Opportunities and limitations of hydrogen storage in zeolitic clathrates

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Opportunities and limitations of hydrogen

storage in zeolitic clathrates

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storage in zeolitic clathrates

Proefschrift

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

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

in het openbaar te verdedigen op maandag 8 mei 2006 om 15.00 uur

door

Annemieke Wilhelmina Charlotte VAN DEN BERG

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Prof. dr. J. Schoonman Prof. dr. J.C. Jansen

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. dr. J. Schoonman Technische Universiteit Delft, promotor

Prof. dr. J.C. Jansen Universiteit van Stellenbosch, Zuid-Afrika, promotor Prof. dr. G.J. Witkamp Technische Universiteit Delft

Prof. dr. H. Gies Ruhr-Universität Bochum, Duitsland

Prof. dr. C.R.A. Catlow FRS University College London, Verenigd Koninkrijk Prof. dr. J. Martens K.U. Leuven, Belgie

Dr. S.T. Bromley Universitat de Barcelona, Spanje

Dr. S.T. Bromley heeft als begeleider in belangrijke mate aan de totstandkoming van het proefschrift bijgedragen.

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1 Introduction

Abstract

This chapter describes:

• The importance of and difficulties associated with small-scale hydrogen storage. • The definition of zeolites and clathrates and the explanation of how they could

be used as H2 storage material.

• A brief overview of the computational modelling techniques employed for my studies.

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1.1 Hydrogen as an energy carrier

The world stock of fossil fuels is limited. Predictions on when the oil famine will start vary from the year 2020 to 2200, in all cases indicating that alternative energy sources and carriers have to be found if mankind does not want to change its habits dramatically. Another important reason for searching for alternatives is the huge global pollution resulting from burning the fossil fuels.

In the next four subsections the following topics will be discussed in detail: 1. An overview and comparison of all known viable energy sources and energy

carriers that could replace fossil fuels.

2. The characteristics of molecular hydrogen important for its application as a fuel. 3. The criteria set for small-scale hydrogen storage methods.

4. A brief comparison between the main H2 storage methods that are currently under investigation.

1.1.1 Energy sources and energy carriers

Currently several options for solving the energy problem, both in the short and the long term, are under investigation. Short-term solutions involve more efficient use of the available remaining fossil fuels (e.g., developing lightweight vehicles, using more efficient burning engines like hybrid systems and fuel cells, and smart conversions of coal and natural gas into oil). Although these short-term solutions are interesting in themselves and sometimes even transferable to enhance the efficiency of other energy carriers that will be used after the fossil fuel stock is consumed [1], it is more important to find a workable long-term solution. Replacements are needed both for the energy source and the energy carrier function of fossil fuels. Preferably, these substitutes are effectively inexhaustible and non-polluting. The various alternative energy sources to oil that are reviewed below are:

• Nuclear energy, fission and fusion

• Biomass

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Nuclear energy - fission

Nuclear energy, obtained by splitting uranium (U-235) and plutonium (Pu-239), is extremely efficient on a weight and volume basis compared to gasoline - the energy in one kg of U-235 equals that in eight million litres of gasoline - and produces, therefore, also less (nuclear) waste per kWh. Even more important, it could provide the world with energy for several generations to come; the current world reserve is 15-20 million ton uranium of which ~4 million ton can be obtained at feasible costs (< 130 $/kg). However, mining of uranium is a dirty and dangerous job1 and the transport of radioactive feed and waste streams is also risky. Furthermore, a nuclear reactor produces dangerous radioactive waste, which takes centuries to decay to safer materials and for which no good permanent storage or destruction solution has been found yet. In addition, nuclear power faces broad social resistance, especially after the Chernobyl disaster. Combining this with the fact that nuclear energy is relatively expensive [1] and not sustainable (contrary to the other energy sources in this list), it will eventually have to be replaced. This leads to the conclusion that nuclear energy is not the final answer to the energy question, although it provides a convenient temporary alternative if no other solution is found before the last drop of oil is used.

Nuclear energy - fusion

Theoretically, nuclear power can also be obtained from the fusion reaction of deuterium with tritium, i.e., the energy production process also happening in the Sun. Deuterium (D) can be extracted from water (reserves for millions of years) and tritium (T) can be manufactured from lithium (reserves for at least 1000 years). Although no working energy reactor exists yet, the first large-scale experimental reactor, ITER (International Thermonuclear Experimental Reactor), will be built in Cadarache in Southern France in the next 10 years. If this reactor will work, nuclear fusion could become a very important energy source, especially because fusion between two D-nuclei is also possible, the process is inherently safe (no chance on a runaway process like with fission), and the radioactive waste decays rapidly and is non-polluting

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(helium). The future has to show whether nuclear fusion can be used as an economically feasible energy source.

Biomass

The two main issues relating to biomass as an energy source are its inefficiency and its so-called two-dimensionality. First, many biomass forms are not suitable for conversion into hydrocarbons, because they either contain too much water, which has to be separated first, and/or the conversion process gives rise to few useful (by)products, both making the process very inefficient and thus expensive. Although this problem is now partially solved, thanks to enzymes obtained from genetically modified bacteria that can convert cellulose into sugar [1], there still remains the 2D-problem: the limited space on earth available for growing the additional biomass makes it impossible to replace all hydrocarbons by their bio-equivalent and, therefore, biofuels can at most only provide a partial solution.

Wind, water (tidal and hydro-electric), and geothermal energy

Wind, water (tidal and hydro-electric), and terrestrial heat can be important sources of energy and have proved to be economically feasible, though their energy is at present still more expensive than that from hydrocarbons [1]. However, waterfalls and hot springs are certainly not ubiquitous and wind is not constantly blowing (hard enough) everywhere and always, making these sources only interesting as main energy source at some specific locations in the world, while for all other places they can at most only fulfil a supporting task. Additionally, extracting energy from wind and water can cause severe distortions in the local ecosystem (e.g., the noise and the sail rotations of a wind-turbine can scare birds and other small animals from their previously undisturbed habitat).

Solar radiation

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because of the need for very pure crystalline silicon. This energy source is, therefore, not (yet) economically viable. Nevertheless, recent research results in this field are promising and indicate much cheaper ways of production [2]. In comparison to the other energy sources, solar radiation has probably the largest potential to supply the final solution for the energy problem.

