaction, the activation

energy for desorption/reaction and the pre-exponential factor used for the rate constant. Numerous

methods have been devised for extracting these parameters, ranging from relatively simple ways to more

accurate yet complicated ways. Jong & Niemantsverdriet (1990) studied a wide sample of analysis methods

and concluded that simple, rough procedures yield unreliable results, but are easy to apply. Furthermore,

they suggest that ‘complete’ methods, which make fewer assumptions and use several TPD curves to

extract parameters, should be used whenever possible, as they give better results. Each method is

discussed separately below.

Redhead’s Method

This is the simplest and most commonly used method for determining kinetic parameters. In a lot of cases,

especially with regards to reactive systems, several parameters that are needed as input for more

complicated methods are not known. Therefore, Redhead’s (1962) method offers a simple and easy to use

procedure that gives approximate results. For a system with no readsorption, the rate of desorption is

equal to the flow rate of desorbed molecules detected by the mass spectrometer. This is not the case with

readsorption because the total flow rate of species leaving the reactor is reduced. In the absence of

readsorption, the normalised rate detected by the mass spectrometer r is given by Equation 3 below. This

assumes a desorption process or a rate limiting reaction of order n in coverage . At the peak temperature

Tp the rate of desorption is a maximum implying that 220 dTddtdr . This condition produces the

relationship given by Equation 4 below, which can be used to calculate Eact if the pre-exponential factor A is

known (or vice versa). The peak temperature and coverage at the peak temperature must also be known;

however, the coverage term cancels out when the order of reaction/desorption is one. The main problem

with Redhead’s method is that the pre-exponential factor is often not known and has to be estimated or

determined using statistical mechanics.

nn

RT

EAk

dT

d

dt

dr

actexp (3)

p

act

1

p

2

p

act expRT

EAn

RT

En

(4)

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Peak Width and Shape Index Methods

The following two methods of quantitative analysis are based around taking two or three points of data

from a single TPD curve and performing brief calculations to determine some kinetic parameters.

Peak width analysis utilises the width of a single TPD peak at half or at three-quarters of the maximum rate

of desorption (W1/2 and W3/4), in addition to the peak temperature Tp, to determine the activation energy

Eact and the pre-exponential factor A. Falconer & Schwarz (1983) and Jong & Niemantsverdriet (1990) have

summarised and rearranged the equations used for this method in situations of first-order and

second-order kinetics into an easier format than those initially developed by Chan et al. (1978). These are

shown in Table 1 below. W1/2 , W3/4, and Tp do not vary with coverage for first-order situations, but do vary

for second-order. Therefore, the values of Eact and A determined for second-order situations are a function

of coverage.

Table 1: Equations used for Peak Width Analysis. θo is the inital coverage (Falconer & Schwarz, 1983; Jong & Niemantsverdriet, 1990).

First Order Second Order

5.0

2

21

2

p

pact

832.511

W

TRTE

5.0

2

21

2

p

pact

117.3112

W

TRTE

5.0

2

43

2

p

pact

353.211

W

TRTE

5.0

2

43

2

p

pact

209.1112

W

TRTE

p

act

p

act expRT

E

RT

EA

p

act

pact

32

o

2

act exp2

pRT

E

RTETR

EA

Another method is based upon calculating a shape index, which is the ratio of slopes at inflection points of

a single TPD curve, as shown in Equation 5 below. Ibok & Ollis (1980) concluded that this method allows

one to distinguish between systems that are first or second-order and to determine the extent of

readsorption. Both Ibok & Ollis (1980) and Criado et al. (1982) showed that when RTEact is large, the

value of the shape index for first and second-order kinetics without readsorption is independent of initial

coverage o . However, Criado et al. (1982) discovered that the values of the shape index for first-order

systems without readsorption and second-order systems with readsorption may be similar and difficult to

distinguish. Table 2 below shows the values the shape index can take under different situations (Falconer &

Schwarz, 1983).

2

2

1

2

2

2

1

2

2

2

2

2

T

T

T

T

dTd

dTd

dTrd

dTrd

IndexShape

(5)

Note: T1 and T2 are the low and high inflection point temperatures, respectively.

Table 2: Values of the shape index when the initial coverage θo = 1, T2/T1 ≈ 1.1 (typical value) and Eact/RT is large.

Without Readsorption

With Readsorption

First-Order 0.76 0.55

Second-Order 1.46 0.86

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Varying the Heating Rate

TPD peak temperatures increase with the heating rate . The problem of not knowing the pre-exponential

factor in Redhead’s method may be overcome by conducting several TPD experiments at different heating

rates, giving a series of TPD curves with different peak temperatures. Rearranging Equation 4 above results

in Equation 6 below; this shows that a plot of 2

pln T vs. p1 T results in a straight line of slope REact .

This method assumes that for reactions of order greater than 1, the coverage at peak temperature p is

constant, which is valid for second-order systems because the TPD curve is symmetrical in these cases. p

is calculated from Equation 1 or 2. The pre-exponential factor can then be determined by the intercept of

the plot generated.

p

act1

p2

p

lnlnRT

ERAn

T

n

(6)

Varying the Initial Coverage

A series of TPD experiments can also be conducted at different initial coverages. Rearranging Equation 3

above gives Equation 7 below; this shows that a plot of rln vs. ln at constant temperature gives a

straight line whose slope is equal to the order of reaction n. The value of at a particular temperature can

be retrieved by using Equation 2 above and the rate r can be read directly off the TPD curve. From a series

of TPD curves at various initial coverages, one may determine several data points (r, ) at the same

temperature. However, when actE is a function of coverage (due to adsorbate-adsorbate interactions) then

the apparent order of reaction will vary with coverage. Falconer & Madix (1977) showed that if the

activation energy decreased with coverage (as is expected for adsorbates that repel each other), then the

apparent order of reaction increases. According to Falconer & Madix (1977), this is an easy and useful

method for determining whether or not the activation energy is a function of coverage. Furthermore, by

plotting rln vs. T1 at constant coverage then the activation energy can be determined from the slope,

and this allows one to derive the dependence of activation energy on coverage. Falconer & Schwarz (1983)

commented that this technique is not appropriate for TPD curves that show significant desorption from

multiple sites.

lnlnln act nRT

EAr

(7)

Readsorption Considerations

Readsorption is when a desorbed species readsorbs onto catalyst further down the reactor. Gorte (1982)

has shown that it is very difficult to eliminate readsorption even when high carrier gas flow rates are used.

(Gorte, 1982) went further to say that analysing TPD data must be done with care and that in many

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scenarios only qualitative results can be deduced. It is commonly found that the overall activation energy

corresponds to the heat of adsorption in this case, rather than the activation energy for desorption. These

parameters will be numerically the same if the adsorption process is non-activated (which is the case for

many systems of interest) (Gorte, 1982).

Non-Constant Activation Energy Considerations

Most of the above methods consider activation energy to be constant; however, in reality Eact can vary with

coverage; additionally, there can be a distribution of activation energies for each type of site on a catalyst.

For example, this could be due to small environmental variations around each site. Such complicating

factors require numerical simulation of a TPD curve, followed by regressional fitting of the model to

experimental TPD data. This type of analysis has been performed less frequently in the literature;

nevertheless, it can be useful to measure the dependence of Eact on coverage or to determine the

distribution of activation energies for a catalytic site. More importantly, this method utilises all the

information in a TPD curve, rather than just using a few data points, and so gives more confidence in the

quantitative results obtained.

Other methods, discussed previously in this section, have difficulty extracting quantitative parameters

from overlapping TPD peaks because the theory behind each method assumes desorption/reaction from a

single site. However, experimental TPD curves are very often a convolution of several overlapping peaks.

This requires analysis by computational methods with regressional curve fitting to model several sites on a

catalyst simultaneously. Moreover, this enables the relative population of different types of site on a

catalyst to be quantified.

This project will focus on numerical modelling of TPD with reaction by assuming there is a distribution of

activation energies for each site. It will be demonstrated later this method can prove very useful for

extracting reasonable quantitative results from complicated and overlapping TPD curves. Furthermore, it is

useful for systems undergoing complicated reaction mechanisms.

