Intrinsic Thermal Management Capabilities of Flexible MetalâOrganic

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Intrinsic thermal management capabilities of flexible metalorganic frameworks for carbon dioxide separation and capture Shotaro Hiraide, Hideki Tanaka, Narutomo Ishikawa, and Minoru T. Miyahara ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b13771 • Publication Date (Web): 25 Oct 2017 Downloaded from http://pubs.acs.org on October 28, 2017

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Figure 1. (a) Adsorption isotherm for CO2 on ELM-11 at 195 K. Closed and open symbols denote adsorption and desorption process, respectively. (b) In-situ synchrotron XRPD patterns measured at the points designated by the numbers in 1a. The XRPD patterns with the same color are those with the same crystal structure. 100x120mm (300 x 300 DPI)


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Figure 2. Rietveld refined XRPD pattern of C ⊃ 3CO2 at 195 K. The bottom panel shows the residual error. 60x43mm (300 x 300 DPI)



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Figure 3. (a) Density distribution of CO2 in the host framework C obtained by GCMC simulation using the final Rietveld refined structure. The color-coded CO2 molecules (red and yellow) represent the two possible configurations in the framework. (b) A snapshot of one configuration of the CO2 molecules in the host framework C, and (c) the other configuration of the CO2 molecules. 52x16mm (300 x 300 DPI)


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Figure 4. Rietveld refined structure of D ⊃ 6CO2 together with the density distribution of CO2 obtained by the GCMC simulation. The site occupancy of the CO2 molecules colored by gray and red is 1.0, and those of the monochromatic CO2 molecules are less than 1.0 (the site occupancy of the purple CO2 molecules is the second biggest, followed by yellow and pink). (a) a view from a-b plane, (b) b-c plane, and (c) a-c plane. 71x29mm (300 x 300 DPI)



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Figure 5. Rietveld refined XRPD pattern of D ⊃ 6CO2 at 195 K. The bottom panel shows the residual error. 60x43mm (300 x 300 DPI)


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Figure 6. Crystal structures of ELM-11 with different CO2 loadings at 195 K: Top views of (a) A, (b) B ⊃ 2CO2, (c) C ⊃ 3CO2, and (d) D ⊃ 6CO2; and side views of (e) A, (f) B ⊃ 2CO2, (g) C ⊃ 3CO2, and (h) D ⊃ 6CO2. The most energetically stable CO2 configuration was chosen. 81x39mm (300 x 300 DPI)



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Figure 7. (a) Fictitious adsorption isotherms for CO2 on frameworks B (blue line), C (green line), and D (red line) at 195 K obtained by GCMC simulations, and the experimental desorption isotherm at 195 K (gray line with circles). (b) Osmotic free energy changes for the B, C, and D state based on the A state. The colorcoding is the same as that for the fictitious adsorption isotherms. A dashed orange line shows an expected free energy change of the real system where the host framework structure gradually deforms from B to C. 91x101mm (300 x 300 DPI)


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Figure 8. Temperature dependence of the Helmholz free energy change of the host, -∆FBAhost (black circles) and -∆FDChost (red triangles), obtained from the free energy analysis. The -∆FBAhost values are from ref. 18. The two lines are determined from the least-squares fitting of eqn. (5). 52x33mm (300 x 300 DPI)



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Figure 9 Schematic diagrams for six operations to evaluate the intrinsic thermal management capabilities of ELM-11. 85x42mm (300 x 300 DPI)


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Figure 10. The total and each component adsorption isotherm for (a) CO2/N2 (10:90) and (b) CO2/CH4 (50:50) mixtures on B and D, and CO2 selectivity at 298 K. The existence of structure C was omitted for the sake of simplicity. 110x146mm (300 x 300 DPI)



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Intrinsic thermal management capabilities of flexible metal-organic frameworks for carbon dioxide separation and capture Shotaro Hiraide, Hideki Tanaka,* Narutomo Ishikawa, and Minoru T. Miyahara* Department of Chemical Engineering, Kyoto University, Nishikyo, Kyoto 615-8510, Japan. Keywords: Metal-Organic Frameworks, Intrinsic Thermal Management, Multi-Gate Adsorption, Carbon Capture and Storage, Free Energy Analysis

