Computational Study of Hydrocarbon Adsorption in ... - ACS Publications

Mar 8, 2011 - I. INTRODUCTION. The organic Rankine cycle (ORC) is an important method employed for the utilization of renewable energy sources such as...
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Computational Study of Hydrocarbon Adsorption in Metal-Organic Framework Ni2(dhtp) Xiuquan Sun,† Collin D. Wick,‡ Praveen. K. Thallapally,† B. Peter McGrail,† and Liem X. Dang*,† † ‡

Pacific Northwest National Laboratory, Richland, Washington 99352, United States Louisiana Tech University, Ruston, Louisiana 71270, United States ABSTRACT: Enhancing the efficiency of the Rankine cycle, which is utilized for multiple renewable energy sources, requires the use of a working fluid with a high latent heat of vaporization. To further enhance its latent heat, a working fluid can be placed in a metal organic heat carrier (MOHC) with a high heat of adsorption. One such material is Ni\DOBDC, in which linear alkanes have a higher heat of adsorption than cyclic alkanes. We carried out molecular dynamics simulations to investigate the structural, diffusive, and adsorption properties of n-hexane and cyclohexane in Ni\DOBDC. The strong binding for both n-hexane and cyclohexane with Ni\DOBDC is attributed to the increase of the heat of adsorption observed in experiments. Our structural results indicate the organic linkers in Ni\DOBDC are the primary binding sites for both n-hexane and cyclohexane molecules. However, at all temperatures and loadings examined in present work, n-hexane clearly showed stronger binding with Ni\DOBDC than cyclohexane. This was found to be the result of the ability of n-hexane to reconfigure its structure to a greater degree than cyclohexane to gain more contacts between adsorbates and adsorbents. The geometry and flexibility of guest molecules were also related to their diffusivity in Ni\DOBDC, with higher diffusion for flexible molecules. Because of the large pore sizes in Ni\DOBDC, energetic effects were the dominant force for alkane adsorption and selectivity.

I. INTRODUCTION The organic Rankine cycle (ORC) is an important method employed for the utilization of renewable energy sources such as geothermal, solar thermal, industrial waste heat, and biomass combustion, to generate the power production.1-7 The ORC utilizes a working fluid that is evaporated in a boiler, which can be heated by renewable sources, followed by its movement through a turbine to create useful work, and then condensation. The selection and design of working fluids for the ORC are vital to the efficiency of the procedure.8-13 Working fluids with high latent heats provide greater work output, and hydrocarbons show promising capability as ORC working fluids.6,13 Enhancing the efficiency of ORCs is an ongoing challenge to improve the viability of renewable energy sources. Recently, metal organic frameworks (MOFs), a new class of porous materials, have been developed to be metal-organic heat carriers (MOHCs), which can reversibly uptake and release selected organic compounds used as working fluids or refrigerants.14 By tuning the binding energy of the MOHC with specific working fluid molecules, a desorption enthalpy significantly greater (2 to 3) than the latent heat of vaporization of the pure fluid phase can be obtained.14 An ORC system utilizing MOHCs, therefore, can extract more heat from the heat source, allowing the delivery of a higher inlet enthalpy of the working fluid to the turbine, increasing its work output. This will reduce r 2011 American Chemical Society

capital costs, increase efficiency of the cycle, and expand the range of geothermal and solar resources suitable for economic power production. One interesting aspect has been found that working fluids with straight chain alkanes have higher heats of adsorption enthalpies than cyclic alkanes.14 However, there is little to no molecular level understanding as to why this is. MOFs, in general, possess unique properties and they can be modified in countless ways.15-25 The building blocks of MOFs consist of inorganic metals that form complexes with organic linkers. Both the inorganic metals, including their valency, and the functional groups in the organic linkers can be modified to develop nearly any structure imaginable. In addition to their use as MOHCs, these properties have the potential to be beneficial for a large number of applications including gas separation, gas storage, catalysis, and drug delivery.19,25-29 Molecular simulation is an ideal tool to gain molecular level insight into a variety of condensed systems, including liquid, solids, networks, and interfaces.30 The reason for this is that molecular level information can be described fairly unambiguously, but molecular simulation has the drawback that it relies on a model that has to be parametrized. One recent molecular Received: December 3, 2010 Revised: January 13, 2011 Published: March 08, 2011 2842

