Experimental and molecular simulation studies of adsorption and diffusion of cyclic hydrocarbons in silicalite-1

Microporous and Mesoporous Materials 55 (2002) 31–49 www.elsevier.com/locate/micromeso

Experimental and molecular simulation studies of adsorption and diffusion of cyclic hydrocarbons in silicalite-1 Lijuan Song a, Zhao-Lin Sun b, Lovat V.C. Rees a

a,*

Department of Chemistry, University of Edinburgh, Joseph Black Building, West Mains Road, Edinburgh EH9 3JJ, UK b Department of Applied Chemistry, Fushun Petroleum Institute, Fushun 113001, Liaoning, China Received 21 January 2002; received in revised form 23 April 2002; accepted 23 April 2002

Abstract The adsorption and diffusion of benzene, p-xylene, cyclohexane, cis- and trans-1,4-dimethylcyclohexane (c- and tDMCH) in silicalite-1 zeolite have been investigated using the frequency response (FR) experimental method and the simulation techniques such as the canonical ensemble Monte Carlo simulation, the force field minimisation and dynamics. It has been found by the FR measurements that two independent fluxes of p-xylene exist in the two channels of silicalite-1 respectively at low loadings and low temperatures, while at high temperatures, only one single, pure diffusion process is observed. The diffusivity of benzene is slower than that of p-xylene and the saturated hydrocarbons diffuse much more slowly than their aromatic equivalents. As found with benzene and p-xylene, t-DMCH has been found to diffuse much more rapidly than cyclohexane. The c-DMCH, on the other hand, diffuses extremely slowly. The theoretical calculations give rational interpretations to these interesting experimental results. Ó 2002 Elsevier Science Inc. All rights reserved. Keywords: Cyclic hydrocarbons; Adsorption; Diffusion; Silicalite-1; Simulation studies

1. Introduction With their unique framework structure and related properties [1,2], MFI type zeolites, ZSM-5 and its pure silica form silicalite-1, have become one of the most versatile and valuable zeolite types in modern petrochemical and hydrocarbon processing. The ‘molecular traffic control’ and shape selectivity features of the MFI zeolites have been very important in the processing of BTX (benzene, tol-

*

Corresponding author. Tel.: +44-131-650-4762/4766; fax: +44-131-650-4733/4766. E-mail address: [email protected] (L.V.C. Rees).

uene, xylene); e.g. toluene disproportionation, xylene isomerization, adsorptive separation of xylene isomers, benzene alkylation, etc. The adsorption and diffusion properties of these aromatics in MFI zeolites are very crucial for understanding the underlying mechanisms behind these processes. Over the past two decades various techniques have been used in the investigations of these systems [3–14]. However, a complete understanding of the anomalous adsorption and diffusion behaviour of these systems has still not been arrived at and contradicting conclusions have been reported mainly due to the complexity of these systems. It has been reported in the literature that at higher temperatures the isotherms of the aromatics

1387-1811/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII: S 1 3 8 7 - 1 8 1 1 ( 0 2 ) 0 0 3 9 4 - 3

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in silicalite-1 are Langmuirian with a maximum adsorption capacity of 4 molecules per unit cell (m./u.c.), but at lower temperatures the isotherms display increased capacities with a step or kink around
4 m./u.c. Additionally, p-xylene has been found to show a large, well-defined hysteresis loop in the sorption/desorption isotherms at loadings between 4 and 8 m./u.c. Our previous studies [7– 10] have demonstrated that this hysteresis loop depends critically on the length and specific features of the sorbate molecules. When the sorbate is p-dichlorobenzene (p-DCB), a rigid molecule with dimensions very similar to p-xylene, a well-defined hysteresis loop very similar to that found with pxylene is again observed. Various techniques (both microscopic and macroscopic) have been used to study the diffusivities of molecules in sorbents [15–20]. Of these, the frequency response (FR) technique has proved to be a very powerful method for determining the intracrystalline mass transfer of molecules through zeolite crystals. An outstanding advantage of the FR method is its ability to distinguish multikinetic processes in an FR spectrum, i.e. various ‘independent’ rate processes which occur simultaneously can be followed by this technique [16]. For example, in the measurement of the diffusivity of p-xylene in silicalite-1 the FR displays two ‘independent’ fluxes of p-xylene diffusing in the straight and sinusoidal channels of the zeolite and, similarly, in silicalite-2 in the two sets of straight channels at loadings <4 m./u.c. [7–10]. These findings are not consistent with the equilibrium spatial distribution results of p-xylene in silicalite-1 obtained from XRD [3,21], NMR [22,23] and computer simulation [10,22] methods which showed that p-xylene molecules are located at the intersections of the two channels of silicalite-1 at loadings 6 4 m./u.c. with their long molecular axis paralleling the straight channel direction and perpendicular to the crystallographic mirror plane. Also interestingly, the diffusion of benzene is much slower than that of p-xylene which has been attributed to the need for a much greater loss of entropy of the ‘freely’ rotating benzene molecule when it jumps from one intersection through a channel segment to the adjacent intersection. However, further evidence is needed to prove this conclusion.

