Studies of unusual adsorption and diffusion behaviour of benzene in silicalite-1

The adsorption and diffusion properties of benzene in silicalite-1 have been investigated using gravimetric techniques, molecular simulation methods and the frequency response (FR) approach.

Two steps at loadings of ca. 4 and 6 molecules per unit cell (m. u.c.−1), respectively, and a hysteresis loop between loadings from 6 to 8 m. u.c.−1 can be found in the isotherms of benzene in silicalite-1.

These stepped isotherms could be classified as showing type VI isotherm behaviour but in this system the reasons behind the steps are of a new and novel nature.

The anomalous adsorption behaviour has been ascribed to the subtle interplay of increased sorbate–sorbate interactions and decreases in the entropy of sorption due to the energetically heterogeneous surfaces which are present in the adsorbent.

The diffusivity of benzene in silicalite-1 also displays an unusual behaviour.

At loadings lower than 4 m. u.c.−1, only a pure, single diffusion process can be observed, while at higher loadings, two diffusion processes are found.

The former case can be ascribed to the movement of the sorbed benzene molecules mainly down the straight channel direction, whereas the latter case has been associated with diffusion processes involving (a) benzene molecules which are part of clusters and (b) molecules which are not clustered, respectively.

It is an entropic driving force which causes the faster diffusivity of the clustered molecules.

Both the adsorption and diffusion properties of this system depend on the composition and structure of the silicalite-1 samples.


The adsorption and diffusion properties of aromatics in MFI zeolites have been of increasing interest over the past two decades due to the fundamental and industrial importance of these properties in catalysis and separation processes.1–20

Various techniques, including gravimetric adsorption measurements,6,8,13,14,18,21–24 sorption uptake rates,8,13,14,21,23,25 calorimetric techniques,10,26,27 temperature programmable desorption (TPD)28 or differential thermal gravimetry (DTG),9 NMR,11,12,17 magnetic resonance imaging (MRI),29 FTIR and Raman spectroscopy,30–33 X-ray and neutron diffraction,4,5,34–37 frequency response (FR),16–18 zero length column chromatography (ZLC),7,38 and molecular simulations,1–3,39–43 have been used in these investigations.

The reported results are, however, not conclusive, and sometimes even contradictory, due to the complexity of the systems.

Experimental isotherms of benzene in silicalite-1 measured previously are not always consistent with one another.

One conclusion, however, can be drawn from the higher temperature isotherms which all show a Langmuir shape with a maximum adsorption capacity of 4 m. u.c.−1.

The isotherms of Talu et al44. and Tsikoyiannis and Wei14 at lower temperatures display a step or kink around 4 m. u.c.−1 and then rise to a final plateau at somewhat below eight molecules per unit cell.

Lee and Chiang6 reported two inflections at ca. 4 and 6 m. u.c.−1, respectively, in benzene isotherms at temperatures of 283, 293 and 303 K but only one inflection at 273 K. Wu and co-workers,8 and Shah and co-workers21 reported isotherms with saturation values around 8 m. u.c.−1 without any step.

Thamm10 reported an isotherm with two steps at loadings of ca. 4 and 6 m. u.c.−1 at 303 K. In addition, a hysteresis loop was found in this isotherm between loadings of about 6 to 8 m. u.c.−1 Thamm10,26 also found that the heat of adsorption of benzene in silicalite-1 showed a characteristic behaviour which was dependent on the temperature and the amount adsorbed.

Tsikoyiannis and Wei14 reported a hysteresis loop, but only for samples with higher aluminium contents.

Efforts have been made to study the spatial distribution of benzene molecules within the silicalite-1 framework1,3–5,11–13,32,34–37,39,40,43,45 using different methods in order to interpret the anomalous adsorption behaviour.

It has generally been accepted that at loadings ≤4 m. u.c.−1, benzene molecules are localised in the intersections of the two channel networks of silicalite-1 although Talu has suggested that the straight channel segments are the preferential adsorption sites for benzene molecules inside the silicalite-1 lattice.40

However, the packing arrangements of benzene molecules in silicalite-1 at loadings higher than 4 m. u.c.−1 are still in doubt.

In addition, most of the previous studies presented only the energetically preferable adsorption sites or the probability for the sorbed benzene molecules being in certain sites rather than the detailed spatial conformation of the sorbate molecules inside the host lattice.

As to the diffusivities of benzene in silicalite-1, most of the experimental data reported in the literature at specific temperatures are within one, or at most, two orders of magnitude.13

These experimental diffusivity values were mostly measured at low loadings.

At high concentrations, the diffusivities are, however, much less documented due to the very strong sorbate–sorbate interactions between the sorbed benzene molecules at high loadings which make the measurements difficult and with some techniques impossible.

The FR technique used in this study is a quasi-steady state relaxation technique in which a parameter influencing the equilibrium state of the system is perturbed periodically at a particular frequency.