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Table 1. Potential Parameters Used in This Study; the Atoms in Parentheses Are Those Atom Types Connected to molecule alkane

Ni DOBDC

atom type

σ (Å)

ε (kcal/mol)

q (e)

CCH4

3.500

0.066

-0.24

CCH3 CCH2

3.500 3.500

0.066 0.066

-0.18 -0.12

H

2.500

0.030

0.06

Ni

2.525

0.015

0.563 -0.444

phenyl O

3.066

0.210

phenyl C(O)

3.400

0.086

0.315

phenyl H

2.600

0.015

0.177

phenyl C(H)

3.400

0.086

-0.192

phenoyl C(Ccarbo) Carboxylate C

3.400 3.400

0.086 0.086

-0.237 0.651

Carboxylate O

2.960

0.210

-0.517

Carboxylate O(Ni)

3.066

0.210

-0.315

should allow for the sorption of fairly high adsorbate concentrations. With these two promising properties, strong adsorbates interactions, and a high pore volume, Ni\DOBDC shows promising attributes to be an effective MOHC. There is a need to understand, on a molecular level, the adsorption properties in Ni\DOBDC to be able to predict the types of working fluids for the ORC it works best with, and possible ways to improve its design to maximize its adsorption enthalpy. In this report, we describe the exploration of the structural, energetic, and dynamical properties of n-hexane and cyclohexane with molecular dynamics simulations. Additionally, the adsorptions of methane, ethane, n-butane, n-hexane, and cyclohexane in Ni\DOBDC were studied with free energy perturbation calculations.

Figure 1. a) Unit cell of Ni\DOBDC. Carbons are represented as cyan, oxygen as red, hydrogen as white, and nickel as blue spheres. b) The fragment of Ni\DOBDC used to calculate partial charges.

simulation study was an investigation of the adsorption and diffusion of n-alkanes, cyclohexane, and benzene in the MOFs bipyridine molecular square and MOF-5 by Sarkisov et al.31 The authors described complex interactions between the guest and host molecules, and different structural and diffusive properties were found for molecules adsorbed in different MOFs. Duren and Snurr investigated the separation of methane and n-butane in five different MOFs, finding that IRMOFs (isoreticular metalorganic-frame) are promising materials for the separation of hydrocarbons.32 Jiang and Sandler performed Monte Carlo simulations to address the adsorption and separation of linear and branched alkanes in IRMOF-1. They found that energetic effects were dominant at low gas concentration, but with higher alkane concentration, entropic effects became dominant.27 Several years ago, a novel nickel-based MOF (Ni2(dhtp) or Ni\DOBDC) was synthesized.33 Ni\DOBDC contains a 3D honeycomb-like network structure, with a large 1D cylindrical channel having a diameter of about 11 Å (part a of Figure 1). The metal nickel sites in the frames are unsaturated following the removal of solvent molecules from the framework, which is expected to allow exceptionally strong binding with adsorbates. Moreover, Ni\DOBDC has a very large pore volume, which