To understand the role sorbate molecules play on the adsorption and diffusion behaviour in the sorbent, the diffusivities of cyclohexane, cis- and trans-1,4-dimethylcyclohexane (c- and t-DMCH) have, also, been studied [9,10]. These saturated hydrocarbons diffuse much more slowly than their aromatic equivalents. As found with benzene and p-xylene, t-DMCH has been found to diffuse much more rapidly than cyclohexane. The c-DMCH, on the other hand, diffused extremely slowly. In this study, the adsorption and diffusion behaviour of benzene, p-xylene, cyclohexane, c- and t-DMCH in silicalite-1 zeolite have been calculated using the canonical ensemble Monte Carlo simulation, and the force field minimisation and dynamics techniques supplied in the Cerius2 4.2 software package developed by Molecular Simulation Inc. (MSI) (now Accelrys). The sorption Demontis, Burchart–Dreiding and PCFF force fields were applied in the simulations. The results were compared with the diffusivities of the sorbed molecules measured by the FR technique. The purpose of this work is to understand the behaviour of the sorbed molecules in terms of the temperature dependence of their interactions with the zeolite channel framework and to interpret the anomalous adsorption and diffusion behaviour of the systems.

2. Experimental and simulation methods 2.1. The FR method In our FR method an equilibrium state is perturbed by applying a small, square-wave modulation to the volume of the gas phase. The theoretical solutions of the FR 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 UZB ¼ UZ  UB is obtained, where UZ and UB 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

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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 in-phase :

ðPB =PZ Þ cos UZB  1 ¼ Kdin þ S

ð1Þ

ðPB =PZ Þ sin UZB ¼ Kdout

ð2Þ

out-of-phase :

can be obtained [16]. 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, din and dout 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 decade [7,15,16,24,25]. The principal features of the FR apparatus developed in our group has been described previously [26]. An accurately known amount of zeolite sample is scattered in a plug of glass wool and outgassed at a pressure of <103 Pa and 623 K overnight by rotary and turbo molecular drag pumps. A dose of purified sorbate is, then, 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 0.001–10 Hz was scanned over some 30 increments. The frequency was controlled by an on-line computer, which was also used for the acquisition of the pressure data from the Baratron transducer. The conversion rate of the analogue-to-digital converter in the interface unit must be fast enough to cope with the 1–4 ms response time of the pressure transducer. The pressure response to the volume change over the whole frequency range

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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 squarewave forms. The silicalite-1 zeolite samples used in this study, silicalite-1 (A) and silicalite-1 (B), have been described previously [9,10]. These samples were calcined, initially, at 823 K for 10 h in an oven to remove the templating material. The crystals were heated from room temperature to 823 K at 2 K min1 . X-ray diffraction patterns and SEM micrographs showed that the samples were highly crystalline and of near spherical shape. The spherical shape arose from the intergrowths of the more common coffin shaped crystals. Benzene and cyclohexane were obtained from the National Physical Laboratory, UK; p-xylene was supplied by Aldrich Chemical Company, Inc.; c- and t-DMCH were produced in Fluka Chemie AG. All chemicals had a purity of 99þ%. 2.2. Simulation procedures The main objective of this study is to understand the behaviour of the sorbed aromatic molecules in terms of the temperature dependence of their binding and mobility in the MFI zeolite channels. In order to investigate the equilibrium configurations of the sorbed molecules inside the channel framework, the adsorption simulations of a single p-xylene or a single benzene in siliceous MFI zeolite 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. MSI’s Cerius2 4.2 software was used to carry out the simulations on a Silicon Graphics workstation. Initially, high energy configurations were rejected to save computational time during the simulations. These configurations are those in which the