An outstanding advantage of the frequency-response technique is its ability to characterise multi-kinetic processes which may be present in a FR spectrum over a broad range of time constants.

Over the past decade, the FR technique has been extensively studied both experimentally and theoretically and has proved to be a powerful method for determining intracrystalline mass transfer of molecules through zeolite crystals.16–18,46–52

The primary objective of this study is to give an insight into the fundamental adsorption and diffusion behaviour of benzene in silicalite-1 at loadings up to the saturation capacity 8 m. u.c.−1 using a gravimetric adsorption method, the frequency-response technique, and molecular simulation calculations.

The effect of differing chemical compositions, hydroxyl nests, etc., of the samples on the adsorption and diffusion properties of the systems has also been investigated.


Model and computational procedures

Solid docking

Simulations of the configurations of benzene inside silicalite-1, using Monte Carlo (MC), energy minimization (EM) and molecular dynamics (MD) procedures, were carried out using the Solid_Docking package of the commercial InsightII software which by rapid searches is able to locate possible low-energy binding sites/packing arrangements for guest molecules within a host lattice.

The unit cell of silicalite-1 used has an orthorhombic Pnma space group with a = 20.022 Å, b = 19.899 Å, c = 13.383 Å containing 96 silicon and 192 oxygen atoms and the zeolite framework was assumed to be rigid during all runs.

The simulation box was defined as a single crystallographic unit cell to which periodic boundary conditions were applied in order to simulate the infinite zeolite structure.

The cff91_czeo forcefield, belonging to the cff91 forcefield, was used to describe the interactions in both the host framework lattice and the guest sorbate molecules.

More details for the methodology used in this study can be found in .ref. 53

The calculations were performed on a Silicon Graphics workstation.

The focus of these simulations is on structural rather than thermodynamic properties of the sorbate molecules.

These simulations are much less computationally demanding and more efficient for simulating configurations of the systems when large molecules and high loadings are involved in a zeolite framework.

Adsorption simulations

In order to understand the behaviour of the sorbed benzene molecules in terms of the temperature-dependence of their binding and mobility in the MFI zeolite channels, the adsorption simulations of a single benzene molecule in silicalite-1 were performed at different temperatures using the rapid Monte Carlo statistical simulation, the canonical ensemble Monte Carlo (fixed loading) simulation in which the Metropolis scheme was used.

The simulations were started by choosing the initial coordinates of the sorbate molecule in a sinusoidal channel segment, a straight channel segment and an intersection of these two channels, respectively.

Sorption module of Accelrys’ Cerius2 4.2 software was used to carry out the simulations on a Silicon Graphics workstation.

Both the benzene molecules and the zeolite framework were treated as rigid units.

The only permitted degrees of freedom are the three translational and three rotational variables associated with the sorbate molecule.

Electrostatic interactions were not included in all of the simulations due to the very low loading and the pure silica framework involved.

The unit cell of silicalite-1 used is the same as that described in section 1.1.

The simulation box was defined as two crystallographic unit cells to which periodic boundary conditions were also applied in order to simulate the infinite zeolite structure.

The various Monte Carlo step sizes for the simulations were adjusted in order to obtain a 50% acceptance probability.

The interaction cutoff distance was fixed at 9.9 Å, which is slightly less than half the smallest parameter for the simulation cell, so it accounts for all of the necessary interactions.

At least 4 million simulation steps were performed and the equilibration of the system was monitored by measuring the configuration energy as a function of Monte Carlo steps.

The Sorption Demontis,54 Burchart-Dreiding55 and PCFF56 Force Fields were applied in the simulations, respectively.

Dynamic simulations

The energy minimisation and molecular dynamics methods supplied in the Cerius2 4.2 software were applied to calculate the minimum energies of benzene down the straight channels of silicalite-1 by using the Burchart-Dreiding forcefield.

The initial position of benzene molecules was in the middle of one straight channel segment.

The framework structure and the dimension of the simulation box are the same as those used in the sorption calculations described above.

During the simulations, the framework is assumed to be rigid, whereas all the atoms of the sorbate molecules are flexible.

The sorbate molecule is forced to diffuse stepwise along the straight channel axis at steps of 0.2 Å.

At each step, the energy minimisation was followed by a quenched molecular dynamics in which 5 short dynamic runs (0.1 ps, 300 K) were applied and the system was re-minimised after each dynamic run.

The minimum energies at each step were recorded to reflect on different orientations and internal degrees of freedom of the sorbate molecules inside the channels.

The periodic boundary conditions were also applied for these simulations.

Molecular dynamics (MD) was also used to simulate the diffusivities of benzene in silicalite-1 framework.

This simulation was carried out by using the Materials Studio software supplied by Accelrys.

The same framework structure and simulation box as those used in the sorption calculations described above were, again, applied.

