Chemical Physics Letters 501 (2011) 345–350

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Chemical Physics Letters

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Rotational dynamics of propylene in ZSM-5 zeolitic frameworks

Siddharth Gautam 1, V.K. Sharma, S. Mitra, S.L. Chaplot, R. Mukhopadhyay ⇑Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 1 November 2010In final form 26 November 2010Available online 30 November 2010

0009-2614/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.cplett.2010.11.080

⇑ Corresponding author. Fax: +91 22 25505151.E-mail addresses: mukhop@barc.gov.in, mukhop@

khopadhyay).1 Present address: Donostia International Physic

Lardizabal, 420018 Donostia-San Sebastian, Spain.

Rotational dynamics of propylene molecules adsorbed in ZSM-5 zeolite as studied by molecular dynamicssimulation technique is reported here. Intermediate scattering functions corresponding to the rotationalmotion indicate a complex and anisotropic rotational motion of the propylene molecule. Orientationalcorrelation functions indicate that propylene molecule performs librations at short times. Calculatedrotational density of states and dynamic structure factor further confirmed this. It is also observed thatwhile diffusing, propylene molecules prefer its orientation along the channel direction mainly becauseof the host structure rather than spatial restriction.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Zeolites are crystalline microporous aluminosilicates, wellknown for their molecular sieving and catalytic properties andare used extensively in petrochemical and refining industries [1].The shape selectivity of zeolitic materials with respect to hydrocar-bons for the cracking reactions has been an ongoing research fieldfor quite some time now [2]. The catalytic properties of zeolites forcracking reactions are influenced by the way hydrocarbons arechosen both on the reactant as well as the product sides by theirshapes. An understanding of these properties of the zeolites re-quires detailed investigation of the diffusive behavior of the ad-sorbed molecules. A number of experimental methods such asquasielastic neutron scattering (QENS) [3–6], pulsed field gradientNMR, dynamic light scattering techniques etc. are available tomeasure self-diffusivity [7–9]. Computational approaches such asmolecular dynamics have provided valuable insight into self-diffu-sivity and do not suffer experimental limitation [10–14]. The re-sults of all these investigations are generally found to be in goodagreement for a number of zeolite–sorbate systems [4–6,11–14].In general, apart from the translational motion, sorbate moleculecan also perform rotational motion inside zeolite. It is interestingto investigate how the rotational motion gets affected in confine-ment and how it couples with the translational motion. This in turncan help in designing better separation and catalytic processes.

In recent times, there have been a number of reports on therotational motion in confined media [15–19]. Effect of confinementon rotational motion of the guest molecules is discussed in detailby Farrer and Fourkas [15]. They showed that it depends on many

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apsara.barc.ernet.in (R. Mu-

s Center, Paseo Manuel de

factors like, host–guest interaction, the shape of the host as well asguest, the relative volume of the cages, temperature, etc. Severalanomalies such as levitation effect, anisotropy in rotational motionwith size and shape of the guest molecules and host matrices havebeen reported in literature. Sharma et al. [16] had shown that for amodel guest tetrahedral molecule, AX4, rotational diffusivity showsa peak at a particular value of lAX (bond length A–X). This was themanifestation of the minimum torque experienced by the mole-cule. Recently Huang et al. [17] have studied the effect of the shapeof guest molecules on the rotational motion where n-pentane and2-methyl butane are the guest molecules adsorbed in MCM-22. Itwas found that while 2-methyl butane is trapped inside the cageand undergoes reorientational motions, n-pentane diffusesthrough the cages in addition to the rotational motion. RecentNMR study [8] speculated the existence of librational motion incase of butane adsorbed in ZSM-5 zeolite. However, no direct evi-dence of librational motion of hydrocarbon adsorbed in zeolite isfound so far. For the present study, we have chosen propylene(an unsaturated hydrocarbon) as an adsorbed species in ZSM-5zeolites. Propylene finds usage in reducing NO under excess oxy-gen condition inside a ZSM-5 zeolite. This is widely employed inautomobile industry [20]. The all silica form of ZSM-5 zeolite iscalled silicalite. ZSM-5 zeolite structure has two different channelsystems, straight as well as sinusoidal. Straight channels with anelliptical cross-section of approximately 5.2–5.7 Å are parallel tothe crystallographic axis b. Sinusoidal channels having circularcross section of 5.4 Å in the ‘a–c’ plane intersect these channels.The resulting intersections are elongated cavities with diameterup to 9 Å. Schematic of ZSM-5 zeolite is shown in Figure 1a. Diffu-sion behavior of several hydrocarbons was studied in ZSM-5 zeo-lite using different experimental and simulation techniques[4,18,21–24].