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sorbate molecules and the framework are very close together; i.e. the distance between the atoms of the sorbate and the framework is less than half their van der Waals radii. The van der Waals energies between the sorbate and the framework were calculated by summing all pair interactions within a specific volume, in which the radius is determined by a cut-off distance. The van der Waals energy term within the zeolite framework is restricted to the minimum image convention, in which an atom is considered to interact with its closest neighbour atoms in a periodic box around it. In the case of sorbate–sorbate energy, the interactions are not limited to the atoms within the minimum image border but to the molecules whose centres of mass are within it. Both the aromatic molecules and the zeolite framework were treated as rigid units. The effect of framework flexibility on the diffusivity has been observed. This effect, however, does not alter the equilibrium configurations calculated for the sorbed molecules in the system [27–30]. The only permitted degrees of freedom are the three translational and three rotational variables associated with the sorbate molecule. The 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 has an ortho, rhombic Pnma space group with a ¼ 20:022 A , c ¼ 13:383 A  containing 96 silicon b ¼ 19:899 A and 192 oxygen atoms. The simulation box was defined as two crystallographic unit cells to which periodic boundary conditions were 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 fifty percent acceptance probability. The interaction , which is cut-off distance was fixed at 9.9 A 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, which should exhibit a small fluctuation around a central value after sufficiently long runs.

The sorption Demontis [31], Burchart–Dreiding [32,33] and PCFF [34] Force Fields were applied in the simulations, respectively. For the sorption Demontis force field, the sorbate–sorbate interactions are described using Buckingham potentials. Partial charges are applied to the hydrogen and carbon atoms of the aromatic molecules to calculate the electrostatic interactions. The sorbate–zeolite interactions take into account the short-range atom–atom interactions between the aromatic compound and the oxygen atoms of the zeolite. The short-range interactions with the silicon atoms are neglected because they are well shielded by the oxygen atoms of the SiO4 framework tetrahedra. The Burchart–Dreiding force field combines the Burchart force field which prescribes the host framework and the Dreiding II force field which treats the guest molecule. The parameters for the framework–molecule interactions are derived from the parameters of both force fields combined by the arithmetic combination rule. The van der Waals interactions in the Burchart force field are expressed by an exponential-6 term and the electrostatic interactions by partial atomic charges and a screened Coulombic term. In the Drieding II force field, the LennardJones potential is applied to describe the van der Waals interactions and the electrostatic interactions are described by atomic monopoles and a screened Coulombic term. PCFF was developed based on CFF91 with parameterisation including the functional groups of zeolites. The van der Waals interactions in this force field were calculated using an inverse 9th-power term for the repulsive part rather than the more conventional Lennard-Jones model. In order to understand the significant influence of the sorbate molecules on the diffusivity in silicalite-1, the energy minimisation and molecular dynamics methods supplied in the Cerius2 4.2 software were applied to calculate the minimum energies of benzene, p-xylene, cyclohexane, c- and t-DMCH down the straight channels of silicalite-1 by using the Burchart–Dreiding force field. The initial position of these sorbate 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

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the sorption calculations described above. Again, the purpose of the simulations is to study the interaction energies between sorbate and sorbent down the diffusion pathway rather than the diffusion coefficient. During the simulations, the framework is, therefore, assumed to be fixed, whereas all the atoms of the sorbate molecules are flexible. The sorbate molecule is forced to diffuse stepwise . At along the straight channel axis at steps of 0.2 A 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 reminimised after each dynamic run. The minimum energies at each step were recorded to reflect on different orientations and the internal degrees of freedom of the sorbate molecules inside the channels. The periodic boundary conditions were also applied for these simulations.

3. Results and discussion As mentioned above, it has been reported that p-xylene molecules are located at the intersections of silicalite-1 at adsorption equilibrium at loadings 6 4 m./u.c. with their long molecular axis paralleling the straight channel direction. This conclusion implies that only one diffusion process along the straight channel direction should be observed in the FR spectrum for the system because the long and rigid p-xylene molecule (
0.9 nm) should have great difficulty rotating around the axis perpendicular to the plane of the aromatic ring in the intersections. However, the FR studies [7–10] suggested that two ‘independent’ fluxes of p-xylene existed. These fluxes represented the diffusions down the straight and the sinusoidal channel directions, respectively, at loadings <4 m./u.c.. The argument that the lower frequency kinetic process should be attributed to the rate of dissipation of the heat of adsorption has been shown to be very unlikely [8,9,24]. To try to resolve these conflicting results, the FR studies of p-xylene in both silicalite-1 (A) and (B) samples have been extended to temperatures up to 533 K and over a range of equilibrium pressures. Some typical FR spectra of such mea-