ABSTRACT: We show that flexible metal-organic frameworks (MOFs) exhibiting ‘gate openings/closings’ for CO2 can intrinsically suppress the exothermic heat released by adsorption and the endothermic heat gained by desorption, both of which reduce the working capacity of CO2 in a separation process under near-adiabatic conditions. We use the elastic layer-structured metal-organic framework11 (ELM-11) [Cu(4,4’-bipyridine)2(BF4)2], which exhibits a two-step gate-adsorption isotherm, as a model system for flexible MOFs, and perform free energy analyses with the aid of grand canonical Monte Carlo simulations for ELM-11 structures that were determined by the Rietveld method using in-situ synchrotron X-ray powder diffraction data. We demonstrate that the thermal management capabilities of ELM-11 showing the two-step gating for CO2 at lower and higher pressures are nearly identical and quite effective (41% and 44% at 298 K, respectively). Moreover, we show that ELM-11 has an extremely high CO2 selectivity for both CO2/N2 and CO2/CH4 mixtures at 298 K that, in addition to the intrinsic thermal management capability, is a crucial factor for application to carbon capture and storage (CCS). The multi-gate closing pressures of ELM-11 are not necessarily matched to the operating pressures used in CCS; however, our findings, and perspectives based on free energy analyses regarding modification of the host framework structure in order to tune the gating pressure, suggest that flexible MOFs exhibiting multi-gate openings/closings are promising materials for further development into systems with intrinsic thermal management mechanisms for CCS applications.

INTRODUCTION Reducing anthropogenic CO2 emissions into the atmosphere is becoming an increasingly urgent environmental issue, and various strategies have been developed, including the use of less carbon-rich fuels like natural gas, renewable energy resources, improvements in energy efficiency, and carbon capture and storage (CCS).1,2 In particular, CCS is a fast growing field of research and the adsorption of CO2 on metal-organic frameworks (MOFs)3,4 has become an intense research subject over recent decades, owing to their high surface areas and tunable pore surfaces.1-4 Temperature swing adsorption (TSA) and pressure swing adsorption (PSA) have been investigated as possible candidates for carbon capture; important requirements of MOFs in real PSA processes are selectivity for CO2, regenerability, and CO2 working capacity.3 The management of thermal fluctuations associated with adsorption and desorption on the adsorbent, in order to obtain large CO2 working capacities, is a challenge for the development of a highly efficient PSA system. The effective thermal management of adsorption towers enables the operation of the PSA system under near-adiabatic conditions, which is essential for reducing the cycle time. The short cycle time enables the size-reduction of adsorption towers, and hence, contribute to cost reduction for CO2 separation. Recently, Mason et al.5 reported that flexible MOFs exhibiting ‘gate-opening’ behavior and stepped (‘S-shaped’) CH4 adsorption isotherms are capable of providing large CH4 working capacities when they are applied to an adsorbed natural gas (ANG) storage system. Moreover, these materials can also suppress the impact of heating due to the exothermic heat liberated

