Temperature Dependence of Volume Change of NaX and NaY

May 19, 2014 - The simulation results show that DAY and NaY monotonously contract over the entire temperature range 50–600 K, but the coefficient of...
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Temperature Dependence of Volume Change of NaX and NaY Zeolites Using Molecular Dynamics Simulations Hyein Guk,† Daejin Kim,† Heeju Lee,‡ Yong Nam Choi,‡ Sun Young Kang,† Seung-Hoon Choi,† and Dong Hyen Chung*,† †

Insilicotech Co. Ltd., C-602, Korea Bio Park, 700, Daewangpangyo-ro, Bundang-gu, Seongnam 463-400, Korea Neutron Science Division, Korea Atomic Energy Research Institute, Daejeon 305-353, Korea

‡

S Supporting Information *

ABSTRACT: The thermal expansion behavior of faujasite zeolites, dealuminated Y (DAY), NaX, and NaY, has been studied by means of molecular dynamics (MD) simulations. In this work, harmonic potential parameters for the bond stretching and the angle bending are optimized for the MD simulations. The simulation results show that DAY and NaY monotonously contract over the entire temperature range 50−600 K, but the coefficient of thermal expansion of DAY is a more negative value (−4.2 × 10−6 K−1) than that of NaY (−2.9 × 10−6 K−1). On the other hand, NaX contracts up to room temperature and expands upon further heating. The analysis of bond lengths and angles shows that the volume change behaviors are highly correlated to the bond angle changes with temperature. The nonmonotonous volume change behavior of NaX is also directly related to the bond angle changes. From the radial distribution function of Na+ ions, we found that the highly concentrated Na+ ions in NaX can exert repulsive forces on each other, such that the volume change direction above room temperature can be reversed.

1. INTRODUCTION Most materials expand with temperature, but there are exceptional materials that contract with temperature. These materials are said to show negative thermal expansion. Zeolites except for cancrinite and sodalite are typical materials having the negative coefficient of thermal expansion.1−3 Zeolites are crystalline aluminosilicate materials that have micropores built by various connections of SiO4 and AlO4− tetrahedra. The size selectivity is the unique property of zeolites, which makes zeolites useful for a wide range of industrial applications, such as gas separation and catalysts. In particular, NaX (Si/Al < 1.5) and NaY (Si/Al > 1.5) with the faujasite framework structure are industrially used as a cracking catalyst to increase the yield of gasoline and diesel fuel from crude oil feedstock by cracking heavy paraffins into gasoline grade naphthas.4 The change of framework structure following the volume change could deeply influence the transport of included guest molecules and the catalytic performances. Therefore, many experiments5−14 and simulations1,15−18 have been carried out to study thermal expansion behavior of zeolites, and through the many research articles and review papers, the mechanism of the negative thermal expansion has been described as the low-frequency vibrating modes of the joint connecting rigid tetrahedral structures of SiO4 and AlO4, which are called rigid unit modes (RUM) of zeolites.25−27 Most simulation studies on the negative thermal expansion of zeolites have been performed by a lattice dynamics method.1,15−17 In the lattice dynamics simulation results, the thermal expansion behaviors of zeolites and AlPO4-17 have been well reproduced, and these articles have described that © 2014 American Chemical Society

volume contraction was caused by the existence of two- and three-dimensional channel systems for zeolites and AlPO4’s,1 decreases in bond distances rather than rocking motions of rigid polyhedra for AlPO4-17,15 and the rotations of rigid unit modes for DAY and NaX.17 In the molecular dynamics (MD) simulation,18 Yamahara et al. dealt with only siliceous MFI-type zeolite (silicalite), so that the effects of Al and Na on the thermal expansion behavior have not been studied. In this work, we performed MD simulations to explicitly deal with the dynamic motions of the frameworks. We reproduced the thermal expansion behaviors of DAY (siliceous faujasite, dealuminated Y) and NaX zeolites, and predicted the thermal expansion behavior of NaY zeolite. We analyzed the bond lengths, bond angles, and Na−Na radial distribution function (RDF) to understand the different thermal expansion behaviors of NaX and NaY zeolites.