Fig. 1. FR spectra of p-xylene in silicalite-1 (A). Lines are the fits from theoretical models (dash and dash-dot lines denote the theoretical characteristic function curves down the sinusoidal and the straight channels, respectively) and the symbols (, ) present experimental in-phase and out-of-phase characteristic function data, respectively.

surements are presented in Figs. 1 and 2. The packing patterns of p-xylene in silicalite-1 at different loadings have been performed using the Solid-Docking package in Insight II software developed by MSI [10]. These calculations were carried out at absolute zero. In order to obtain the equilibrium adsorption configurations of p-xylene in silicalite-1 at higher temperatures the procedures described in Section 2.2, which take the temperature dependence of the sorbate/sorbent interactions in the framework channels into account, have been performed. Figs. 3–6 demonstrate the mass distribution and the sorption trajectory energy profiles of p-xylene in silicalite-1 with the initial coordinates of the sorbate molecule in a sinusoidal channel segment and a straight channel segment, respectively, using the sorption Demontis force field.

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Fig. 2. FR spectra of p-xylene in silicalite-1 (B). The notations are the same as in Fig. 1.

Fig. 3. Simulation results for the mass distribution of p-xylene adsorbed initially in a sinusoidal channel segment of silicalite-1 at different temperatures. Dots indicate the centre of mass of p-xylene and the molecules demonstrate the configurations at the adsorption equilibrium state.

It can be seen from Figs. 3 and 4 that the orientation of the long molecular axis of the sorbed

p-xylene molecule inside the silicalite-1 framework channels at adsorption equilibrium tends to

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Fig. 4. Simulation results for the mass distribution of p-xylene adsorbed initially in a straight channel segment of silicalite-1 at different temperatures. Dots indicate the centre of mass of p-xylene and the molecules demonstrate the configurations at the adsorption equilibrium state.

remain unchanged at lower temperatures. At higher temperatures, however, the molecule sorbed initially in a sinusoidal channel segment reorientates at an intersection of the two channels to become lined-up in the straight channel direction. The snapshot pictures (not shown) support this conclusion explicitly. The sorption trajectory energy profiles as presented in Figs. 5 and 6 indicate that the repulsion components of the sorption energies of p-xylene inside the sinusoidal channel segment are much higher than those in the intersections between the sinusoidal channel segments and also higher than the corresponding energies in the straight channel segments and their intersections. If the molecule was firstly sorbed into a sinusoidal channel segment, the molecule will

move to a lower energy site, i.e. an intersection, when adsorption equilibrium is reached as shown in Fig. 3. The difference in the sorption energies of p-xylene in the intersections with orientations of the long molecular axis either down the straight channel direction or down the sinusoidal channel direction is very small as shown in Figs. 5 and 6. These results imply that, when adsorption equilibrium is reached, the adsorbed p-xylene molecules will occupy the intersections of the two channels at lower loadings (<4 m./u.c.) and low temperatures with the orientation of the long molecular axis along either the sinusoidal channel direction or the straight channel direction. These arguments strongly support the FR experimental results that two independent diffusion processes

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Fig. 5. Sorption trajectory energy profiles of p-xylene in silicalite-1 with the initial coordinates of the sorbate molecule in a sinusoidal channel segment.

Fig. 6. Sorption trajectory energy profiles of p-xylene in silicalite-1 with the initial coordinates of the sorbate molecule in a straight channel segment.

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of p-xylene down the straight and the sinusoidal channel directions, respectively, can be detected at temperatures lower than 448 K as shown in Figs. 1(a), (b) and 2(a), as well as our previous studies [7–10]. It has been well documented that it is difficult for even flexible, long linear hydrocarbon molecules to lose their conformational ‘memory’ quickly inside the host framework channels [35– 37], suggesting that molecules aligned along a particular channel will tend to move along that channel at lower loadings. The FR measurements of p-xylene in silicalite-1 (A) were also carried out at different pressures at 398 K. The ratio of the intensity of the lower frequency peak, K2 , (i.e. diffusion down the sinusoidal channels) to the intensity of the higher frequency peak, K1 , (i.e. diffusion down the straight channels) decreases slightly, justifying further that the bimodal FR out-of-phase curve of p-xylene in silicalite1 can be ascribed to the two diffusion processes down the two channels rather than the adsorption heat effect which should result in an increase of the ratio of K2 /K1 as the pressure increases [15]. At temperatures higher than 473 K, the sorption mass distributions (cf. Figs. 3 and 4) and the snapshot pictures (not shown) show that, at adsorption equilibrium, the sorbed p-xylene molecules occupy the intersection sorption sites and orient themselves with their long axis down the straight channel direction regardless of whether the molecules were sorbed initially in a straight channel or a sinusoidal channel segment. This result implies that the thermal energies of the sorbed p-xylene molecules are high enough to overcome the energy barrier (
40 kJ/mol), which can be seen in the energy profiles (cf. Fig. 5(c) and (d)), for a pxylene molecule to rotate from the sinusoidal channel direction to the straight channel direction in an intersection. The NMR deuterium spectra of p-xylene-d10 sorbed in ZSM-5 [38] show that the sorbed p-xylene molecule is not reorienting about the long axis at 198 K, while at 373 K a relatively unhindered wobble or nutation of the long axis can be detected. These findings imply that at higher temperatures it is possible for the long axis of p-xylene to reorient in the intersections of sili-

