Hexane Isomers in Faujasite: Anomalous Diffusion and Kinetic

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Hexane Isomers in Faujasite : Anomalous Diffusion and Kinetic Separation Angela Mary Thomas, and Yashonath Subramanian J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04795 • Publication Date (Web): 15 Jun 2017 Downloaded from http://pubs.acs.org on June 21, 2017

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The Journal of Physical Chemistry

Hexane Isomers in Faujasite : Anomalous Diffusion and Kinetic Separation Angela Mary Thomas and Yashonath Subramanian∗ Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012,India E-mail: [email protected]

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Abstract Adsorption and diffusion properties of the five hexane isomers in zeolite Y have been obtained from molecular dynamic simulations. The self-diffusivities (Ds ) of the isomers exhibit an anomalous dependence on their molecular diameter where larger diameter doubly branched isomer, 2,2-dimethyl butane, shows the maximum Ds among all isomers. This anomalous dependence of Ds as well as the computed activation energies Ea are in excellent agreement with the predictions of Levitation Effect (LE). These findings also explain the trends in Ea of hexane isomers in zeolite BEA which was observed by Bárcia et al. in their experimental study. The order of exit of different isomers from a zeolite Y column depends on the order of their Ds at different temperature range. n-hexane shows a tendency to bend by increasing its gauche conformer population in order to reduce the energetic barrier it experiences at the 12-ring window of the zeolite Y cage.

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Introduction Porous solids like zeolites, metal-organic frameworks (MOFs) and zeolitic imidazolinium frameworks (ZIFs) are extensively used for separation of hydrocarbons in several petrochemical industries. 1,2 Investigations into properties of hydrocarbons that are adsorbed in these materials show many interesting effects such as the window effect, single file diffusion, Levitation effect, enhancement of viscosity, etc. 3–7 Diffusion and sorption properties of many hydrocarbon mixtures in zeolites have been widely studied to understand the effect of this confinement. 8,9 Study of dibranched hexane isomers as well as separation of such branched hexane isomers from their linear counterpart, n-hexane (nC6) using zeolites is of great interest due to high research octane number (RON) of the branched isomers. Haag et al. used gas chromatography to compare the diffusivities of linear nC6, a single branched isomer such as 3-methyl pentane (3MP) and a double branched isomer such as 2,2-dimethyl butane (22DMB) in medium pore zeolite ZSM-5 and found that the branched isomers show lower diffusivities than nC6. 10 This observation has been verified by Gump and coworkers using nC6/22DMB mixture in ZSM-5 membranes and also by Schuring et al. using nC6/2-methyl pentane (2MP) mixture in zeolite silicalite. 11,12 Gump et al. also found that the permeation of 22DMB is reduced significantly when nC6 is present in large amounts but the presence of 22DMB in higher concentration does not affect the permeation of nC6. The results of these experiments are in agreement with the molecular simulations of Krishna and coworkers. 13–15 They attributed this exclusion of the branched isomers by the medium pore zeolite to the configurational entropy or packing efficiency effects and have observed that the linear molecules prefer the zeolite channel and the branched isomers prefer channel intersections. 13,14 After examining a number of zeolites, they found that MFI zeolites have high selectivity in favour of nC6. 15 Several studies on these systems have also been reported which attempt to understand the dependence of this separation on various parameters like aluminium content in zeolites, the shape selectivity of nC6 and surface modification of zeolites. 16–19 The adsorption and diffusion properties of hydrocarbons in large pore-zeolites have not been investigated in great detail. Huddersman and Klimczyk have compared the diffusivi3



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ties of 3MP and 2,3-dimethyl butane (23DMB) in large pore zeolites BEA and MOR using gas chromatography and found that the doubly branched counterpart showed maximum diffusivity at very high temperatures of around 600 K. 20 Bárcia et al. found that the activation energies for diffusion for branched isomers were lower than that of the linear molecule. 21 Quasi elastic neutron scattering (QENS) and molecular dynamics studies on pentane isomers by Borah et al. found that the linear n-pentane had lower diffusivity than the branched isomers (isopentane and neopentane) in zeolite NaY in the temperature range of 150 K- 300 K. 22 Such a behaviour has been predicted earlier by MD simulations. 23 The NMR studies on this system showed a higher diffusivity for the linear isomer which has been attributed to the millisecond time scale over which diffusivity is measured by NMR as compared to QENS and MD. Larger time scale leads to lower diffusivity which arises from defects the in zeolite crystals. 24 The present study employs molecular dynamic simulations to investigate the properties of hexane isomers in the large pore zeolite, namely, zeolite Y. Methods section presents intermolecular potential model employed in the simulation as well as the computational details. The next section presents both structural and dynamic properties of the guests in the system. The structural properties include the guest-guest radial distribution function as well as the distribution of the guest molecules inside the α-cage of zeolite. The dynamic properties computed includes the diffusion behaviour, rates of cage to cage migrations, the energetic barriers at the window, and the reorientational motion of the isomers. Subsequent subsections discuss kinetic separation of the isomer mixtures and its strong dependence on temperature. The variation of the end to end length of nC6 as a function of both temperature and, more interestingly, during its passage through the bottleneck 12-ring window is also discussed.

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Methods Interaction Potential for Zeolite NaY Zeolite NaY crystallises in the cubic space group Fd¯3m with cell dimension a = 24.8536 ˚ A. The composition of the zeolite is Na48 Si144 Al48 O384 . There are eight super-cages (α-cages), of approximate diameter ∼ 12.0 ˚ A each, in one unit cell of the zeolite. These cages are tetrahedrally connected through twelve oxygen atoms forming a 12-ring window of approximate free diameter ∼ 7.5 ˚ A. Sodium ions occupy the SI, SI′ and SII sites in the zeolite. 25 Interaction potential proposed by Demontis et al. is modified for the host zeolite. 26 The potential has a Si-O harmonic bond stretching term and an O-(Si)-O harmonic stretching term between the non-bonded O atoms connected to same Si/Al which is modified into a quartic bond angle potential for O-Si-O bond angle by Borah et al.. 22 Na ions are kept frozen in this potential. We term this potential as Potential A. Thus, potential A is given by,

Uzeo =

X X

harm USi−O (rij ) +

i∈nSi j∈nO

X X X

quar UO−Si−O (θijk )

(1)

i∈nO j∈nSi k∈nO

rij is the bond distance between ith Si and j th O and θijk is the bond distance between ith O and j th Si and k th O at each timestep. Two additional potentials, Potential B and Potential C are considered for zeolite Y to study the effect of mobile Na ions and Al atoms on the diffusion of nC6 in zeolite Y. Potential B includes mobile Na ions which interact with nearby oxygen atoms with a Na-O bond potential. It also distinguishes Al atoms from Si atom by having a different potential for Al-O interaction. Potential C considers mobile Na ions with Na-O bond potentials but Al is indistinguishable from Si atoms. The differences in parameters in potentials are given in Table S2 in SI. Complete details of the potential are given in SI.