During the simulations, however, both the framework and the sorbate molecules were allowed to vibrate.

Only one benzene was loaded in the simulation box and initially located at one of the intersections between the two channels.

The PCFF Force Field was selected and both van der Waals interactions and electrostatic interactions were included in non-bond interactions with summation methods of atom-based and Ewald for these two kinds of interactions, respectively.

The interaction cutoff value was set to 12.5 Å with a spline width of 3.0 Å and a buffer width of 1.0 Å.

For the coulomb term calculations, a dielectric constant of 1.0 was used.

The constant-temperature, constant-volume ensemble (NVT), i.e., the canonical ensemble, was specified in the simulations.

Again, all the simulations had the periodic boundary conditions applied.

The time step used in MD runs was 0.5 fs with total simulation time of 1.0 ns.

Prior to the MD runs, an energy minimisation and an equilibration stage with a simulation time of 10 ps were utilised.

The FR method

In our frequency response method an equilibrium state is perturbed by applying a square-wave modulation to the volume of the gas phase.

The theoretical solutions of the frequency-response technique have been comprehensively developed over the past decade.

The full FR parameters (phase lag and amplitude) are experimentally derived from a Fourier transformation of the volume and pressure square-waves.

The phase lag ΦZB = ΦZΦB is obtained, where ΦZ and ΦB are the phase lags determined in the presence and the absence of zeolites, respectively.

The amplitude is embodied in the ratio PB/PZ, where PB and PZ are the pressures response to the ±1% volume perturbations in the absence and presence of sorbents, respectively.

From the solution of Fick's second law for the diffusion of a single diffusant in a solid subjected to a periodic, sinusoidal surface concentration modulation, the following equations can be obtained47in-phase: (PB/PZ) cos ΦZB − 1 = in + Sout-of-phase: (PB/PZ) sin ΦZB = outwhere K is a constant related to the gradient of the adsorption isotherm, S is a constant that represents a very rapid adsorption/desorption process, which may co-exist with the diffusion process being measured, δin and δout are the overall in-phase and out-of-phase characteristic functions, respectively, which depend on the theoretical models describing the overall kinetic processes of a system.

These theoretical models have been comprehensively developed over the past decade46,47,49,50,57.


A gravimetric balance (Sartorius) was used to measure the isotherms of benzene in ca. 200 mg of the silicalite-1, which had been outgassed under a vacuum of <10−3 Pa at 673 K for more than 20 h prior to the sorption measurements.

The isotherm temperature was controlled by a Eurotherm temperature controller.

The pressures were determined using two high-accuracy Baratron pressure transducers of type MKS 626 (0–10 Torr) and type MKS 220CA (0–1000 Torr), respectively.

The zero drift of the apparatus was always found to be negligible.

Buoyancy corrections were found to be insignificant in this balance at the equilibrium pressures involved in the measurements.

A more accurate, fully automated and computer controlled gravimetric system [IGA (Intelligent Gravimetric Analyzer), Hiden Analytical Ltd., Warrington, UK] was also employed in this study.

A sensitive microbalance (resolution of 0.1 μg) is mounted in a thermostated enclosure and thus provides higher accuracies and stabilities.

The sample temperature was regulated to ±0.1 °C by either a water bath or a furnace.

The IGA system has been used to carry out temperature programmable desorption (TPD) measurements for benzene sorbed in silicalite-1.

In this method a sorbate gas is brought into adsorption equilibrium with the sorbent at room temperature at a specified pressure which was chosen from the isotherm to give the required loading.

The system was then heated at rates of 5 to 20 K min−1 from room temperature to ca. 653 K. The above equilibrium pressure was maintained during the heating.

The weight of the sorbent was recorded as a function of temperature from which TG (Thermal Gravimetry) and DTG data could be derived.

The principal features of the FR apparatus developed in our group have been previously described.51

An accurately known amount of zeolite sample is scattered in a plug of glass wool and outgassed at a pressure of <10−3 Pa and 623 K overnight.

A dose of purified benzene is brought into sorption equilibrium with the zeolite in the sorption chamber at a chosen pressure and temperature.

A square-wave modulation of ±1% was then applied to the gas phase equilibrium volume, Ve.

The pressure response to the volume perturbation was recorded with a high-accuracy differential Baratron pressure transducer (MKS 698A11TRC) at each frequency over three to five square-wave cycles (256 readings per cycle) after the periodic steady-state had been established.

The volume, Ve, is 80 cm3 in the FR system.

A frequency range of 0.001 to 10 Hz was scanned over some 30 increments.

The conversion rate of the analogue-to-digital converter in the interface unit must be fast enough to cope with the 1 to 4 ms response time of the pressure transducer.

The pressure response to the volume change over the whole frequency range was measured in the absence (blank experiment) and presence of sorbent samples to eliminate time constants associated with the apparatus.

