Adsorption

Adsorption describes the binding of gas or liquid molecules to a liquid or solid surface. In conventional surface science, adsorption is studied on open, atomically- smooth surfaces of metal single crystals with well defined Miller indices. Molecules may be bound to surfaces by eitherphysisorptionorchemisorption.[161] Physisorbed molecules are bound to a surface by weak Van der Waals interactions, such as dispersive forces or dipole-dipole interactions, with enthalpies of between a few kJ mol−1 _{to tens of kJ mol}−1_{. Due to the small interaction enthalpy, physisorption}

is only observed at low temperatures and is a non-activated and fully reversible process. Chemisorption involves the transfer of electronic charge between adsorbate and surface to form a chemical bond, which may also lead to the dissociation of adsorbing species. Adsorption enthalpies vary from tens of kJ mol−1 to a few hundred kJ mol−1_{. Due to the stronger interaction, desorption becomes an activated}

process. Chemisorption is not a fully reversible process and chemisorbed species may still be adsorbed at room temperature or higher.

For open surfaces various models of adsorption have been developed, including the Langmuir and Brunauer Emmett Teller (BET) models. Both the Langmuir and BET models assume that surface adsorbates are in dynamic equilibrium with a fluid phase above the surface, with adsorbates able to freely adsorb and desorb from the surface. Adsorption is also assumed to occur at a fixed temperature (i.e. isothermally).

In the Langmuir model adsorbent surfaces are assumed to be uniform with all adsorption sites equivalent, whilst neighbouring adsorbed molecules are assumed not

Chapter 2. Synthesis and Characterisation Techniques

Figure 2.7: The Langmuir isotherm.

Coverage tends asymptotically towards

θ= 1.

Figure 2.8: The BET isotherm, showing several values of c. After Atkins & de Paula[128].

to interact. Furthermore, adsorption is limited to a coverage of one monolayer.[128] The rate of adsorption is dependent on the pressure of the adsorbate gas (p) and the number of vacant surface sites (n(1−θ), where n is the total number of adsorption sites andθ is the percentage surface coverage). The rate of desorption is dependent only on the number of occupied adsorption sites (nθ). At equilibrium these rates may be equated which gives the Langmuir isotherm:[161]

θ= Kp

1 +Kp (2.4)

where K = kAds

kDes and kAds and kDes are the rate constants for the adsorption and

desorption processes respectively.

The BET model extends the Langmuir model to multilayer adsorption. Addi- tional layers adsorb on top of the first monolayer, as if onto the free surface, with the adsorption of each isolated layer described by the Langmuir model. The BET equation is expressed in terms of fractional monolayer volumes:[162]

V VM ono = cp (p0−p) h 1 + (c−1)_pp 0 i (2.5)

whereVM ono is the volume of one monolayer,pis the equilibrium pressure, p0 is the

saturation pressure of the adsorbate at the isotherm temperature, andcis a constant dependent on the enthalpies of desorption from the monolayer and the enthalpy of vaporisation:

c=e(∆HDes−∆HV ap)/RT _.

When c 1, the monolayer forms rapidly, followed by the gradual assembly of subsequent multilayers. For c≤ 1 the monolayer forms slower than or at the same

Chapter 2. Synthesis and Characterisation Techniques

rate as multilayers (Figure 2.8).[162] Rearranging eqn. (2.5) to a linear form, the slope and the intercept of a plot of _pp

0 against

p/p0

V(1−p/p0) can be used to determine

the surface area, provided the molecular cross-section of the adsorbate is known. The surfaces involved in adsorbing molecules in porous solids differ, however, from the open surfaces on which the Langmuir and BET models of adsorption were developed. In these materials small molecules capable of diffusing through the pore openings may access the internal surface which is many times larger than the external surface of the particle. These internal surfaces are neither open, nor atomically flat, nor do they have a homogenous distribution of adsorption sites. Also the enclosed nature of micropores may hinder multilayer formation. As a result, the Langmuir and BET are not strictly valid for assessing the surface area of porous solids, though both are commonly used to provide comparisons between different materials.

Pore volumes may be measured as an alternative to surface area to characterise the porosity of a porous material. Dubinin-Radushkevich (D-R) theory is based on the Pol´anyi potential theory in which physisorption isotherm data may be expressed as a temperature invariant characteristic curve.[163] The Dubinin-Radushkevich equation is, V V0 =e− [−RT ln(p/p_0)]2 (βE0)2 where _VV

0 is the fractional filling of the micropore volumeV0;E0 is the characteristic

energy; and β is a scaling factor. Using a linear form of the D-R equation, the micropore volume of a material may be determined from the intercept of a plot of

A2 (whereA= −RTln(p/p0)

β ) against lnV.