Interaction Potential for Hexane Isomers There are five isomers of hexane : n-hexane (nC6), 2-methyl pentane (2MP), 3-methyl pentane(3MP), 2,3-dimethyl butane (23DMB) and 2,2-dimethyl butane (22DMB) (Figure

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1). All these isomers are modelled using united atom approach where each of the groups CH3 , CH2 , CH and C is represented by a single interaction site. Thus each isomer is defined by six sites. The C-C bond lengths for all the isomers are constrained to an equilibrium bond distance of 1.53 ˚ A (Figure 1). The C-C-C bond angle potentials, C-C-C-C dihedral angle potentials and non bonded intramolecular potentials for the isomers are given by,

Uhex =

X X X

hcos UC−C−C (θijk )+

X X X X

OP LS (φijkl )+ UC−C−C−C

i∈nC j∈nC k∈nC l∈nC

i∈nC j∈nC k∈nC

X

X

12−6 UC−C (rij )

i∈nC j=i+4,∈nC

(2)

where θijk is the Ci − Cj − Ck bond angle, φijkl is the Ci − Cj − Ck − Cl dihedral angle and rij is the Ci − Cj distance beyond the fourth atom at each timestep. The details of all the intramolecular interactions are given in SI.

Intermolecular Interaction Potential between the Hexane Isomers and Zeolite All intermolecular non-bonded interactions among hexane-hexane and hexane-zeolite atoms are given by Lennard Jones (LJ) potential,

U

LJ

σ 12 σ 6 (r) = 4ǫ 12 − 6 r r ·

¸

(3)

where σ is the LJ interaction diameter, ǫ is the well depth of the LJ potential and r is the distance between the particles. More details of the interaction are given in SI. 27,28

Simulation Details Simulation cell is made up of 2 × 2 × 2 unit cells of zeolite NaY with edge length L = 49.7072 ˚ A of the cube. Isomers are placed uniformly at the centre of each α-cage at a concentration of one molecule/cage. Thus there are a total of 64 molecules of hexane in the simulation

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cell (Figure 2). Cubic periodic boundary conditions are imposed in all three directions. Simulations are performed both with frozen and mobile Na ions. Simulations are performed in the NVE ensemble and integration is carried out with velocity Verlet algorithm. The integration timestep is 1 fs and the energy conservation is good (better than 1 in 10−5 ) . A spherical cutoff of 15 ˚ A has been employed for non-bonded interactions. Simulations are carried out at five different temperatures : 250 K, 300 K, 330 K, 350 K and 400 K. The length of equilibration is 500 ps and the production run is 20 ns long for all the runs. Positions, velocities and forces are accumulated every 5 fs for first 2 ns run and then every 1 ps for the rest of the simulation. All simulations were performed using DLPOLY package. 29

Results and Discussion Structure Radial Distribution Function Centre of mass (c.o.m) - c.o.m radial distribution function (RDF), g(r), between the guest molecules of all the five isomers at 250 K is shown in Figure 3. The RDF for nC6 has its first g(r) peak at 5.0 ˚ A, whereas RDFs for others show a maximum between 5.4 ˚ A (2MP) and 6.1 ˚ A (22DMB). The first peak for nC6 is at a shorter value of distance as it has smaller molecular diameter perpendicular to the long axis. Also note that the intensity of the first g(r) peak for nC6 is higher than 6.0. For other isomers, the maximum value of the g(r) first peak is between 3 and 4. This is surprising since the LJ interaction parameters for all the isomers are almost similar. In order to check if this is due to the presence of the zeolite or intrinsic to the guest molecules, a liquid phase simulation was carried out for nC6 and 2MP to compare the liquid phase behaviour with the adsorbed phase behaviour. The available volume for the hexane isomers in the zeolite is calculated (4/3)πrc 3 , where rc is the radius of the α-cage taken as 5.5 ˚ A which yielded a simulation box of length l = 34.92 ˚ A . Hence, the density of the simulated pure liquid phase is identical to the adsorbed phase. It was

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observed that the peak heights of both nC6 as well as 2MP are similar with a value ∼ 3 in the liquid phase as opposed to their behaviour in the adsorbed phase (see Figure S1). In the adsorbed phase, the larger height of nC6 is due the ability of several nC6 molecules to closely pack in an α-cage. In contrast, the probability of accommodating more than one branched isomer in a single cage is less. This is because the branched isomers of hexane (i) are unable to bend as nC6 (as shown in a subsequent section) and (ii) have their molecular diameters larger than the nC6. Adsorption Site The adsorption sites of the linear (nC6) and one branched (22DMB) hexane isomers have been examined. Adsorption sites have an important role and determine many of the properties of guests when they are in the host zeolite. Many of the lattice models use the knowledge about adsorption sites to carry out longer calculations on larger systems. Demontis and coworkers have investigated many guest-zeolite systems using such models. 30,31 A set of points representing the c.o.m positions of nC6 and 22DMB with energy close to the adsorption site at 250 K are shown in Figure 4. For nC6, the c.o.m points shown correspond to those guests which have a guest-host interaction energy of less than -44.0 kJ/mol(see Figure 4a). These set of points indicate their positions within α-cage, where the energies are close to the absolute energy minima of -46.7 kJ/mol. There are more number of points corresponding to their adsorption minima for nC6 and 22DMB when compared to the mono atomic guests like Xe, where there are much fewer points or positions close to the energy minimum. 32 In other words, the degeneracy of the points associated with the adsorption site and the spread of these points is higher for hexane isomers. The presence of degenerate energy levels in case of nC6, arising from the availability of higher number of internal degrees of freedom, can help optimise its energy even if the contribution from the guest-zeolite interaction is not favourable. The three dihedral angles available to nC6 molecule help in optimising the energy at many locations in the α-cage. Such an optimisation would be less for a molecule like 22DMB where there is only one dihedral angle available. The loci of all points with energies less than -44.0 kJ/mol for 22DMB

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molecule, where the global minimum is at -45.8 kJ/mol is shown in Figure 4b. The adsorption sites for 22DMB are closer to the cage atoms especially near the four membered rings. Since it is not clear from the figure whether the adsorption sites are located in the vicinity of the 12-membered ring, the angle between the vector connecting c.o.m of the guest to the centre of cage (c.o.c) and the vector connecting the centre of window (c.o.w) to c.o.c is computed. In Figure 5, the distribution of these angles for points satisfying guest-zeolite interaction energy less than -44 kJ/mol for both nC6 and 22DMB is shown. The maximum value of the angle is limited to half the tetrahedral angle (∼ 54◦ ).For nC6, a narrow distribution with a maximum around 33◦ is seen. This suggests that nC6 essentially passes through the periphery of the 12-ring window. In contrast, 22DMB has a wide distribution around 40◦ . The adsorption energies of the isomers calculated at a low temperature of 10 K are listed in Table 1. nC6 has the highest adsorption enthalpy whereas 22DMB has the lowest energy of adsorption. The figures indicating the positions of all the molecules at their adsorption sites are given in Figure S3 in SI. Efficient separation of hexane isomers using zeolite Y can not be performed through adsorption since their adsorption energies are very close to each other. Centre of Cage - Centre of Mass Distribution In Figure 6, c.o.c-c.o.m radial distribution functions for the isomers at temperatures 250 K and 400 K is shown. For nC6, the distribution shows a maximum around 3 ˚ A at all five temperatures. Branched isomers exhibit a maximum closer to the centre of the α-cage at lower temperatures only. This is expected of a larger sized molecules like the branched isomers. At higher temperatures, the maxima are shifted closer to the periphery. The approximate temperature at which the maximum shifts from close to the cage centre to the periphery is rather abrupt and different for different isomers. The temperature at which this shift occurs is 350 K for 2MP, 330 K for both 3MP and 23DMB and 300 K for 22DMB. These distribution functions have an implication on the properties of rate of cage-to-cage diffusion. It is seen that there is a one-to-one correspondence with the rate of cage-to-cage jumps and these curves. These are discussed in SI.