The FR spectra were derived from the equivalent fundamental sine-wave perturbation by a Fourier transformation of the volume and pressure square-wave forms.

The silicalite-1 zeolite samples used in this study are summarised in Table 1.

Silicalite-1 (A) was synthesised by Van-Den-Begin et al. from a gel containing a TPA-water solution (20 wt.% TPAOH) and a Ludox solution (40 wt.% colloidal SiO2).52

Silicalite-1 (B) is a commercial zeolite, RD 1051/87, produced by LAPORTE Inorganic.

The sample was separated by sedimentation in a column of water to produce a narrow distribution of particle size prior to the diffusion measurements.

All of the samples were used for the adsorption and the FR studies after calcination at 823 K for 10 h in an oven.

The crystals were heated in air from room temperature to 823 K at 2 K min−1.

X-ray diffraction patterns and SEM micrographs showed that these zeolite samples were highly crystalline and contained crystals of nearly uniform size.

Benzene was supplied by the National Physical Laboratory, UK, with a purity of 99+%.

Results and discussion


The isotherms of benzene in silicalite-1 (A) and silicalite-1 (B) at higher temperatures are shown in Fig. 1.

A marked inflection can be seen in the isotherm in silicalite-1 (B) at 323 K at loadings above 4 m. u.c.−1, while no step is found in the isotherms of silicalite-1 (A), suggesting that the conflicting isotherms reported in the literature, as mentioned above, may result from differences in the samples used.

The synthesis gel composition for silicalite-1 (A) sample had no aluminium present and, thus, the Si/Al ratio of the product should be almost infinite.

The large number of internal silanol groups (cf. Table 1), measured by 1H-MAS NMR,52 existing in the bulk phase of the silicalite-1 (A) crystals induced by the presence of TPA ions during the pentasil-type synthesis is, therefore, the most probable factor influencing the adsorptive properties.58

The adsorption behaviour of the system is also influenced by the Si/Al ratios of the samples.10,18,27

It is worth noting that the defect effect is more pronounced, for the case of aromatics/MFI systems, than that for n-alkanes/MFI systems due to the fact that an additional interaction between sorbate molecules and the sorbent framework will be involved in the aromatics/MFI systems compared with the simple dispersion/repulsion forces which are involved with the alkanes.

Fig. 2 presents the isotherms of benzene in both silicalite-1 samples at lower temperatures.

The results reported by Lee and Chiang6 that two steps at ca. 4 and 6 m. u.c.−1, respectively, in each benzene isotherm at temperatures of 283, 293 and 303 K and only one step at 273 K were confirmed in this study using the silicalite-1 (B) sample.

A hysteresis loop which appeared in the isotherm of Thamm10 can also be observed in the isotherm at 303 K. However, the isotherm in silicalite-1 (A) at 273 K levels off at about 9 m. u.c.−1 without any inflection.

Step-like isotherms have been attributes to phase transitions occurring in the sorbent induced by sorption of the sorbate molecules.1,6,31,59,60

This suggestion was discarded in our previous study18 as (i) the phase transitions can occur at loadings in the range ca. 0–2 m. u.c.−16,45,59,61,62 where no steps are found; and (ii) the symmetry changes also occur on change of temperature.

The higher the temperature, the lower the loading at which the phase transition takes place.59,63

However, the loadings at which the steps are found are independent of temperature in most cases.

Thirdly, a phase transition of silicalite-1 from monoclinic to orthorhombic was observed when trichloroethene was sorbed in silicalite-1 at a loading of ca. 7 m. u.c.−1 using an in situ neutron diffraction technique,35 but no inflection in the isotherm was found.

Finally, the transformation of silicalite-1 from monoclinic to orthorhombic symmetry involves only minor displacements of the atomic positions within the framework structure which, under appropriate conditions, are highly reversible and cause only very small changes in size and shape of the channel system.36,64

The fact that the structural differences between the topologically equivalent orthorhombic and monoclinic forms of MFI framework are very small is generally overlooked by many workers who ascribed the changes in the adsorptive properties simply to these phase transitions.

Neutron diffraction investigations give further support to this argument.35,36

As mentioned in the Introduction section, the intersections of the two channel systems of silicalite-1, of which there are four per unit cell, are the most preferred sorption sites for benzene, which is consistent with the fact that a step occurs in the isotherm when the loading increases above 4 m. u.c.−1.

Thamm10 has ascribed the inflections of the benzene isotherms in silicalite-1 to the redistribution and/or reorientation of benzene molecules occurring in the system at the loadings where the steps occur.

These redistribution and/or reorientation processes will result in a large entropy loss in the adsorbed phase, as shown in Fig. 3b, but this entropy decrease is balanced by the large increases in the corresponding heats of adsorption, as shown in Fig. 3a.