2.4 Brief description of isopropylamine/ZSM-5 system

Isopropylamine is basic in nature and can adsorb onto acid sites within zeolites such as ZSM-5. The

structure of isopropylamine is shown in Figure 6 below. If a TPD experiment is performed on a sample of

ZSM-5 that has been fully covered with isopropylamine, then at temperatures below 500 K some weakly

bound isopropylamine desorbs unreacted; however, at temperatures between 550 K and 650 K,

isopropylamine reacts to form ammonia and propene (Parrillo, et al., 1990; Miao, 2012). The overall

reaction is shown below. Our goal is to extract quantitative kinetic parameters relevant to the

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isopropylamine/ZSM-5 system. It is believed that the reaction to form propene and ammonia might be rate

limiting because ammonia and propene are reported to desorb at the same temperature in TPD

experiments (Parrillo, et al., 1993). However, some issues have been raised regarding this system, including

the fact that propene is known to undergo reaction at high temperatures which may complicate the

modelling process. Also, the reaction step may not be entirely rate limiting; desorption of propene and

ammonia may potentially be slow enough that the TPD peaks observed are dependent on desorption

rather than the reaction kinetics. Finally, readsorption in a porous catalyst such as ZSM-5 is likely and this

will complicate the analysis.

H3C NH2

HC

CH3

Figure 6: Structure of isopropylamine.

323323 NHCHCHCH)CHCH(NHCH

Parrillo et al. (1990) discovered that the amount of isopropylamine that reacted in ZSM-5 corresponded to

a 1:1 ratio with aluminium atoms present. Brønsted sites are formed in ZSM-5 when an Al and a Si atom

are linked by a bridging OH hydroxyl group on the surface of a pore. As a result, Parrillo et al. (1990)

concluded that isopropylamine only reacts on strong Brønsted acid sites, with one isopropylamine

molecule adsorbing per Brønsted site. This is useful because the TPD with reaction experiment with

isopropylamine is thus giving information specific to Brønsted acid sites, rather than any other sites that

may be present. Furthermore, Parrillo & Gorte (1992) showed that the heat of adsorption of

isopropylamine on ZSM-5 is constant at 240 kJ/mol, up to a coverage of one molecule per Al atom. As a

result, they concluded that all Brønsted acid sites in ZSM-5 are of equal strength, which is also supported

by Kresnawahjuesa et al. (2002) and by the results of this report (discussed later). Assuming adsorption is

not activated, the heat of adsorption will equal the activation energy for desorption. Using Redhead’s

method with assuming A = 1013 s-1 (the expected value for a unimolecular desorption process)

(Barrie, 2012), an activation energy of 240 kJ/mol results in a peak temperature of about 870 K for a

heating rate of 1 K/s. This explains why the isopropylamine on Brønsted sites are observed to react before

desorbing because the temperature at which desorption is expected (870 K) is much higher than that at

which the reaction occurs (550-650 K).

3. Experiments My role within the project was mainly in developing and validating a general model for TPD with reaction;

however, during the first half of the project, I conducted some experiments in collaboration with my

partner, Qing (Chely) Miao. These experiments will be discussed in the following two sections, but due to a

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lack of space, only experiments that produced useful data will be covered. My partner and I performed

many more experiments that yielded unreliable data due to difficulties experienced with the experimental

set-up (especially with regards to the isopropylamine experiments). My partner later performed more

experiments on the isopropylamine/ZSM-5 system on her own, the details of which may be found in her

report.

The experiments described in this section aim to answer the following questions addressed in section 3.4:

Does propene react to form other species within the temperature range relevant for the

isopropylamine/ZSM-5 system?

At what temperature does desorption of propene from ZSM-5 occur? Is it rate limiting in the

temperature range of the isopropylamine/ZSM-5 reaction?

Unfortunately, we could not perform experiments with ammonia because it was unavailable. Moreover,

issues regarding safety prevented my partner from using ammonia in further experiments.

3.1 Experimental procedure

The apparatus used consists of an integrated microreactor and quadrupole mass spectrometer (see

Figure 1), manufactured by Hiden CATLAB Systems. Up to four gas cylinders could be connected, whereby

the flow rate of different gases entering the reactor could be individually controlled. The reactor used

consists of a hollow quartz tube that is able to withstand high temperatures. The tube was cleaned using

hexane, isopropanol and acetone (in that order) and allowed to dry completely before use. Quartz wool

was inserted in the tube before and after the catalyst sample to ensure the catalyst remained in place and

to prevent any particulates from entering the mass spectrometer. A heating element surrounding the tube

facilitated programming the temperature automatically with feedback from a thermocouple placed inside

the tube. The temperature could be controlled from 323 – 1173 K. A split-stream from the reactor is sent

to the mass spectrometer for analysis.

The first experiment conducted aimed to determine the temperature range over which propene undergoes

thermal decomposition. No catalyst was used for this experiment. A continuous flow of propene (2 ml/min)

and helium (38 ml/min) were passed through the reactor tube while the temperature was ramped from

323 K to 1148 K at a rate of 2 K/min. The mass spectrometer was set to scan mass-to-charge (m/e) ratios

1 – 42. This allowed us to determine the main products of reaction. The second experiment aimed to

perform TPD on a sample of ZSM-5 with full initial coverage of propene. The ZSM-5 sample used weighed

25 mg. ZSM-5 adsorbs water vapour from air so samples were pre-treated by heating at 873 K for about

one hour in a continuous flow of helium. The mass spectrometer was set to detect water leaving the

reactor so as to ensure all water was eliminated at the end of pre-treatment. The reactor was then cooled

14

down to 323 K while maintaining the flow of helium over the catalyst. Propene was then injected into the

helium carrier gas by using small pulses (volume = 250 μl at atmospheric pressure) while the concentration

of propene leaving the reactor was detected. Pulsing continued until the peak height of pulses, on a plot of

concentration versus time, came to a steady height. This indicates that the catalyst has been fully loaded

with propene (11 pulses were required). The temperature was then ramped from 323 – 1148 K at a

constant rate of 5 K/min. The helium carrier gas flow rate of 40 ml/min was maintained, while the mass

spectrometer was set to detect m/e = 41 (corresponding to the main peak of propene’s spectrum).

Sections 3.2 and 3.3 below present the experimental results my partner and I obtained from the

experiments described above. The results are also discussed and subjected to a critical analysis.

3.2 Thermal decomposition of propene

The results obtained from the experiment to determine when thermal decomposition of propene occurs is

shown in Figure 7 below. As can be seen, propene passes unreacted until about 1050 K where the

concentration of propene (m/e = 41) drops suddenly and the concentration of other species increases.

Unfortunately, the experiment could not be continued at higher temperatures to see the extent of reaction

because of equipment limitations. The m/e ratios shown in Figure 7 were selected because they were the

only ones that showed significant change upon reaction. The m/e ratios of 2, 15, 16, 26 and 28 were seen

to increase once decomposition occurred. These have been attributed to hydrogen, methane and ethene,

as shown in Table 3 below. An extremely minute increase in the m/e = 30 was also detected, indicating

very small quantities of ethane were being produced as well. It is relevant to note that some propene ions

fragment in the mass spectrometer to give signals at m/e = 15 and m/e = 26. Laidler & Wojciechowski

(1960) reported the same major products for propene decomposition. The temperature range over which

propene was detected in my partner’s isopropylamine/ZSM-5 TPD experiment is 550 – 660 K (Miao, 2012).

Therefore, this indicates that the thermal decomposition of propene will not be a complicating issue in

modelling this system.

Figure 7: Continuous flow of propene with a constant heating rate. Decomposition occurs at about 1050 K. m/e ratios of 2, 15,

16, 26 and 28 are seen to increase upon reaction.

Table 3: A tick indicates the m/e value is present in the spectrum. A double tick indicates the m/e

value is the major peak. An indicates the m/e value is not present in the spectrum (NIST, 2011).

m/e Propene Ethene Methane Hydrogen

2

15

16

26

28

41

0.00E+00

5.00E-09

1.00E-08

1.50E-08

2.00E-08

2.50E-08

3.00E-08

3.50E-08

4.00E-08

350 550 750 950 1150

Mas

s Sp

ec

Sign

al (

au)

Temperature (K)

m/e = 41

m/e = 28

m/e = 26

m/e = 16

m/e = 15

m/e = 2

15

3.3 Desorption of propene from ZSM-5

The result of our TPD experiment involving propene on ZSM-5 is shown in Figure 8 below. The coverage of

propene at each temperature has been calculated using Equation 1 and is shown in Figure 9 below.

Figure 8: TPD of propene on ZSM-5 with full initial coverage.

Figure 9: Calculated coverage of propene on ZSM-5 during TPD.