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Dynamical Properties This section mainly deals with the time dependent properties to understand the kinetics of diffusion in zeolite NaY. Mean Square Displacement Mean square displacement (MSD) of hexane isomers at 250 K is given in Figure 7. These computed curves are essentially straight over a period of 2.25 ns which suggest good statistics. The diffusivities have been obtained by computing the slope of MSDs from the relation,

Ds =

< r2 (t) > 2dt

(4)

where < r2 (t) > is the mean square displacement at time t and the dimensionality d = 3 for the present system. The diffusivities Ds obtained from the slope of MSD curves at various temperatures are listed in Table 2. At low temperatures (250 K), the order of diffusivities is Ds (nC6) < Ds (2MP) < Ds (3MP) < Ds (23DMB) < Ds (22DMB). This trend is similar to the diffusivity trend obtained by Bárcia et al. for hexane isomers in zeolite BEA at 423 K (Ds (nC6) < Ds (3MP) ∼ Ds (23DMB) < Ds (22DMB); they did not include 2MP in their study (see Table 8 of Bárcia’s paper). 21 The trends in the diffusivities at various temperatures can be understood in terms of previously observed dependence of Ds on molecular diameter, σ. 5,22,33 It has been observed that Ds decreases with σ for small σ values. For larger σ, when it is comparable to the bottleneck diameter, the diffusivity increases and reaches a maximum before it decreases rapidly to zero. The nature of the dependence is depicted in Figure 8. Two distinct regimes are seen from the figure. In the region where σ is small as compared to the bottleneck diameter, Ds ∝ 1/σ 2 . This regime is called the linear regime (LR). At larger σ, Ds first increases and then decreases. This region is referred to as the anomalous regime (AR). This surprising behaviour is referred to as the Levitation Effect (LE). 5 Experiments have verified the existence of the Levitation Effect. 22 The maximum in diffusivity in the anomalous regime arises from the reduction in the net force exerted on guest molecules by the host. For a guest which has a σ comparable to the bottleneck diameter, the force exerted by the zeolite (host) is the least thereby increasing its 10


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Ds . The force reaches a minimum since force exerted on the guest along a given direction cancels the force exerted on it along the diagonally opposite direction. Since 22DMB has the largest cross sectional diameter which is close to the bottle neck diameter (diameter of the 12 ring window ∼ 7.5 ˚ A), it diffuses faster. The maximum diffusivity is always seen for the molecule or isomer whose value of the dimensionless levitation parameter, γ, is close to unity. γ is defined for mono atomic molecules in the expression,

γ=

2.21/6 σgz σw

(5)

σ⊥ σw

(6)

For polyatomic molecules γ is given by,

γ=

where σgz is the guest-zeolite interaction parameter of the mono atomic molecule, σ⊥ is the molecular diameter perpendicular to the long axis of a polyatomic molecule and σw is the window diameter of the zeolite. When γ = 1, the interaction between the guest and zeolite is optimum. In other words, the interaction is dominated by the attraction between the guestzeolite atoms (methyl/methylene group of the guest and the oxygen atom of the zeolite framework) and the interatomic distance is close to the LJ minimum. When the molecular diameter and window diameter are comparable, the guest experiences equal attractive forces from opposite oxygen atoms of the zeolite window which effectively cancels each other, thus making the net force negligible. The guest then will be weakly bound to the zeolite surface and behaves like a free particle though it is confined inside the zeolite. This results in higher diffusivity. Table 3 lists the molecular diameter of various isomers of hexane. As these molecules are not spherical, the molecular diameter that is relevant for diffusion is the diameter perpendicular to the long axis. These can be obtained from the geometry of the molecules (shown in S5 of Supporting information). The diameter increases in the order σ(nC6) < σ(2MP) < σ(3MP) < σ(23DMB) < σ(22DMB). The computed γ values are also listed. A plot of Ds vs. γ at 250 K is shown in Figure 9. A lowering of the net force on the guest with values of γ close to unity at various points in 11



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configuration space translates to smaller undulations in energy (F = −∇φ). This manifests as a lower activation energy for particles in anomalous regime. In order to validate this in the case for hexane isomers in zeolite Y, we have obtained Ea values from the Arrhenius plots for diffusion (see Figure 10). The values of Ea is tabulated in Table 4. Ea is the highest for nC6 followed by 2MP, 3MP, 23DMB and 22DMB. The Ea values for nC6 and 22DMB are 11.17 and 7.42 kJ/mol respectively. It is clear that the isomer with the larger cross sectional diameter (22DMB) has lower Ea . This confirms that the increase in Ds with increase in cross sectional diameter of the isomer has its origin in the Levitation effect. Previous work by Rajappa and Yashonath on the dependence of levitation effect on concentration suggests that up to rather high loading, ρ (= vs /vc , where vs is the total volume of guests and vc is the total volume of cage), the anomalous maximum persists, although the intensity of the maximum is lower. 34 More recently, Rajappa and coworkers also reported calculations on pentane isomers in zeolite Y up to a loading of 3 molecules/cage. They found that the branched isomer, isopentane, show higher diffusivity than n-pentane at 298 K. This suggests that anomalous behaviour with its origin in the levitation effect is seen up to reasonably higher loadings. 24 We have been using the intramolecular potential for zeolite-Y with rigid Na ions (referred to as potential A) for our simulations whose parameters and other details are described earlier. Additionally, we have carried out MD calculations with two other intramolecular potentials (potentials B and C). Potential B includes mobile Na ions which interact with nearest oxygen atoms with a bond potential. This potential also distinguishes between Si and Al atoms by specifying an additional Al-O potential. In potential C, the Na ions are interacting with nearest oxygen atoms (as in potential B), but there is no distinction between Si and Al atoms. The diffusivity of nC6 in zeolite Y with the earlier potential A with frozen Na ions is 3.59. The zeolite potentials B and C yielded values of Ds for nC6 as 3.10 and 4.36 respectively. As is evident, the diffusivities do not vary significantly from each other. Therefore, the effect of mobile Na ions and Al atoms on the diffusivities is very less. This is to be expected as the number of Na ions are very less and Al atoms are buried deep within the oxygen to interact explicitly with the guest atoms. We have therefore carried out further calculations only with potential A. 12


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Velocity Autocorrelation Function Velocity autocorrelation function (VACF) is calculated from the c.o.m velocities vi at time t using the formula,

Cv (t) =

*

vi (0).vi (t) vi (0).vi (0)

+

(7)