Next to an energy source, there is also the need for an energy carrier that can store the obtained energy in a convenient form for later use. Current scientific opinion suggests three energy carriers that could replace fossil fuels:

• Hydrocarbons from biomass • Electricity (in batteries) • Hydrogen

Hydrocarbons from biomass

As argued before, biomass cannot produce enough hydrocarbons to reach the worldwide demand for fuel. Additionally, hydrocarbons (from oil) are currently used for the production of a lot of important products such as plastics and medicines. Therefore, it seems more useful to employ the future hydrocarbons from biomass as starting materials for the production of these goods instead of as a fuel. Otherwise, alternatives have to be found for these consumer products as well.

Electricity (in batteries)

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Hydrogen

Hydrogen (H2) is the most interesting alternative energy carrier, because it is available in effectively infinite amounts in the form of water, which can be split into oxygen and hydrogen (by means of the electrolysis reaction: 2 H2O (l) à 2 H2(g) + O2 (g)) with the help of electricity or another energy form. Although it is also possible to obtain hydrogen from other starting materials like hydrocarbons, water is favoured from a sustainable point of view, i.e., it is not scarce and gives no CO2 as a by-product like hydrocarbons.

When H2is burned the only exhaust gas is H2O, so in this sense hydrogen seems to be an environmentally friendly fuel. However, the energy source for electrolysis determines the overall friendliness of H2 as a fuel. In general, the higher the number of energy conversion steps before final usage, the lower the overall efficiency of the energy source. The most ideal situation would, therefore, be to use sunlight directly for the electrolysis of water, i.e., photoelectrochemical (PEC) splitting. Some promising results are already obtained in this field [3] and if this conversion process can be commercialized it will probably be the best option for producing H2 as a sustainable energy carrier.

1.1.2 Properties of molecular hydrogen

Table 1.1 Properties of molecular hydrogen

relevant for its application as a fuel

Property Value Unit

Boiling point (Tb) -252.87 °C Melting point (Ts) -259.14 °C Density 0.090 (273 K) 70.8 (Tb) 70.6 (Ts) kg/m3 kg/m3 kg/m3 Inflammability limits 4.65 - 93.9 % Explosion limits 4 - 74.5 %

Molecular weight 2.0158 g/mol

Heat of combustion a 241 - 285 kJ/mol

a_{lower value: H}

2(g) + ½O2(g)à H2O(g)

upper value: H2(g) + ½O2(g)à H2O(l)

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from safety and energetic considerations. The possibility of leakages of ultra-cold hydrogen from fuel tanks or refuelling lines presents potentially hazardous working environments for which extensive precautions are necessary. Cooling hydrogen to such low temperatures also costs a lot of energy, thus, making this type of storage energetically less efficient and expensive.

Additionally, H2 has a very low density in the gas phase (for comparison, the density of gasoline is 720 kg/m3 at 293 K), which, in combination with the broad inflammability and explosion limits, makes it not attractive to store H2 as a (compressed) gas, because of the required large tank volume and the fire and explosion hazard. A benefit of hydrogen is its high energy content on a mass basis resulting from its low molecular weight in combination with the relatively high heat of combustion. For example, the energy content of 1 kg of H2 equals that of 2.7 kg of gasoline.

Large-scale storage of hydrogen has already been performed for many years now, usually as a compressed gas or a cryogenic liquid in very robust large tanks. However, when hydrogen has to be used on a small scale, like for normal household practice, this method is not feasible. The most important consumer application of hydrogen as energy carrier will most likely be that of replacement for hydrocarbons as car fuel. In section 1.1.3 the specific technical difficulties of storing H2 for that purpose will be discussed. Besides solving the storage problem, other difficult issues like social acceptance of massive use of H2 and a complete reorganisation of the fuel supply systems need to be taken care of before society can really exchange hydrogen for fossil fuels, but this discussion falls outside the scope of this thesis.

1.1.3 Technical criteria for small scale H2 storage methods

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currently used in fossil fuel driven cars. The European Union has comparable targets [6].

Ref. 5 gives some insight into the background of these criteria; the proportions of an average gasoline tank are given as 61.7 kg (50.8 kg of gasoline and 10.9 kg of casing) and 84 litres (70.6 litres of gasoline and 13.4 litres of casing). The fuel consumptions of gasoline and hydrogen are given as 11.5 km/kg and 84.8 km/kg, respectively, in which the gasoline is burned in the conventional way, while the hydrogen is burned in the twice as efficient Proton Exchange Membrane (PEM) fuel cell. With the stated average gasoline tank capacity one can thus drive 584 km. In order to drive that distance using hydrogen as a fuel, the corresponding tank should contain 6.9 kg of H2. This would mean that for a H2 storage tank with a weight equal to that of the stated gasoline tank, the content of hydrogen should be 11.2 wt%, and the volume usage of the hydrogen should be at least 82.1 kg/m3 (note that this is higher than the density of liquid H2 at its boiling point at 1 atm, see Table 1.1).

It would be ideal if the conventional hydrocarbon-driven car could be replaced by a hydrogen-driven equivalent. However, the former type of car is known to disappear in the future anyhow. Therefore, it is fairer to compare the H2-driven car to a type that is already an alternative, the car using electricity stored in batteries as a fuel2. If the criterion would be that a hydrogen powered car should be able to drive a distance of 120 km, a typical range for the current commercial electric vehicles mentioned above2 [7], on a full tank, assuming a tank casing weight equal to that of a gasoline tank, the hydrogen weight content required is as low as 2.8 wt%. Alternatively, when the design of the regular car is improved by using lightweight material etc. the number of kilometres that can be driven with a given amount of H2 increases, thus reducing significantly the total amount and corresponding weight percentage needed onboard [1].

Although investigations into H2 storage methods have been pursued for more than thirty years, no method has been found yet that can fulfil the demanding DOE-criteria of uptake rate and volumetric and gravimetric storage capacity. Besides these technical criteria, many other criteria like cost, safety, reliability, and availability are playing an important part in determining the feasibility of hydrogen storage methods. A

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brief overview of the storage methods currently under investigation is given in the next section.