II. MODELS AND METHODS Ni\DOBDC, with DOBDC referring to 2,5-dioxido-1,4-benzene-dicarboxylate, has a molecular formula of C8H2O6Ni2, and is also known as Ni2(dhtp). The crystalline form is triagonal and has a space group of R3 with a = b = 25.7856 Å, c = 6.6883 Å, R = β = 90, and γ = 120. A unit cell is shown in part a of Figure 1. There is a hexagonal channel that can be observed with nickel atoms complexed with carboxylate and deprotonated hydroxyl organic ligands. These ligands are substituents of aromatic rings, which result in the organic linkers forming a side of the hexaganol channel with the nickel atoms present at the vertices. One unit cell in this case represents a ringlike segment along a channel with six aromatic rings, which we will define as a channel segment for our further discussion. These channels are then repeated in the direction normal to plane shown in part a of Figure 1, forming a well-segmented channel. The MOF is assumed to be rigid in this work. The dimensions of our simulation box were 51.6  44.7  47.4 Å3. The atomic coordinates were determined from experimental crystallographic data.33 The partial charges for the atoms in the MOF were derived from density functional theory (DFT) calculations using the NWCHEM computational package34,35 with the B3P86 functional and 6-31G* basis set. The CHELPG electrostatic potential method was used to extract the partial charges.36 The cluster used to perform the DFT calculation is shown in part b of Figure 1. The Lennard-Jones (LJ) parameters for nickel were taken from the UFF force field,37 and those for the organic ligands were taken from the general Amber force field.38 2843

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The LJ parameters used in this work may not reflect the unsaturated nature of the Ni atoms, but this is expected to have a minor effect on the adsorption of hydrocarbons due to the general electrostatic repulsion between Ni and the hydrogens in alkanes. For adsorption of CO2, properly accounting for the unsaturated nature of Ni is more important since oxygen could donate electron density to the metal sites, which would increase the strength of interactions between Ni and CO2, but this is outside the scope of the current work. How to accurately model the interactions between adsorbates and adsorbents in classical molecular dynamics simulations is still open for further research, and building more accurate and realistic MOF models will be addressed in future work. Both partial charges and LJ parameters for our atomic alkane model were taken from the OPLS-AA force field.39 The parameters used in this study are listed in Table 1. The LJ parameters for the interaction between unlike atoms were evaluated with the Lorentz-Berthelot combining rules.30 The 3D particle mesh Ewald summation technique was used to calculate the long-range electrostatic interactions.40 All simulations were carried out in the NVT ensemble using the Amber 9 computational package.41 The temperature was set using the Andersen coupling scheme.42 The systems were equilibrated for 1 ns and 5 ns trajectories were used to calculate structural, and 3 ns trajectories obtained in microcanonical ensemble (NVE) were used to calculate diffusion properties. To calculate the free energy of sorption for our gases, a staged free energy perturbation (FEP) method was used.43 The staged FEP method allows the free energy difference between two states to be calculated as follows, ΔG ¼ G1 - G0 ¼

∑i Gλðiþ1Þ - GλðiÞ

 Gλði þ 1Þ - GλðiÞ ¼ - kB T ln

ð1Þ

  Eλðiþ1Þ - EλðiÞ exp kB T λðiÞ ð2Þ

where G0 and G1 are the free energies of states 0 and 1. Eλ(i) is the potential energy of the system in state λ(i), and kB is the Boltzmann constant. For our work, we carried out the FEP method in four different stages, with each having a different strength of interaction between the adsorbate and MOF. It should be noted that throughout the whole calculation the full solute intramolecular interactions were included. For all of our adsorbates, there were four stages (to integrate between five points) with λi = [0, 0.3, 0.6, 0.8] and λiþ1 = [0.3, 0.6, 0.8, 1.0]. Different sets of λi values (smaller steps and more stages) were tested for the calculation of the free energy with λ between 0 and 0.3, and the same results were obtained, so a first step from 0 to 0.3 was deemed sufficient. For each stage, a total of 1 ns of simulation time was carried out. The isosteric heat of adsorption for zero loading was calculated from ΔH ¼ RT - ðUad - UMOF - Ualkane Þ

ð3Þ

Where Uad is the total potential energy with alkanes adsorbed in MOF, and UMOF and Ualkane are the intramolecular potential energies for the MOF and alkanes, respectively. This value is important to estimate the usefulness of the MOF for a MOHC as described in the introduction.