The VACF for the the c.o.m velocities of various isomers at 250 K is shown in Figure 11. At 250 K, it is seen that nC6 has the largest backscattering. The value of the minimum in VACF is less than -0.1 for nC6. The other isomers have relatively less backscattering. The higher backscattering of nC6 arises from larger undulations in the potential energy landscape. The other isomers are associated with less undulating potential energy landscape leading to lower backscattering. With increase in temperature, the backscattering in the case of nC6 decreases significantly and can be compared to the other isomers. 22DMB in particular shows oscillations because of the high γ value (1.02). When γ > 1.0, the molecule is slightly larger than the bottleneck diameter. However, since the zeolite framework is flexible and can expand, 22DMB is able to diffuse through the window. The Ds values obtained from the VACF are also comparable to the values obtained from MSDs. Rate of Cage Visits Normally, a guest molecule diffuses by migrating from one α-cage to another. At every MD step, a guest is assigned to a given α-cage. All cage-to-cage migrations are then counted and this number, nc gives the number of intercage migrations. This number per guest per second gives the rate of intercage migrations, kc . However, it is seen that a guest which moves from cage i to j returns to cage i and this is some times repeated many times. Such recrossings lead to no net movement and depend only on the local potential energy profile at or in the vicinity of the 12-ring window. To get an idea of the correct rate, we define rate of cage visits from nv which is nc minus number of recrossing events. This is termed by us as kv , the rate of cage visits. This quantity is expected to give a realistic value for the cages visited during the simulation and this quantity will be similar or proportional to the self-diffusivity

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of the guest. Figure 12 shows the variation of the guest-host interaction energy as a function of distance from the window plane. This was obtained from molecular dynamics data by averaging over all cage-to-cage migration events. One can see that nC6 alone shows a slight positive energy barrier for the passage through the window which is absent for other isomers. The behaviour of kv does not depend on the potential energy landscape near the window, but on the overall potential energy landscape. The behaviour of kv and Ds are very similar as they both yield properties that depend on longer duration. The behaviour of kc with temperature is discussed in detail in SI. Table 5 gives the values of kv at all temperatures for all the isomers. The Arrhenius plot for kv is shown in Figure 13 and the activation energy barriers, Ea are calculated (Table 6). All the isomers have positive energy barriers for kv with nC6 having the highest and 22DMB having the lowest Ea values. These values are of the same order and show similar trend to those values of Ea which was obtained from the Ds . This demonstrates the similarity between Ds and kv . In SI, we report the variation in the cage residence times for various isomers at different temperatures which is derived from kv . Reorientational Motion nC6 is asymmetric with one of its molecular dimensions much larger than the other two. Other isomers are more symmetric and closer to globular shape. The reorientational time of all five isomers at five different temperatures have been obtained by computing C 2 (t),

C 2 (t) =< P2 (x) >

(8)

where P2 (x) is the second degree Legendre polynomial in x and is given as P2 (x) = (3x2 − ˆ i (t).ˆ ˆ i is the longest end-to-end unit vector for each 1)/2, where x = cosθ =< u ui (0) > and u isomer and their directions are depicted in Figure 1. The values of τ1 and τ2 have been derived by fitting a biexponential of the form y(t) = A1 exp(−t/τ1 ) + A2 exp(−t/τ2 ) to the curve of C 2 (t) obtained from the MD data. The fitted values of τ1 and τ2 are given in Table 7 and the C 2 (t) curves at 250 K are shown in Figure 14. τ1 corresponds to the fast decay 14


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and τ2 to the slow decay. Oscillations in C 2 (t) are seen up to 2 ps for branched isomers. The doubly branched isomers show significant oscillations as compared to the singly branched ones. The latter exhibit some change in curvature at around 0.5 ps. The oscillations are associated with the difficulty that the doubly branched isomers have in passing through the 12 ring window which is the bottleneck for diffusion. Singly branched isomers 2MP and 3MP as well as nC6 being relatively smaller in diameter have no difficulty in going through the window. A short movie, Movie S1, taken from the MD trajectory corroborates this view. From the movie it is evident that 23DMB slows down as it approaches the 12 ring window and there is a back and forth oscillation when it is about to enter the window. The value of τ2 is large for nC6 and decreases with increase in the globular shape of the isomer. The least value of τ2 is seen for 22DMB. With increasing temperature, the value of τ2 decreases for all the isomers. Figure 15 shows the Arrhenius plots for the reorientational motion, ln(τ2 ) vs. T. It is evident that the reorientational motion is generally Arrhenius for all isomers over the temperature range of 250 K - 400 K. The Ea values for reorientational motion is given in Table 8. It is seen that nC6 has the highest Ea with a magnitude of 14.13 kJ/mol. Interestingly Ea for 3MP and 23DMB are higher than that of 2MP. 22DMB has the least activation energy barrier for reorientation. These trends can be understood, again, in terms of the deviation from the globular shape with 22DMB being closest to the globular shape.

Kinetic Separation of Hexane Isomers The Arrhenius plots for Ds of various isomers cross each other at some temperature (see Figure 10). For example, the plots of nC6 and 2MP intersect at 300 K. Thus below 300 K, 2MP will have higher diffusivity while above this temperature nC6 will diffuse faster. Similarly, the plots of other isomers intersect with that of nC6 at certain temperatures, above which nC6 will have higher diffusivity than the other branched isomer. We shall refer to the temperature at which the lines of two isomers cross as the inversion temperatures, Tinv . Table 9 lists the inversion temperatures of all the hexane isomers. From the table it 15



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is seen that singly branched isomers have Tinv with nC6 at 300 K (2MP) and 347 K (3MP), whereas the Tinv for doubly branched isomers with nC6 are at 387 K (23DMB) and 418 K (22DMB). Thus, it is evident that the nC6 has higher inversion temperatures with doubly branched isomers than with the singly branched ones. The above discussion is of relevance to the separation of mixtures of hexane isomers. In a kinetic-based separation, the mixture is loaded at the top of a zeolite column and the separated components are collected at the bottom. The component with the highest diffusivity reaches the bottom of the column faster than the one with a lower diffusivity. As we have seen, in a binary mixture of hexane isomers, this difference in diffusivities can be controlled by altering the temperature. When the temperature is below Tinv , the isomer counterpart with higher Ds will exit the zeolite column first and above Tinv those with lesser diffusivity will elude out first. Thus one can separate out a preferred isomer from the binary mixture by controlling the temperature. The general scheme to obtain Tinv for any given multicomponent mixtures is given in Figure 16 which is derived from the Arrhenius plot, ln(Ds ) against (1000/T), for all the hexane isomers. The plots intersect at different Tinv points for a pair of isomers and are indicated by vertical dashed lines in the figure. The region between two vertical dashed lines correspond to a particular order of diffusivities. In Table 10 the order of diffusivities of the hexane isomers for each of the regions is tabulated. The linear isomer has the least diffusivity at low temperatures. This is in contrast to the diffusion in small pore zeolites such as silicalite where the linear isomer has the highest diffusivity. Bárcia and coworkers found, in an experimental study, that the branched isomers have higher diffusivity than the linear isomer (nC6). 21 However, they attributed this to large contribution from macropore diffusivity. Our calculations here in the intracrystalline pores (without any intercrystalline macropores) clearly suggest that in large pore zeolite such as zeolite BEA or zeolite Y, the branched isomers invariably have higher diffusivities than linear isomer. The contribution of the macropore diffusivity appears to be not responsible for the observed higher diffusivity of the branched isomers in BEA zeolite. For a multicomponent mixture, from Table 9, it is clear that the Tinv between the linear isomer and singly branched isomers are at the lowest temperature range (T613 K).