We have earlier reported the translational motion of propylenein ZSM-5 zeolite and compared the results obtained from both MD

Figure 1. Schematic of (a) ZSM-5 zeolite and (b) propylene molecules as used in the present study.

346 S. Gautam et al. / Chemical Physics Letters 501 (2011) 345–350

simulation and QENS experiment [4]. Here we report on the rota-tional dynamics of propylene inside ZSM-5 zeolite using MD simu-lation techniques. MD simulation results reveal many interestingfeatures, such as existence of librational motion of propylene inZSM-5 and preferential ordering of the propylene molecule insidethe channel. This letter is organized in four sections. Details per-taining to molecular dynamics simulation for the present systemsare given in section 2, results and discussion are given in section 3and conclusions are listed in section 4.

2. Simulation details

Molecular dynamics simulations of propylene molecules con-fined in ZSM-5 zeolite have been carried out in the micro-canonicalensemble. Atomic positions of ZSM-5 zeolite as reported by Kon-ingsveld et al. [25] have been used in the simulation. The simula-tion cell consisting of (2 � 2 � 2) unit cells of ZSM-5 zeolite withsize of 40.044 � 39.798 � 26.766 Å. Test runs made with largersystem sizes did not lead to significant changes in the results. Peri-odic boundary conditions are used in all three directions. Theframework of zeolite was fixed and propylene molecules were al-lowed to move. Propylene molecule was modelled as three inter-acting sites (CH3–CH–CH2) under united atom model as shown inFigure 1b. The propylene is considered as a rigid molecule andtherefore the bond angle and bond lengths between the sites arekept constant throughout the simulation. The rotational degreesof freedom are modeled using quaternion formalism [26]. Equa-tions of motions for both translational and rotational motion areintegrated using the leapfrog form of the Verlet algorithm. MDsimulations were carried out for different loading of propylenemolecules, namely 1, 2 and 8 molecules per unit cell of ZSM-5 zeo-lite. A simulation time step of 1 fs was used in the simulation,which gave good energy conservation. The temperature of the sys-tem was adjusted to 300 K at each step for the first 300 ps. Subse-quently production run of 1.3 ns was carried out.

Intermolecular interactions were modelled by Lennard–Jones(6–12) potential. The guest–guest as well as the guest–zeoliteinteraction could thus be written as

UðrijÞ ¼ 4eijrij

rij

� �12

� rij

rij

� �6" #

ð1Þ

where U is the potential between the interacting species i and j,separated by a distance rij. The interaction parameters eij and rij

used in the simulation are as available in the literature [27,28].The Lorentz–Berthelot combination rule was used to obtain thecross or mixed terms. A cutoff radius of 13 Å is employed forguest–guest and guest–zeolite interaction.

In a recent MD simulation study, a comparison between thedynamics of n-alkanes in rigid and flexible frameworks has beendiscussed [29]. It reports that only small molecules at low loadings

show some enhancement in diffusivity in a flexible framework.However, for larger molecules and at higher loadings, guest–guestinteractions mostly control the diffusion and hence the effects of aflexible framework become almost negligible.