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calite-1 channels as obtained from our simulation calculations. The FR spectra of p-xylene in both silicalite-1 (A) and silicalite-1 (B) displayed in Figs. 1 and 2 show that the slow diffusion process down the sinusoidal channel direction is not observed at 448 K. A perfect single, pure diffusion FR spectrum is always found at higher temperatures for both of these samples. These results could be ascribed to the argument, as observed from the simulation calculations, that the p-xylene molecules sorbed, from the external surface of the crystals, into the sinusoidal channels will reorient their long axis from the sinusoidal channel direction to the straight channel direction at intersections as they diffuse down the sinusoidal channels. The higher the temperature is, the easier this rotation becomes. On the other hand, a p-xylene sorbed in a straight channel, because of the non-spherical shape of the intersection, finds it much more difficult to rotate and reorientate its long axis along the sinusoidal channel direction. Thus, at higher temperatures only diffusion down the straight channels is observed. In summary, sorbed p-xylene molecules diffuse along the straight and the sinusoidal channel directions as two single-file diffusion processes at low temperatures and low loadings. At high temperatures, the long axis of pxylene molecules can rotate at the intersections from the sinusoidal channel direction to the preferred straight channel direction, resulting in diffusion down the straight channel direction dominating the system. It should be noted that the surface resistance, which depends very much on the size of zeolite crystals, as observed in our previous single-file diffusion studies [39,40] becomes too insignificant to be measured with pxylene because of the small crystals used in the present work. The activation energy (21  2 kJ/mol) for diffusion derived from the FR spectra in Fig. 1(c)–(f) is quite similar to that (19  2 kJ/mol) obtained from the diffusivities of the sorbed p-xylene molecules in the straight channel direction at lower temperatures when two ‘independent’ fluxes of p-xylene were observed in the FR spectra [7–10]. This finding supports further the above arguments.

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Table 1 Average adsorption energy DE and isosteric heat of adsorption DH of p-xylene and benzene in silicalite-1 obtained from the canonical ensemble Monte Carlo adsorption simulations by using the sorption Demontis, Burchart–Dreiding and PCFF force fields at temperature of 673 K Sorbate p-Xylene Benzene

Demontis

Burchart–Dreiding

PCFF

DE (kJ/mol)

DH (kJ/mol)

DE (kJ/mol)

DH (kJ/mol)

DE (kJ/mol)

DH (kJ/mol)

)98.2 )70.4

104.1 76.1

)71.1 )58.5

76.8 65.6

)63.5 –

69.1 –

Similar simulation results were obtained when the other two different force fields were used, i.e. the Burchart–Dreiding and the PCFF, although the sorption energy values listed in Table 1 are different from those derived from the sorption Demontis force field. It can be seen that the heat of adsorption calculated by applying the Burchart– Dreiding force field is more consistent with the experimental results [12] than the other two force fields. The sorption Demontis force field gives a higher heat of adsorption, whereas the PCFF produces a lower heat of adsorption. From the sorption trajectory energy profiles, one can also conclude that the energy barrier for the sorbed p-

xylene molecule jumping from one intersection to another through a straight channel segment is much smaller than that for the molecule jumping between adjacent intersections via a sinusoidal channel segment. Once again this is consistent with the FR experimental results where the activation energy (19  2 kJ/mol) in the straight channel direction is much smaller than that (35  4 kJ/mol) down the sinusoidal channel direction [7]. The FR diffusivity measurements show that only a single, pure diffusion process can be observed for the benzene/silicalite-1 system at loadings <4 m./u.c. and that the diffusivity of the smaller benzene molecule is slower than that of the

Fig. 7. FR spectra of benzene in (a) silicalite-1 (B) and (b) silicalite-1 (A) at a pressure of 133.3 Pa. Lines are the fits of theoretical models and the symbols (, ) present experimental in-phase and out-of-phase characteristic function data, respectively.