End-to-end Length Variation of nC6 End-to-end Length Variation of nC6 with Temperature The variation in the average end-to-end length (Le−e ) of nC6 as a function of temperature is shown in Figure 17. In order to understand the significant decrease in Le−e on increase in temperature from 250 K - 400 K, the distribution of Le−e , f(Le−e ) has been computed at various temperatures which is given in Figure 18. The peak between 5.9 ˚ A and 6.4 ˚ A arises when nC6 is in all trans conformation. Here, all three dihedral angles of nC6 are in the range of 160◦ - 180◦ . The distribution of dihedral angles is shown in Figure S9 of Supporting Information. As can be seen from the figure, with increase in temperature, the population of gauche conformation increases for all the three dihedral angles. The percentage of gauche conformation at each temperature for each of the three dihedral angles of nC6 is given in Table 11. The increase in gauche leads to the increase in intensity of shoulder in Figure 18. Thus, the decrease in hLe−e i arises from the increase in the population of gauche conformers in nC6 over the temperature range of 250 K - 400 K. End-to-end Length Variation of nC6 during Diffusion Variation in the end-to-end length, Le−e , in nC6 during its migration from one cage to another through a 12 ring window has also been investigated. The region inside the cage is divided into two distinct regions based on the perpendicular distance from the window plane to the c.o.m of the molecule, dw.p−c.o.m . When dw.p−c.o.m is ≤ 1.0 ˚ A, the molecule is considered to be near the window and when dw.p−c.o.m ≥ 2.0 ˚ A, the molecule is considered to be inside the zeolite cage. The variation of Le−e at various temperatures near the window and inside the cage were calculated from the trajectory and is given in Table 12. From the table it

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is evident that at lower temperatures, molecules near the window have a lower Le−e value compared to those in the cage. With increase in temperature, Le−e gradually decreases and eventually the difference in Le−e disappears at 400 K. The distribution of Le−e , f(Le−e ) is also computed at various temperatures, both in the cage and near the window to get a clear picture of these variations (shown in Figure 19). There is a reduction in the distribution for higher Le−e values, when the molecule is closer to the window. This means that the molecule takes on a gauche conformation when it has to pass through the window to another cage. This increase in the gauche conformers is verified by plotting the variation of dihedral angle distribution at both the regions (shown in Figure S10 in Supporting Information). It is evident that only the second dihedral angle φ2 has an increase in gauche conformers when it is approaching the window, while the other two dihedral angles show little or no variation. The changes in Le−e of nC6 when it passes from one cage to other is given in Figure 20. These changes in Le−e indicate that nC6 tries to ‘curl up’ and bend to increase its diameter perpendicular to the long molecular axis as it passes through the window. This can be attributed to the Levitation effect as nC6 tries to mimic an anomalous regime particle to increase its diffusivity. As we have already seen, an anomalous regime particle has a lower activation energy to diffuse through the zeolite and nC6 will have a relatively facile diffusion through the zeolite and the 12-ring window due to bending.

Conclusions This comparative study of hexane isomers in zeolite Y brings out interesting aspects in both structural as well as dynamical properties especially during diffusion. The study has been performed at a low loading of one molecule/cage. Note that the levitation effect is observed to persist up to reasonably high loading. 24,34 The guest-guest RDF of nC6 shows significantly higher intensity as compared to its branched isomers. It is shown that this is not the case for the liquids which are not confined within the zeolite. The higher intensity of nC6 in the zeolite arises from its ability to conform to the zeolite wall curvature and its lower diameter. The density distribution of the c.o.m of the branched isomers within the α-cage shows marked changes with temperature. The observed trend in the Ds exhibit 18


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markedly different trends as compared to small-pore zeolites such as MFI. These are in good agreement with the experimental results of hexane isomers in zeolite BEA by Bárcia et al. Here branched isomers have higher diffusivities as compared to the linear nC6. The computed activation energies, Ea for the branched isomers are lower than that for nC6. These surprising trends are counter-intuitive and can be understood in terms the Levitation effect based on levitation parameter, γ. The activation energy obtained from self-diffusivity of linear nC6 in a defect-free zeolite is the highest at 11.2 kJ/mol whereas the doubly branched 22DMB has the lowest Ea at 7.4 kJ/mol. These values are lower than those obtained by Bárcia et al. We attribute the higher values for activation energies obtained by Bárcia et al to the BEA zeolite whose structure is different from zeolite Y and to the intercrystalline or macropores. The reorientational relaxation times of nC6 is highest since nC6 being a linear molecule encounters maximum hindrance to its rotation. The Ea value for its reorientation is also the highest at 14.1 kJ/mol. A general way to carry out the kinetic separation of hexane isomers is also discussed. The exact order of exit of hexane isomers from a zeolite Y column is seen to depend on the temperature at which the separation is being carried out. The inversion temperatures of all pairs have been obtained and an effective separation of isomers can be carried out with this knowledge. The inversion temperatures reported might be slightly different from those listed if longer simulations are carried out. The intermolecular potential employed will also have an effect on the derivation of Tinv . The end-to-end distance of linear isomer, nC6, decreases with increase in temperature due to bending. Such a decrease arises from an increase in the gauche conformer population of all three dihedral angles in nC6. A similar bending is also seen when nC6 approaches the window plane of the 12-ring window. This is attributed to the tendency of the nC6 molecule to increase its value of levitation parameter, γ, by increasing its cross-section diameter which can be achieved by the bending. Interestingly, only the central dihedral angle φ2 showed a visible change in its population as a function of dw.p−c.o.m while φ1 and φ3 show no significant change in gauche conformer population. Acknowledgements : The authors would like to thank the Thematic Unit of Excellence 19



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on Computational Material Science (TUE- CMS) funded by Department of Science and Technology (DST), Govt. of India, for the computational facilities. The authors are also grateful to University Grants Commission (UGC) for the financial support.

Supporting Information Available The Supporting Information contains following information: a. Computational Details. b. Details about the alternate potentials. c. The liquid phase RDFs of pure nC6 and 2MP. d. The temperature dependence of RDFs of hexane isomers in zeolite Y. e. Adsorption site of hexane isomers inside zeolite Y at low temperature. f. The temperature dependence of MSDs of hexane isomers in zeolite Y. g. The calculation of Levitation parameter, γ. h. The rate of cage migrations of hexane isomers in zeolite Y. i. Configuration of hexane isomers at window plane of the zeolite Y cage. j. Cage residence time of each hexane isomers in zeolite Y. k. Change in dihedral angles of nC6 as functions of temperature and distance from the window plane of zeolite Y. Movie shows the reorientational oscillations of the doubly branched 23DMB when it tries to cross the window. • Filename: suppinfo.pdf • Filename: 23DMB.mpg • Filename: nC6adspos.cif • Filename: 2MPadspos.cif • Filename: 3MPadspos.cif • Filename: 23DMBadspos.cif 20