Figure 8 shows that propene mainly desorbs between 360 K and 650 K. Three overlapping peaks can be

distinguished, indicating at least three sites of different binding energies. The peak temperature of the site

with the highest binding energy is about 607 K. The reaction of isopropylamine on ZSM-5 occurs between

550 K and 660 K, with a peak temperature of about 630 K. Therefore, propene desorption is quicker than

isopropylamine reaction at all temperatures. Using Redhead’s method for a first order process (assuming

A = 1013 s-1, = 1 K/s), peak temperatures of 607 K and 630 K result in activation energies of 166 kJ/mol

and 172 kJ/mol. Using Equation 3, the ratio of the rate of desorption to the rate of reaction at unity

coverage has been calculated and is shown in Figure 10 below. As can be seen, the rate of propene

desorption is about four times as large as the rate of reaction between 550 K and 660 K. This indicates that

a peak temperature difference of 23 K is large enough that desorption will not limit the progress of the

reaction. It also means that propene can be considered to desorb instantly once produced by the reaction

for the purposes of modelling. On a separate note, coke was found to form in the ZSM-5 catalyst during the

experiment. This indicates that propene undergoes reaction on ZSM-5; however, it is believed that only

trace amounts of coke formed and thus the extent of reaction is small.

Figure 10: The ratio of the rate of desorption to the rate of reaction at full coverage has been calculated using Equation 3.

0.E+00

1.E-10

2.E-10

3.E-10

4.E-10

5.E-10

300 500 700 900 1100

Mas

s Sp

ec S

ign

al (

au)

Temperature (K)

0.0

0.2

0.4

0.6

0.8

1.0

300 500 700 900 1100

Cal

cula

ted

Co

vera

ge

Temperature (K)

0

1

2

3

4

5

6

500 550 600 650 700

Temperature (K)

Rati

o o

f D

eso

rpti

on

to

Reacti

on

Rate

s

16

4. Model description The following section will describe the model which I developed with guidance from my supervisor

Dr. Patrick Barrie. My partner did not contribute to the development of this model.

The model developed uses fundamental rate laws to fit computationally calculated TPD curves to

experimental data. As a result, quantitative parameters may be determined such as distribution of

activation energies for sites, pre-exponential factors and the relative population of different sites on a

catalyst. Another useful characteristic of the model is the fact that it is general, rather than being specific

to a particular reactant/catalyst system. This allows a wide range of systems to be analysed with relative

ease and practicality, as opposed to individually deriving and programming different sets of differential

equations for each system. The model can also be used on systems not undergoing reaction, as will be seen

shortly.

Quantitative analysis of TPD with reaction data is challenging because of the complexity of some reactive

systems and the presence of readsorption. The model developed enables extraction of meaningful kinetic

parameters from complex reacting systems; however, due to time restrictions, readsorption has not been

accounted for in the model. MATLAB was used as the programming environment because of its utilisation

of matrix variables that make manipulation of large quantities of data more efficient.

4.1 Background knowledge

The details of the programming code will not be covered in this report, but have been deposited with my

supervisor. In order to define the equations forming the foundation of the model, the following will review

some necessary background knowledge.

Reaction set:

The simplest way to explain how a set of reactions is input into the model is by way of example. Let us

consider we have a molecule (ads)A that has been adsorbed on to a catalyst.

(ads)A undergoes simple

desorption to form (g)A without reaction.

(g)A is then carried away quickly enough such that readsorption

does not occur. Therefore, in this system the ‘reaction set’ consists of one ‘reaction’, shown in Reaction Set

1 below:

(g)(ads) AA

Reaction Set 1

(g)(ads)(ads)(g) 2B2BAA

Reaction Set 2

Note that even though only desorption and no reaction is occurring, for the purposes of the model, (ads)A

and (g)A can be considered to be two separate species with a non-reversible reaction taking place between

them. Reaction Set 1 thus consists of two species and one ‘reaction’. Therefore, within the model, species

are differentiated not only by their atomic makeup, but also by their physical state (i.e. adsorbed or

17

gaseous). Let us consider another example, where this time molecule (ads)A can also undergo a reversible

surface reaction to form two molecules of (ads)B that later desorb non-reversibly to give two molecules of

(g)B ; this scenario is illustrated in Reaction Set 2 above. This situation can be modelled using four species

(ads)A ,(g)A ,

(ads)B and (g)B , and the reaction set will consist of four ‘reactions’, namely:

(g)(ads) AA ,

(ads)(ads) 2BA , (ads)(ads) A2B and

(g)(ads) BB .

The stoichiometric matrix S stores the stoichiometric coefficients for each species in each reaction taking

place. Therefore, the stoichiometric matrix for Reaction Set 1 above is 11S , where the -1 represents

(ads)A being consumed and the 1 represents (g)A being produced. Similarly, the stoichiometric matrix for

Reaction Set 2 above is shown below. The first row represents(g)(ads) AA , the second row

(ads)(ads) 2BA ,

the third row (ads)(ads) A2B and finally the fourth row represents

(g)(ads) BB .

1100

0210

0210

0011

S

The physical state of species matrix, isAdsorbed, stores information on whether each species is adsorbed or

gaseous. For the species involved in Reaction Set 2 above, 0110isadsorbed where a 0 means the

molecule is not adsorbed and a 1 means the molecule is adsorbed. This feature is required because if the

products of a surface reaction occupy more sites than the reactants, such as(ads)(ads) 2BA , then the rate

of reaction is given by BAA 1 kr , where BA1 is the coverage of ‘empty sites’ on the

catalyst. As a result, the model must know which molecules are adsorbed and which are in the gaseous

state in order to calculate sitesempty . Therefore, to define a reaction set, one must input four pieces of

information into the model:

The number of species being modelled, which is called numOfMolecules.

The number of reactions being modelled, which is called numOfReactions.

The stoichiometric matrix S, which is of size (numOfReactions x numOfMolecules).

The physical state of molecules matrix called isAdsorbed, which is of size (1 x numOfMolecules).

Number of sites and distribution of activation energy for each site:

In order to reproduce TPD curves with multiple sites, such as that shown previously in Figure 4, the model

needs to be able to simultaneously compute reaction/desorption from multiple sites. The relative

population of each type of site will thus need to be considered. For example, site type 1 may make up 30%

and site type 2 may make up 70% of the catalyst. This information does not need to be known beforehand

18

because it is considered a variable than can be changed in order to fit experimental data. In this way, the

relative population of different sites is one of the quantitative results produced by the model.

Every reaction being modelled, be it in reality desorption or an actual reaction, has associated with it an

activation energy. Most quantitative techniques found in the literature assume there is a single activation

energy for each site; however, this is not always the case, and this model considers a normal distribution of

activation energy for each type of site. Not only is this more realistic, but it also allows the model to

produce a better fit to experimental TPD data and gives an idea of how wide is the distribution of

activation energies is for each type of site. This may potentially provide critical information about the

environment in which adsorbed species are present and the reaction mechanisms at work.

The normal distribution of activation energy for each type of site is accounted for by considering every

type of site to consist of numerous ‘points’, each of which have a single activation energy. The activation

energy of the ‘points’ will be spread across the distribution of activation energy for the site type. For

example, if we have one type of site with a normal distribution of activation energy, then we can model

that distribution by considering the site type to consist of say 50 ‘point sites’, each of constant activation

energy. These smaller sites or ‘points’ will have activation energies between 3mean E and 3mean E ,

where meanE and are the mean activation energy and the standard deviation for the site type. Figure 11

below illustrates the difference between a site type and a site point. Each point can be considered to be a

stand-alone site when modelling, so if there are two types of site, each of which having a distribution

modelled using 50 points, then effectively we can consider there to be 2x50 = 100 sites present. However,

the relative population of the different points being used for each site distribution needs to be considered.

A matrix called ε will store the fractional weighting every point has for each site distribution. For example,

a point with activation energy equal to meanE will have a larger fractional weighting than a point with

activation energy 3mean E , because there are more sites with the mean activation energy than with an

activation energy on the outskirts of the distribution.

Figure 11: The difference between a site type and a site point.

19

Finally, the pre-exponential factor for the rate constant in each reaction must be defined. This is assumed

not to vary with temperature or between sites because it is intrinsic to the molecules taking part in the

reaction/desorption. In reality the pre-exponential factor may in fact vary with temperature (Miller, et al.,

1987); however, the assumption that it is constant is commonly made by most analytical methods to allow

feasible progress in quantifying kinetic parameters. So in summary the following parameters are in use:

The number of sites, called numOfSites.

The fractional population of each site matrix, called α of size (1 x numOfSites).

The mean activation energy matrix called meanE which is of size (numOfReactions x numOfSites).

The standard deviation of activation energy matrix called σ which is of size

(numOfReactions x numOfSites).

The number of points to consider for each site, called numOfPoints.

The fractional weighting matrix called ε which is of size

(numOfReactions x numOfSites x numOfPoints).

The pre-exponential factor matrix A which is of size (1 x numOfReactions).

Note that the model allows the user to define a different activation energy distribution for every reaction

on each site. However, it is assumed that the activation energy is perfectly correlated to the site binding

strength; as such, the distributions of activation energy for all reactions on a particular site will have the

same standard deviation. This assumption has been made through valid physical insight in order to simplify

computation.