1.1.4 Known hydrogen storage methods – a comparison

The first four methods in Table 1.2 have been the subject of study for many years now while the others are relatively new [5, 8-14]. The storage methods can be divided into three categories, which will be discussed separately:

• Storage as a pure gas or liquid • Chemi- and physisorption • Encapsulation

Table 1.2 Overview of known possible techniques for hydrogen storage

Method Weight capacity [wt%] a Volume capacity [kg/m3] Cost [$/kg H2]

Refilling time Safety Ref.

Liquefaction 16 36 72 5 min -- 5

Compression 13.5 21 81 - 160 < 3 min -- 5

Rechargeable metal hydrides

3.4 40 221 20-60 min ++ 5

Carbon carrier 2 - 5b,c 34 - 67b 191 - 397 Unknown + 5, 8

MOF carrierd 4.5 b,e 27b Unknown Unknown + 9

Molecular compounds 7b 65b Unknown Unknown ++ f 10 Glass microspheres 4.3 13 Unknown Replacement cassetteg - 5 Water clathrates 5.0 b,h 46b,h Unknown Replacement cassetteg - 11

Desired value i > 6.5 > 62 < 133 < 2 min ++ 5

a_{Measured maximum values.}

b_{Not including tank and auxiliary equipment weight and volume.} c

Much higher numbers are reported, however, these are later found to be due to H2O

adsorption instead of H2 [12]. d_{MOF = metal organic framework.}

e_{Reported value at 78 K and 20 bar, value for 293 K is 1 wt%, later measurements are}

less positive [13]: 1.6 and 0.2 wt% were found at the same conditions.

f_{Lower if a carcinogenic chemical like benzene is used.}

g_{The entire tank (content) is replaced in one turn by a new one.}

h_{Given value belongs to a pure binary solid at ~2000 bar and 250 K [11]. The more}

feasible ternary system with tetrahydrofuran (THF) only contains 0.5 1.0 wt% and 5 -10 kg/m3 H2 at 50 bar and 280 K [14].

i_{These values are based on the DOE targets for 2010, the targets for 2015 are 9 wt%,}

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H2 storage as a pure gas or liquid

At first glance, the most attractive option seems to be to store hydrogen in its pure form either as a liquid or as a gas. Liquid hydrogen has the highest H2 weight percentage in combination with one of the highest H2 densities and the uptake rate is also quick. However, the liquefaction process requires a lot of energy, making this option quite expensive and inefficient, and the H2 losses due to boil-off (1-2 % per day) are inevitable causing safety and possibly environmental problems (i.e., H2 is thought to affect the ozone layer). Compressed gaseous hydrogen (345 bar) also has a good weight capacity and uptake rate. However, the volume occupancy is relatively large and compressing the H2 is also expensive and dangerous.

H2 storage by chemi- or physisorption

An alternative is to store hydrogen by attaching it to another material. This can be achieved either by chemisorption, i.e., dissociating the H2 molecule and forming new chemical bonds, or by physisorption, i.e., keeping the H2 as a molecule at the surface of a support material by means of non-bonding attractive interactions. Chemisorption is the storage principle found in metal hydrides and molecular compounds that allow for reversible hydrogenation (e.g., with benzene, toluene, or fullerenes) or irreversible onboard H2 generation (e.g., with methanol or gasoline). Physisorption is the storage principle employed by carbon and metal organic frameworks (MOF’s).

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Encapsulation

A third group of storage methods uses a principle in between the above options, i.e., encapsulation of small amounts of pure hydrogen, like in the voids of water clathrates and glass microspheres (diameter 25-500 µm). Although hydrogen is not immediately released in case of an accident, the melting of the water hydrate and the breaking of the glass spheres can be quite fast. Additionally, water clathrates can only exist in combination with a stabilising compound like tetrahydrofuran (THF) at reasonable pressures like 50 bar [14], reducing storage capacity dramatically compared to a pure binary solid mixture at a technically unfeasible pressure of 2000 bar (5 wt% à 1 wt%, see Table 1.2) [11]. The glass microcapsules only contain a relevant amount of H2 for 200<P<500 bars and need to be heated to 200-400 °C for filling and release. Refilling within a reasonable time (< 2 min) is, thus, only possible with replacement cassettes (see Table 1.2). At this moment no encapsulation method has been found yet for which the storage capacity is large enough to fulfil the DOE-criteria.

Hydrogen encapsulation is also possible within some zeolite types (see also section 1.2.4). This encapsulation is comparable to that in glass microspheres in the sense that uptake and release is facilitated by elevated temperatures and that the structure can exist at ambient conditions. On the other hand, a zeolitic cavity is much smaller than the void of a microsphere, resulting in the average attractive H2-wall interaction to be practically absent in the glass sphere, while present in the zeolite and comparable to that in a water clathrate. Additionally, a zeolite is considerably more stable and robust than glass spheres and water clathrates and, therefore, a more promising candidate.

1.2 Zeolitic clathrates as hydrogen storage materials

In this section the following topics will be discussed: 1. Zeolites and their applications.

2. Zeolitic clathrates3. 3. Flexibility in zeolites.

4. Zeolites as hydrogen storage materials: facts, figures and future.

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1.2.1 Zeolites - description and applications

Figure 1.1 The construction of a zeolite: The T-atoms, here Si and Al, are

surrounded by four O-atoms in a tetrahedral arrangement. The O-atoms are shared between two tetrahedra and the spatial distribution of the tetrahedra gives the specific zeolite structure (in this example the silicalite [MFI] framework).

Zeolites are inorganic porous crystalline materials containing pores and/or chambers with access diameters varying from 3 to 9 Å, allowing for sieving on a molecular level. A property exploited for example by LTA membranes to obtain pure ethanol by sieving away the smaller water molecules [15]. The elemental composition of a zeolite is M_{n v}_/ (Al Si O_n _m ₂₍_{n m}₊ ₎)⋅wH O₂ in which M is the type of counterbalancing cation, n is the number of Al-atoms, v is the valence of M, m is the number of Si-atoms in the framework and w is the number of hosted water molecules. The Si- and Al-atoms are tetrahedrally coordinated by the oxygen atoms and are, therefore, called the T-atoms of the zeolite. All oxygen atoms are shared between two tetrahedra and the way in which they are spatially arranged determines the exact structure of the zeolite. This is schematically depicted in Figure 1.1.