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• Filename: 22DMBadspos.cif • Filename: nC6winpos.cif • Filename: 2MPwinpos.cif • Filename: 3MPwinpos.cif • Filename: 23DMBwinpos.cif • Filename: 22DMBwinpos.cif

References (1) Herm, Z. R.; Wiers, B. M.; Mason, J. A.; van Baten, J. M.; Hudson, M. R.; Zajdel, P.; Brown, C. M.; Masciocchi, N.; Krishna, R.; Long, J. R. Separation of Hexane Isomers in a Metal-Organic Framework with Triangular Channels. Science 2013, 340, 960–964. (2) Chen, L.; Yuan, S.; Qian, J.-F.; Fan, W.; He, M.-Y.; Chen, Q.; Zhang, Z.-H. Effective Adsorption Separation of n-Hexane/2-Methylpentane in Facilely Synthesized Zeolitic Imidazolate Frameworks ZIF-8 and ZIF-69. Ind. Eng. Chem. Res. 2016, 55, 10751– 10757. (3) Gorring, R. Diffusion of normal paraffins in zeolite T. J. Catal. 1973, 31, 13 – 26. (4) Hahn, K.; Kärger, J. Molecular Dynamics Simulation of Single-File Systems. J. Phys. Chem. 1996, 100, 316–326. (5) Yashonath, S.; Santikary, P. Diffusion of Sorbates in Zeolites Y and A: Novel Dependence on Sorbate Size and Strength of Sorbate-Zeolite Interaction. J. Phys. Chem. 1994, 98, 6368–6376. (6) Hu, H.-W.; Carson, G. A.; Granick, S. Relaxation time of confined liquids under shear. Phys. Rev. Lett. 1991, 66, 2758–2761.

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(7) Granick, S. Motions and Relaxations of Confined Liquids. Science 1991, 253, 1374– 1379. (8) Combariza, A. F.; Sastre, G. Influence of Zeolite Surface in the Sorption of Methane from Molecular Dynamics. J. Phys. Chem. C 2011, 115, 13751–13758. (9) O’Malley, A. J.; Catlow, C. R. A. Molecular dynamics simulations of longer n-alkanes in silicalite: state-of-the-art models achieving close agreement with experiment. Phys. Chem. Chem. Phys. 2015, 17, 1943–1948. (10) Haag, W. O.; Lago, R. M.; Weisz, P. B. Transport and reactivity of hydrocarbon molecules in a shape-selective zeolite. Faraday Discuss. Chem. Soc. 1981, 72, 317–330. (11) Gump, C. J.; Noble, R. D.; Falconer, J. L. Separation of Hexane Isomers through Nonzeolite Pores in ZSM-5 Zeolite Membranes. Ind. Eng. Chem. Res. 1999, 38, 2775– 2781. (12) Schuring, D.; Koriabkina, A. O.; de Jong, A. M.; Smit, B.; van Santen, R. A. Adsorption and Diffusion of n-Hexane/2-Methylpentane Mixtures in Zeolite Silicalite: Experiments and Modeling. J. Phys. Chem. B 2001, 105, 7690–7698. (13) Calero, S.; Smit, B.; Krishna, R. Configurational Entropy Effects during Sorption of Hexane Isomers in Silicalite. J. Catal. 2001, 202, 395 – 401. (14) Krishna, R.; van Baten, J. Diffusion of hydrocarbon mixtures in MFI zeolite: Influence of intersection blocking. Chem. Eng. J. 2008, 140, 614 – 620. (15) Krishna, R.; van Baten, J. Screening of zeolite adsorbents for separation of hexane isomers: A molecular simulation study. Sep. Purif. Technol. 2007, 55, 246 – 255. (16) Ferreira, A. F.; Mittelmeijer-Hazeleger, M. C.; v.d. Bergh, J.; Aguado, S.; Jansen, J. C.; Rothenberg, G.; Rodrigues, A. E.; Kapteijn, F. Adsorption of hexane isomers on MFI type zeolites at ambient temperature: Understanding the aluminium content effect. Microporous Mesoporous Mater. 2013, 170, 26 – 35.

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(17) Ferreira, A. F.; Mittelmeijer-Hazeleger, M. C.; Bliek, A.; Moulijn, J. A. Influence of Si/Al ratio on hexane isomers adsorption equilibria. Microporous Mesoporous Mater. 2008, 111, 171 – 177. (18) Vandegehuchte, B. D.; Thybaut, J. W.; Marin, G. B. Unraveling Diffusion and Other Shape Selectivity Effects in ZSM5 Using n-Hexane Hydroconversion Single-Event Microkinetics. Ind. Eng. Chem. Res. 2014, 53, 15333–15347. (19) Gobin, O. C.; Reitmeier, S. J.; Jentys, A.; Lercher, J. A. Role of the Surface Modification on the Transport of Hexane Isomers in ZSM-5. J. Phys. Chem. C 2011, 115, 1171–1179. (20) Huddersman, K.; Klimczyk, M. Separation of hexane isomers on zeolites mordenite and beta. J. Chem. Soc., Faraday Trans. 1996, 92, 143–147. (21) Bárcia, P. S.; Silva, J. A.; Rodrigues, A. E. Adsorption equilibrium and kinetics of branched hexane isomers in pellets of BETA zeolite. Microporous Mesoporous Mater. 2005, 79, 145 – 163. (22) Borah, B. J.; Jobic, H.; Yashonath, S. Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY. J. Chem. Phys. 2010, 132, 144507. (23) Bhide, S. Y.; Yashonath, S. Anomalous diffusion of linear and branched pentanes within zeolite NaY. Molecular Physics 2004, 102, 1057–1066. (24) Rajappa, C.; Krause, C.; Borah, B.; Adem, Z.; Galvosas, P.; Kärger, J.; Subramanian, Y. Diffusion of pentane isomers in faujasite-type zeolites : NMR and molecular dynamics study. Microporous Mesoporous Mater. 2013, 171, 58 – 64. (25) Fitch, A. N.; Jobic, H.; Renouprez, A. Localization of benzene in sodium-Y-zeolite by powder neutron diffraction. J. Phys. Chem. 1986, 90, 1311–1318. (26) Demontis, P.; Suffritti, G. B.; Quartieri, S.; Fois, E. S.; Gamba, A. Molecular dynamics studies on zeolites. 3. Dehydrated zeolite A. J. Phys. Chem. 1988, 92, 867–871. 23



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(27) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. Optimized intermolecular potential functions for liquid hydrocarbons. J. Am. Chem. Soc. 1984, 106, 6638–6646. (28) Wender, A.; Barreau, A.; Lefebvre, C.; Di Lella, A.; Boutin, A.; Ungerer, P.; Fuchs, A. H. Adsorption of n-alkanes in faujasite zeolites: molecular simulation study and experimental measurements. Adsorption 2007, 13, 439–451. (29) Todorov, I. T.; Smith, W.; Trachenko, K.; Dove, M. T. DLPOLY3: new dimensions in molecular dynamics simulations via massive parallelism. J. Mater. Chem. 2006, 16, 1911–1918. (30) P. Demontis, F. G. P.; ; Suffritti, G. B. A Lattice-Gas Cellular Automaton to Model Diffusion in Restricted Geometries. J. Phys. Chem. B 2006, 110, 13554–13559. (31) Demontis, P.; Pazzona, F. G.; Suffritti, G. B. Introducing a Cellular Automaton as an Empirical Model to Study Static and Dynamic Properties of Molecules Adsorbed in Zeolites. J. Phys. Chem. B 2008, 112, 12444–12452. (32) Santikary, P.; Yashonath, S.; Ananthakrishna, G. A molecular dynamics study of xenon sorbed in sodium Y zeolite. 1. Temperature and concentration dependence. J. Phys. Chem. 1992, 96, 10469–10477. (33) Yashonath, S.; Ghorai, P. K. Diffusion in Nanoporous Phases: Size Dependence and Levitation Effect. J. Phys. Chem. B 2008, 112, 665–686. (34) Rajappa, C.; Yashonath, S. Levitation Effect and Its Dependence on Sorbate Concentration. The Journal of Physical Chemistry B 1997, 101, 8035–8037.