Figure 2. Radial distribution functions of a) n-hexane-n-hexane, nhexane-nickel, and n-hexane-organic ligand, b) cyclohexane-cyclohexane, cyclohexane-nickel, and cyclohexane-organic ligand at 300 K and a loading of 3 guest molecules per channel segment, chex is cyclohexane in the legend of the figure. In all the figures, ring refers to a channel segment.

The adsorption entropy ΔS is evaluated from adsorption free energy ΔG and heat of adsorption ΔH according to, ΔG ¼ - ΔH - TΔS

ð4Þ

III. RESULTS AND DISCUSSION A. Structure. The radial distribution functions (RDFs) for nhexane in Ni\DOBDC with a loading ratio of 3 guest molecules per channel segment, as defined in section II, are shown in part a of Figure 2. The RDFs were calculated from the center of mass distances between the species. The first peak of the n-hexanen-hexane RDF is around 6.1 Å, which we attribute to n-hexanes in the same channel segment interacting with one another, whereas the small peak at 9 Å are from n-hexanes that are bound to different segments in the same channel. It should be noted that the Ni\DOBDC structure is such that the center of the channel segments are separated by 6.7 Å from each other. The RDFs between n-hexane and the center of mass of the organic linkers, as shown in part a of Figure 2, give a strong first peak, showing strong binding. The RDFs do not show as strong of binding between n-hexane and Ni, but a moderately sized peak is apparent. We attribute this to interactions between n-hexane and the organic linker, which causes a peak in the RDF between 2844

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Figure 3. Orientation distributions of a) n-hexane and b) cyclohexane as a function of loading.

Ni and n-hexane, because Ni has a rigid bond with the organic linker. These results indicate that n-hexane prefers to reside much closer to the organic linker than to Ni. This is expected because n-hexane can form more contacts with the organic linker than with Ni, which is not as assessable, and also the positively charged hydrogens on the alkanes would not be expected to strongly interact with positively charged Ni. There are only a small fraction of n-hexane molecules that reside closer to Ni than to the organic linker, as there is a small first peak between n-hexane and Ni at 4.5 Å. The RDFs of cyclohexane in Ni\DOBDC are shown in part b of Figure 2. The RDFs were calculated between the centers of masses of the species. As for the n-hexane system, there appears to be no strong binding between Ni and cyclohexane. There is a strong first peak in the cyclohexane-organic linker RDF, similar to what was observed for the n-hexane-organic linker RDF, but the peak is somewhat lower and broader for cyclohexane. Furthermore, the first cyclohexane-cyclohexane RDF peak is higher than the n-hexane-nhexane peak. In fact, whereas the first cyclohexane-cyclohexane RDF peak is higher than the cyclohexane-organic linker peak, the opposite is true for n-hexane, in which its n-hexane-organic linker peak is the higher than its first n-hexane-n-hexane RDF peak. These results show stronger binding between n-hexane and the linker in comparison with itself, whereas cyclohexane shows the opposite. As n-hexane and cyclohexane have similar interaction types, this is somewhat unexpected. One possible explanation is that the shape of cyclohexane molecules does not allow them to lie flat on one of the faces of the hexagonal channel in the

Figure 4. Snapshots taken from simulations of a) n-hexane and b) cyclohexane adsorbed in Ni\DOBDC at 300 K and a loading of 3 hexane molecules per channel segment. Only guest molecules in one segment in the channel of MOF are shown for a better view. The MOF is represented as blue and guest molecules are represented as red.