The results displayed in Fig. 3 are in good agreement with Thamm’s calorimetric data.10,26

The simulation results presented in the following section justify these arguments and elucidate explicitly at molecular levels the factors which cause the anomalous steps and the hysteresis loop in the isotherms of this system.

Neutron diffraction studies35 also suggested that the steps observed in the isotherms of benzene in silicalite-1 are not signatures of phase transitions of the sorbent structure but are related to three stages in the filling process induced by the three kinds of sites present in silicalite-1.

One can, therefore, conclude that the unusual isotherms of benzene in silicalite-1 can be attributed to energetically heterogeneous surfaces which are present in the adsorbent.

These heterogeneities, arising from sorbate–sorbent and sorbate–sorbate interactions, cause spatial configuration changes as the loading increases.

It is interesting to point out that the isotherms in Figs. 1 and 2 which show one or more steps are examples of Type VI isotherms.65

However, these inflections are not due to the accepted mechanism for such steps, i.e. second and third layer adsorption on very homogeneous surfaces but are due to adsorption on different sets of sites where heat/entropic factors introduce distinct differences to the sorption process at well-defined adsorbate concentrations.

Simulation calculations

The configurations of benzene within silicalite-1 with the lowest potential energies at loadings from 4 to 8 m. u.c.−1, derived from the solid docking simulations, are presented in Figs. 4 and 5.

The structures displayed here can explain explicitly the unusual adsorption isotherms of the system and the diffusivity discussed in the subsequent section even though these simulations determine the arrangements for a temperature of 0 K.

At loadings up to 4 m. u.c.−1, the molecules are located in the intersections with the aromatic-ring plane normal to the xz plane (cf.

Fig. 4(a,4) and 4(b,4)).

The sorbate–sorbate interactions will be negligible at these loadings.

Fig. 6 displays the mass distributions of benzene adsorbed initially in a sinusoidal channel segment and a straight channel segment of silicalite-1 at 673 K calculated using the adsorption simulation technique.

Dots indicate the centre of mass of the benzene molecules sorbed during the simulation.

It is clearly shown that the intersections are still preferred positions for the sorbed benzene molecules at high temperature.

Similar simulation configurations were obtained using the different forcefields listed in section 1.2 but the heat of adsorption calculated on applying the Burchart-Dreiding forcefield is more consistent with the experimental results26 than the other two forcefields.66

At a loading of 5 m. u.c.−1, however, a dramatic change occurs in the structure of the system as shown in Fig. 4(a,5) and (b,5).

Four molecules are distributed in the intersection and the straight channel segments forming a cluster along the straight channel direction with those molecules in the intersections now parallel to the xz plane.

The fifth molecule which does not join the chain remains in an intersection site of an adjacent straight channel and retains the same orientation as observed at the loadings ≤4 m. u.c.−1.

At a loading of 6 m. u.c.−1, the chain remains unchanged but now there are two molecules located in the intersection sites of the adjacent straight channels as shown in Fig. 4(a,6) and (b,6).

The formation of such strong sorbate–sorbate chains of molecules has been proposed by Sacerdote and Mentzen et al5. by comparing X-ray powder diffraction data and calorimetrically determined differential adsorption heats, with computer simulated atom–atom interactions for this system at a loading of 8 m. u.c.−1

As the loading increases to 7 m. u.c.−1, the chain still exists but now the seventh molecule does not go into the remaining straight channel site to form another chain down the straight channel adjacent to the one with the existing chain, as suggested by the X-ray researchers,5 but resides in one of the sinusoidal channel segments to form a side-chain along the sinusoidal channel direction (cf.

Fig. 5(a,7) and 5(b,7)).

At a loading of 8 m. u.c.−1, a similar configuration can be seen with the eighth molecule located in another sinusoidal channel segment at a site opposite to that of the seventh molecule as can be seen in Fig. 5(a,8) and 5(b,8).

Thus, one can conclude that the configuration of benzene in silicalite-1 at a loading of 8 m. u.c.−1 consists of clusters down the straight channels with side chains along the sinusoidal channel direction.

These findings confirm, again, the statements made by Thamm10 from his calorimetric data that redistribution and/or reorientation occurs twice in the system at loadings of ca. 4 m. u.c.−1 and 6 m. u.c.−1, respectively.

As mentioned above, for lower loadings (up to 4 m. u.c.−1), the configuration of the sorbed benzene molecules in silicalite-1 resulted from this study is in fair agreement with those reported in the literature.

For loadings higher than 4 m. u.c.−1, the locations of the molecules derived from different studies are inconsistent.

X-ray and FT-Raman investigations4,5,32 presented a conformation of benzene molecules sorbed in silicalite-1 at loadings between 4 and 6 m. u.c.−1 with four molecules located at the intersections and the other added molecules occupying the sinusoidal channel segments.

For loadings higher than 6 m. u.c.−1, four molecules remain in the intersections and the rest of the benzene molecules move to the straight channel segments forming infinite chains in the straight channels.