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Table 1: Adsorption energies, Eads of different hexane isomers adsorbed in zeolite Y. They are obtained from potential energy calculations at 10 K. (Eads values are in units of kJ/mol.) Isomer nC6 2MP 3MP 23DMB 22DMB

Eads -46.7 -45.9 -46.4 -45.9 -45.8

Table 2: Diffusivities, Ds of hexane isomers inside zeolite Y obtained from MSD calculations at different temperatures. (Ds values are in units of 10−9 m2 /s.) Isomer

250K nC6 1.43(0.24) 2MP 1.79(0.09) 3MP 2.04(0.12) 23DMB 2.57(0.19) 22DMB 2.91(0.38)

300K 3.59(0.35) 3.17(0.21) 3.92(0.24) 4.68(0.32) 5.67(0.29)

Ds 330K 5.07(0.40) 4.58(0.50) 5.49(0.42) 6.63(0.30) 7.39(0.39)

350K 400K 7.27(0.61) 10.47(0.50) 6.44(0.55) 9.78(0.57) 6.23(0.44) 10.44(0.66) 7.26(0.61) 10.60(0.8) 7.75(0.46) 11.43(0.38)

Table 3: The molecular diameter perpendicular to the long axis, σ⊥ , and the levitation parameter, γ, values of all hexane isomers when adsorbed in zeolite Y. (σ⊥ values are in units of ˚ A.) Isomer σ⊥ γ nC6 6.905 0.69 2MP 8.09 0.80 3MP 9.55 0.95 23DMB 9.96 0.98 22DMB 10.31 1.02

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Table 4: Activation energies for diffusion, Ea , of different hexane isomers adsorbed in zeolite Y. They are obtained from the slope of ln (Ds ) vs. 1/T Arrhenius plot at different temperatures, viz. 250 K, 300 K, 330 K, 350 K and 400 K. (Ea values are in units of kJ/mol.) Isomer Ea nC6 11.2 2MP 9.5 3MP 8.8 23DMB 7.8 22DMB 7.4

Table 5: Rate of cage visits, kv by hexane isomers in zeolite Y at different temperatures. (kv values are in units of 1010 molecule-1 . s-1 and Temperatures are in K.) Temperature 250 300 330 350 400

nC6 2MP 0.94 1.40 1.93 2.40 2.47 2.97 2.86 3.06 3.50 3.45

kv 3MP 23DMB 22DMB 1.73 2.05 2.36 2.71 2.99 3.24 3.17 3.32 3.84 3.20 3.62 4.12 3.66 4.17 4.65

Table 6: The activation energies for the cage visits, Ea , of hexane isomers in zeolite Y at different temperature ranges. (Temperatures are in K and Ea values are in kJ/mol.) Isomer nC6 2MP 3MP 23DMB 22DMB

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Ea 7.4 5.2 4.2 3.9 3.8


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Table 7: Reorientational time of hexane isomers within a zeolite Y cage at different temperatures. (The values are in units of ps.) Reorientational Time Isomer 250K 300K 330K 350K τ1 τ2 τ1 τ2 τ1 τ2 τ1 τ2 nC6 2.04 23.35 1.05 9.09 0.90 6.32 0.71 4.08 2MP 1.06 11.90 0.73 6.49 0.62 4.31 0.59 4.44 3MP 1.09 13.69 0.61 4.50 0.53 3.53 0.52 4.04 23DMB 0.67 9.80 0.61 8.84 0.52 4.34 0.43 3.84 22DMB 0.50 3.90 0.41 2.26 0.38 2.04 0.35 1.89

400K τ1 τ2 0.33 1.66 0.50 2.92 0.42 2.42 0.38 2.00 0.31 1.10

Table 8: Reorientational activation energies, Ea of hexane isomers within a zeolite Y cage. This is obtained from the slope of ln(τ2 ) vs. 1/T Arrhenius plots at temperature 250 K, 300 K, 330 K, 350 K and 400 K. (Ea values are in units of kJ/mol.) Isomer Ea nC6 14.1 2MP 7.7 3MP 9.2 23DMB 8.9 22DMB 6.5

Table 9: Inversion temperatures for diffusivities, Tinv , of hexane isomers inside zeolite Y. ( Tinv values are in units of K.) Molecules inverted 2MP/nC6 3MP/nC6 23DMB/nC6 22DMB/nC6 23DMB/3MP 23DMB/2MP 3MP/2MP 22DMB/2MP 22DMB/3MP 22DMB/23DMB

27

Tinv 300 347 387 418 528 549 586 613 627 1172



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Table 10: Different regions according to order of diffusivities of hexane isomers in zeolite Y. (Temperatures are in units of K.) Region Temperature Range I T1172

Order of diffusivities nC6 < 2MP < 3MP < 23DMB < 22DMB 2MP < nC6 < 3MP < 23DMB < 22DMB 2MP < 3MP < nC6 < 23DMB < 22DMB 2MP < 3MP < 23DMB < nC6 < 22DMB 2MP < 3MP < 23DMB < 22DMB < nC6 2MP < 23DMB < 3MP < 22DMB < nC6 23DMB < 2MP < 3MP < 22DMB < nC6 23DMB < 3MP < 2MP < 22DMB < nC6 23DMB < 3MP < 22DMB < 2MP < nC6 23DMB < 22DMB < 3MP < 2MP < nC6 22DMB < 23DMB < 3MP < 2MP < nC6

Table 11: Percentage gauche conformations for each dihedral angle of nC6 inside zeolite Y at various temperatures. (Temperatures are in units of K.)

Temperature 250 300 330 350 400

% Gauche Conformers φ1 φ2 φ3 24.9 19.0 24.7 29.5 23.8 29.4 32.3 26.4 32.5 34.3 28.2 34.3 36.5 30.4 36.6

Table 12: End to end length variation, Le−e , in nC6 during diffusion inside zeolite Y. (Le−e values are in units of ˚ A.)

Isomer 250 300 330 350 400

Le−e ˚ dw.p−c.o.m >2.0 ˚ dw.p−c.o.m < 1.0 A A near window inside the cage 5.67 (0.065) 5.75 (0.060) 5.63 (0.062) 5.65 (0.063) 5.56 (0.069) 5.60 (0.065) 5.51 (0.066) 5.53 (0.067) 5.48 (0.069) 5.48 (0.070)

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Figure 1: The five isomers of hexane. Note that each molecule is made of six interaction sites.The bond length, dihedral angle and the longest end-to-end vector are also shown for each isomer.