4.2 Generating a TPD curve

TPD with Simple Desorption:

Consider(ads)A , of coverage , undergoing desorption to produce

(g)A without readsorption. The governing

rate equation is shown below.

n

RT

EA

dT

d

actexp (8)

Our aim is to produce a graph of dTd versus T . In order to do that, must first be calculated for all

temperatures. Assuming no distribution of activation energy, this is done by numerically integrating

Equation 8 above to yield the coverage as a function of temperature, T , which is later plugged back into

Equation 8 to calculate dTd as a function of temperature. We have chosen to plot dTd rather

than dtd versus T so that area beneath the curve equals initial coverage. This eases analysis and

comparison with experimental data, as shown later.

20

The situation changes when there is a distribution of activation energy. Recall that each ‘site point’ could

be considered as a stand-alone site for the purposes of modelling. Thus, we need to distinguish between

isite , which is the overall coverage of site type i, and betweenji point,site , which is the coverage of site

point j corresponding to site type i, i.e. the population of occupied site point j divided by the total

population of site point j. Equation 8 above will now apply to each site point, rather than applying to the

entire site type, and the coverage as a function of temperature for each site point will have to be

determined. The rate of desorption from all site points are then summed up to yield the overall rate of

desorption from site type i, see Equations 9 and 10 below. The population weighting of every site point, is

stored in matrix , whereby the element ij equals (population of site point j corresponding to site type i) /

(population of all site points corresponding to site type i).ijE is the activation energy of site point j

corresponding to site type i.

snumOfPoint

j

ji

ij

i

dT

d

dT

d

1

point,sitesite

(9)

snumOfPoint

j

ij

ij

i

RT

EA

dT

d

1

siteexp

(10)

Extra consideration is needed when more than one site type is present. The overall rate of desorption

dTd , is given by Equation 11 below. The population fraction for site type i is given by i , which is a

number between 0 and 1, such that if site type i makes up 30% of all sites on the catalyst, then 30.0i .

numOfSites

i

snumOfPoint

j

ji

ijidT

d

dT

d

1 1

point,site

(11)

Therefore, Equation 8 must be solved to give the coverage of each site point, which then allows

dTd jisite point, to be calculated for each site point. This in turn is used in Equation 11 to yield the

desorption rate of A molecules as function of temperature.

Example TPD Simulation: Effect of varying Emean, σ and β:

Consider the desorption (g)(ads) AA from a catalyst with full initial coverage of

(ads)A . There is only one

type of site on the catalyst, which has a normal distribution of activation energy for desorption of(ads)A .

The base case considered has the following parameters: meanE = 100 kJ/mol, σ = 10 kJ/mol, A = 1013 s-1,

= 1 K/s. Figures 12, 13 and 14 below are plots of desorption rate (K-1) versus temperature (K). They show

the effect of changing meanE , σ and , respectively. Note, that the y-axis in these figures is called

‘Desorption Rate of A’, which refers to dTd rather than dtd . The area under each curve was

verified to be 1 for all cases considered below.

21

Figure 12: The effect of changing Emean, with σ = 10 kJ/mol and β

= 1 K/s.

Figure 13: The effect of changing σ, with Emean = 100 kJ/mol and

β = 1 K/s.

Figure 14: The effect of changing β, with Emean = 100 kJ/mol and σ = 10 kJ/mol.

Digression: Defining the units for amount of gaseous species:

We need to incorporate the presence and reaction of multiple species, both in adsorbed and gaseous

states. The concentration of adsorbed species is defined using the dimensionless value of coverage, which

is the ratio of occupied sites to total sites on a catalyst, as explained before. Since the total number of sites

on a catalyst remains constant, this means coverage is directly proportional to the amount of adsorbed

species. Recall that this model does not include readsorption; therefore, the concentration of a species in

the gas phase is never included in any rate equation because it is assumed that gaseous species are

transported away quickly enough not to readsorb. Consequently, the model will only keep track of the

amount of each gaseous species that has desorbed from the catalyst and the rate at which gaseous species

being produced, not the concentration. The unit of gaseous amount used is defined such that if a

monolayer of coverage 1 desorbs completely, this will correspond to a gaseous amount of 1. This is

done for convenience and for simplifying comparison of the amount of adsorbed species in terms of

coverage to the amount of gaseous species desorbed. Also, in this way, the rate of desorption of an

adsorbed species will equal the rate of production of its corresponding gaseous species - had we used

moles for the amount of gaseous species, a constant of proportionality would be required to equate these

two rates. Moreover, to simplify the equations involved (and to simply the code underlying the model), the

nomenclature for gaseous amount used will also be , such that for the specific case of (g)(ads) AA , the

0.000

0.002

0.004

0.006

0.008

0.010

0.012

200 300 400 500

No

rmal

ise

d D

eso

rpti

on

Rat

e (

K-1

)

Temperature (K)

Emean = 90 kJ/mol

Emean = 100 kJ/mol

Emean = 110 kJ/mol

0.000

0.004

0.008

0.012

0.016

0.020

200 250 300 350 400 450 500

No

rmal

ise

d D

eso

rpti

on

Rat

e (

K-1

)

Temperature (K)

Sigma = 5 kJ/mol Sigma = 10 kJ/mol Sigma = 15 kJ/mol

0.000

0.002

0.004

0.006

0.008

0.010

0.012

200 250 300 350 400 450 500

No

rmal

ise

d D

eso

rpti

on

Rat

e (

K-1

)

Temperature (K)

Beta = 0.1 K/s Beta = 1 K/s Beta = 10 K/s

22

following equation will hold: dTddTd A(g)A(ads) . Note, however, this equation is not generally

applicable to all scenarios. For example, in Reaction Set 2 discussed above and reproduced below, the rate

of production of (g)A does not equal dTd A(ads) because

(ads)A is also being converted to(ads)B .

(g)(ads)(ads)(g) 2B2BAA

In future work, if readsorption is to be incorporated, then the concentration of gaseous species can be

simply worked out from the amount of gaseous species desorbing per second divided by the carrier gas

flow rate (assuming the amount of gas desorbing is small compared to the carrier gas flow rate, which is

normally the case).

TPD with Reaction:

In TPD with reaction, Equation 8 will have to be modified to account for multiple species present and for

multiple reactions occurring. As site points were indexed with the letter j and site types with the letter i

previously, reactions will be indexed with letter k and species with letter n, such that we will refer to

reaction k and to species n.

The rate of production of a species n due to reaction k occurring on site point j of site type i is given by

Equation 12 below. Recall that S is the stoichiometric matrix, such that knS is the element of matrix S

corresponding to the stoichiometric coefficient of species n in reaction k. The species q in Equation 12

refers only to reactants involved in reaction k and kA refers to the pre-exponential factor of reaction k.

RTEAS

dT

d ijk

q

S

jiqkn

kjin kqexp

reactants

point,site,species

reaction,point,site,species (12)

It is important to keep in mind that dTd is the rate of production. For example, if species n was a

product of reaction k then knS would be positive, making dTd positive. However, if it was a reactant

then knS would be negative, making dTd negative, indicating that species n is being consumed.

Equation 12 is only valid when the number of sites occupied by adsorbed products is less than or equal to

the number of sites occupied by adsorbed reactants. Otherwise, an extra term sitesempty raised to the power

of (number of adsorbed products – number of adsorbed reactants) would need to be incorporated.

However, in order to avoid clutter, this will not be shown in the equations that follow, because it is not

applicable in the case studies analysed later on. Nevertheless, the model does accommodate for this term,

if appropriate.

Equation 12 only considered one reaction, but reactions occur simultaneously on each site point. Equation

13 below includes the contribution of all reactions.

23

ionsnumOfReact

k

ijk

q

S

jiqkn

jin RTEAS

dT

dkq

1 reactants

point,site,species

point,site,species exp

(13)

Finally, the rate of production from all site points of all site types must be added together to give the total

rate of production of species n, as shown in Equation 14 below.

numOfSites

i

snumOfPoint

j

jin

iji

n

dT

d

dT

d

1 1

point,site,speciesspecies

(14)

Therefore, the coverage of each species on each site point as a function of temperature will need to be

determined by numerical integration of Equation 13. This then allows calculation of the rate of production

of each species from each site point dTd jin point,site,species . Finally, this is plugged into Equation 14 to yield

the overall rate of production of each species dTd nspecies as a function of temperature.

5. Model validation and discussion of results This section will attempt to validate the model by applying it to several TPD experiments found in the

literature and to my partner’s experimental results for the isopropylamine/ZSM-5 system. Furthermore,

the current model will be compared to another independently produced model, in order to detect any

programming errors t. The following model validation is the result of my own work, with valuable help and

guidance from my supervisor Dr. Patrick Barrie. My partner did not contribute to validation of this model.