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different zeolite and zeotype structures known [16], however, every year a few more are found and a very large number is theoretically predicted [17-20].

In addition to the above-mentioned application as molecular sieve, zeolites can also be used as heterogeneous catalysts and as ion exchangers. Washing powder contains up to 30 % of sodium-containing zeolite to soften hard water and every year worldwide ~1·109 kg of zeolite LTA (Linde Type A [16]) and zeolite Na-P1 (Gismondine [16]) is produced for that purpose. Some zeolites like FAU (Faujasite [16]) possess a strong acidity that, in combination with the high thermal and chemical resistance, makes them attractive catalysts for use in the petrochemical industry. The study in this thesis will tell if the application as H2 storage material can be added to this list of useful purposes of zeolites.

1.2.2 Zeolitic clathrates

The first clathrate structures were discovered in 1810 and are unrelated to zeolites. They are crystalline porous ice structures in which gas molecules occupy cages made up of hydrogen-bonded water molecules, and they are known by several names; water clathrate, clathrate hydrate, and gas hydrate. The cages are unstable when empty, collapsing into the conventional ice crystal structure, but they are stabilised by the inclusion of gas molecules (e.g., O2, N2, CO2, CH4, H2S, Ar, Kr, Xe). Clathrates are non-stoichiometric compounds, because the amount of enclosed gas is temperature and pressure dependent. Recently, also the existence of a H2 hydrate at 2000 bar and 250 K has been proven [11].

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Figure 1.2 Schematic representations of the zeolitic clathrates MEP, MTN, and

DOH, in which the shapes of the cages and the connectivities between the cages are clearly visible. The three- and four-connected vertices are T-atoms and O-atoms lie in the middle between two such vertices. These structures are equivalent to the sI, sII, and sH water clathrates, in which case the vertices are the O-atoms of the water molecule and the H-atoms lie in the middle between two such vertices.

For water clathrates there only exist three topologies (see Figure 1.2); i) structure I (sI) corresponding to clathrasil MEP, ii) structure II (sII) corresponding to clathrasil MTN, and iii) structure H (sH) corresponding to clathrasil DOH. For zeolitic clathrates a considerably larger number of topologies is known (see Table 1.3).

Another important difference between zeolites and water clathrates is the need for the presence of small gas molecules in the cages. As said before, the water clathrate cannot exist without the encapsulated gas molecules. In case of the zeolites, the structure is formed around a large organic template molecule or a hydrated cation usually only present in (some of) the large cages, while all other cages are allowed to be empty. Although the smaller cages often contain N2 or CO2 molecules, this is shown to be non-essential for formation [27]. Furthermore, the zeolite structure does not collapse after removal of the template molecules, provided that the pores are large enough to let the decomposition products pass, and are even stable up to 1000°C and from vacuum to high pressures in this empty state. Water clathrates on the other hand can only exist at sub-ambient temperatures and high pressures.

Unfortunately, it is often very difficult to remove an organic template out of a zeolitic clathrate because of its limited pore diameter. Although this is a practical problem that needs further study, it will not be a part of this thesis. Some clathrasils can be synthesized with only a small portion of their large cages occupied by a template

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molecule [28]. Additionally, some zeolitic clathrates can be synthesized around a hydrated cation and the water can later be removed relatively easily leaving an empty structure [29].

1.2.3 Flexibility in zeolites

Figure 1.3 Three examples of expression of flexibility in zeolites. As a measure

for the magnitude of the flexible deformation of the zeolite pore the maximum movement of its O-atoms is chosen (comparing the original state to the maximally deformed state). SOD: the breathing mode of the six-ring during H2 passage [this work]. RHO: shrinkage of the eight-ring pore windows (circular à elliptic) after dehydration of the zeolite [21]. ZSM5: deformation of the ten-ring pore in order to fit adsorbed para-xylene molecules [22].

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For a long time people assumed zeolites to be rigid systems and on a macroscopic level they indeed show the behaviour of a plain rock. However, on the molecular level a completely different picture is encountered. Figure 1.3 illustrates some examples of remarkable phenomena measured in zeolites that cannot be explained without taking the zeolitic framework flexibility into account.

Alternating translations and rotations of the six TO4 tetrahedra around their O-atom connection points, at effectively no energetic cost, are known to locally change the accessible opening of a SOD (and FAU) six-ring, thus enabling a better interaction with the charge-compensating cations or facilitating easier passage of molecules of a size similar to the ring opening [23]4. The small top graph in Figure 1.3 shows how the six-ring opening represented by the areas of the two indicated triangles in the picture above the graph, changes under the influence of a H2 molecule moving through the centre of the six-ring (see also section 4.4.1).

On the left- and the right-hand sides of the small top graph the H2 is positioned far away from the six-ring and the large changes in the triangle areas shown in the middle of the graph correspond to the situation in which H2 passes through the ring centre. If a triangle area becomes smaller, the three O-atoms forming it, move closer together and vice versa, i.e., the passage of H2 does not cause a homogeneous expansion of the six-ring. Instead the six-ring moves in a peristaltic-like fashion, a so-called breathing mode, to let the H2 pass. Although this kind of flexible movement (for more examples see ref. 23) is in general modest, it can still have a large influence on adsorption and diffusion.

A more apparent manifestation of flexibility, which changes the entire zeolite framework, can be induced by the presence or absence of adsorbed molecules like water in the RHO example [21] or p-xylene in the ZSM5 example [22]. Also the type of counterbalancing cation can have such effects [24]. Additionally, applying pressure on a zeolite crystal can in some frameworks cause the framework to reversibly deform. Some zeolites are even predicted to show auxetic behaviour [25]: a simultaneous rotation of

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An important simulation method in this field is the rigid unit mode (RUM) theory [23], which assumes the TO4 tetrahedra to be rigid units that can bend and rotate on their connection points

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some specific tetrahedra throughout the framework, induced by an outside pressure or pulling force, causes the structure to shrink or expand in all directions.