MOF. The RDFs at other loading ratios were calculated for nhexane and cyclohexane (data not shown). In general, no drastic differences were observed for the RDFs shown for n-hexane and cyclohexane. The only noticeable change for n-hexane was that the second peak of n-hexane-n-hexane RDF disappeared when the loading ratio reached 0.43 n-hexane molecules per channel segment. Parts a and b of Figure 3 show the loading dependence of the orientational distributions for n-hexane and cyclohexane respectively in Ni\DOBDC at 300 K. The angle for n-hexane was calculated between the end-to-end carbon vector for n-hexane and the vector aligned down the open MOF channel. For cyclohexane distribution, the angle is defined between the vector that is normal to the cyclohexane ring and the vector aligned down the open channel. For the distributions at all loading ratios for n-hexane, two symmetric peaks can be observed at an angle of ∼53 degrees 2845

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Table 2. Calculated Diffusion Coefficients for n-Hexane and Cyclohexane Adsorbed in Ni\DOBDC at 300 K loading (molecule/

diffusion coefficient

channel segment)

(  10-10 m2 s-1)

0.43

n-hexane 44.11

cyclohexane 12.61

1

17.70

4.25

2

7.38

3.46

3

0.73

0.57

or cos(θ) ≈ 0.6. The angle between the vector from one carboxylate group to another of the same aromatic ring, and the direction down the channel would yield an angle around 53 degrees also. This indicates that n-hexane molecules are aligned with the organic linkers to maximize the number of contacts with it. With increased loading of n-hexane, the angle becomes even more populated at ∼53 degrees. A snapshot taken from a simulation with 3 n-hexane molecules per channel segment at 300 K is given in part a of Figure 4. As was discussed previously, the n-hexane molecules show clear alignment with the aromatic rings, showing a primary interaction with one side of the hexagonal channel, but secondary interactions with the two adjacent hexagonal sides. The orientational distributions of n-hexane molecules were also investigated at 77 K for different loadings (data not shown). For high loadings (3 n-hexanes per channel segment), the distribution was found to be very similar to that at 300 K. However, at low loadings, the distribution narrowed significantly at the lower temperature for all the peaks in comparison with the higher temperature. For cyclohexane, as shown in part b of Figure 3, the angle of the cyclohexane ring perpendicular vector relative to the channel direction is most populated at ∼75 degree or cos(θ) ≈ 0.26. This value is very close to the angle between the normal of the aromatic ring and down the channel. The similar values for the two angles indicate that the cyclohexane ring is parallel to the aromatic ring in the organic linker group. With this kind of packing, the number of contacts between the two rings is also maximized. The orientation of cyclohexane shows only a weak loading dependence. Part b of Figure 4 gives a snapshot of cyclohexane in the MOF at 300 K with 3 guest molecules per channel segment. The cyclohexane molecules show a degree of alignment with the aromatic rings, but this alignment does not appear as strong as for n-hexane. Further evidence of this is in parts a and b of Figure 3, which shows higher peaks at 3 molecules per channel segment for the orientational distribution for n-hexane (of around 1.2) than for cyclohexane (0.9). As with n-hexane, we also carried out a similar calculation at 77 K (data not shown), and the distributions were much narrower at the lower temperature for all loadings. The strong correlations of orientations of guest molecules and organic linker groups indicate strong interactions between nhexane, cylcohexane, and Ni\DOBDC. B. Self-Diffusion. The transport rate is an important property for the efficiency of a porous material to facilitate adsorption and separation of guest species. Because of experimental challenges, the only experimental diffusion data for hydrocarbons in MOFs, to our knowledge, were obtained from an NMR study in MOF-5.44 From this referenced study, the diffusion coefficient of n-hexane was found to be 3.2  10-9 m2 s-1. For the same system, molecular simulation work by others found a diffusion coefficient of 2.2  10-9 m2 s-1, in good agreement with the experimental value.31 Whereas the described system is different than Ni\DOBDC, it

holds many similar characteristics as it, and diffusion in both systems should be somewhat similar. There are often three coefficients used to characterize gas dynamics in MOFs: self, transport, and corrected diffusivity.24,45-48 All of these become the same at the limit of infinite dilution, and we will focus our investigation on self-diffusivity. The self-diffusivity in one dimension (as the channels are 1D) can be obtained from the Einstein relation, * + N 1 1 2 jri ðtÞ - ri ð0Þj ð5Þ Ds ðcÞ ¼ lim t f¥ 2t N i ¼ 1