3. Results and discussion

Molecular motion inside the channels of zeolite can be typifiedby a fast regime corresponds to the rattling of the trapped mole-cule, the intermediate regime to the escape process of this mole-cule and the slowest regime to the cage relaxation with itscollective character. Motion of a molecular species inside the zeo-lite channels involves translation as well as rotation. In MD simu-lation, the center of mass position as a function of time providesinformation about the translational motion, while the evolutionof the orientation of the molecules depicts the rotational motion.The position vector of an interacting species of propylene moleculecan be written as a sum of the position vector of the center of massof the molecule with respect to a space fixed reference frame, rCM,and the position vector of the species with respect to the center ofmass of the molecule d,

r ¼ rCM þ d ð2Þ

This decomposition of the position vector of an interacting spe-cies in the space fixed frame can be used to separate the two com-ponents – translational and rotational motion of the molecule. Therotational motion can be investigated by studying the evolution ofthe position vector of a species belonging to the guest moleculewith respect to the center of mass of the molecule as stated inEq. (2). Intermediate scattering functions corresponding to therotational motion can be calculated as,

IrotðQ ; tÞ ¼ hexp½iQ :ðdðt þ t0Þ � dðt0ÞÞ�i ð3Þ

In the present study we have followed the orientation of a CH3

site with respect to center of mass to study the rotational motion.Averaging was done over all possible orientations of the Q vector.

Intermediate scattering functions, Irot(Q,t), for rotational motionof propylene adsorbed in ZSM-5 zeolite at different concentrationof loading is shown in Figure 2a. As can be seen from 2a, unliketranslational motion, rotational intermediate scattering functionsdoes not decay to zero at long time. Values of Irot(Q,t) at long timecan be compared with the elastic incoherent structure factor (EISF)as observed in QENS experiment. It can be seen from the figure thatIrot(Q,t) decay more rapidly at lower loading which implies that thepropylene molecules undergo faster rotational motion. However,the behavior of Irot(Q,t) and their long time values remain samefor different loading suggesting that the nature of rotations donot change with the loading. In view of this, here onwards, only re-sults of the simulation carried out for 8 molecule/unit cell will bediscussed. Variations of Irot(Q,t) with Q values are shown in Figure2b. To understand the detailed mechanism of the rotational motion

0.2

0.4

0.6

0.8

1.0

0 25 50 75 100 0.01 0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0Q=1.45 Å-1

Irot (Q

,t)

t (ps)

1 Mol/UC 2 Mol/UC 8 Mol/UC

ba

t (ps)

Q=0.46 Å-1

Q=0.58 Å-1

Q=1.45 Å-1

Q=2.44 Å-1

Irot (Q

,t)

Figure 2. (a) Intermediate scattering functions for rotational motion at different loading of propylene molecules per unit cell of ZSM-5 zeolite. (b) Variation of Irot(Q,t) for 8propylene molecules per unit cell of ZSM-5 zeolite.

1 10 100

0.0

0.2

0.4

0.6

0.8

1.0

l = 1

l = 6l = 5l = 4l = 3

l = 2

<P

l(e(t

).e(

0)>

Time (ps)

Figure 3. The behavior of the first six orientational correlation functions,<Pl(e(t).e(0))> with time.

S. Gautam et al. / Chemical Physics Letters 501 (2011) 345–350 347

inside zeolitic channels, the intermediate scattering function Ir-

ot(Q,t) was compared with theoretical models. For isotropic rota-tion, the rotation axis is not unique and distributed isotropically.In this case, Irot(Q,t) can be written as [30].