2. SIMULATION MODELS AND METHODS 2.1. Unit Cell Construction and Parameter Optimization. The unit cells of NaX and NaY were constructed on the basis of the literature data.19,20 The lattice constants of cubic NaX and NaY are 25.03 and 24.76 Å, respectively. The unit cell of NaX has 384 O, 104 Si, 88 Al, and 88 Na atoms, and that of NaY is composed of 384 O, 136 Si, 56 Al, and 56 Na atoms. The atomic coordinates in the crystal structures of NaX and Received: February 4, 2014 Revised: May 16, 2014 Published: May 19, 2014 12811

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50, 100, 200, 300, 400, 500, and 600 K, and the temperature and pressure were controlled by the Andersen thermostat23 and the Parrinello barostat,24 respectively. The simulation time was 500 ps, and the data collected for the last 200 ps were used for the analysis of thermal expansion behavior.

NaY are listed in the Supporting Information. The crystal structures have substitutional disorder positions. To find stable atomic configurations for the disorder positions, Metropolis Monte Carlo (MMC) simulations were performed. To build the initial structures for the MMC simulations, the disordered unit cells of NaX and NaY were converted into the corresponding primitive cells, which are a quarter of the unit cell. The Si, Al, and Na atoms were distributed on the substitutional disorder positions according to the occupancy probability. In the case of NaX, there are two Wyckoff positions of 96g for Si and Al atoms. One 96g position has 24 points only for Si atoms, and the other is for 24 mixture atoms with Si occupancy of 0.0833 and Al occupancy of 0.9167, which were approximated to 2 Si and 22 Al atoms. Because 24 Na atoms located on another Wyckoff position 96g have partial occupancy of 0.25, 18 Na atoms among them were randomly selected and removed. There is one mixture atom position called the Wyckoff position 192i in NaY, and the occupancy of Si is 0.7083 and that of Al is 0.2917. 48 points corresponding to the Wyckoff position 192i were occupied by 34 Si and 14 Al atoms in accordance with Loewenstein’s rule.21 14 Na atoms in NaY were located on one 16c and two 32e positions with partial occupancies of 0.55, 0.46, and 0.97, respectively, which were approximated to 0.5, 0.5, and 1.0. Therefore, 2 out of 4 points of the Wyckoff position 16c, 4 out of 8 points of the Wyckoff position 32e, and 8 points of the other Wyckoff position 32e were randomly occupied by Na atoms. Using these initial structures, we performed MMC simulations. The total number of MMC simulation steps was 1 × 106. At every MMC step, we randomly chose a pair of Si− Al, or vacancy−Na within the same Wyckoff positions and exchanged their positions with each other, and the energies of the generated structures were calculated with the Krokidas parameter set. The most stable primitive cells of NaX and NaY from MMC simulations were converted again into a conventional cell. These structures were used for the initial structures of MD simulations. By repeating MD simulations with the initial optimized structures at 50, 100, 300, and 600 K and manual variation of potential parameters, we did the first optimization of the potential parameters to fit the thermal expansion behaviors of the zeolites. Using these first optimized parameters (Supporting Information Table S3), we carried out MMC simulations to find the most stable configurations of NaX and NaY, and henceforth we used these optimized structures for all simulations. With these stable structures, we tried again to optimize potential parameters. At this time, we used the Monte Carlo procedure to optimize the potential parameters, which is explained in detail in section 3.1, and the final optimized parameters were used for the following simulations. The unit cell of DAY was obtained on the basis of the NaY structure. The Si atoms were substituted for all Al atoms, and all Na atoms were removed, and the geometry optimization was performed by the Dmol3 program in the Materials Studio 6.1 package.22 The optimized unit cell of DAY has a lattice constant of 24.44 Å, and consists of 384 O and 192 Si atoms. 2.2. Molecular Dynamics Simulations. The MD simulations were performed using the Forcite program in the Materials Studio 6.1.22 The force field parameters were taken from ref 17, and harmonic bond and angle potential parameters were optimized for the MD simulations. NPT (isothermal− isobaric ensemble) simulations were performed at 0.0 GPa and