∑

where ri(t) is the position of particle i at time t, N is the total number of particles, and t is the time. We calculated the selfdiffusion coefficient for n-hexane and cyclohexane molecules, and the values for these as a function of loading are listed in Table 2. The calculated value for n-hexane at the lowest loading is 4.41  10-9 m2 s-1. This is fairly close to the diffusion of n-hexane in MOF-5. One interesting observation pointed out by other studies is that the diffusion coefficients of guest molecules in larger pore sized MOFs are similar to those obtained in silica zeolites.24,31 The reason was attributed to the confinement of the guest molecules to the pore wall due to high-energy barrier for the transportation of molecules. Our simulation results support this explanation, as although the channel diameter is relatively large (11 Å), the diffusion coefficient of n-hexane is similar to the values calculated for MOF-5 and silicalite.31 There are strong interactions between n-hexane and the Ni\DOBDC, and large separation between segments along the channel direction. This results in a relatively high energy barrier to move from one channel segment to another, which appears to limit the mobility of the n-hexane molecules, confining the n-hexane molecular position to be near the vicinity of the channel wall. This is consistent to our structural analysis mentioned above. The diffusion coefficient of cyclohexane in Ni\DOBDC at low loading and 300 K is 1.26  10-9 m2 s-1. This is about 4 times slower than n-hexane. The slower diffusivity of cyclohexane is possibly due to its inability to change configurations in comparison to n-hexane. Because of the unrestricted linear nature of n-hexane, its dihedrals can sample a much larger degree of phase space. During molecular transport, n-hexane can adjust its structure to maximize interactions with the pore volume in a much large number of configurations, reducing energy penalties for movement through the channel. In contrast, cyclohexane cannot maximize the number of contacts with the pore easily, and any movement from one channel segment to another requires the breaking of more contacts between cyclohexane and the MOF. This is similar to what was observed previously by Sarkisov et al. for cyclohexane in bipyridine molecular squares and MOF-5.31 The diffusion coefficients show a very strong loading dependence for both n-hexane and cyclohexane. With increasing loading of guest molecules, the diffusion coefficients decrease rapidly. This is expected due to the increased crowding between guests at higher concentrations. The loading dependence of the self-diffusivity of guest molecules in MOFs has been investigated for other gases, and similar trends as to what has been observed in our work have been found.47 However, the degree of reduction in our diffusion coefficients is much greater than has been found for lighter gases. C. Free Energy Calculation. Part a of Figure 5 shows the temperature dependence of the adsorption free energy for a series of 2846

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Table 3. Heat of Adsorption and Adsorption Entropy of Alkanes in Ni\DOBOC at 300 K alkane

ΔH (kcal/mol)

ΔS (cal/mol/K)

methane

3.92

-7.67

ethane n-butane

5.78 9.64

-8.72 -13.33

n-hexane

14.27

-16.86

cyclohexane

12.02

-13.92

Figure 6. Heats of adsorption and adsorption entropies as a function of the number of alkane carbons at 300 K. In this Figure, the heats of adsorption are defined as the negative of enthalpies.

Figure 5. Adsorption free energies of a) methane, ethane, n-butane, and n-hexane, b) cyclohexane, n-hexane as a function of temperature at zero loading in Ni\DOBDC (solid lines), and in Zn\MOF (dashed lines).

alkanes, including methane, ethane, n-butane, and n-hexane. The free energies increase with increasing temperature for all of them, which is expected, as the structure of Ni\DOBDC is rigid, and, as a result of this, the only difference with increasing temperature is the alkane structural movement. Alkane structural movement is hindered by the rigid MOF, reducing its entropy contribution to the free energy, which becomes more of a factor at higher temperatures. Even at the highest temperature studied, 400 K, the alkane free energy of adsorption is still negative. The adsorption free energy changes decrease with the number of carbons, as expected. Also, the free energy of adsorption as a function of temperature increase by a similar degree for each of the species investigated. Comparing the free energies of transfer in Ni\DOBDC with that of MOF-5 for alkanes27 shows that Ni\DOBDC and MOF-5 have similar adsorption free energies for alkanes. The temperature dependence of the adsorption free energy of cyclohexane was also calculated, and can be compared with that for n-hexane as shown in part b of Figure 5. The free energies are more positive for cyclohexane than n-hexane over the temperature range examined. This difference can be related to the ability of n-hexane to make more contacts with the MOF surface than cyclohexane (as discussed in part A of section III). Also, the large pore size of Ni\DOBDC reduces the entropic penalty for flexible molecules in comparison with a more confined environment. A similar trend was found when comparing the adsorption of linear and branched alkanes in MOF-5.27 The heat of adsorption and