Experimental TPD data modelled include the following systems:

Carbon monoxide desorption from a surface of Ni(111) (Miller, et al., 1987).

Formic acid decomposition from a surface of Cu(110) (Ying & Madix, 1980).

Isopropylamine reaction and desorption from zeolite ZSM-5.

Since the model does not consider readsorption, the first two case studies were chosen because the

experiments on metal crystal surfaces were conducted in ultra high vacuum, ensuring that readsorption

was negligible. The case study of CO on Ni(111) contains multiple overlapping peaks, but no reaction. The

case study of formic acid on Cu(110) has both reaction and desorption. The third case study was conducted

on a system in which readsorption is present; nonetheless, this scenario demonstrates the potential

usefulness and flexibility of the model, and gives an example of modelling TPD with reaction systems. If

readsorption is included into the model within future work, this case study may be revisited to obtain more

accurate results.

24

5.1 Comparison with specific model

At the beginning of this research project, a simplified model for TPD with reaction for isopropylamine on

zeolite ZSM-5 was developed. This model is specific to the isopropylamine/ZSM-5 system and assumes a

single activation energy for each reaction, rather than a distribution. The specific model contains the

reaction steps shown in Reaction Set 3 below.

The model assumes that propene is produced in the gaseous state rather than in an adsorbed state. This

assumption was made because of two reasons. Firstly, results of the experiment discussed in section 3.3

indicate that desorption of propene can be considered to be instantaneous for the purposes of modelling.

Secondly, isopropylamine bonds to Brønsted acid sites on ZSM-5 through the nitrogen atom, which means

when decomposition occurs, propene could be severed directly into a gaseous state (see Figure 15 below).

On the other hand, ammonia is modelled as being produced in an adsorbed state which may later desorb

because it is expected that nitrogen atom remain bonded to the site immediately after reaction. A program

to model this reaction scheme was written in Visual Basic and also in Java. The results of the general model

developed in this project could then be compared to these programs, in order to validate the model and

detect any programming errors.

H3C CH3

AlSi

+NH3

CH

O-

Figure 15: Structure of adsorbed isopropylamine on a Brønsted

site.

(g) 3 (ads) 3

(ads) 3 (g) 2 3 (ads)3 2 3

(g) 3 2 3 (ads) 3 2 3

NH NH3.

NH CHCHCH )CH (NHCH CH2.

)CH (NHCH CH )CH (NHCH CH1.

Reaction Set 3: The set of reactions input into the current model

for comparison with the independent model.

The reaction set which was input into the current model is shown in Reaction Set 3 above. The value of

activation energy for each of the above reactions was set to be 100 kJ/mol. The pre-exponential factor was

set to be 1013 s-1 for each reaction and the initial coverage of isopropylamine was set to be unity. This

means that reactions 1 and 2 above will occur at the same rate; therefore, it is expected that the

desorption peaks for isopropylamine and propene will overlap completely. However, the peak for

ammonia will be delayed to higher temperatures because it is produced in the adsorbed state. The

coverage of ammonia is initially zero and reaction 2 needs time to produce enough ammonia such that the

rate of desorption of ammonia is appreciable. The simulated TPD curves for this situation are shown in

Figure 16 below. Note that both the general model and the specific program for this reaction predict

exactly the same results.

It is relevant to note here that the general model was also subjected to a large battery of other tests, in

which it performed as expected, but these tests will not be discussed in this report due to lack of space.

25

Figure 16: Both general and specific models predict the same results. Propene and isopropylamine curves are overlapping.

5.2 Case Study: CO on nickel

The desorption of carbon monoxide from a surface of Ni(111) was modelled using experimental data found

in the literature (Miller, et al., 1987). This system was chosen because readsorption is negligible and

because the results exhibit multiple overlapping peaks. Other quantitative methods struggle to extract

parameters from overlapping peaks. This example will demonstrate the strength of the model in dealing

with such complications. The process of fitting the model to experimental TPD data has not been

automated; therefore, a manual fitting procedure was conducted, explained in Figure 17 below. For

simpler cases with fewer variable parameters, such as that of formic acid on Cu(110), a more rigorous

sensitivity analysis could be conducted by also varying the pre-exponential factor (discussed later).

However, for the following case study of CO on Ni(111), the curves were fitted ‘by eye’ because there were

too many parameters to conduct a manual optimisation (due to the presence of multiple peaks). Ideally

(and potentially in future work), an automated non-linear and multiple variable optimisation algorithm

could be used; however, for the purposes of demonstrating and validating the model, the approximate

procedure utilised is sufficiently accurate.

Define set of

reactions

Choose

number of

sites

Determine most

suitable pre-

exponential factor

from literature

Simulate TPD

0

0.002

0.004

0.006

0.008

0.01

0.012

230 280 330 380 430 480 530

Rat

e o

f De

sorp

tio

n (a

rbit

rary

un

its)

Temperature (K)

Is model

consistent with

experimental

results?NO YES

Adjust activation

energy

distribution and

site population

Guess activation

energy

distribution and

site population

Done

Figure 17: Process of fitting a model to experimental results.

Miller et al. (1987) published TPD experiments for the desorption of carbon monoxide adsorbed at

temperatures of 300 K and 87 K on Ni(111) , shown in Figures 18 and 19 below. For each adsorption

0

0.005

0.01

0.015

0.02

0.025

290 310 330 350 370 390 410

No

rmal

ise

d R

ate

of

Des

orp

tio

n

(K-1

)

Temperature (K)

Isopropylamine (Specific) Isopropylamine (general) Ammonia (Specific) Ammonia (General) Propene (Specific) Propene (General)

26

temperature, TPD was performed at different initial coverages. The saturation coverage for 300 K

adsorption was found to be 0.50 CO molecules per Ni atom (CO/Ni), while that for 87 K adsorption

corresponded to 0.57 CO/Ni. For CO adsorbed at 300 K, the main peak has a ‘shoulder’ on the left. This can

be explained by the presence of at least two binding states of similar binding energy for the CO molecule

on Ni(111). A new low temperature peak appears for CO adsorbed at 87 K, which corresponds to a new

lower binding energy state of the CO molecule. Furthermore, as the initial coverage is increased, the peak

temperature can be seen to decrease. Since desorption of CO on nickel is expected to be first-order

(discussed in the next paragraph), this can only be explained by the decrease of activation energy with

increasing coverage i.e. adsorbed CO molecules interact unfavourably with each other. Therefore, the

activation energy is expected to be a function of coverage, which was confirmed by Christmann et al.

(1974). Also, the high energy binding state is occupied before the low energy binding state at low

coverages, indicating that CO is mobile on the surface of Ni(111).

Figure 18: TPD of CO adsorbed on Ni(111) at 300 K performed at

a heating rate of 6 K/s (Miller, et al., 1987).

Figure 19: TPD of CO adsorbed on Ni(111) at 87 K performed at a

heating rate of 6 K/s (Miller, et al., 1987).

Simple desorption of CO is expected as shown in Reaction Set 4 below which was used to model the

experimental data. However, CO is known to dissociate and disproportionate on some transition metals

(Steinruck, et al., 1986); therefore, it is imperative to determine whether dissociation occurs on Ni(111) in

the temperature range sampled as this will affect the reaction set used in the model. Tomanek &

Bennemann (1983) determined that the activation energy for dissociation of CO on Ni(111) is 209 kJ/mol,

which means this reaction will only be significant at temperatures above 600 K (determined by simulating a

first-order dissociation reaction with Eact = 209 kJ/mol). Given that nearly all CO desorbs at a temperature

significantly lower than 600 K on Ni(111), the dissociation surface reaction may be safely neglected. On a

further note, Nakamura et al. (1989) support this by saying that dissociation does not occur at the

desorption temperatures for CO on Ni(111). Another possible factor is the disproportionation reaction

27

2CO(ads) → C(ads) + CO2 , where two CO molecules combine to produce an adsorbed surface carbon species

and CO2. However, when CO is adsorbed at temperatures lower than 300 K, molecular CO desorbs when

heated to 500 K without any trace of adsorbed carbon or oxygen, indicating that neither dissociation nor

disproportionation occurs within the temperature range of the experiment (Steinruck, et al., 1986).

(g)(ads) COCO

Reaction Set 4: Simple desorption of CO.

The TPD data for adsorption at 300 K and saturation coverage of 0.50 CO/Ni was modelled using two sites

(site 1 = low temperature shoulder, site 2 = high temperature main peak), each with a distribution of

activation energies.

The pre-exponential factor used for desorption of CO was taken to be A = 1013 s-1 because this is the value

expected for unimolecular desorption – it corresponds to the frequency of a bond vibration. In any case, an

order of magnitude change in A affects the activation energy by only 5 % (Barrie, 2012). The parameters

that were varied to fit experimental data are shown in Table 4 below along with their optimised values

(note that a fit was not possible unless a distribution of activation energy was used for each site):

Table 4: Parameters used to fit the model to experimental TPD data for absorption at 300 K.