3. RESULTS AND DISCUSSION 3.1. Force Field Parameters for Molecular Dynamics Simulations. There are some experimental data explaining the effect of temperature on the faujasites in the literature.8,9,17 The DAY shows monotonic contraction from 25 to 570 K,8 but the NaX contracts up to the ambient temperature9 and expands above it.17 Krokidas et al. have developed a potential parameter set for NaX (Krokidas potential) and successfully reproduced the thermal expansion behaviors of NaX using their own parameter set in lattice dynamics simulations. We have applied the Krokidas potential parameter set to our MD simulations. To quantitatively compare the simulation results with the experiments, the coefficient of thermal expansion was calculated by the following equation: Δl α= l0ΔT (1) where Δl is the change in average lattice constant, l0 is the initial average lattice constant, and ΔT is the change in temperature. Although the coefficient of thermal expansion of DAY calculated from the MD simulation results (−2.6 × 10−6 K−1) is different from −4.2 × 10−6 K−1 experimentally obtained by Attfield et al.,8 as Figure 1 shows, the volume change

Figure 1. Relative volume of DAY (square) and NaX (triangle) from experiments8,9,17 and the present simulation using the Krokidas potential in the temperature range of 50−600 K. The experimental data of NaX below 300 K are for NaX with Si/Al ratio of 1.54, and those above 300 K are for NaX with Si/Al ratio of 1.15. The open symbols are for the experimental data, and the filled symbols are for the simulation data.

tendency of DAY seems similar to the experimental data. However, we did not succeed in reproducing the thermal expansion behavior of NaX with the Krokidas potential in MD simulations. Figure 1 shows that NaX monotonically expands as the temperature increases. Therefore, we needed modifications of the Krokidas potential for MD simulations. First, we increased the force constant of the harmonic bonding potential for Si−O bond from 17 to 34 eV/Å2 to describe the experimental results of DAY. Second, we optimized the other potential parameters using Monte Carlo procedures: we varied harmonic potential parameters of Al−O bond and Si−O−Al 12812

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angle, and then using those parameters we performed MD simulations of NaX at 50, 100, 300, and 600 K, and finally we obtained a harmonic potential parameters set minimizing the differences in volume change profiles between simulation results and experimental data. Potential parameters for nonbonded interactions such as Coulombic and Buckingham potentials took the values of the Krokidas potential. The modified force field parameters for MD simulations are shown in Table 1. Table 1. Modified Force Field Parameters for the MD Simulations harmonic bonding potential Si−O KR (eV/Å2) R0 (Å)

2

Kθ (eV/rad ) θ (deg)

Al−O

34 11.05 1.64 1.72 harmonic angle potential Si−O−Si

Si−O−Al

0.5 149.8

3.47 140.0

3.2. Thermal Expansion Behaviors of Faujasites. The MD simulation results using the modified potential parameters are shown in Figures 2 and 3. We reproduced the thermal Figure 3. Relative volume of NaX from experiments9,17 (△) and simulation (▲-dotted line) data using the modified potential parameters in the temperature range of (a) 50−300 K, where the Si/Al ratio of NaX in the experiments is 1.54; (b) 300−600 K, where the Si/Al ratio of NaX in the experiments is 1.15.

the MMC simulation, and the same MD simulations with these structures were performed. We observed a measurable difference in the thermal behavior depending on the ion distribution, although the general trend of the thermal behavior is very similar from each other. Simulation results are shown in the Supporting Information (Figure S1). We found that thermal expansion behaviors of NaX and NaY are similar up to room temperature but become different at high temperature. We analyzed the MD trajectories to explain the volume change behaviors in terms of bonds and angles. There is one type of bond (Si−O) and two types of angles (Si− O−Si and O−Si−O) in DAY. On the other hand, there are two types of bonds (Si−O and Al−O) and four types of angles (Si− O−Si, Si−O−Al, O−Si−O, and O−Al−O) in the NaX and NaY. We calculated the average bond length and average bond angle averaged over all bonds and angles through the trajectory analysis. Figure 4 shows that there are two competitive processes. One is the increase of the average bond length, which is the volume-increasing process, and the other is the decrease of the average bond angle, which is the volumedecreasing process. For all faujasites, the average bond length is increased with temperature, and the average bond angle is decreased. However, there is a difference in the average bond angle between NaX and the others. For DAY and NaY, the gradient of the average bond angle is almost constant with temperature, but that is gradually decreased above 200 K for NaX. In other words, in the case of NaX, the effect of the average bond angle on the volume contraction with temperature is reduced, and therefore the volume expands above room