Neutron diffraction studies35 showed that up to a loading of 4 m. u.c.−1, the sorbed benzene molecules fill the intersections.

At a loading of 6 m. u.c.−1, the two additional molecules are located in the straight and sinusoidal channel segments, respectively, to form dimers with the molecules already in the intersections.

The sorbed benzene molecules at the higher loading of 8 m. u.c.−1 occupy the three types of sites in a new arrangement of interconnected chains.

Obviously, the configurations obtained from this study are different from those mentioned above.

However, all display a three-stage process of porosity filling, suggesting that the three types of adsorption sites are energetically heterogeneous.

The two steps observed in the above sorption isotherms can then be ascribed to the dramatic change of the spatial configurations of the system at loadings of around 4 m. u.c.−1 and 6 m. u.c.−1, respectively.

The discrepancies might be ascribed to the difference in temperature for different studies or/and to the different silicalite-1 samples used in the experiments.

As far as the hysteresis loop is concerned, however, the conformation of benzene molecules presented in Figs. 4 and 5 are the most plausible, as discussed below.

The saturation adsorption capacity for benzene in silicalite-1 determined experimentally (cf.

Fig. 2) is ca. 8 m. u.c.−1, which is consistent with previously reported data.8,10,67,68

This value is much smaller than the theoretical value of 12 m. u.c.−1 based on the crystallographic data for silicalite-1 and the liquid density of benzene.

The spatial configuration of the sorbed benzene at a loading of 8 m. u.c.−1 (cf.

Fig. 5(a,8) and (b,8)) shows that there are still two straight channel segments and two sinusoidal channel segments per unit cell left available, implying that the adsorption occurs on energetically preferred centers rather than a process of volume filling within the microporous network.

As mentioned above, a large entropy loss is involved at high loadings.

This entropy decrease can, however, be balanced by the large increase in the corresponding heats of adsorption (cf. Fig. 3).

For loadings in excess of 8 m. u.c.−1, a further entropy loss would occur due to the very tight packing of the sorbed benzene molecules.

The corresponding heats of adsorption will, nevertheless, decrease at very high loadings and are not able to balance the entropy decrease.

The saturated adsorption capacity of ca. 8 m. u.c.−1 is, therefore, controlled by both the entropy and enthalpy effects of the sorbed benzene molecules.

In the light of the solid docking simulation results, a possible interpretation of the hysteresis loop found in the isotherm of benzene in silicalite-1 (B) at 303 K is proposed.

At loadings lower than 6 m. u.c.−1, the sorbed molecules are associated with one another only via the straight channel direction as shown in Figs. 4 and 5.

In the hysteresis loop region, the sorbed benzene molecules form a large sorbate–sorbate cluster throughout the framework channels, leading to strong sorbate–sorbate interactions which can be seen from the heat of adsorption of this system, as shown in Fig. 3.

On increasing the loading some reorientation and relocation of the molecules already sorbed may occur to give clusters with maximum sorbate–sorbate interaction energy.

At maximum loading the final sorbed benzene molecule is sorbed on the least preferred sites, i.e. a sinusoidal segment site.

On desorbing from this maximum loaded state, molecules have to be removed from these strongly bound clusters, i.e., the first molecule will be removed along the straight channel which offers the minimum diffusional resistance, thus, adsorption and desorption involves different processes and paths, resulting in two different configurations with essentially identical free energies at the same partial pressure and hysteresis occurs.


Some FR spectra of benzene in the silicalite-1 (A) and silicalite-1 (B) at lower loadings (<4 m. u.c.−1) are shown in Fig. 7.

An excellent agreement between the theoretical model for a single diffusion constant and the experimental data for the two silicalite samples indicates that the mass transfer of benzene in the MFI zeolite network is dominated by a pure, single diffusion process at lower loadings.

This pure, single diffusion process could arise either from the movement of the sorbed benzene molecules along only one channel direction, most probably down the straight channel direction, or from an average single diffusion process along the two channel systems.

XRD and NMR studies show that benzene is an almost perfect spherical rotator at the intersections of the two channels in the MFI structure,11,12,45,52 indicating that the sorbed benzene molecules could diffuse readily along either of the two channel networks resulting in an average single diffusion coefficient at lower loadings.

The energy minimization simulations of the sorbed benzene molecule in silicalite-1 show, however, that the energy barrier for the benzene molecule diffusing down the straight channel direction (29.6 kJ mol−1) is in good agreement with the experimental activation energy (28.8 kJ mol−1),18,66 implying that the single diffusion process measured, at high temperatures or lower loadings, by the FR method may result from the sorbed benzene molecules moving mainly along the straight channel direction.

Results obtained from an MD simulation run, shown in Fig. 8, support this assumption since the mass transport down the straight channel direction greatly overweighs the transport processes along the other two directions.