IrotðQ ; tÞ ¼X1l¼0

ð2lþ 1Þj2l ðQRÞClðtÞ ð4Þ

where jl’s are Bessel functions, R is the radius of gyration and Cl arethe orientational correlation functions defined as,

ClðtÞ ¼ hPlðeðtÞ:eð0ÞÞi ð5Þ

Pl is the Legendre polynomial of order l and e is a unit vector di-rect towards the CH3 site with respect to center of mass of the pro-pylene molecule. Therefore, evolution of e with time can beanalysed to get the details of rotational motion of the propylenemolecule. In particular, in the case of isotropic rotational diffusionthrough small angular jumps, the orientational correlation func-tions in Eq. (5) can be expressed in terms of the rotational diffusioncoefficient (DR) as

ClðtÞ ¼ expð�lðlþ 1ÞDRtÞ ð6Þ

It has been shown in Ref. [18] that in case of propylene, the fac-tor (2l + 1)jl

2(QR) in Eq. (4) has significant contributions only up tol = 6 for all the Q values up to 2.5 �1 and the summation over infi-nite terms can be truncated at l = 6. It was found that Irot(Q,t) func-tions do not follow the simple exponential decay characteristic ofisotropic rotational diffusion model. In addition, data show someoscillations at short times (Figure 2b), which are investigated fur-ther as described below.

As can be seen from Eq. (4) above, the time dependence of theintermediate scattering function for rotational motion comesexclusively from the orientational correlation functions. The orien-tational correlation functions of different orders were calculatedand shown in Figure 3. The functions show conspicuous wobblingbefore decaying to lower values instead of a simple exponential de-cay. Oscillations in these functions indicate that the molecules un-dergo librational motion [31]. Rotational dynamics of the trappedmolecule inside the channel may consist of oscillations of the mol-ecule as a whole until the molecule experiences a suitable torqueand the space to rotate freely. Oscillations of the trapped moleculeas a whole also known as librational motion was also observed byNMR studies on butane adsorbed in ZSM-5 zeolite [8].

Existence of libration motion for propylene in ZSM-5 zeolite isfurther confirmed from the calculated Fourier transform (FT) of Ir-

ot(Q,t) and angular velocity auto correlation functions (AVACF)which are related to dynamical structure factor S(Q,) and rotationaldensity of state respectively. FT of Irot(Q,t) and AVACF are shown inFigure 4a and b respectively. The peak at 7 meV as observed in both

the figures corresponds to the existence of libration of propylenemolecule.

Torque autocorrelation function (TACF) is also calculated forpropylene adsorbed in ZSM-5 zeolite in order to investigate thenature of torque responsible for the rotational motion of propylenemolecule inside the zeolitic cavity. Large amplitude oscillation inTACF is found as shown in Figure 5a. The torque on a particularpropylene molecule consists of two parts; first arises due to allother propylene molecules present in the zeolitic cavity (guest–guest) and second is due to the zeolite framework atoms (guest–host). In order to examine the origin of large oscillations in TACFfor ZSM-5 zeolite, torque due to guest–guest interactions and tor-que due to guest–host interactions are separately calculated. TACFdue to guest–guest interaction and guest–host interaction for ZSM-5 zeolite are separately shown in Figure 5b. It can be seen from thefigure that the large oscillations are mostly due to guest–hostinteraction rather than guest–guest interaction.

One can obtain the value of the libration angle for propylenemolecules in ZSM-5 zeolite by using Eq. (5) and settingPlðcosðhmÞÞ = Cl(tm), where tm is the time at which the first mini-mum occurs in the orientational correlation functions (Figure 3).This leads to a mean libration angle of 40� for propylene adsorbedin ZSM-5 zeolite. Correlation times, sl, associated with orienta-tional correlation functions can be calculated as

sl ¼Z 1

0ClðtÞdt ¼

Z 1

0hPlðeðtÞ:eð0ÞÞidt ð7Þ

Values of correlation times, s1 and s2 obtained from the orienta-tional correlation functions using Eq. (7) are 38 ± 3 and 94 ± 4 psrespectively.

0 5 10 15 200

1

2

3b

FT (

AV

AC

F)

E (meV)0 5 10 15 20

0

4

8

Q=1.83 Å-1FT

(IR

(Q,t)

)

E (meV)

a

Figure 4. (a) Fourier Transform of Irot(Q,t) for propylene in ZSM-5 zeolite at typical Q-value of 1.83 �1. A peak around �7 meV is observed. (b) Fourier Transform of AVACF forpropylene in ZSM-5 zeolite.