Figure 2. Relative volume of DAY (square) and NaY (circle) from experiments8 and simulations in the temperature range of 50−600 K. The open symbols are for the experimental data, and the filled symbols are for the simulation data.

expansion behaviors of both DAY and NaX, and predicted thermal expansion behavior of NaY. The thermal expansion tendency of DAY and NaX is in good agreement with the experimental data.8,9,17 The average lattice parameters obtained in simulations are shown in Table 2, and using these data, we calculated the coefficients of thermal expansion. The coefficient of thermal expansion of DAY is the same as the experimental value (−4.2 × 10−6 K−1). The coefficient of thermal expansion of NaX is −8.1 × 10−7 K−1 up to room temperature and 7.8 × 10−7 K−1 above 300 K. The coefficient of thermal expansion of NaY is predicted to be −2.9 × 10−6 K−1. Thermal expansion behavior of NaX is followed only by the c axis, and the other two display the opposite behavior. For NaY, only a and b axes are decreasing in line with the volume contraction. Presumably this anisotropic volume change occurs by nonsymmetric model of NaX and NaY. Additionally, we took four different structures for NaX with different distributions of Si, Al, and Na ions from 12813

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Table 2. Lattice Parameters of Faujasites Obtained from MD Simulation DAY T (K)

a (Å)

b (Å)

c (Å)

α (deg)

β (deg)

γ (deg)

50 100 200 300 400 500 600

24.664 24.660 24.648 24.638 24.628 24.619 24.608

24.665 24.659 24.649 24.639 24.629 24.619 24.609

24.664 24.660 24.650 24.638 24.626 24.617 24.604

90.001 90.001 89.996 90.001 90.002 90.006 89.999

89.998 90.000 89.999 90.002 89.996 89.997 89.999

89.999 90.002 90.002 90.002 90.003 90.005 90.002

NaX T (K)

a (Å)

b (Å)

c (Å)

α (deg)

β (deg)

γ (deg)

50 100 200 300 400 500 600

24.728 24.777 24.794 24.798 24.802 24.787 24.797

25.029 25.069 25.079 25.090 25.083 24.951 24.896

24.872 24.773 24.743 24.726 24.731 24.890 24.938

88.663 88.738 88.719 88.762 88.787 88.832 88.879

89.456 89.730 89.731 89.736 89.749 90.008 90.089

89.800 89.685 89.392 89.378 89.376 89.643 89.739

NaY T (K)

a (Å)

b (Å)

c (Å)

α (deg)

β (deg)

γ (deg)