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Table 2 Diffusion coefficients of the cyclic hydrocarbons along the straight channel direction, D01 , and the sinusoidal channel direction, D02 , of silicalite-1 measured by the FR method Sorbate

T (K)

n (m./u.c.)

D01 1013 (m2 s1 )

D02 1013 (m2 s1 )

Benzene p-Xylene Cyclohexane c-DMCH t-DMCH

435 373 423 398 398 448

1.1 3.9 – – – –

1.24 160 0.06 <0.01 0.55 2.9

– 15 – – – –

larger p-xylene molecule as presented in Fig. 7 and Table 2. The sorption simulation results of the system presented in Fig. 8 can be used to give a reasonable explanation of these experimental results. It can be seen from Fig. 8 that the intersections are the energetically preferred adsorption sites for the sorbed benzene molecules at low loadings. Unlike the sorbed p-xylene molecules, the sorbed benzene molecule at equilibrium does not orient itself along a specific direction but resides at the intersection, still rotating even at temperatures as low as 173 K. These configurations of the sorbed benzene molecule can be readily seen from the snapshot pictures of the sorption simulations, indicating that benzene molecules can easily rotate in the intersections as confirmed from XRD and NMR experimental data [11,23]. The simulation results also indicate that the single diffusion process detected by the FR method is the average diffusivity of benzene molecules diffusing along both the straight and the sinusoidal channels of the silicalite-1 framework. The slower diffusivity of benzene compared with that of p-xylene can then be ascribed to the high orientational disorder of the benzene molecules in the intersection sites which restrain the molecules in these sites from easily moving into the channels segments. There is a need for a much greater loss of entropy of the freely rotating benzene molecule in an intersection when it jumps from one intersection to another through a channel segment. These results are in agreement with the Bluemoon simulations of benzene in silicalite-1 [29]. The influence of subtle differences in molecular shape and size on the diffusivities of the sorbate molecules in silicalite-1 can be clearly demonstrated in Fig. 9 and Table 2 which present the

diffusivities of cyclohexane, c- and t-DMCH and their aromatic equivalents, benzene and p-xylene, in silicalite-1 measured by the FR technique. For comparison, a FR spectrum of p-DCB, a long and rigid molecule similar to p-xylene, is also presented in Fig. 9. It can be seen that the saturated hydrocarbons diffuse much more slowly than the aromatics, while t-DMCH has been found to diffuse much more rapidly than cyclohexane. These findings are in agreement with the results obtained from the simultaneous thermal analyzer and the zero length chromatography techniques [41]. The energy minimisation calculations described in Section 2.2 were performed on these systems to try to understand this interesting diffusion behaviour at the molecular level. From the calculations, spatial configurations of the sorbed molecules inside both the straight channel segments and the intersections as well as related potential energies are obtained. Some of these configurations are presented in Figs. 10–12, and the average potential energies of the sorbed molecules in the channel segment and the intersection sorption sites are listed in Table 3. The results show that it is difficult for the long, rigid p-xylene to reorient its long axis when it diffuses along the straight channel direction and the change in the configurations of the molecule is insignificant (only the rotation of p-xylene around the long axis is found). For the smaller and rigid benzene, however, several different configurations inside the channel segment are found as shown in Fig. 10, indicating that the sorbed benzene still has some freedom of rotation around the C6 axis even within the channel segment. The difference in the potential energies between these configurations is noticeable. In the intersection, consistent with the above adsorption simulation results no specific

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Fig. 8. Snapshots and the mass distribution of benzene adsorbed in a intersection of silicalite-1 at 173 K (a–c), and the mass distributions of the benzene adsorbed initially in a sinusoidal channel segment (d) and a straight channel segment (e) of silicalite-1 at 673 K. The molecules demonstrate the configurations at the adsorption equilibrium state.

orientation of the sorbed benzene is found. This is again in accordance with the conclusion derived from experiments [11,23,38] that the sorbed benzene molecules can undergo a reorientation of the C6 axis as well as the rapid rotation about the

C6 axis. The difference in the potential energies between benzene molecules with different orientations in the intersection is minor. The potential energy barriers of benzene and p-xylene diffusing down the straight channels of silicalite-1

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Fig. 9. FR spectra of the cyclic hydrocarbons and p-DCB in silicalite-1 (B). The notations are the same as in Fig. 1.