Emean (kJ/mol) σ (kJ/mol) α

Site 1 99.3 8.9 0.38

Site 2 115.7 5.4 0.62

Note that α1 + α2 must always equal 1. Figure 20 shows how the model compares to experimental TPD data

observed by Miller et al. (1987). The fit was good with an error of about 0.9 % (see Equation 16 below),

especially given that there were five independent parameters to vary and that it was done manually.

2

ExperimentModelError SquareofSum

(15)

100

2

2

Experiment

ExperimentModelPercentageError

(16)

Figure 20: Comparison of model to experimental TPD data for CO adsorption at 300 K on Ni(111).

Figure 21: Optimisation of pre-exponential factor on TPD curve of initial coverage equal to 0.032 CO/Ni for 300 K adsorption of CO on Ni(111). The sum of square error is given in Equation 15.

The line drawn is to guide the eye.

28

The peak temperature of the high binding energy peak of CO (i.e. site 2) was determined to be 444 K from

the experimental data in Figure 20. Redhead’s method (described in Section 3) was applied using this peak

temperature and a pre-exponential factor of 1013 s-1, and the resulting activation energy was determined

to be 113.7 kJ/mol. This compares very well to our value of Emean, 2 = 115.7 kJ/mol. Furthermore,

Christmann et al. (1974) determined an activation energy for desorption of 111 kJ/mol at medium

coverages. None of the other quantitative methods can be easily applied to compare values for the

activation energy of the low binding energy peak (i.e. site 1) due to the two peaks overlapping.

During the TPD experiment, coverage of CO gradually decreases; therefore, the activation energy is

expected to change accordingly. However, in the limit of low coverage (see Figure 18 above) a single peak

is observed for the high energy binding state of CO (site 2). Miller et al. (1987) used the peak width analysis

method (described in Section 3) to determine an activation energy of 128 kJ/mol and a pre-exponential

factor of 1.4 x 1014 s-1, for a single peak at an initial coverage of 0.04 CO/Ni. As expected, the activation

energy is higher for lower coverages.

The standard deviation of activation energy gives, in this case, a quantitative indication of how much the

activation energy varies with coverage. In fact the activation energy determined by Miller et al. (1987) for

the high binding energy state at very low coverage is within Emean, 2 + 2.3σ2. This agrees well with our

predictions because values of activation energy at 2.3σ2 are at the outskirts of the distribution, in line with

the fact that Miller et al. (1987) calculated the activation energy in the limit of very low coverage.

Furthermore, Christmann et al. (1974) reported values of the isosteric heat of adsorption Est of CO on

Ni(111), which is related to the activation energy of desorption by Eact = Est - 0.5RT, for the non-activated

adsorption of CO (Miller, et al., 1987). The values calculated for the activation energy of desorption from

the results of Christmann et al. (1974) over a wide range of coverages are approximately 81.9 –

126.4 kJ/mol, which corresponds to Emean, 1 - 2σ1 and Emean, 2 + 2σ2, this also supports our findings since

values within Emean ± 2σ contain about 95 % of the distribution.

In order to better compare the model results to the peak width analysis method used by Miller et al.

(1987), the model was fitted to the low coverage peak of 0.032 CO/Ni in Figure 18 using a single site

without a distribution of activation energy. In this case only two parameters needed variation (Eact and A);

therefore, a more rigorous optimisation procedure was followed, shown in Figure 21 above. For every

value of A plotted, the value of Eact was optimised by minimising the sum of the square error between the

model and experimental data. As a result, the best fit parameters deduced were approximately A = 1013 s-1

and Eact = 119.7 kJ/mol. This further supports our use of 1013 s-1 as the pre-exponential factor. The different

values between our model and the peak width method used by Miller et al. (1987) may be due to the fact

29

that there was a fitting error of approximately 9.4 %. This error can explain the discrepancy in activation

energy reported. It is believed that a good fit was not obtained in this case because a single activation

energy was used, rather than a distribution, given that Christmann et al. (1974) reported a sudden, large

variation in activation energy for small coverages. Furthermore, two types of site (two-fold and three-fold

bridged sites) have been suggested to occur at very low coverages of CO on Ni(111) (Surnev, et al., 1988)

which may also explain the discrepancy.

The experimental TPD curve at saturation coverage (0.57 CO/Ni) for adsorption at 87 K (see Figure 19) was

also modelled, but this time using three sites to account for the new lower energy binding state that

appeared (see Figure 22 for comparison of the model with experimental data). The fit was good with an

error of about 0.7 %. The parameters determined are summarised in Table 5 below. The sites are labelled

in Figure 23, which shows the rate of desorption from each site separately, as predicted by the model.

Figure 22: Comparison of model with experimental results for CO adsorbed at 87 K.

Figure 23: Rate of desorption of CO, as predicted by the model, for each site. The total desorption rate is also shown.

Table 5: Summary of parameters used to model CO adsorbed at 87 K with an initial coverage of 0.57 CO/Ni.

Emean (kJ/mol) σ (kJ/mol) α

Site 1 102 9.9 0.402

Site 2 115 4.8 0.493

Site 3 75.4 5.9 0.105

The activation energies and standard deviations for sites 1 and 2 were approximately the same as for CO

adsorbed at 87 K and 300 K. Miller et al. (1987) also discovered similar activation energies at the limit of

low coverage for adsorption at 300 K and 87 K. The peak temperature of site 3 is difficult is discern;

however, an approximate value is 293 K. Redhead’s method was used using this peak temperature (and

A = 1013 s-1) to determine an activation energy of 74.1 kJ/mol for site 3. This compares very well with our

value of 75.4 kJ/mol.

0.000

0.002

0.004

0.006

0.008

0.010

0.012

200 300 400 500

No

rma

lise

d D

eso

rpti

on

Ra

te

Temperature (K)

Model

Experiment

30

A key quantitative result of the modelling process is the population fraction of sites present on the catalyst,

a figure that is usually difficult to obtain from overlapping peaks. It is interesting to note that the

population fraction of site 2 dropped significantly from α2 = 0.62 at an adsorption temperature of 300 K to

α2 = 0.49 at an adsorption temperature of 87 K. The population fraction of site 1 increased slightly from

α1 = 0.38 to α1 = 0.40. In addition, the saturation coverage increased from 0.50 CO/Ni to 0.57 CO/Ni. This

means that some CO molecules in the high energy binding state of site 2 are moving into the lower binding

energy state of sites 1 and 3. These results can be explained by the fact that Surnev et al. (1988) and Tang

et al. (1986) reported the presence of two-fold bridged and terminal CO sites on Ni(111), which are

illustrated in Figures 24(a) and 24(b) below. In particular, it was reported the relative populations of two-

fold bridged sites to terminal sites is both temperature and coverage dependent. Also, the two-fold

bridged site has a stronger binding energy than the terminal site (Tang et al., 1986). This leads us to believe

that site 1 is mainly due to desorption from terminally bound CO molecules, while site 2 is that due to two-

fold bridged molecules. Site 3 may be attributed to neighbouring CO species at high loadings, because

there will be unfavourable interactions between neighbouring CO species due to the partial negative

charge of CO on Ni(111) (Somorjai, 1994), as shown in Figure 24(c). In support, King (1975) notes that

repulsion between adsorbed species can cause multiple TPD peaks from a crystal metal surface. The

population fraction determined from the model may also be used to validate quantitatively proposed

binding models of CO on Ni(111); however, due to a lack of time and space, this was not performed.

Figure 24: (a) Terminal site (b) Two-fold bridged site (c) Unfavourable interactions between neighbouring CO molecules at high surface

coverages.

The model developed has proven to be useful and accurate in determining the range of activation energies

for CO desorption from multiple overlapping sites, which is normally difficult to perform using other

quantitative methods. The population fraction of sites was also determined, which allowed insights to be

made on the binding structure of CO on Ni(111).

5.3 Case Study: formic acid on copper

TPD with reaction of formic acid adsorbed onto a crystal surface of Cu(110) was modelled using

experimental results published in the literature. The reaction mechanism for formic acid decomposition on

Cu(110) has been studied by Ying & Madix (1980) and is shown below in Figure 26. Formic acid adsorbs

dissociatively to produce an adsorbed hydrogen atom (ads)H and formate species

(ads)HCOO . As the

temperature is increased during TPD, the adsorbed hydrogen atoms present recombine to desorb as

31

molecular hydrogen. At yet higher temperatures, the formate species decomposes to produce gaseous

carbon dioxide and an adsorbed hydrogen atom, which desorbs rapidly because the temperature at which

formate decomposition occurs is much higher than that for hydrogen desorption. The experimental TPD

results used are shown in Figure 25 below.