0 1 2 3

-0.5

0.0

0.5

1.0

t (ps)

a

TA

CF

t (ps)0 1 2 3

-0.5

0.0

0.5

1.0

Guest-Guest Guest-Host

b

Figure 5. (a) Torque auto correlation function (TACF) for propylene in ZSM-5 zeolite. Presence of oscillations is observed. (b) TACF for due to guest–guest as well as guest–host interaction. TACF due to guest–host interaction is seen to be responsible for the oscillations.

348 S. Gautam et al. / Chemical Physics Letters 501 (2011) 345–350

To probe the nature of motion, the time evolutions of cos(h), hbeing the angle of a unit vector e attached to a tagged propylenemolecule adsorbed in ZSM–5 with the X, Y and Z-axis in the spacefixed frame are shown in Figure 6a. It is found that the angularjumps do not comprise all the possible angles uniformly in allthe X,Y,Z directions. It is found that while these are similar in Y& Z directions it is different in X direction indicating a clear aniso-tropic motion. The angular jumps in Y and Z direction are limitedto a small angular band indicating restricted rotations. However,in X direction, the distribution of angular jumps is limited to a

0 30 60 90 120 150 180

-1

0

1

Cos

θ

X direction Y direction Z direction

t (ps)

a b

Figure 6. (a) Projection of a unit vector e (directed towards CH3 site) with respect to cenzeolite. (b) Torque exerted on the molecules in the X direction due to guest–guest inter

much smaller value and the molecule found to flip at �140 psand again performs restricted rotation. Due to comparable size ofpropylene molecules and ZSM-5 channel diameter, reversal of ori-entation of the molecule is possible in two cases: (1) while trans-lating, the molecule finds a channel intersection which providesan opportunity to change its orientation before entering into an-other channel again and (2) due to the collision with the otherguest molecule. To probe the cause of this reversal of orientation,torque due to guest–guest and guest–zeolite interaction is calcu-lated. Time evolutions of torque experienced by the same molecule

0 30 60 90 120 150 180

-200

0

200

Tx (

GG

) (i

n ar

b. u

nit)

t (ps)

ter of mass in space fixed coordinate for short time for a tagged molecule in ZSM-5action.

-1

0

1

X (Å)

up to 140 ps

Y (

Å)

X (Å)

- 1 0 1 - 1 0 1

-1

0

1up to 200 ps

Y (

Å)

a b

Figure 7. Trajectory of the tip of unit vector associated with a tagged molecule in ZSM-5 zeolite in X–Y plane for (a) up to 140 ps and (b) up to 200 ps.

S. Gautam et al. / Chemical Physics Letters 501 (2011) 345–350 349

due to guest–guest and guest–zeolite interaction are calculated.Figure 6b shows the time evolutions of torque in the X directiondue to guest–guest interactions only. It can be seen from Figure6b, that around 140 ps, torque in the X direction due to guest–guest interaction shows some peaks suggesting collisions due toother guest molecules. Although not shown here, torque due toguest–host interaction shows no such change. Therefore, the flip-ping orientation of the molecule is mainly due to guest–guestinteraction.

Therefore, in general, rotation of a propylene molecule insideZSM-5 zeolite is characterised by restricted rotations for shorttimes, then flips its orientation and continues restricted rotations.This is clearly shown in Figure 7, where trajectories of the tip of theunit vector attached to a tagged molecule is plotted in X–Y planefor (a) up to 140 ps and (b) up to 200 ps. Restriction of h to a smallvalue suggests that the molecule confined in ZSM-5 zeolite per-forms a restricted rotation, possibly libration as indicated in therotational density of states. This indicates that the rotational mo-tion in ZSM-5 zeolite is much more complex in nature to modelit through simple isotropic rotation characterised by uniformangular jumps.