during adsorption, and cooling due to the endothermic heat of desorption, both of which result in reduced working capacity. They performed high-pressure CH4 adsorption measurements at various temperatures (273–323 K) and microcalorimetry experiments for Co(bdp) (bdp2- = 1,4-benzenedipyrazolate), which belongs to a family of flexible MOFs, and showed that the heat released by CH4 adsorption at the gate-opening pressure is reduced by 28% because the endothermic expansion of the Co(bdp) framework partially offsets the exothermic heat of CH4 adsorption. As well as the ANG system, the intrinsic thermal management capability of flexible MOFs should be useful for developing the highly efficient PSA system that can reduce the cost for CO2 separation in CCS; however, to the best of our knowledge, there have been no studies on intrinsic thermal management for CO2 separation using flexible MOFs, and thus the effectiveness of intrinsic thermal management with distinct multi-gate openings, which is a characteristic feature of flexible MOFs,6 is completely unknown. Moreover, the desorption isotherms of flexible MOFs are typically characterized by hystereses (‘gate-closing’ pressure is lower than the ‘gate-opening’ pressure); however, the relationship between their intrinsic thermal management capabilities and these hystereses is unclear. Therefore, the development of a thermodynamic model describing the gateopening/closing behavior is required as a tool for evaluating and predicting the intrinsic thermal management capability of flexible MOFs. A thermodynamic model for gate-opening behavior based on the osmotic statistical ensemble was first developed by Coudert et al.7 These researchers proposed a free energy analysis method to evaluate the difference in the Helmholtz free energies of the


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initial and final flexible MOF structures during gate opening. This method is simple and useful because it only relies on an experimental adsorption isotherm fitted to a Langmuir isotherm over its plateau region after gate opening; this method has been applied successfully to a variety of different flexible MOFadsorbate systems.8-16 Mason et al. also used this thermodynamic model to gain insight into the mechanism of intrinsic thermal management within the Co(bdp) framework during gate opening.5 The free energy analysis method involving Langmuir isotherm fitting provides a reasonable approximation of the difference in the Helmholtz free energies of the host framework, and if it is combined with molecular simulations instead of relying on Langmuir isotherm fitting, precise thermodynamic quantities can be obtained. In previous studies,17-18 we conducted a free energy analysis with the aid of grand canonical Monte Carlo (GCMC) simulations for CO2 adsorption on atomistic-structure models of elastic layer-structured metal-organic framework-11 (ELM-11: [Cu(BF4)2(bpy)2]; bpy = 4,4’-bipyridine), which were determined by in-situ synchrotron X-ray powder diffraction (XRPD) measurements at 195−298 K and Rietveld analysis. This analysis found that changes in both internal energy and entropy of the host framework upon deformation of the host are important factors that control the gateclosing pressure. ELM-11, having a two-dimensional (2D) grid framework, is the first flexible MOF for which CO2-adsorption gate opening was observed,19 and depending on adsorption pressure and temperature, it also exhibits gate adsorption phenomena for a variety of gases such as N2, CH4, Ar, and n-butane.20-29 In particular for CO2, ELM-11 exhibits a very sharp and typical gate-adsorption isotherm that arises from the encapsulation of two CO2 molecules per monomer unit [monomer unit (MU) = Cu(BF4)2(bpy)2],17-18 and thus the adsorption behavior of ELM11 for gas mixtures containing CO2 was investigated by some groups for the purpose of application to CCS.24, 30-31 More interestingly, a few groups recently reported that ELM-11 also exhibits a second gate opening at moderate pressure and 195 K, and at high pressure and 298 K,32-34 which indicates that ELM11 is a suitable model and reference compound to further our understanding of the mechanism of intrinsic thermal management in multi-gate-opening/closing systems. In the present study, we aim to demonstrate the possibility of application of the intrinsic thermal management capabilities of flexible MOFs to CCS by a rigorous thermodynamic model. We therefore determined the crystal structures of ELM-11 encapsulating six and three CO2 molecules per monomer unit, before and after the closing of the higher gate at 195 K (hereafter referred to as D ⊃ 6CO2 and C ⊃ 3CO2, where D and C denote the ELM-11 framework structures) obtained by structural refinement combined with molecular simulations and Rietveld analysis using in-situ synchrotron XRPD data, which was developed in our previous study.18 We then performed free energy analyses for the two-step gate-desorption isotherm of CO2 on ELM-11 with the aid of GCMC simulations using the two framework structures D and C. Framework structure B, from the previously determined crystal structure of ELM-11 that had encapsulated two CO2 molecules per monomer unit (B ⊃ 2CO2) immediately prior to the lower gate closing, was also included.18 The crystal structure of ELM-11 after the lower gate closing (closed structure in vacuo) is designated as A in this paper. We then evaluated the intrinsic thermal management capability of ELM-11 using the thermodynamic quantities obtained from the free energy analyses at 195 K, and discuss the intrinsic thermal

management capability at each stage of the gate-opening/closing process. The CO2 separation characteristics of ELM-11 at 298 K including the intrinsic thermal management capability and the CO2 selectivities for CO2/N2 and CO2/CH4 mixtures are also predicted. Finally, based on our results, a guideline for designing new flexible MOFs for CCS is proposed.