Figure 25: TPD experiment of formic acid on Cu(110) using a

heating rate of β = 3.4 K/s (Ying & Madix, 1980).

(ads)(g)2(ads)

2(g)(ads)

(ads)(ads)(g)

HCOHCOO3.

H2H2.

HHCOOHCOOH1.

Figure 26: Reaction mechanism for Formic Acid on Cu(110).

As can be seen, adsorbed hydrogen atoms that formed upon adsorption of formic acid desorb at low

temperature; furthermore, the hydrogen formed due to decomposition of the formate species is

coincident with the evolution of carbon dioxide [carbon dioxide cannot adsorb on Cu(110) because it does

not have a binding state (Ying & Madix, 1980)]. The low temperature hydrogen peak was modelled

separately to the other peaks, and two important issues were discovered:

Due to the stoichiometry of the process, the low temperature hydrogen peak should have an area

equal to that of the high temperature hydrogen peak. However, it was realised that the area of the

low temperature hydrogen peak is in fact ≈ 51% of the high temperature peak. Ying & Madix (1980)

also realised this discrepancy (but they quoted it as being 70%) and commented that during

adsorption, formate species may compete with adsorbed hydrogen atoms for available sites, which

may cause some hydrogen to desorb upon adsorption of formic acid, explaining this apparent

inconsistency. A more agreeable observation was that the area of the high temperature hydrogen

peak equals almost exactly half that of the CO2 peak, as expected by stoichiometry.

The shape of the hydrogen peak is somewhat ‘triangular’ and does not correspond to that expected

for second-order desorption kinetics. The presence of formate species on the surface is known to

cause a reduction in the desorption temperature for hydrogen (Wachs & Madix, 1979) indicating

that formate species do affect hydrogen desorption. This interaction may account for the irregular

shape observed. The irregular shape makes fitting a curve difficult, as discussed below.

The reaction set used for modelling the low-temperature hydrogen peak consists of one reaction

2H(ads) → H2(g). The model used consists of one type of site with a single activation energy, rather than a

32

distribution, because it was found that if a distribution was used the pre-exponential factor obtained is

unreasonably high. Furthermore, a uniform surface of Cu(110) contains only one type of site and this

supports the use of a single activation energy. A manual optimisation fitting by altering both the pre-

exponential factor and the activation energy was not useful in this case because the irregular shape of the

low temperature hydrogen peak resulted in similar fittings for all cases. Consequently, a pre-exponential

factor of 4 x 108 s-1 was chosen because Wilmer et al. (2003) reported this value for desorption of

hydrogen from a supported copper catalyst. The activation energy was optimised with respect to the

chosen pre-exponential factor and was found to be 49.8 kJ/mol; the optimisation curve is shown in Figure

27 below. The model and experimental TPD curves are given in Figure 28 below and as can be seen, an

exact fit was not possible (fitting error of about 16 %) due to the ‘triangular’ shape of the experimental

curve and the human error involved in reading experimental data from published graphs.

Figure 27: Optimisation with respect to activation energy of desorption for the low temperature hydrogen peak, assuming a pre-exponential factor of 4 x 10

8 s

-1. The line drawn is to guide

the eye.

Figure 28: Model and experimental TPD curves for the low temperature hydrogen peak from formic acid on Cu(110).

On a supported copper catalyst, Wilmer et al. (2003) reported the activation energy for desorption of

hydrogen to be 58 kJ/mol. The reduced activation energy we determined in the presence of formate

species is supported by the fact that Ying & Madix (1980) reported a significantly lower peak temperature

(about 50 K lower) for hydrogen in the presence of formate species on Cu(110). Furthermore, Wachs &

Madix (1979) reported an activation energy of 50.2 ± 4.2 kJ/mol for D2 from a Cu(110) surface, this

compares very well to our value of 49.8 kJ/mol. Finally, Redhead’s method for quantitative analysis on the

low temperature hydrogen curve (using Tp = 274 K and p equal to half the initial coverage) results in a

calculated activation energy of 48.2 kJ/mol, which is also similar to our value.

The decomposition of formate species was modelled using Reaction Set 5 shown below. The kinetic

parameters resolved from the low temperature hydrogen peak were used for reaction 2 in this model. In

this case, the CO2 curve could not be modelled using a distribution of activation energies because the

33

simulated curve would not fit experimental results unless a very small standard deviation was used i.e. a

single activation energy was needed. This is supported by the fact that a uniform Cu(110) surface contains

only one type of site. Not having a distribution of activation energies facilitates the manual simultaneous

optimisation of both the pre-exponential factor and the activation energy for formate decomposition. This

was performed by first selecting a pre-exponential factor and then conducting an optimisation for

activation energy, as done with hydrogen above. Numerous values for the pre-exponential factor were

tested, producing Figure 29 below. This resulted in an optimum pairing of A = 7.5 x 1015 s-1 and

Eact = 149.8 kJ/mol. The model and experimental results for both the CO2 and high temperature H2 peaks

are shown in Figure 30 below. Note that the CO2 peak shows a good fitting, with an error of 2.4 %.

(g)2(ads)

(ads)(g)2(ads)

H2H2.

HCOHCOO1.

Reaction Set 5: Decomposition of adsorbed formate.

Figure 29: Optimisation of A for formate reaction. Eact was

optimised for each plotted point above. The line drawn is to guide the eye.

Figure 30: Model and experimental TPD curves for the CO2 and

high temperature H2 peaks from formic acid on Cu(110).

Ying & Madix (1980) normalised the high-temperature hydrogen and carbon dioxide peaks and showed

that they overlap precisely, as expected because formic acid decomposition is rate limiting. However, when

this was performed using data read from the published graphs, the hydrogen curve overshot the CO2 curve

slightly. This proves that error in extracting data points from graphs over 30 years old is unavoidable. As a

result, the experimental hydrogen curve overshoots the model, as can be seen in Figure 30 above.

Ying & Madix (1980) conducted quantitative analysis on formic acid decomposition using three methods:

variation of heating rate, variation of initial coverage and fitting a model to experimental data. The results

reported were A = 9.4 x 1013 s-1 and Eact = 133.3 kJ/mol. In order to illustrate why our parameters differed

from those of Ying & Madix (1980), Figure 31 shows a plot of ln(rate constant) vs. 1/T for our values of A

and Eact and for those of Ying & Madix (1980) over a temperature range of 425-500 K. As can be seen, both

sets of parameters yield very similar values for the rate constant. This is because it is possible to have

34

different pairs of A and Eact that predict similar values for the rate constant. When the same

pre-exponential factor of A = 9.4 x 1013 s-1 used by Ying & Madix (1980) was input into our model and fitted

to the experimental CO2 curve in Figure 25, the resulting optimised activation energy was found to be

Eact = 132.8 kJ/mol. This compares very well to the value of 133.3 kJ/mol reported by Ying & Madix (1980).

Figure 31: Comparison of the rate constant calculated using the parameters determined from our model (A = 7.5 x 10

15 s

-1 and

Eact = 149.8 kJ/mol) and those determined using the results of Ying & Madix (1980) (Eact = 133.3 kJ/mol, A = 9.4 x 1013

s-1

).

5.4 Case Study: Isopropylamine on ZSM-5

My partner’s experimental TPD data for isopropylamine on ZSM-5 (with full initial coverage) is shown in

Figure 32 below (after correcting for baseline drift). The m/e ratios of 44, 41 and 17 correspond to the

strongest peaks in the spectra of isopropylamine, propene and ammonia, respectively. However, it is

important to note that isopropylamine produces a m/e = 41 fragment in the mass spectrometer as well.

0

2E-10

4E-10

6E-10

8E-10

1E-09

1.2E-09

300 400 500 600 700 800 900 1000

Mas

s Sp

ect

rom

ete

r Si

gnal

(au

)

Temperature (K)

m/e = 44

m/e = 41

m/e = 17

Figure 32: TPD of isopropylamine on ZSM-5 with full initial coverage and a heating rate of 0.17 K/s (Miao, 2012).

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

300 350 400 450 500 550 600

No

rmal

ise

d D

eso

rpti

on

Rat

e (K

-1)

Temperature (K)

Model

m/e = 41

Figure 33: Comparison of fitted model to experimental results for

isopropylamine desorption.