One can conclude, then, that the single peak in the FR signal at low loadings results from the sorbed benzene molecules being transported along the straight channels rather than an average single diffusion process along both channel systems.

At low temperatures and loadings >4 m. u.c.−1, pronounced and, very much unexpected, bimodal FR spectra were observed for benzene diffusing in silicalite-1 with a new peak appearing at a frequency much higher than that observed at low loadings, as shown in Fig. 9.

It does not seem rational to assign the new peak to either the effect of the dissipation of the adsorption heat or to a finite-rate mass exchange between transport channels and stationary storage channels because, in both cases, no bimodal behaviour would be observed in the FR spectra when the rate of the diffusion is slower than the rates of these two processes.49,50

Two thermodesorption processes were observed at high loadings in DSC (differential scanning calorimetry) and DTG9 studies, implying that more than one mass transfer process take place in the system.

NMR measurements11,12,69 also detected two types of motion of the sorbed benzene molecules at higher loadings and no evidence from the line shapes of exchange between these two types could be observed.

It is, therefore, reasonable to propose that the bimodal FR spectra can be ascribed to two independent diffusion processes taking place in the system.47,48

As discussed above, sorbed benzene molecules diffuse down the straight channels at lower loadings.

At high loadings, it is unreasonable to assign the new high frequency peak of the FR spectra to the transport of the sorbed molecules along the sinusoidal channel direction as (i) there are no molecules sorbed in the sinusoidal channel segments at loadings of 5 and 6 m. u.c.−1 according to the solid docking results shown in Fig. 4 and (ii) diffusion down the sinusoidal channel direction should be energetically more difficult than that along the straight channel direction as the benzene molecules suffer a large repulsive interaction when located in the sinusoidal channel segments.

The two observed diffusion processes must, therefore, be associated with two different states of the sorbed benzene molecules in silicalite-1 channels at high loadings.

The solid docking simulation results, as presented in Figs. 4 and 5, show that some of the sorbed molecules are clustered at high loadings, leading to two different states of the sorbed benzene molecules existing in the framework, i.e. a clustered state and an unclustered state, respectively.

Fig. 10 displays the DTG profiles of benzene molecules sorbed in silicalite-1 derived from the temperature programmed desorption results at various adsorption loadings measured using the IGA apparatus.

Only a single high temperature peak was observed in these DTG profiles when the initial adsorption loadings were lower than 4 m. u.c.−1, whereas at higher loadings two peaks were found.

The new lower temperature peak can, therefore, be associated with the desorption of molecules sorbed above a loading of 4 m. u.c.−1 The results clearly demonstrate that the initial 4 m. u.c.−1 sorbed in the preferred channel intersection sites require higher temperatures before desorption occurs compared to molecules sorbed in the other sites at loadings in excess of 4 m. u.c.−1 As these latter molecules are sorbed with higher heats of adsorption (cf. Fig. 3), mainly from increased sorbate–sorbate interactions, the ease with which they are desorbed must be due to gains in entropy on desorption as the main driving force.

In Fig. 10 the higher temperature peak in the DTG curves for molecules sorbed in the channel intersection sites increase in temperature from ca.

343 K for a loading of 1.5 m. u.c.−1 to ca.

403 K for a loading of 8 m. u.c.−1 This increase arises from the increase in equilibrium pressure that is maintained in these DTG measurements as the loading increases (see Experimental section for the conditions used in the IGA apparatus).

The experimental results also showed that changing the heating rate had little or no effect on the TG and DTG profiles.

The TG and DTG profiles of the benzene molecules sorbed in silicalite-1 (B) with a initial loadings of 6 m. u.c.−1 are shown in Fig. 11a.

The complete desorption of the two molecules in excess of 4 m. u.c.−1 occurs over the temperature range of 298–323 K. If the initial equilibrium system is heated to 323 K the molecules in excess of 4 m. u.c.−1 will, thus, be removed.

Following this low temperature heating if the system is cooled to room temperature and then a second temperature programmed desorption is initiated but now using the reduced equilibrium pressure over the sorbent appropriate for a loading of 4 m. u.c.−1 The resulting TG and DTG profiles, presented in Fig. 11b, match exactly the profiles generated previously starting with the sorbent loaded only with 4 m. u.c.−1 This perfect match indicates that when the benzene molecules sorbed in excess of 4 m. u.c.−1 are removed, the remaining 4 m. u.c.−1 will be redistributed back to their preferred intersection sorption sites.

These thermogravimetric findings support the concept that the bimodal FR spectra at high loadings should be ascribed to two diffusion processes arising from the two states of the sorbed benzene molecules.

The additional high frequency peak at low temperatures and high loadings should be related to the diffusion process of the sorbed benzene molecules associated with the cluster state and the low frequency peak, which has a similar time constant to that for the single frequency peak at high temperatures and low loadings, should be associated with the diffusion of the sorbed molecules located in the intersection sites and not part of the clusters.