EXPERIMENTAL AND METHODOLOGY CO2 adsorption. Pre-ELM-11 was purchased from Tokyo Chemical Industry Co., and was transformed into ELM-11 by heating at 373 K for 10 h under vacuum (< 0.1 mPa). The CO2 adsorption isotherms of ELM-11 at 195, 200, and 205 K were measured by BELSORP-max (Microtrac Bel) and a cryostat equipped with a two-stage Gifford–McMahon refrigerator.35 The sample-cell temperature was kept within ±0.01 K of the required temperature during the adsorption measurements. In-situ synchrotron XRPD. The pre-ELM-11 sample was placed in the end of a 0.4-mm-diameter Lindemann glass capillary, which was attached to a stainless steel tube with an epoxy adhesive. The sample was then evacuated for 10 h at 373 K for transforming it to ELM-11. In-situ synchrotron XRPD patterns of ELM-11, at 195 K and various CO2 pressures up to 100 kPa, were measured on the BL02B2 beamline of the SPring-8 synchrotron facility, Japan, using a large Debye-Scherrer-type diffractometer with a multi-modular system constructed with six MYTHEN detectors. The temperature of the capillary was controlled by a nitrogen gas blower and the CO2 gas pressure was controlled by a laboratory made gas-handling system. The capillary was oscillated by 60° to obtain uniform diffraction intensities, and the wavelengths of the incident X-rays was 0.099928 nm. Structural analysis using in-situ synchrotron XRPD data. The primary crystal structures of C ⊃ 3CO2 and D ⊃ 6CO2 were obtained by the previously developed method,18 which is similar to a hybrid reverse Monte Carlo technique.36 In this method, Monte Carlo trial moves are performed for the Cu ions, bpy molecules, BF4 anions, and CO2 molecules, until the reliability factor (an index of the deviation between the observed and calculated XRPD patterns), Rwp, becomes sufficiently small under a potential energy constraint. We realized this structure refinement method by combining a home-made code for the Monte Carlo trials with the RIETAN-2000 software package to evaluate the Rwp factor.37 The hydrogen atoms attached to the bpy molecules of the structure obtained in this manner were then removed, and the resulting structure was used as the input for structural refinement using the Rietveld method (RIETAN-FP software package38). Soft constraints for all the bond lengths and angles were imposed during refinement. The split pseudoVoigt function was adopted to describe the peak profiles of the calculated XRPD patterns, and partial profile relaxation39 was applied for fourteen refractions for C ⊃ 3CO2 and thirteen refractions for D ⊃ 6CO2. The hydrogen atoms of the bpy molecules were then reattached to the final structures with bond lengths of 0.108 nm. The framework structures, C and D, which were obtained from the Rietveld-refined structures, C ⊃ 3CO2 and D ⊃ 6CO2 by removing the CO2 molecules, were used to estimate the density distribution of the encapsulated CO2 at a given pressure and 195 K by the GCMC method (see next section). The obtained density distributions for C and D were used to determine possible configurations (sites) of the CO2 in the host frameworks; the



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site occupancies were determined from the frequency of appearance of the configuration. The Debye-Waller factor for each CO2 was then evaluated from the standard deviation of a Gaussian fit to the CO2-density distribution, σ, by assuming an isotropic temperature factor (= 8π2σ2). The specified configurations, site occupancies, and the Debye-Waller factors were utilized as the fixed parameters for further Rietveld refinement. The GCMC method and the Rietveld refinement were repeated until a sufficiently small Rwp value was obtained and the Rietveld-refined CO2 configurations coincided reasonably with the CO2 density distribution obtained by the GCMC method.