The porosity of activated forms of open-pore framework materials in this work was initially investigated by N2 adsorption at 77 K. Materials were activated at

elevated temperature (100–200°C) and reduced pressure (∼ 1×10−4 _{Torr) for 2–}

4 hours, with isotherms collected using a Micromeritics Tristar II 3020 volumetric porosimeter. If the sample was found to be porous, a lower starting pressure N2

isotherm was collected at 77 K using a Micromeritics 2020 volumetric porosimeter. Where insufficient sample was available for either of these porosimeters, data was collected using a Hiden-Isochem IGA. Adsorption isotherms for CO2 adsorption

at 195, 273 and 298 K and CH4 at 195 and 273 K were collected using a Hiden-

Isochema IGA gravimetric instrument. High-pressure adsorption measurements of CO2, methane, ethane, propane and butane adsorption were collected at 298 K using a bench-scale open-flow adsorption/desorption volumetric apparatus described in detail elsewhere.[164]

Chapter 2. Synthesis and Characterisation Techniques

Simulating Adsorption

In addition to experimental adsorption measurements, the adsorption of gas molecules by porous solids may be investigated by computer simulation. Two approaches are commonly used for this: quantum mechanical calculations and molecular simulations. Both methods parameterise the intermolecular interactions in terms of electrostatic and dispersive (i.e. van der Waals) interactions. Keskinet al. provide a comprehensive review of simulation techniques applied to MOFs.[165] Quantum mechanical approaches use approximations of the multibody Schr¨odinger equation to determine not only adsorptive properties of a system, but also physical properties such as lattice constants and point charges.[165] The most common approach used is density functional theory (DFT), as it relatively computationally cheap. DFT has been widely used in predicting structural properties of MOFs, though for adsorption it has been less successful as it does not predict dispersive interactions with sufficient precision. A more precise description may be achieved us- ing high levelab initio methods, though these tend to be extremely computationally intensive.[165]

By contrast, molecular simulation is much less computationally intensive, as van der Waals interactions are approximated using aforce field approach.[165, 166] Adsorbents are modelled using an atomistic representation of the MOF, derived from the desolvated structure. The framework is assumed to be rigid and periodic boundary conditions are applied to avoid finite size effects.[166] Force fields define the interactions between each pair of atoms in the adsorbate/adsorbate and adsorbate/adsorbent systems, using Lennard-Jones parameters and partial charges to describe van der Waals and electrostatic interactions respectively. Bond deformations of the adsorbate may also be included in the force-field.[166] For framework elements the UFF,[167] DREIDING[168] or OPLS-AA[169] force fields are commonly used. Adsorbates may be modelled either atomistically (like the framework), in which case the same force field may be used, or alternatively groups of atoms may be modelled together by a so-called united atom approach, modelling for example a CH2 group as a single sphere. The TraPPE force field contains interaction

parameters for adsorbates modelled by this approach.[170]

Isotherms may be obtained by predicting adsorption equilibria using Grand Canonical Monte Carlo (GCMC) simulations. GCMC mimics experimental con- ditions by fixing the chemical potential, volume and temperature of the system, whilst allowing the number of molecules to vary.[166] At every pressure step of the isotherm, millions of Monte Carlo insertion, deletion, translation or rotation steps are performed with acceptance criteria based on Boltzmann weighting. Of

Chapter 2. Synthesis and Characterisation Techniques

these steps, an initial fraction (usually 40 %) are used for equilibration, with the remaining 60 % used to calculate the simulation average for a given pressure.[166]

In this work the MUSIC general purpose simulation code will be used to simulate adsorption isotherms,[171] using the UFF force field[167] to describe the framework and either UFF or TraPPE[170] for the adsorbate.

Determination of Surface Area - Experiment vs Simulation

Using an atomistic model of the framework, the surface area may be directly computed and compared against experimentally derived BET and Langmuir surface areas. However, different authors define surface area in different ways: the van der Waals surface (also Corey-Pauling-Koltun) assumes atoms are hard overlapping spheres of van der Waals radius and the surface area is the combined surface area of all spheres; the Connolly surface describes the surface mapped out by the outer edge of a probe molecule “rolled” over a surface; and the solvent accessible surface area is the surface mapped out by the centre of a probe molecule “rolled” over a surface[172] (Fig. 2.9).