induced from the calculations are in excellent agreement with the activation energies obtained from the experimental measurements as shown in Table 3. These calculations justify further that the slower diffusivity of benzene compared with pxylene arises from the combination of the entropic effect as discussed above and the somewhat higher activation energy of benzene than that of pxylene. Compared with the aromatics, the repulsions between the equivalent saturated cyclic hydrocarbons and the silicalite-1 framework are much higher as presented in Table 3, suggesting that molecular dimension and flexibility are crucial factors to the sorbent/sorbate interactions when the size of the sorbate molecule is comparable with the

pore size of the framework. These high repulsions give a reasonable explanation to the much slower diffusivities of the saturated cyclic hydrocarbons in silicalite-1 than those for the equivalent aromatics detected by the FR measurements. It is rational to envisage that the three-dimensional saturated cyclic hydrocarbons should find access to the nearly circular straight channels (0:54 0:56 nm) easier than to the elliptic sinusoidal channels (0:51 0:55 nm) of silicalite-1. Much higher repulsions between the molecules and the walls of the sinusoidal channels should be expected. A calculation for cyclohexane diffusing down a sinusoidal channel segment of silicalite-1 has been made. The repulsion energy is found to be as much as two times larger than that for the straight

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Fig. 10. Minimisation simulation results for the configurations and related potential energies of benzene (a–c) and p-xylene (d,e) in a straight channel segment (a–c,d) and an intersection (e) of silicalite-1.

channel segment. These repulsions should be even greater for the larger dimethylcyclohexanes, indicating that these saturated hydrocarbons will be adsorbed into the sinusoidal channels only with great difficulty. The molecules are preferentially

adsorbed into the straight channels and located at energetically preferred intersection sorption sites when adsorption equilibrium is attained. This is in agreement with the measured maximum adsorption capacity of 4 m./u.c. for these molecules

L. Song et al. / Microporous and Mesoporous Materials 55 (2002) 31–49

45

Fig. 11. Minimisation simulation results for the configurations and related potential energies of cyclohexane (a–d) and t-DMCH (e,f) in a straight channel segment (a,b,f) and an intersection (c,d,e) of silicalite-1. The cyclohexane molecules in (a) and (c) are in chair conformation and those in (b) and (d) are in boat conformation.

in silicalite-1 [9,10]. However, the flat aromatics, benzene and p-xylene, should find it much easier to be sorbed in the sinusoidal channel segments than the corresponding three-dimensional satu-

rated hydrocarbons. A higher maximum adsorption capacity of 8 m./u.c. is, therefore, obtained for the aromatics/silicalite-1 systems. In addition, the sorbate–sorbate interactions between the sorbed

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L. Song et al. / Microporous and Mesoporous Materials 55 (2002) 31–49

Fig. 12. Minimisation simulation results for the configurations and related potential energies of c-DMCH in a straight channel segment (a,b) and an intersection (c–f) of silicalite-1.

aromatic molecules are much stronger than those between the saturated hydrocarbons, which also play an important role in the high adsorption capacities found for the aromatics.

In the light of these simulation calculations, one can conclude that, like benzene, cyclohexane can rotate in the intersections of silicalite-1. In addition, due to the high internal degrees of freedom of

L. Song et al. / Microporous and Mesoporous Materials 55 (2002) 31–49

47

Table 3 Experimental activation energies, Ea , and the average potential energies of the cyclic hydrocarbons in the straight channel segment, Es , and the intersection, Ei , of silicalite-1 Sorbate

Es (kJ/mol)

Ei (kJ/mol)

DE (kJ/mol)

Ea (kJ/mol)