MOLECULAR SIMULATIONS AND THEORY Grand canonical Monte Carlo simulations. We conducted GCMC simulations for CO2 adsorption on B, C, and D in order to obtain fictitious adsorption isotherms that are required in order to conduct free energy analyses. The details of the GCMC simulations are given in the Supporting Information†. Free energy analyses. The osmotic free energy of a system, ΩiOS, when the host framework structure is in state i, can be written as:7 ΩiOS (N ihost , P, T ) = Fi host (N ihost ,Vi , T ) + PVi + Ωiguest (P,Vi , T ) ,

(1)

where Nihost is the number of host framework atoms, P the external gas pressure, T the temperature, Fihost the Helmholtz free energy of the host, Vi the volume of the host, and Ωiguest the grand potential of the guest. The grand potential can be calculated by integrating the fictitious adsorption isotherm of a guest on the host framework in state i, Niguest, by assuming that the host framework structure does not change during adsorption: Ω

guest i

(P,V ,T ) = −k TN B

i

guest i

( P ,V , T ) − ∫ id

i

P

Pid

N

guest i

(P' ,Vi ,T )Vm dP' , (2)

where kB is the Boltzmann constant and Vm is the molar volume of the external gas [Vm = (∂µ/∂P)T, where µ is the chemical potential of the gas]. The first term on the right-hand side of eqn. (2) is the grand potential at a sufficiently small pressure, Pid. The osmotic free energy difference of state k on the basis of the state i, ∆ΩikOS, is expressed as:

− Ω iguest , ΔΩ ikOS = ΔFikhost + PΔV + Ω guest k

(3)

where ∆Fikhost is the Helmholtz free energy change required to deform the host framework from state i to state k in vacuo, ∆V is the volume change of the host, and the P∆V term is negligible in most cases. Considering an equilibrium transition at a pressure, Pikgate, the ∆ΩikOS value should be zero and hence, the following equation is derived from eqns. (2) and (3):

ΔFikhost (T ) − k BT {N kguest (Pid , T ) − N iguest (Pid , T )} Pikgate

− ∫Pid

{N (P' , T ) − N (P' , T )}V dP' = 0 guest k

guest i

.

(4)

m

Note that the experimental adsorption isotherm for CO2 on ELM-11 at 195 K shows two hysteresis loops corresponding to each gate opening and closing.33-34 In previous studies, we found that the gate-closing pressure is close to the thermodynamic equilibrium transition pressure by conducting a free-energy analysis for a simplified flexible MOF model with a stackedlayer structure,40 and atomistic models of ZIF-8.35 In other

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words, gate opening can be regarded as a transition from a metastable state. We therefore adopted the experimental gate-closing pressure as Pikgate, and basically discuss desorption processes (the changes in the framework structure are D → C and B → A) in this study. The thermodynamic relationship for ∆Fikhost is then given by:

∆Fikhost (T ) = ∆U ikhost − T∆S ikhost ,

(5)

where ∆Uikhost and ∆Sikhost are differences in the internal energy and entropy of the host framework resulting from the deformation of the host, and we assume that the both values are independent of temperature. Transition enthalpy. The enthalpy change of the system, ∆Hiktrs, owing to the transition from state i to state k at the gate-closing pressure, Pikgate, can be expressed as:

ΔH iktrs ≈ ΔU ikhost − ΔN ikguest ( Pikgate , T )Qi int ( Pikgate , T ) − N kguest ( Pikgate , T ){Qkint ( Pikgate , T )

,

(6)

− Qi int ( Pikgate , T )} where ∆Nikguest (= Nkguest − Niguest) is the difference in the number of guest molecules in states i and k, and Q jint (j = i, k) is the molar integral heat of adsorption defined as: Q jint ( P, T ) �= −

H guest ( P, T ) − H gas ( P, T ) j N guest ( P, T ) j

,

(7)