Isopropylamine desorbs between 320 K and 585 K; however due to noise in the signal, it is difficult to

model the m/e = 44 curve. It is apparent from Figure 32 and from others (Parrillo, et al., 1990) that

-7

-6

-5

-4

-3

-2

-1

0

1

0.0019 0.002 0.0021 0.0022 0.0023 0.0024 ln

(rat

e c

on

stan

t)

1/T (K-1)

Model

Ying & Madix

35

propene desorbs only slightly between 550 K and 585 K. Therefore, the m/e = 41 fragment of

isopropylamine will be used (after normalisation and correction for slight propene desorption) to extract

the kinetic parameters for desorption of isopropylamine. A shoulder on the right of the m/e = 41 curve

indicates that there are at least two sites from which isopropylamine desorbs. It is expected that ZSM-5

contains some weak acid sites with a distribution of activation energy because the pore structure contains

two types of channels – one straight and one zig-zag (Structure Commission of the International Zeolite

Association, 2008). Moreover, sites located at intersections between channels might have yet another

binding energy. As a result, desorption of isopropylamine is modelled using simple desorption from two

sites, each with a distribution of activation energy. The pre-exponential factor for desorption was taken to

be A = 1013 s-1, as expected for unimolecular desorption (Barrie, 2012). The model was fitted to the

normalised and corrected m/e = 41 curve with an error of 0.24 %, and is shown in Figure 33 above. The

kinetic parameters extracted for both sites are shown in Table 6 below. The only other quantitative

method that can be applied (with caution) to overlapping peaks is Redhead’s method. However, in this

case only the peak temperature of site 1 can be distinguished to be about 410 K. Redhead’s method (with

A = 1013 s-1, = 0.17 K/s) gives an activation energy of 116.6 kJ/mol, which compares well with our value

of 118.4 kJ/mol. Our simulations show that both sites have similar standard deviations of 8.8 kJ/mol and

8.7 kJ/mol, indicating that the distribution of activation energies for each site varies over a range of about

2σ = 17.5 kJ/mol.

Table 6: Summary of kinetic parameters extracted for isopropylamine desorption.

Emean (kJ/mol) σ (kJ/mol) α

Site 1 118.4 8.8 0.57

Site 2 139.1 8.7 0.43

(g)3(ads)3

(ads)3(g)23(ads)323

NHNH2.

NHCHCHCH)CHCH(NHCH1.

Reaction Set 6

Figure 32 shows that reaction to produce propene and ammonia takes place between 550 K and 650 K. The

propene peak has a shape consistent with a first-order reaction (as expected); however, the ammonia peak

is shifted to higher temperatures and has a long tail. The heat of adsorption for ammonia on ZSM-5 was

reported to be 150 kJ/mol by Parrillo & Gorte (1992), which is expected to equal the activation energy of

desorption because the adsorption process is not activated. This means that a peak temperature of 550 K

is expected for simple desorption of ammonia from ZSM-5; however, Figure 32 shows a peak of about

650 K for ammonia. Given the fact that propene desorbs significantly sooner than ammonia, we know that

the reaction is not limiting the desorption of ammonia. This indicates that the emergence of ammonia is

controlled by readsorption. The propene peak will thus be modelled to extract kinetic parameters for the

reaction of isopropylamine. The strong Brønsted sites are expected to have a full coverage of

isopropylamine until reaction occurs (see Section 2.4). We can therefore perform simulations using one

36

site with full initial coverage of isopropylamine. Reaction Set 6 above was input into the model for reasons

given in Section 5.1. Since the model does not consider readsorption, the peak shape of ammonia cannot

be simulated by assuming first-order desorption of ammonia. As a result, the ammonia curve cannot be

fitted to the model and the parameters for ammonia desorption cannot be determined. The model and

experimental propene curves are shown in Figure 34 below, the fitting error was about 8 %. It was found

that a good fit could not be attained with the propene peak (using a pre-exponential factor of A = 1013 s-1)

unless a single activation energy was used i.e. no distribution. This is supported by the fact that

experimental evidence shows that these Brønsted sites on ZSM-5 are of equal strength i.e. will give equal

activation energies (Parrillo & Gorte, 1992; Kresnawahjuesa, et al., 2002). This enabled a more rigorous

optimisation procedure for A to be performed as shown in Figure 35 below. The activation energy for the

isopropylamine reaction was determined to be 187.9 kJ/mol with a pre-exponential factor of

A = 5 x 1013 s-1. Redhead’s method gives an activation energy of 187.3 kJ/mol, which compares very well to

our value. Note that the activation energy for reaction is lower than that for isopropylamine desorption

from Brønsted sites (240 kJ/mol, see Section 2.4), which is as expected because decomposition is observed

to occur before desorption.

0.000

0.005

0.010

0.015

0.020

0.025

540 560 580 600 620 640 660

No

rmal

ise

d D

eso

rpti

on

Rat

e (K

-1)

Temperature (K)

Model

Experiment

Figure 34: Plot of model and experiment for the propene curve.

Figure 35: Optimisation of pre-exponential factor for reaction of isopropylamine. The line drawn is to guide the eye.

0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 4.0E-05

1.E+12 1.E+13 1.E+14 1.E+15

Sum

of

Squ

are

Erro

r

Pre-exponential Factor (s-1)

37

6. Conclusion A general model for temperature programmed desorption (TPD) with reaction has been developed and

successfully validated. The model can cope with multiple overlapping sites and can attribute a distribution

of activation energies to each site. The flexibility of the model in allowing the specification of a set of

reactions to describe any system proved to be very useful. Quantitative information such as distribution of

activation energies for each site, pre-exponential factors, and relative site populations, may be determined

by fitting the model to experimental TPD data. Three case studies were undertaken, from which

quantitative parameters were extracted that agreed well with values reported in the literature. In order to

understand better the underlying dynamics of one of the case studies (isopropylamine/ZSM-5), some

experiments were performed to determine the temperature range of propene desorption from ZSM-5 and

the extent of thermal decomposition of propene. The ability of the model to extract parameters from TPD

with reaction experiments and the strength of the model in dealing with multiple overlapping peaks was

demonstrated, a feat rarely accomplished using other methods.

7. Further work Future work that may be performed in continuation of this research include:

Incorporation of readsorption effects into the model.

TPD experiments of ammonia on ZSM-5 in order to model more accurately the

isopropylamine/ZSM-5 system.

Case studies involving more complicated reaction systems such as CO on a supported-ruthenium

catalyst, on which I have already done significant work, but did not have space to write about in this

report.

8. Nomenclature English

A Pre-exponential factor in rate constant 1/s

E Activation energy J/mol

isAdsorbed Matrix storing state of species (adsorbed or gaseous) -

k Rate constant 1/s

m/e Mass to charge ratio -

n Order of desorption/reaction -

numOfMolecules Number of species in model -

numOfPoints Number of site points considered for the distribution on each site type -

numOfReactions Number of reactions in model -

numOfSites Number of site types in model -

R Universal gas constant J/mol K

T Temperature K

r Rate of Desorption 1/s

S Stoichiometric matrix -

38

t Time s

W Width of desorption peak K

Greek α Fractional propulation of site types matrix -

β Heating rate during TPD K/s

ε Fractional weighting matrix -

θ Coverage -

σ Standard deviation of distribution J/mol

Subscripts 1/2 Half peak rate of desorption conditions

3/4 Three-quarters peak rate of desorption conditions act Activation f Final i Corresponding to site type i j Corresponding to site point j k Corresponding to reaction k mean Mean value of distribution n Corresponding to species n o Initial p Peak rate of desorption conditions st Isoteric heat of adsorption

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41

10. Safety appendix All possible precautions were taken to minimise the risks involved while performing experiments. The risks

involved and precautions undertaken are listed below:

High pressure gas cylinders

Only qualified personnel were allowed to handle gas cylinders. Regulators and pressure gauges

were used at all times. The cylinders were kept secured and stable to prevent them from

accidentally falling. Cylinder valves were always closed when not in use.

Flammable (propene and isopropylamine)

The flow rate of propene was kept to a minimum (about 2 ml/min). Propene was either combusted

in a safe manner or discharged externally to the environment. Possible sources of ignition in the

laboratory were avoided.

Asphyxiation (helium gas)

A low flow rate of helium was maintained (40 ml/min); therefore, this did not constitute a

significant risk of asphyxiation. Nevertheless, we were made very aware of the risk of an accidental

gas leak and a gas sensor alarm was always in use in the laboratory, as a precautionary measure.

Toxic/irritant substances (isopropylamine and organic solvents)

Isopropylamine is a volatile liquid at room temperature; therefore, it was necessary to handle the

substance in a fume cupboard. This minimised the risk of lung irritation caused by isopropylamine

vapours. In addition, nitrile gloves were used at all times when handling such toxic or irritant

substances to avoid skin contact.

The risks involved in developing the model include back ache, repetitive strain injury, and computer eye

strain. The steps taken to avoid such problems involved taking frequent breaks with occasional stretching

in order to relive muscle tension.