Figure 1.4 The effect of framework deformation on the energy path of H2 through the eight-ring of an all-silica CHA structure.

If the framework deformation changes the access diameters of pores, this effect can be employed for controlling transport [26]. For example, Figure 1.4 shows a qualitative computational study of how compressing a chabazite (CHA) crystal in the [111] direction influences the eight-ring pore and the corresponding energetic barrier for H2 passage through it:

A) In absence of force the eight-ring forms an adsorption spot.

B) When a small deformation is applied a small energetic barrier is encountered. C) A large deformation gives rise to a high energetic barrier for H2 passage, thus,

effectively blocking the pore for passage.

In summary, framework flexibility can (i) play an important role in enabling solid-state phase transitions in zeolites, (ii) can be an important parameter for enhancing adsorption and thereby facilitating catalytic reactions, and (iii) can dominate transport phenomena of adsorbed molecules in zeolites. Therefore, when studying applications of

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zeolites, this flexibility should never been overlooked and also for the work presented in this thesis, it will be explicitly shown to be of large importance in chapter 2.

1.2.4 H2 storage mechanisms in zeolites

Zeolites are potentially attractive materials for hydrogen storage because: i) their starting compounds, silica and alumina, are widely available, cheap, and environmentally friendly, ii) they are easy to manufacture, iii) they are stable and resistant to elevated temperature and pressure conditions, to chemicals, and to mechanical impact, iv) they are non-toxic and easy to handle.

The storage of hydrogen in zeolites can be achieved in two ways: physisorption at low temperatures and encapsulation at ambient conditions. Since the uptake in case of physisorption is in general low this is not a very attractive option for zeolites, because they are quite heavy themselves making it difficult to reach the weight target for small-scale storage. Some research has already been performed in this area and the findings are given in appendix 1.1 [30-37], showing that the maximum loading found so far is only 1.8 wt% for zeolite NaA at 40 K [36]. Combining this low capacity with the (expensive and difficult) requirement for cryogenic cooling, makes zeolites undesired for H2 storage by means of physisorption.

In case of encapsulation the size selectivity of zeolites is used for the storage and controlled uptake and release of hydrogen. This storage method involves trapping small gas molecules inside the zeolitic cavities by changing the effective pore window opening to these cavities. This window can be opened and closed by applying force [26], like for the example in Figure 1.4, by using a cation as a “sliding door” [38], or by varying temperature [39]. In each case, it is necessary that the largest pore aperture can adopt a similar size to the passing molecule.

For hydrogen this size approximately corresponds to the diameter of a non-deformed six-ring, i.e., a ring containing six O-atoms and six T-atoms, which happens to be the largest ring present in a zeolitic clathrate5. The energetic barrier for hydrogen

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The Lennard-Jones diameter of H2 is 2.9 Å and the diameter of a non-deformed six-ring is 2.6

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passing through such a six-ring can be overcome at elevated temperatures. This means that theoretically a clathrasil can be loaded at high temperature and pressure and that the

Table 1.3 Overview of all existing and all predicted energetically feasible

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hydrogen can become encapsulated by cooling at that pressure. Heating the zeolite up at a lower pressure allows the hydrogen to escape from the zeolite again. Alternatively, one could apply a force to deform an eight-ring (for example, in CHA; Figure 1.4) in order to control the energetic barrier for passage [26] or employ a bulky cation type that partly closes an eight-ring like in zeolite LTA [38]. However, applying force is unpractical and bulky cations occupy a lot of free space, reducing storage capacity, hence from a technical point of view the heating option is currently the most feasible.

All existing zeolitic clathrates that possess six-rings as largest access portals are gathered in Table 1.3 together with the predicted hypothetical structures that are energetically feasible. A hypothetical structure is considered to be feasible, i.e., it is likely that it can be really synthesized, if its heat of formation (∆Hf) falls within the

range of∆Hf-values of the existing structures, see sixth column of Table 1.3.

The structure of the clathrates is described in the third column: Each cage type has its own description in between the brackets and the ratio between the different cage types is given by the superscripts outside the brackets. In between brackets the ring types (normal text) and their occurrence (superscript) in the cage are given. If the cages are connected via mutual rings (faces) the structure is called a simple tiling (ST) structure, and if (part of) the faces are shared by more than two cages it is called a non-simple tiling (NST) structure (fifth column in Table 1.3).

Storage by means of encapsulation was already proposed forty years ago. However, it has received little attention since, despite the apparent benefit of storage at ambient conditions. The experimental results given in the literature are listed in appendix 1.2 [38-46], showing that the emphasis is placed on research on zeolite LTA using the principle of cation blocking, which gives a maximum storage of 1.4 wt% in NaA at 293 K [38]. In this thesis, the possibility of hydrogen storage by encapsulation in zeolites is further explored for the complete subclass of zeolitic clathrates.

1.3 Modelling H2 encapsulation in zeolitic clathrates

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for the Schrödinger or Dirac equation is employed. In between these two main areas, a multitude of other approaches can be found, such as semi-empirical [47] and tight-binding [48] calculations. These techniques were not used in this work and are, therefore, further omitted. Additionally, it is possible to combine QM with other lower level techniques in so-called embedded cluster calculations. This section gives a general description of the following three calculation types used for the studies in this thesis: 1. Classical force field calculations

2. Quantum mechanical calculations 3. Embedded cluster calculations

Specific simulation details for the calculations used in this thesis can be found in later chapters.

1.3.1 Classical force field calculations

A force field [49] defines the energy of a system as a parametric function of the nuclear coordinates in that system. The parameters are empirically or ab initio determined constants designed to reproduce molecular geometry and possibly also other selected properties such as, for example, bond vibrations. The function defining system energy is often a summation of potentials defining, for example, the energy of a specific bond, angle, torsion, or non-bonding interaction. Some characteristic potentials are given by equations 1.1-1.3 (see also appendix 2.1):

6 r buck E A eρ C r − − = ⋅ − ⋅ (1.1) 2 0 1 2 ( ) 2 three E = ⋅ ⋅ −k q q (1.2) 12 6 . . 4 (( ) ( ) ) L J E r r σ σ ε = ⋅ − (1.3)

Equation 1.1 gives the Buckingham potential, describing energy (Ebuck) as a

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energy (Ethree) as a function of the angle q between three specific nuclei. The potential

parameters in this equation are k2 and q0. Equation 1.3 gives the non-bonding

Lennard-Jones potential, describing the VanderWaals energy (EL.J.) as a function of the

non-bonding distance r between two specific nuclei. The potential parameters in this equation areε andσ.