≈ −u jguest ( P, T ) + RT

where Hjguest − Hgas means the enthalpy change when Njguest mol of gas molecules are encapsulated in the host framework in state guest is the molar interaction potential energy of the guest in j, u j state j, and R is the gas constant. Note that Q jint is defined to be was obpositive when heat is released to the system, and u j tained as the ensemble average using the GCMC simulations in this study. A more detailed derivation of eqn. (6) is given in the Supporting Information. According to eqn. (6), the transition enthalpy can be divided into three contributions: the internal energy change of the host framework (exothermic shrinkage), the heat removed by the guest molecules that desorb from the host framework in state i, and the heat released from the guest molecules remaining in the host framework in state k, which is caused by changes in host-guest interactions upon host deformation. We then combine the right-hand side of eqn. (6) into two contributions, which represent exothermic and endothermic contributions, and express them as: guest

Qik+ = −ΔU ikhost + N kguest ( Pikgate , T ){Qkint ( Pikgate , T ) − Qi int ( Pikgate , T )}

Qik− = ΔN ikguest ( Pikgate , T )Qi int ( Pikgate , T ) .

, (8)

(9)

Intrinsic thermal management capability. The total heat, Qj, removed from the system as the gas pressure is decreased from Po to P can be written as:


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Q j ( P o , P, T ) = N guest ( P, T )Q jint ( P, T ) j

,

( P o , T )Q jint ( P o , T ) � − N guest j

(10)

where the host framework in state j (j = i, k) is assumed to be rigid. On the other hand, assuming that the host framework is flexible and the transition from state i to state k (gate-closing) occurs at Pikgate (P < Pikgate < Po), the net heat, Q'ik, removed from the system is given by:

discussed later. Subsequently, we measured the XRPD patterns for C ⊃ 3CO2 and D ⊃ 6CO2 (14 and 98 kPa during the desorption process) and determined the crystal structures as described in the next section.

Q'ik = Qi ( P o , Pikgate , T ) − ∆H iktrs + Qk ( Pikgate , P, T ) . (11)

In this study, we define the intrinsic thermal management capability, eik, when guest molecules are desorbed at the gate-closing pressure, Pikgate, as:

eik = (Qik− − Q 'ik ) / Qik− = −Qik+ / Qik− ,

(12)

where, in order to obtain the right-hand side of eqn. (12), we used the relationship: Q'ik = −∆Hiktrs, which comes from eqn. (11) by substituting Qi (Pikgate, Pikgate, T) = Qk (Pikgate, Pikgate, T) = 0, as well as: −∆Hiktrs = Qik+ + Qik− from eqns. (6), (8), and (9). In other words, eik represents the ratio of the exothermic heat caused by host deformation to the total endothermic heat resulting from guest desorption.

RESULTS AND DISCUSSION CO2 adsorption isotherms and in-situ XRPD. Figure 1a shows the adsorption isotherm for CO2 on ELM-11 at 195 K (hereafter, the temperature is 195 K unless otherwise specified), in which two steps with hysteresis loops at 0.2−0.4 kPa (the lower gate closing/opening) and 14−30 kPa (the higher gate closing/opening) are observed. The in-situ synchrotron XRPD patterns were measured at points along the adsorption and desorption processes (designated by the numbers 1−11 in Figure 1a), and the data are shown in Figure 1b. The XRPD patterns of the same color are those with the same crystal structure, and color changes as functions of pressure indicates cyclic characteristics. The XRPD patterns obtained after the steep rises that follow the gate openings (1 and 5, Figure 1b) are completely different to those before the gate opening ("in vacuo" and 4), which suggests that the ELM-11 framework structure becomes dramatically deformed. The same can be said about the desorption processes (points 8 and 9 for the higher gate-closing, and 11 and "in vacuo" for the lower gate-closing). We also found that the crystal structure of ELM-11 changes gradually as a function of CO2 loading (2−3 mol-CO2/mol-MU), which is evidenced by the shift of the peak in the 10.8−11° range (see 1−4 and 9−11 in Figure 1b). This confirms our previous speculation,18 namely that ELM-11 exhibits two structural transitions and one gradual deformation, and has four typical crystal structures along the desorption process: D ⊃ 6CO2, C ⊃ 3CO2, B ⊃ 2CO2, and A, as designated in Figure 1a, which are the crystal structures before the closing of the higher gate, just after the closing of the higher gate, just before the closing of the lower gate, and in vacuo, respectively. Note that the framework structure of D ⊃ 5.5CO2 observed just before the higher gate closing can be regarded to be the same as that of D ⊃ 6CO2, which is