50 100 200 300 400 500 600

24.798 24.796 24.793 24.786 24.746 24.719 24.707

24.882 24.881 24.876 24.874 24.836 24.818 24.806

24.869 24.865 24.858 24.851 24.892 24.912 24.916

89.626 89.636 89.647 89.660 89.735 89.787 89.805

89.840 89.846 89.852 89.855 89.965 90.019 90.042

90.283 90.287 90.293 90.295 90.063 89.961 89.915

temperature due to increased average bond length and the decreased effect of the average bond angle on the volume contraction. For DAY and NaY, although the average bond length is increased with temperature, the volume contraction induced by a decrease of the average bond angle predominates over the volume expansion by an increase of the average bond length. From these results, the volume change of faujasites is closely related to the change of the average bond angle. Especially, the average M−O−M angle (Figure 4c) changes in a very different way for NaX, while the average O−M−O angle shows almost the same behavior for all zeolite models and its change with temperature is ignorable, which indicates MO4 tetrahedral structures are rigid units. These results are in line with experimental data8 that the tetrahedra rotate without changing their shape and RUM theory.25,28,29 Additionally, we performed a Na−Na RDF analysis to understand the effect of Na+ ion concentration on the volume change. Na−Na RDF of NaX and NaY is shown in Figure 5. In the case of NaX, the first peak position of Na−Na RDF varied as the temperature increased from 50 to 200 K. The first peak position of NaX at 50, 100, and 200 K is about 4.4, 4.3, and 4.5 Å, respectively. This shift is closely related to the volume contraction and the Coulomb repulsion between Na+ ions, and thus we calculated the electrostatic energy between Na+ ions divided by the number of Na+ ions, which is shown in Figure 6. As for NaX, the electrostatic energy of a Na+ ion steeply increases due to volume contraction in the temperature range of 50−300 K, and slowly decreases as the volume expands. As the temperature increases from 50 to 100 K, the shortened distances between Na+ ions result in a steep increase of the repulsive energy. Although the first peak position of Na−Na

Figure 4. (a) Average bond length, (b) average bond angle, and (c) average O−M−O and M−O−M angles (M = Si, Al) of DAY (square), NaX (triangle), and NaY (circle). The open symbols are for the average O−M−O angle, and the filled symbols are for the average M− O−M angle.

RDF above 100 K shifts to a longer distance, the repulsive energy still increases up to 300 K. These results indicate that as the volume contracts, the induced large repulsive energy between Na+ ions hinders the further contraction, and the volume then begins to expand to reduce the repulsive energy. Consequently, the large repulsive energy between Na+ ions can be considered as a driving force for the volume expansion above 300 K. On the other hand, there is no variation in the position of the first peak of NaY on the heating. This means that Na− Na distance is far enough because of the lower concentration of Na+ ion than NaX. Although the electrostatic energy between Na+ ions of NaY constantly increases due to volume contraction, this is much lower than NaX, and therefore the volume expansion does not happen in the NaY. 12814

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range 200−600 K. The hindrance to reduction of the bond angle in NaX could be caused by the difference in concentration of Na+ ions between NaX and NaY. As for NaX, the large repulsion between Na+ ions prohibits the decrease of the average bond angle, and the average bond length is increased with temperature; hence NaX has a positive thermal expansion above 300 K. The analysis of the simulation results shows that the volume change of faujasites is closely related to the average bond angle, especially the average M− O−M, and this is in line with RUM theory.25,28,29 Additionally, the results of the Na−Na RDF analysis showed that highly concentrated Na+ ions in NaX exert repulsive forces on each other, which is the main driving force for the volume expansion above room temperature.

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ASSOCIATED CONTENT

S Supporting Information *

Atomic coordinates of NaX and NaY based on the literature, the first optimized parameter set, thermal expansion behavior of four different structures for NaX, and fractional coordinates of the initial structure of NaX and NaY for MD simulations. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +82-31-628-0310. Fax: +82-31-628-0333. E-mail: [email protected]. Notes

Figure 5. Na−Na radial distribution function of (a) NaX and (b) NaY.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Creative Research Program (2012-2014) of the Korea Atomic Energy Research Institute. We thank Accelrys Korea for the support of modeling software.

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REFERENCES

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Figure 6. Electrostatic energy of Na+ ions in NaX (▲) and NaY (●).

4. CONCLUSIONS We have optimized force field parameters for the MD simulations and performed the MD simulations using the modified potential parameters to understand the thermal expansion behavior of faujasites in the temperature range of 50−600 K. The MD simulations showed that DAY and NaY contract with temperature. On the other hand, NaX contracts up to room temperature and expands above it. An analysis of the simulations showed that there are two competing processes in the volume change of faujasites. One is the increase in the average bond length, and the other is the decrease in the average bond angle. The monotonous decrease of the average bond angle predominates in DAY and NaY, and thus the volume monotonously decreases. In the case of NaX, there is almost no change of the average bond angle in the temperature 12815

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