Figure 2.9: Accessible surface area de- termined by “rolling” a probe molecule over the surface. After D¨uren et al.[173]

Figure 2.10: The effect of edges and corners on the accessible surface area. After D¨uren et al.[173]

D¨uren et al. calculated the accessible surface area geometrically using probe molecules of varying sizes and compared this with experimentally determined BET surface areas for a range of MOFs.[173] The accessible surface area is sensitive to structural factors such as the proportion of the surface made up of edges and corners (Fig. 2.10) and also to the size of the probe molecule, which does not affect the Connolly surface, leading to the suggestion that the accessible surface rather than

Chapter 2. Synthesis and Characterisation Techniques

Figure 2.11: Snapshots showing the change in adsorbate distribution with increasing load- ing (A–D) from the simulation of N2 adsorption in IRMOF-16. After Walton et al.[174]

also show good agreement between experimentally determined BET surface areas and the accessible surface area.

In two recent papers Snurr and co-workers have used the geometrically de- termined accessible surface area to evaluate the validity of the BET method for determining surface areas in microporous materials. Walton et al. compared BET surface areas calculated using data from both GCMC simulations and experiments with the accessible surface areas of a series of IRMOF materials with increasing length linkers (and hence pore sizes),[174] whilst Bae et al. performed similar experiments for a series of nanoporous (<7 ˚A diameter pores) MOFs and zeolites.[175] Walton et al. used simulations to investigate whether multilayer formation (a primary assumption of BET theory) occurs during adsorption in microporous MOFs and reported how adsorbate distribution within the pores changes with loading (Fig. 2.11). At low loading the adsorbates preferentially adsorb at corner metal-oxide sites. As the loading increases a complete monolayer is formed within the pore and following this, for large pore MOFs, multilayers form with complete pore filling achieved at low partial pressures: for MOF-5 (IRMOF-1)

p

p0 ≈ 0.2. Standard BET surface area analysis is usually carried out in the range

0.05 < _pp

0 < 0.3. However, for microporous solids with small pore sizes this range

may be inappropriate as pores in the solid fill rapidly. Rouquerol et al. proposed two criteria for selecting a pressure range over which the BET surface area should be determined for microporous solids:[176] firstly, the intercept of the linear form of the BET equation (eqn. (2.5)) must be positive; and secondly, a pressure range should be selected such that VM ono

1− _pp 0

increases with increasing _pp

Chapter 2. Synthesis and Characterisation Techniques

(a) (b)

Figure 2.12: Comparison of the BET surface areas calculated from experiment and simulation (using both standard and consistency criteria pressure ranges —right) against accessible surface area calculated geometrically[173] for a range of MOFs and zeolite. After Walton et al.[174] (left) & Bae et al.[175] (right).

consistency criteria were used to calculate BET surface areas from simulated data which were found to be in good agreement with both experimental BET surface areas and also calculated accessible surface areas for all IRMOFs except IRMOF-14 (Fig. 2.12a). IRMOF-14 is thought to have a much lower surface area due to either crystal defects, interpenetration or pore blocking in the experimental sample. All of the simulated BET surface areas slightly over-predict the experimental values since the simulated data use perfect crystals, whereas experimental data were collected from real materials which will contain some defects and blocked pores.

Bae et al. also found good agreement between simulation BET and accessible surface areas using the consistency criteria for nanoporous adsorbents (Fig. 2.12b), though experimental surface areas were found to be much smaller, thought to be due to the standard BET range being used to calculate the surface area. Using the standard BET range with the simulated data, good agreement was found between simulated and experimental surface areas.[175] Baeet al. also investigated the variation of heat of adsorption (Qst) with loading in the consistency criteria

pressure range (Fig. 2.13). A plateau inQst is found at the start of the consistency

criteria BET linear region, with a value greater than the heat of condensation of the adsorbate (N2: 5.56 kJ mol−1), indicating first monolayer formation (adsorbent-

adsorbate interactions), which is the correct region to calculate the surface area of the adsorbent from. Both these papers provide some validation for the use of the BET to obtain quantitive experimental surface area values, even though the absence of multilayer formation invalidates the BET theory.

Turneret al. calculated surface areas of a series of MOFs usingprocrystal electron density, by calculating the sum of the spherical electron densities located about

Chapter 2. Synthesis and Characterisation Techniques

Figure 2.13: Variation of Qst (red dashes) with N2 loading at low pressure IRMOF-13. Blue circles are data points used in calculating the BET surface area. The initial decrease inQst is due to preferential adsorption in small pores. After Bae et al.[175]

appropriate nuclear positions.[172] For MOFs, the 0.0003 au isosurface was used as this reduces the contribution of re-entrant pores. Reasonable agreement was found with both reported Langmuir and BET surface areas, though the procrystal isosurface over-predicts the surface area in all cases due to the presence of small adsorbate inaccessible pores which contribute to the surface area of the framework, especially with catenated MOFs, as well as the reasons outlined previously (vide supra). A very good agreement was found between the procrystal surface area and the experimental pore volumes calculated from D-R equation.[172]