(a) n-hexane (nC6)

(b) 2-methyl pentane (2MP)

(c) 3-methyl pentane(3MP)

(d) 2,3-dimethyl butane (23DMB) (e) 2,2-dimethyl butane (22DMB)

Figure 2: The placement of nC6 at the centre of zeolite cage. (blue - nC6 atoms, green - Si atoms, red - O atoms.)

29



Figure 3: The c.o.m-c.o.m radial distribution functions of hexane isomers inside zeolite Y at 250 K. 7 6

gc.o.m-c.o.m(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 40

nC6 2MP 3MP 23DMB 22DMB

5 4 3

2 1 0 0

2

4

6

8

10

12

14

16

18

20

r (Å)

Figure 4: The distribution of c.o.m of nC6 and 22DMB near the adsorption site inside a zeolite Y cage at 250 K averaged over all molecules and all timesteps.

(a) nC6

(b) 22DMB

30


Page 31 of 40

Figure 5: The c.o.m-c.o.c-c.o.w angle distribution of nC6 and 22DMB at 250 K averaged over all molecules and all timesteps.

Figure 6: The c.o.c-c.o.m Distance Distribution Functions of Hexane Isomers at temperatures 250 K and 400 K. 3

2


2


1.5

gc.o.c-c.o.m (r)

2.5

gc.o.c-c.o.m (r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.5 1

1

0.5 0.5 0 0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

0 0.5

1

1.5

2

2.5

3

3.5

r (Å)

r (Å)

(a) 250 K

(b) 400 K

31


4

4.5

5

5.5

6


Figure 7: Mean square displacement of hexane isomers inside zeolite Y at 250 K. Diffusivities are calculated from the slopes of MSD plots. 4500


4000

3000 2500 2000

2

2

< r (t) > (Å )

3500

1500 1000 500 0 0

250

500

750 1000 1250 1500 1750 2000 2250

t (ps)

Figure 8: The dependence of diffusivity, Ds on molecular diameter σs for zeolite Y. The vertical dashed line demarcates the Linear regime (LR) from the Anomalous regime (AR). 5 1 0.8

AR

LR

2

Ds (x10 m /s)

0.6

-9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.4

190 K

0.2 0 0

0.03

0.06

2

0.09 -2

0.12

1/σs (Å )

32


0.15

Page 32 of 40

Page 33 of 40

Figure 9: The variation of diffusivities of hexane isomers with levitation parameter, γ, inside zeolite Y at 250 K. The linear regime (LR) and Anomalous regime (AR) have been separated by a vertical dashed line. 3

250 K

22DMB

AR

LR

2.5

23DMB

-9

2

Ds (x10 m /s)

2.75

2.25 2

3MP

1.75 1.5 1.25 0.65

2MP

nC6 0.7

0.75

0.8

0.85

γ

0.9

0.95

1

1.05

Figure 10: The Arrhenius plots obtained from self diffusivities of hexane isomers inside zeolite Y at temperatures 250 K, 300 K, 330 K, 350 K and 400K.

nC6 2MP 3MP 23DMB 22DMB nC6 fit 2MP fit 3MP fit 23DMB fit 22DMB fit

-18 -18.5

ln Ds

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-19 -19.5 -20 -20.5 2.5

2.75

3

3.25 3.5 -1 1000/T (K )

33

3.75

4



Figure 11: The velocity autocorrelation function of hexane isomers inside zeolite Y at 250 K. Inset gives an expanded view of VACF from 0 to 3 ps. 1 0.025 0

0.8


Cv(t)

0.6 0.4

-0.025 -0.05 -0.075 -0.1 0

0.5

1

1.5

2

2.5

3

0.2 0 -0.2 0

1

2

3

4

t (ps)

5

Figure 12: Potential energy landscape for hexane isomers inside zeolite Y at 250 K obtained by averaging over all cage to cage migration events.

-36

Window plane


-38

Ugh (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 40

-40

-42

-44 -3

-2

-1

0

1

2

3

dw.p-c.o.m (Å)

34


Page 35 of 40

Figure 13: The Arrhenius plots obtained the rate of cage visits, kv of hexane isomers inside zeolite Y at temperatures 250 K, 300 K, 330 K, 350 K and 400 K. -3 nC6 2MP 3MP 23DMB 22DMB

ln kv

-3.5

-4

-4.5 2.5

3

2.75

3.25

-1

3.5

4

3.75

1000/T (K )

Figure 14: The reorientational time correlation function of hexane isomers inside zeolite Y at 250 K. Inset gives an expanded view of the function from 0 to 2 ps. 1


0.8

1 0.8 0.6 0.4

0.6

0.2

2

C (t)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

0.4

0

1

0.5

2

1.5

0.2 0 0

1

2

3

4

5

t (ps)

35

6

7

8

9


10


Figure 15: The Arrhenius plots obtained from the reorientational time of hexane isomers inside zeolite Y at temperatures 250 K, 300 K, 330 K, 350 K and 400 K. 4

nC6 2MP 3MP 23DMB 22DMB nC6 fit 2MP fit 3MP fit 23DMB fit 22DMB fit

ln τ2

3

2

1

0 2.5

3

-1

4

3.5

1000/T (K )

Figure 16: Diffusivity order changes of hexane isomers in zeolite Y at temperature range 250 K - 1200 K.

XI


-16 X -17 V

ln Ds

IV

III

II

I

VIII

-18

VII

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 40

VI

-19 IX -20 0.5

1

1.5

2

2.5

-1

3

3.5

1000/T (K )

36


4

Page 37 of 40

Figure 17: The Le−e variations in nC6 within zeolite Y at different temperatures. 5.8 5.75

(Å)

5.7 5.65 5.6

5.55 5.5 5.45 5.4 250

275

300

325

T (K)

350

400

375

Figure 18: The distribution of Le−e of nC6 inside zeolite Y with temperatures. 0.125 0.1

f (Le-e)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


250 K 300 K 330 K 350 K 400 K

0.075 0.05

0.025 0

3.2

3.6

4

4.4

4.8

5.2

5.6

6

Le-e (Å)

37


6.4


Figure 19: The variation in the distribution of Le−e of nC6 in the two regions, one close to the window plane, dw.p−c.om < 1.0 ˚ A and another deep inside the α-cage, dw.p−c.o.m > 2.0 ˚ A during diffusion at 250 K. 0.1

molecule near window (dw.p-c.o.m 2.0 Å)

0.08

f(Le-e)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 40

0.06 0.04

0.02 0 3.5

4

4.5

5

5.5

6

6.5

7

Le-e (Å)

Figure 20: The changes in Le−e of nC6 when it passes from one zeolite Y cage (parent cage) to another (daughter cage).

38


Page 39 of 40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Graphical TOC Entry The bending of n-hexane during the cage-to-cage diffusion.

39



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Conformational changes in n-hexane during passage through 12-ring window interconnecting two neighboring supercages. 866x294mm (100 x 100 DPI)


Page 40 of 40

Hexane Isomers in Faujasite: Anomalous Diffusion and Kinetic

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