It is clear from Figure 6a that the tagged molecule prefers aspecific orientation inside ZSM-5 zeolitic channel in X direction.To probe whether this is the case in general for all the propylene

0 30 60 90 120 150 1800

7000

14000

21000

28000

35000

a

Tot

al N

umbe

r of

Ori

enta

tions

Theta (degree)

X Y Z

Figure 8. (a) Histogram of the distribution of projection angles of unit vector (from cenzeolite. (b) Schematic of a sphere covered by the tip of a unit vector e performing isotro

molecules inside the zeolite, the projection angles of the unit vec-tor e was binned for all the molecules for all times. Histogram ofthe distribution of projection angles of unit vector e to differentaxis in case of propylene adsorbed in ZSM-5 zeolite is shown in Fig-ure 8a. Two extra peaks apart from the peak at 90 degree are ob-served for projection angles with respect to X and Y axis asshown in Figure 8a. These extra peaks are found to be absent forprojection angles with respect to Z axis. The origin of the peakaround 90 degree in the distribution of projection angles can be ex-plained as follows: When a unit vector performs isotropic rotation,after a sufficient time, tip of the vector covers a sphere as shown inFigure 8b. Surface of the sphere is equally populated by the trajec-tories of the tip of the vector. At any given time, orientational con-figuration of the unit vector will be determined by the position ofthe tip in the surface of the sphere. Total number of orientationalconfigurations having projection angle h will depend on the lengthof circumference of the circle with radius sin(h) as shown in Figure8b. All the points (representing orientational configurations of theunit vector) in that circumference will have the same projectionangle h. Since circumference is maximum for the projection angleh = 90 degree, total number of orientational configurations willbe maximum for projection angle, h = 90 degree. Distribution cen-tered around 90 degree with respect to to X, Y and Z-axis is thus aconsequence of purely isotropic distribution of the projections.

b

ter of mass to a CH3 site) to different axis in case of propylene adsorbed in ZSM-5pic rotation.

350 S. Gautam et al. / Chemical Physics Letters 501 (2011) 345–350

Appearance of two extra peaks that are observed for projection an-gles with respect to X and Y axes (Figure 8a) shows that insideZSM-5 zeolite channel, molecules do not have random orienta-tions; instead, there exists a preferred orientation. Calculationshowed that the preferred angles correspond to the orientationwhen the molecular axis lies parallel to the channel axes. Further,these preferred orientations were observed only in X and Y direc-tion, and not in Z direction. This is expected as ZSM-5 zeolite con-sists channels in X and Y direction only and no channels in Zdirection. Therefore, it can be inferred that while translating, pro-pylene molecules are aligned along the channels. To check that thisis a consequence of channel structure or geometrical restriction orboth, MD simulation of propylene adsorbed in another zeolite,AlPO4-5 has been carried out. AlPO4-5 has only straight channelwith larger diameter (�11 Å) than ZSM-5 zeolite (�5.4 Å) and pro-vides enough space for propylene molecules to orient itself insidethe channel. Preferred orientation of propylene inside AlPO4-5was also observed along the channel direction. However, no signa-ture of libration motion was found in this case, due to the largerdiameter of the channels. Thus, the preferred orientation of theguest molecule inside a host zeolite is mainly due to the shape ofhost structure rather than size of channels whereas librational mo-tion arises mainly due to the geometrical restriction.

4. Conclusion

From the present study, it is found that the rotational dynamicsof propylene adsorbed in ZSM-5 zeolite is quite complex and sim-ple isotropic rotation could not explain the rotational intermediatescattering function. In addition, orientational correlation functionshows presence of librational motion at short times before it flipsits orientation. This was confirmed by rotational density of statesand the dynamic structure factor calculated by Fourier transforma-tion of angular velocity auto correlation function and intermediatescattering function respectively. MD simulation also showed thatthe propylene molecules prefer its orientation along the channeldirection during diffusion through the ZSM-5 zeolite. It is foundthat the preferred orientation of the guest molecule inside a hostzeolite is more due to the shape of host structure rather than the

size of the channels whereas librational motion arises mainly dueto the geometrical restriction.

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