With increasing the loading, more molecules will be in the clustered state and fewer molecules will remain in the unclustered state.

This conclusion is supported by the FR spectra displayed in Fig. 9 where the intensity of the lower frequency peak decreases as loading increases.

It can also be seen from Fig. 9 that the formation of the clusters of the sorbed benzene molecules in silicalite-1 depends on temperature.

At the same loading, more molecules will be in the clustered state at lower temperature than those at higher temperature.

It is worth noting that the Darken equation may be invalid at such high loadings because of the complex nature of the adsorption isotherm.

Thus only transport diffusivities are presented in Table 2 instead of self-diffusivities at these loadings.

The diffusivities of benzene in silicalite-1 (A) and silicalite-1 (B) zeolite samples obtained from the FR measurements in this study are summarized in Table 2 and Figs. 7, 9, 12 and 13.

At low loadings or high temperatures, the diffusivities of benzene in both samples are similar with a single diffusion process being observed.

As is commonly observed in zeolite systems,70 the intracrystalline self-diffusion coefficients of benzene in silicalite-1, obtained by the use of Darken equation, decreases with increasing loading, while the transport diffusivities increase slightly as the loading increases for both samples.

At high loadings or low temperatures remarkable discrepancies in the diffusivities between these two samples can be observed, as shown in Figs. 9 and 13.

The FR bimodal behaviour can be obtained at loadings of just above 4 m. u.c.−1 for silicalite-1 (B) sample (cf. Fig. 9) while for silicalite-1 (A) sample, this bimodal phenomenon cannot be observed until loading higher than 8 m. u.c.−1 (cf. Fig. 13).

This FR bimodal behaviour for silicalite-1 (A) is not as distinct as that for silicalite-1 (B).

All these findings indicate that the heterogeneity of the channel networks and the formation of clusters of benzene sorbed in silicalite-1 (A) are decreased.

In addition, the diffusivities of benzene in the silicalite-1 (A) sample are higher than those in the silicalite(B) sample.

Apart from differences in morphology, the major difference between these two samples is the chemical or structural differences of the framework, as mentioned above.

The results deduced by 13C CP NMR spectra clearly showed an increase in the molecular mobility of the sorbed benzene in MFI zeolites with a high concentration of structural defects.71

Obviously, structural defects handicap the formation of clusters.

The increase in diffusivity of benzene in silicalite-1 with increase in loading was detected by Shah et al. using a gravimetric technique and large crystals.24

This technique is, however, not able to distinguish different kinetic processes occurring in the system and the explanation for this phenomenon offered by Shah et al. is not satisfying.

The present study demonstrates once again that the FR technique is a very powerful, more useful one for measuring the complicated processes occurring in some sorbate/sorbent systems.


Molecular simulations show that the intersections of the two channel networks of silicalite-1 are the energetically preferred adsorption sites for the sorbed benzene molecules.

After all, the intersections are fully occupied by benzene molecules, i.e. loading approaches 4 m. u.c.−1, further adsorption will cause a redistribution or rearrangement of the sorbed molecules with some molecules forming strongly sorbate–sorbate bonded chains.

Sorption isotherms of benzene in silicalite-1 show two interesting steps which occur at loadings of ca. 4 and 6 m. u.c.−1, respectively.

Such steps have been shown to occur after the first 4 m. u.c.−1 to be sorbed have filled the four, energetically preferred, channel intersection sites.

The steps are due to the subtle interplay of increased sorbate–sorbate interactions and decreases in the entropy of sorption when molecules, at loadings in excess of 4 m. u.c.−1, have to occupy sinusoidal and straight channel segment sites.

Such stepped isotherms could be classified as showing type VI isotherm behaviour.

The hysteresis loop found in the isotherm of this system results from the strong sorbate–sorbate interactions, the energetically heterogeneous surfaces of the sorbent framework and the close packing of the sorbed benzene molecules, which lead to packing differences of the sorbed molecules on adsorption and desorption branches of the isotherm.

The adsorption behaviour of this system is affected by the chemical nature of the silicalite-1 samples.

Structural defects can result in the disappearance of the steps in the isotherms.

One of the important features of the FR method is its ability to distinguish processes with different time constants which are simultaneously operating in the system.

This method is capable, therefore, of detecting the different diffusivities of different states of sorbed benzene molecules.

At loadings lower than 4 m. u.c.−1, the sorbed benzene molecules diffuse mainly down the straight channels, while at higher loadings, the sorbed benzene molecules which belong to a cluster diffuse faster than the unclustered sorbed molecules because of an entropic driving force for the molecules sorbed in clusters.

Temperature programme desorption studies and simulation calculations, using Accelrys software, have helped greatly to elucidate the underlying features controlling the diffusion of benzene molecules sorbed in the two types of channel networks present in silicalite-1.