The simplest calculation that can be performed with a force field is a structure optimisation [49, 50]. In this case the force field is combined with an optimisation algorithm in order to find the geometry corresponding to the lowest energy state of the molecule (sometimes with additional constraints such as fixed pressure or volume) at effectively zero Kelvin; the so-called equilibrium geometry. This state can be used for comparison purposes. In this thesis it is used i) to calculate the change in energy as a function of position in order to determine the energetic barrier for diffusion, and ii) to find the energy change as a function of the number of H2 molecules encapsulated in a zeolite cage in order to determine the maximum storage capacity.

A second type of classical simulation is the so-called Monte Carlo (MC) simulation [49]. During these calculations a large number of systems with a different microscopic state but with an identical macroscopic (thermodynamic) state are generated. This collection of systems is called an ensemble. There exist four different ensembles:

• Microcanonical ensemble (NVE): The thermodynamic state (an isolated system) is characterized by a constant number of atoms/ions, N, a constant volume, V, and a constant energy, E.

• Canonical ensemble (NVT): The thermodynamic state is characterized by a constant number of atoms/ions, a constant volume, and a constant temperature, T.

• Isobaric-Isothermal ensemble (NPT): The thermodynamic state is characterized by a constant number of atoms/ions, a constant pressure, P, and a constant temperature.

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The practical sampling of an ensemble is performed by making a random small change in the system, accepting this new system if it falls within the criteria of the ensemble and rejecting it if it does not, and repeating these steps until a statistically viable number of systems is found. In case of the first three ensembles it is only possible to change the position of the atoms/ions, while in case of the grand canonical ensemble [49] also the number of atoms can be varied. This last characteristic is of particular interest to the study for hydrogen storage, because it allows for the calculation of adsorption isotherms, which show the hydrogen loading capacity in a certain zeolite at a given pressure and temperature, by means of so-called grand canonical Monte Carlo (GCMC) simulations (see chapters 7 and 8).

If a force field is combined with Newton’s equations of motion [49, 50], the underlying model can be solved for its evolution in time for a given ensemble (with a fixed N). These calculations are called molecular dynamics (MD) simulations and can be used to study time dependent phenomena such as diffusion. The hydrogen diffusion in a zeolite determines the uptake time and can, therefore, be used to show if this criterion is fulfilled. To calculate the diffusion and the corresponding uptake time as a function of temperature, the NPT and NVT ensembles can be employed.

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1.3.2 Quantum mechanical calculations

Quantum mechanical calculations are based on a general theory, represented by the Schrödinger equation

2 2m V i t ∂Ψ     −_ _∇ Ψ + Ψ = _ _ ∂     h _h _(1.4)

in which h is Planck’s constant divided by 2π, m is mass, ∇2

is the nabla-squared operator (= 2 2 2 2 2 2 x y z ∂ ₊ ∂ ₊ ∂

∂ ∂ ∂ ),Ψ is the wave function, V is the potential energy, i is the imaginary number (i2 = -1), and t is the time. This equation is in principle applicable to every system and for all conditions. Unfortunately, it is not possible to solve this equation directly for existing systems larger than simple one-electron systems such as the H-atom (if the nucleus is treated as a classical particle), and approximations have to be adopted in order to use it. The applicability of the resulting (approximate) solutions to real physical systems follows directly from the approximations made. Furthermore, despite the approximations, the calculations are computationally still very demanding, limiting the calculations to relatively small systems of up to a number in the order of hundreds of atoms/ions.

The first important approximation is stating that the potential energy is not a function of time, allowing equation 1.4 to be separated in a time dependent and a time-independent part. The time time-independent Schrödinger equation is the most interesting one and can be written as

E

ψ ψ

Η = (1.5)

in which H is the Hamiltonian operator describing all particle interactions,ψ is the time independent wave function, and E is energy. As can be seen from equation 1.4, the

Hamiltonian operator can be written as

2 2

2

H V

m

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hydrogen atom V becomes 2 0 4 e r πε

− with e being the elementary charge, ε0 the vacuum

permittivity and r the distance between the electron and the hydrogen nucleus.

A second approximation always employed to make equation 1.5 solvable is assuming the nuclei of the atoms/ions to be fixed and separating the classical nuclear and quantum electron behaviour (the Born-Oppenheimer approximation), so the equation has to be solved only for the electrons in the system. In reality, the nuclei are vibrating, also at zero Kelvin, causing the space they occupy to be larger than predicted by this simplified model. This so-called zero point motion is, for example, of importance when calculating the maximum hydrogen loading in confined space like the cage of a zeolitic clathrate. The motion is caused by zero-point energy, i.e., the lowest energy a particle can have. This energy is non-zero for all particles limited by a potential field (“particle in a box”), because the Heisenberg uncertainty principle [50] states that the finite uncertainty in the position of the particle automatically leads to a non-zero uncertainty in the momentum. Consequently, the kinetic energy cannot be zero. For electrons this effect is accounted for by treating them on a quantum mechanical level, but the nuclei, which are treated as classical particles, need an additional correction. It is, for example, possible to calculate an approximate zero-point motion based on the energy landscape around the equilibrium structure and assuming that the resulting correction is equivalent to the corresponding QM harmonic oscillator.

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field used as input is consistent with the field of the solution. Usually6, this state is the ground state of the system (i.e., the system at minimum energy) and can be used in the same way as the optimized system in classical mechanics to determine energetic barriers for diffusion and maximum storage capacities.