p-Xylene Benzene Boat cyclohexane Chair cyclohexane c-DMCH t-DMCHg

)58.5 )34.4 53.9 32.4 75.2 35.5

)78.5 )64.0 )8.8 )14.6 )37.6 )11.7

20.0 29.6 62.7 47.0 112.8 47.2

19.0 28.8 – 48.1 56.0 38.9

the molecule, different conformations of the molecule and the alternation between chair and boat conformations are found in the intersections even though the probability of this alternation is very low. In the straight channel segment these motions of cyclohexane are highly restrained because of the very tight fit of the molecule. No conversion between chair and boat conformations is found when the molecule diffuses inside the straight channel segment. It can be, therefore, concluded that entropic effects play a significant role in the slower diffusivity of cyclohexane compared with tDMCH, i.e. there is an entropy loss associated with the loss of rotation of freedom for the cyclohexane molecule in an intersection when it jumps from one intersection to another through a straight channel segment. It can be seen from Fig. 11 that the sorbed t-DMCH molecule spans an intersection of silicalite-1 with the two methyl groups entering into the adjacent straight channel segments. This configuration reduces very much the ability of the molecule to change its orientation and/or to maximise its interactions with the framework. The sorbed molecule will then jump between the adjacent intersections directly through the straight channel segments without a need for a large loss of entropy of the molecule which leads to a higher diffusivity for this molecule than that for cyclohexane. The energy barrier of cyclohexane diffusing down the straight channel direction of silicalite-1 with a chair conformation inside the channel segment, as shown in Fig. 11(a), is similar to that for the sorbed t-DMCH as listed in Table 3. The repulsions between the sorbed cyclohexane with a boat conformation, as presented in Fig. 11(b), and the wall of the straight channel segment are higher than those for the former case, resulting

[7] [9] [41] [41] [41]

in a higher energy barrier for the cyclohexane molecule in boat conformation to jump between the intersections. The diffusivity measured experimentally should be mainly the diffusivity of cyclohexane in chair conformation in the straight channels of silicalite-1 because the chair form is much favoured over the boat form. These energy values show that the much faster diffusivity of tDMCH in silicalite-1 than that of cyclohexane arises mainly from the entropic effect on the diffusion process of cyclohexane. Because of the very high flexibility and the asymmetric structure of the c-DMCH molecule, the diffusion behaviour of this molecule is quite different from that of the other two saturated cyclic hydrocarbons mentioned above even though the measured maximum adsorption capacities are the same. The attractions between this molecule and the framework of silicalite-1 in the intersection are higher than those of the other two hydrocarbons because c-DMCH has a high ability to maximise its interactions with the framework walls in the intersections as presented in Fig. 12. In the channel segments, on the other hand, the repulsions are much higher because of the very gauche conformation of c-DMCH. The energy barrier for the sorbed c-DMCH diffusing down the straight channels is then much higher than those for the other two molecules as listed in Table 3, which will then slow down the diffusivity of c-DMCH pronouncedly. In addition, the sorbed c-DMCH has much higher degrees of reorientation freedom in an intersection compared with t-DMCH which can be easily seen from Fig. 12(c)–(f). One can envisage that there will be a great difficulty for a c-DMCH molecule in a configuration shown in Fig. 12(d) to move into the next straight channel segment. The

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L. Song et al. / Microporous and Mesoporous Materials 55 (2002) 31–49

molecule has, therefore, to change its orientation in the intersection until one of the methyl groups enters the straight channel segment which will then lead the whole molecule jumping into the adjacent intersection via the channel segment. Again, a large entropy loss is involved in this diffusion process. The combination of this entropic effect and the very high energy barrier results in the extremely slow diffusivity of c-DMCH in silicalite-1 as observed by using the FR method.

for the equivalent aromatics/silicalite-1 systems, which reduce the diffusivities of the former systems significantly. The entropic effect is also a major reason for the much slower diffusivity of cyclohexane than that of t-DMCH. The extremely slow diffusivity of the sorbed c-DMCH can be attributed to the combination of this entropic effect and the very high energy barrier between the intersection and the channel segment which hinder the molecule from jumping from one intersection via a channel segment into another intersection.

4. Conclusions Acknowledgements The two independent fluxes of p-xylene detected by the FR technique at low temperatures arise from the movement of the sorbed p-xylene molecules down the straight channel and the sinusoidal channel directions, respectively. At adsorption equilibrium the sorbed p-xylene molecules are located at the intersections of the two channels of silicalite-1 with their long molecular axis aligned either along the straight channel direction or along the sinusoidal channel direction. As the temperature increases above 448 K, the molecules gain thermal energies which are high enough to reorient those molecules aligned along the sinusoidal channel direction to the straight channel direction at the intersections so that at high temperatures molecules diffuse to a large extent only along the straight channel direction. The one diffusion process measured by the FR method at higher temperatures is thus associated with this movement. The slower diffusivity of benzene in silicalite-1 compared with p-xylene can be ascribed to the need for a greater loss of entropy of the ‘freely’ rotating benzene molecule located at the intersections when it jumps from one intersection through a channel segment to the adjacent intersection. The influence of subtle differences in molecular shape and size on the diffusivities of the sorbate molecules in silicalite-1 is crucial. Unlike the equivalent aromatic molecules, the slightly larger saturated cyclic hydrocarbons can only be adsorbed in the straight channels and diffuse only along that direction. The repulsions between these molecules and the framework atoms of the channel segments of silicalite-1 are much higher than those

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