adsorption entropy were calculated for alkanes in Ni\DOBDC at 300 K, and the values are provided in Table 3. For linear alkanes, the heats of adsorption increase and adsorption entropy decreases with increasing chain length. The results are expected since the contacts between guest and host molecules increase with longer alkane chain. The adsorption of guest molecules is more energetically favorable for longer alkanes, but the entropic penalty is increased for longer alkane chains for adsorption. The energetic effect is dominant for the adsorption of alkanes here due to the large pore size. The energetic interactions and entropic penalties are less for cyclohexane in comparison to those of n-hexane for reasons stated before. The adsorption heat and entropy as a function of the number of carbons in linear alkanes are shown in Figure 6. The relationship is pretty linear. Similar results were observed for n-alkanes adsorbed in MOF-5.27 Figure 7 shows the loading dependent adsorption free energy of n-hexane and cyclohexane at 300 K. The free energies for both molecules are more negative at higher loadings than at lower loading. These results are expected, as moderate loadings will increase the number of interactions available for subsequent adsorbing species. This amounts to approximately a 30% decrease in free energy when 3 guest molecules per channel segment are present with respect to the bare MOF. As with the free energies at no loading, n-hexane has a more negative free energy than cyclohexane, showing that n-hexane over all the conditions investigated is adsorbed more strongly than cyclohexane. This is consistent with what has been observed for these two species in MOF-5.31 However, their adsorption in the smaller pore size MOF, bipyridine molecular squares, showed different properties.31 At low loadings, the adsorption of n-hexane in bipyridine molecular squares was more favorable, but, at higher loadings, the 2847

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Figure 7. Adsorption free energies of n-hexane and cyclohexane adsorbed in Ni\DOBDC as a function of loading at 300 K. In the figure, ring refers to a channel segment.

adsorption of cyclohexane was found to be more favorable. The reason is that the interaction between guest molecules and MOFs are more important at low loadings, and, at higher loadings, confinement of the n-hexane flexibility may start to hinder its adsorption in comparison with the smaller cyclohexane. In general, it appears that the pore size has a significant effect on how loadings influence solvation of different species. The primary reason the metal organic framework, Ni\DOBDC was studied in this article is that Ni\DOBDC systems have been thoroughly studied experimentally and demonstrated excellent capability for the adsorption of CO2.49,50 We started the effort by using Ni\DOBDC as the model system to calibrate our simulation methods, and compare the results to other MOFs. We believe our simulation results of alkanes adsorbed in Ni\DOBDC will provide useful information for understanding the selectivity of different gases in Ni\DOBDC, such as CO2, CH4, and so forth. We have also studied the adsorption of alkanes into another MOF, Zn\MOF (tetrakis[4-(carboxyphenyl)oxamethyl]methane, which has the metal, Zn2þ, and an organic pillar, 4,40 -bipyridin) using molecular dynamics simulations.51 The calculated free energies for the adsorption of n-hexane and cyclohexane in these MOFs are shown in part b of Figure 5 for comparison. We found the temperature dependence of the free energies is similar in both MOFs with n-hexane having a lower free energy of adsorption than cyclohexane. However, the free energy difference for the two alkanes in Zn\MOF is consistently about 0.5-1.0 kcal/mol throughout all temperatures investigated, whereas it is around 1.5-2.0 kcal/mol in Ni\DOBDC, showing a greater difference. This result shows that Ni \DOBDC has a higher selectivity toward n-hexane than Zn\MOF. Furthermore, from our analysis of the guest dynamics,51 the adsorption of longer chain alkanes at low pressures in Zn\MOF is quite limited in comparison with Ni\DOBDC. This implies that more Zn\MOF is required to add into the working fluids to enhance the latent heat in comparison to Ni\DOBDC, for which the channel is wide open and free volume is relative large, allowing relatively easy uptake of adsorbates.