Mathematically, the electrons can be considered effectively independent by approximating the overall many-electron wave function ψ for N electrons by a so-called Slater determinant (eq. 1.6) containing NxN one-electron wave functionsχ_i

( )

r_j (with rj = position including spatial and spin coordinates, i = 1 - N and j

= 1 - N):

( )

1 1 1 1 1 ! N N N N r r N r r χ χ ψ χ χ = K M O M L (1.6)

Each one-electron wave function, χ_i

( )

r_j , can in turn be approximated by a weighed summation of functions chosen in such a way that together they represent an orbital for the electron. The full collection of such functions is called a basis set of functions, or simply a basis set. A suitably chosen basis set (normally a set of Gaussian functions) combined with the single determinant approximation, allows for the extremely efficient practical calculation of electronic properties of molecular and solid state systems.

Due to the approximation of employing one Slater determinant, although the exchange energy (i.e., due to the non-local repulsive QM exchange “interaction” between electrons of the same spin) is accounted for correctly, information about the electron correlation energy (i.e., due to the electron-electron Coulombic interactions) is averaged out, leading to systematically higher calculated energies. Two popular solutions exist for this deficiency; i) the configurational interaction (CI) approach in which the wave function is not approximated by only one determinant, but by a weighed summation of multiple Slater determinants, and ii) the density functional theory (DFT)

6

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approach for which a so-called functional is introduced in order to take this lost energy term into account. Additionally, the functional also gives the exchange energy. The functional is only a function of the electron density ρ, which in this simplified case can be written as

( )

2 1 N i i r r ρ χ = =

∑

.

Functionals are usually based on the theoretical description of the infinite homogeneous electron field. Often corrections are further added to such functionals to better reproduce experimental values in actual calculations. In such cases the DFT methodology is arguably not really ab initio any more. From a physical point of view, the CI approach gives the most reliable results, however, it is a computationally very intensive technique and can, therefore, only be applied to very small systems (a few atoms). Therefore, the QM calculations presented in this thesis are all based on DFT.

The functionals employed for the DFT studies in this Ph.D.-thesis are briefly discussed below. In the Local Density Approximation (LDA) the density is a slowly varying function, allowing for treating it as a uniform electron gas [51]. The correlation energy obtained with this method is often overestimated, leading to overestimated bond strengths. The exchange energy is often underestimated by about 10% [49].

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A third group of methods are the so-called hybrid methods. These methods write the exchange energy as a weighed summation of the LSDA formula, exact exchange (obtained via Hartree-Fock theory [49]), and a gradient correction term. Similarly, the correlation energy is taken as the LSDA formula plus a gradient correction term times a weight factor. The only hybrid method employed in this work is B3LYP [53,56]. It employs the Becke 3 (B3) parameter functional [56], containing both exchange and correlation energy terms, in combination with the LYP functional [53] for correlation. The parameters in the B3 functional are determined by fitting to experimental data.

An important fact, pointed out by quantum mechanics, is that classical mechanics is overdefined (for example, position and momentum cannot be known at the same time) or alternatively that particles show diffracting behaviour. As a result, an energetic barrier that cannot be crossed according to classical mechanics (i.e., the energy of the crossing particle is not high enough to overcome the barrier) still has a small chance to be crossed according to quantum mechanics. This phenomenon is called tunnelling [47] and can be important for activated diffusion of hydrogen in clathrasils. Like with zero-point motion, it becomes less important at elevated temperatures.

1.3.3 Embedded cluster calculations

The third type of calculation employed for the research in this thesis is the embedded cluster calculation [49]. A small selected cluster is treated at a quantum mechanical level (e.g., DFT), while the rest of the system, not directly involved in the event under study (e.g., chemical reaction, energetic diffusion barrier), is calculated with a lower, more computationally efficient, method (e.g., a force field, or semi-empirical method). In this way it is possible to model a centre of interest with high accuracy whilst also taking the mechanical influence of the surrounding on the event into account.

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calculations in the core and ending with a classical force field description of the outer shell.

1.4 Overview of the Ph.D. thesis

The main goal of research presented in this Ph.D. thesis is to reveal if zeolitic clathrates are suitable small-scale hydrogen storage materials by assessing how well they fulfil the criteria set in section 1.1.3. Since crystalline materials lend themselves very well for computational modelling, it was decided to solve this question largely by simulations, however, always with a strong link to experimental data where possible.

Chapter 1 gives the background information of the main topics of this thesis, being the role hydrogen can play in solving the world’s energy problem, the issues related to small-scale hydrogen storage and the known storage techniques, the definition of zeolites and clathrates, a description of the importance of flexibility of zeolite frameworks, the explanation how zeolites could be used as H2 storage material, and a brief overview of the computational modelling techniques employed for the present studies.

In chapter 2, the force field employed to represent the clathrate, the hydrogen molecule, and the interactions between them is tested by comparing the energetic barriers for H2 diffusion through six-rings resulting from FF- and DFT-based calculations for all silica sodalite and AlPO4-20. It is shown that for both the covalent silica and the ionic AlPO4, the FF gives a good representation of the repulsive forces during six-ring passage. In case of all-silica the framework vibrations are also well represented by the FF. Furthermore, the importance of framework flexibility for diffusion is explicitly demonstrated.

In chapter 3 the self-diffusion of hydrogen in three different clathrasils (SOD, MTN, LOS) and in AlPO4-20 is calculated by means of molecular dynamics simulations. The results are translated into hydrogen uptake rates, which can be linked directly to the uptake criterion given in section 1.1.3, showing that this criterion is fulfilled for most clathrasils at 573 K.

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six-rings can severely hinder transport in the framework and how on the other hand a fully ordered positioning can help.

Chapter 5 illustrates that the influence of elemental composition on the maximum loading capacity in clathrasils (~5 wt%) is low by calculating it for four different clathrates with the sodalite structure by means of molecular mechanics energy minimizations.

Additionally, in chapter 6 the loading in all silica SOD is also calculated with a FF developed for small H2-clusters and by means of periodic DFT calculations with different functionals (LDA, PW91, BLYP, PBE), showing little difference among the results of FF methods and large differences among the results obtained with the various DFT functionals. The various results with DFT show no agreement with the FF results at first glance, but when the total system energy is split into the H2-H2 and the H2-SOD interaction contributions, the former one is nicely reproduced by the PW91 functional and the latter one is reasonably well reproduced by the LDA functional. It is deduced from this work that DFT with the employed functionals is not reliable for predicting H2 loading in clathrasils and that it is better to use the classical FF instead.

In chapter 7 the absorption isotherms of hydrogen into different compositions of sodalite are calculated by means of GCMC-simulations in order to find the conditions needed to obtain reasonable storage capacities, such as the maxima reported in chapter 5. The calculated storage capacities at technically feasible conditions are compared to the criteria mentioned in section 1.1.3. Additionally, the obtained results are compared to experimental data to illustrate the suitability of the FF for predicting absorption. It is shown that the loading in SOD at technically interesting conditions is very low (~0.1 wt%) and is independent of elemental composition.

In chapter 8 the absorption isotherms of hydrogen in all known existing and seven energetically favourable hypothetical clathrasils are presented, showing that none of these structures is currently interesting for small-scale hydrogen storage.

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However, further research is necessary to determine if interesting capacity values can be reached in this way.

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Appendix 1.1 Literature results for H2 physisorption in zeolites

Name Structure T [K] P [bar] Loading [wt%] Loading [cm3/g] Ref.

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Appendix 1.2 Literature results for H2 encapsulation in zeolites

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Appendix 1.2 Continued.

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2

2 Importance of framework flexibility for the diffusion of

H

2 through clathrasils and force field validation

Abstract

The importance of framework flexibility in facilitating the passage of H2 molecules through confining silica framework materials is probed in sodalite (SOD) via both periodic energy minimizations using a dedicated force field (FF), and embedded quantum mechanical/semi-empirical cluster calculations. It is found, regardless of methodological differences, that the quantitative and qualitative agreement between the different techniques is surprisingly good, tending to confirm the quality and suitability of each respective method. In all calculations, the energetics of molecular transport through a confining porous environment is found to be strongly dependent on the flexibility of the framework. Additionally, the interaction between H2 and AlPO4-20, the aluminium phosphate analogue of SOD, is investigated for a rigid framework by comparing results from density functional theory (DFT) cluster calculations and periodic energy minimizations using a dedicated FF. A good agreement has been found between the DFT and FF results for the repulsive non-bonding interaction of the AlPO4 -framework with the H2 molecule.

____________________

The contents of this chapter have been published in:

A.W.C. van den Berg, S.T. Bromley, N. Ramsahye , Th. Maschmeyer, J. Phys Chem. B 2004, 108, 5088.

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2.1 Introduction

Atomistic computer simulations are often employed for predicting diffusion rates and adsorption properties of gaseous species in solid porous frameworks [1]. Frequently, in such studies the framework structure is taken to be rigid. This has proven to be a suitably accurate assumption in a number of studies for molecules that are considerably smaller than the smallest pore aperture [2-5]. Such rigid-framework simulations also have the additional benefit of a great reduction in computer calculation time over simulations using fully flexible frameworks and, thus, have been utilized often. For molecules that are relatively more confined by the surrounding framework, having effective diameters of a similar size to that of the largest framework pore, the approximation of an unresponsive inflexible framework can introduce significant errors [6-9]. In numerous simulations the influence of the framework flexibility on the ease of diffusion has been indicated clearly [10-12], although with different conclusions as to its extent.

As a model system for investigating the influence of framework rigidity on diffusion, several authors have investigated the passage of inert gases through the clathrasil sodalite (SOD), which has a rather small largest pore aperture. Kopelevich et al. [13] investigated the influence of incorporating framework flexibility in the calculation of diffusion of Ne, Ar, and Kr in all-silica (all-Si) SOD by performing calculations using force field (FF) energy minimizations combined with transition-state theory, finding a small difference in the predicted diffusion barrier for Ne, and larger differences for Ar and Kr. Murphy et al. [14] used a comparable calculation method to determine the diffusion of He, Ne, and Ar in an all-Si SOD structure assuming the lattice to be rigid. Finally, Nada et al. [15] calculated the diffusion of He, Ne, and Ar in an all-Si SOD structure with symmetry-simplified periodic Hartree–Fock calculations using a rigid framework. When comparing the corresponding activation energies predicted by this series of computational investigations [13-15] large discrepancies between the results are observed.

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experimental data exist regarding the diffusion of guest molecules. Therefore, currently the above-mentioned literature results cannot be compared directly with experimental data to test their accuracy. In calculations employing the empty all-Si SOD framework one must be careful, therefore, to use computational methods known to accurately reproduce all-silica structures when preparing an appropriate reference rigid framework structure. In this study it is demonstrated that the choice of reference structure is particularly important in assessing the influence of flexibility on the transport of small molecules.

This chapter contains the first study of the energetics of a diatomic molecule passing through the SOD framework. Specifically, the energetic barrier for the diffusion of molecular hydrogen through the Si6O6pores (or six-rings) of all-Si SOD is calculated both by means of (i) periodic framework energy minimizations employing a dedicated FF, and by (ii) embedded quantum mechanical ONIOM1 [17] calculations employing a large terminated silica cluster of 90 atoms cut from the SOD crystal structure. By comparing the respective rigid and flexible framework calculations for both calculation types, a strong dependence of the energetic barrier height for hopping between cages on the framework flexibility is observed. Furthermore, a comparison of the barrier heights using both methods shows that, considering the large difference in calculation type, each approach gives remarkably comparable results with respect to both absolute barrier magnitudes and predicted relative effects of framework flexibility.

The importance of modelling the barrier for molecular hydrogen hopping through the confined environment of a porous structure is of immediate relevance to questions relating to materials for hydrogen storage. As with other molecular modelling studies on hydrogen storage and diffusion [18-19], in the present FF energy minimizations the approximation is made that the diatomic hydrogen molecule can be represented as a single-centred Lennard-Jones (LJ) particle. By examining the present quantum mechanical embedded calculations, which make no approximations as to the molecular nature of hydrogen, the suitability of this single-centre approximation for H2 is also assessed for the relatively extreme case of passage though a confined pore.

As discussed in section 1.2.2, zeolitic clathrates exist in various compositions. The opposite of the almost covalent all-Si SOD structure is AlPO4-20 (AlP(3:3)) in

1

Opportunities and limitations of hydrogen storage in zeolitic clathrates