IV. CONCLUSIONS Molecular dynamics simulations were performed to investigate the structural properties, diffusion, and adsorption of alkanes in Ni\DOBDC. Both n-hexane and cyclohexane oriented in a way to maximize contact with the MOF at infinite dilution, but n-

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hexane clearly showed stronger RDF peaks with the MOF, showing a greater degree of contact. This was found to be the result of the ability of n-hexane to reconfigure its structure to a greater degree than cyclohexane. Higher alkane loading in the MOF had little effect on the RDFs. Moreover, strong orientational order was found for the alkanes with the MOF surfaces. The calculated diffusion coefficients for n-hexane and cyclohexane were greatly reduced at higher loadings. For cyclohexane, its diffusivity was found to be much less than n-hexane, which was attributed to its inability to change configurations. The adsorption free energies were found to be consistent with the structural analysis. Namely, we found that the more flexible nhexane, due to its ability to maximize contacts with the MOF surface, had the lower free energy of adsorption in comparison with cyclohexane. Finally, at higher loadings, the free energies of a subsequent n-hexane or cyclohexane molecule decreased. This was due to the increased number of available interactions, but also due to the large pore size, allowing a high degree of sorption without too much crowding between the adsorbed species.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]

’ ACKNOWLEDGMENT This work was supported by the Division of Chemical Sciences, Geosciences and Biosciences, Office of Basic Energy Sciences, and by the Office of Energy Efficiency and Renewable Energy, Geothermal Technologies Program, U.S. Department of Energy (DOE). This manuscript has been authored by Battelle Memorial Institute, Pacific Northwest Division, under Contract No. DEAC05-76RL01830 with the DOE. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. ’ REFERENCES (1) Hettiarachchia, H. D. M.; Golubovica, M.; Worek, W. M.; Ikegami, Y. Energy 2007, 32, 1698. (2) Dai, Y. P.; Wang, J. F.; Gao, L. Energy Convers. Manage. 2009, 50, 576. (3) Schuster, A.; Karellas, S.; Kakaras, E.; Spliethoff, H. Appl. Therm. Eng. 2009, 29, 1809. (4) Delgado-Torres, A. M.; Garcia-Rodriguez, L. Energy Convers. Manage. 2010, 51, 2846. (5) Gang, P.; Jing, L.; Jie, J. Appl. Therm. Eng. 2010, 30, 998. (6) Nguyen, T. Q.; Slawnwhite, J. D.; Boulama, K. G. Energy Convers. Manage. 2010, 51, 2220. (7) Yari, M. Renewable Energy 2010, 35, 112. (8) Andersen, W. C.; Bruno, T. J. Ind. Eng. Chem. Res. 2005, 44, 5560. (9) Drescher, U.; Bruggemann, D. Appl. Thermal Eng. 2007, 27, 223. (10) Tchanche, B. F.; Papadakis, G.; Lambrinos, G.; Frangoudakis, A. Appl. Therm. Eng. 2009, 29, 2468. (11) Heberle, F.; Bruggemann, D. Appl. Therm. Eng. 2010, 30, 1326. (12) Papadopoulos, A. I.; Stijepovic, M.; Linke, P. Appl. Therm. Eng. 2010, 30, 760. (13) Chen, H. J.; Goswami, D. Y.; Stefanakos, E. K. Renewable Sustainable Energy Rev. 2010, 14, 3059. 2848

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