Figure 1. (a) Adsorption isotherm for CO2 on ELM-11 at 195 K. Closed and open symbols denote adsorption and desorption process, respectively. (b) In-situ synchrotron XRPD patterns measured at the points designated by the numbers in 1a. The XRPD patterns with the same color are those with the same crystal structure.

Figure 2. Rietveld refined XRPD pattern of C ⊃ 3CO2 at 195 K. The bottom panel shows the residual error.



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Figure 3. (a) Density distribution of CO2 in the host framework C obtained by GCMC simulation using the final Rietveld refined structure. The color-coded CO2 molecules (red and yellow) represent the two possible configurations in the framework. (b) A snapshot of one configuration of the CO2 molecules in the host framework C, and (c) the other configuration of the CO2 molecules.

Figure 4. Rietveld refined structure of D ⊃ 6CO2 together with the density distribution of CO2 obtained by the GCMC simulation. The site occupancy of the CO2 molecules colored by gray and red is 1.0, and those of the monochromatic CO2 molecules are less than 1.0 (the site occupancy of the purple CO2 molecules is the second biggest, followed by yellow and pink). (a) a view from a−b plane, (b) b−c plane, and (c) a−c plane.

Structural analyses using in-situ synchrotron XRPD data. We found that six possible CO2 sites exist in the monomer unit of the framework structure of C, and that all the site occupancies are 0.5 using a combination of the GCMC method and Rietveld refinement. The averaged σ value for all of these sites was 0.021 nm, and corresponds to a Debye-Waller factor of 0.035 nm2, which is physically meaningful.41 The resulting Rietveld-refined pattern of C ⊃ 3CO2 is shown in Figure 2, and the crystallographic parameters are listed in Tables 1 and S4. The space group of C ⊃ 3CO2 was determined to be P2/c (No. 13), which is a subgroup of C2/c (No. 15) previously assigned to B ⊃ 2CO2, and its unit-cell volume is slightly larger than that of B ⊃ 2CO2 (Table S5). The final density distribution of CO2 obtained by the GCMC method, and two types of CO2 configuration obtained by Rietveld refinement, are compared in Figure 3a; the good agreement suggests that our structural analysis is accurate. Note that although there are six CO2 sites, there are only two possible CO2 configurations with the same interaction potential energy, as shown in Figures 3b and 3c.

Table 1. Crystallographic data for C ⊃ 3CO2 and D ⊃ 6CO2 obtained from the Rietveld analyses. structure formula P(CO2) [kPa]

C ⊃ 3CO2 CuB2C20N4H16F8⋅3CO2 14

D ⊃ 6CO2 CuB2C20N4H16F8⋅6CO2 98

T [K] crystal system

195 monoclinic

195 triclinic

space group a [nm]

P2/c (No. 13) 1.36866(4)

P1 (No. 1) 1.10894(7)

b [nm] c [nm]

1.10884(2) 1.84649(5)

1.11193(5) 1.43930(9)

α [deg]

β [deg]

90 94.172(2)

86.608(6) 75.513(5)

γ [deg] V [nm3]

90 2.7948(1)

86.791(9) 1.7137(2)

Z Rwp

4 0.02851

2 0.03622

RP RI

0.02190 0.06555

0.02689 0.08105

S

2.0757

2.7527


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Seventeen possible CO2 sites were found in the two monomer units of the framework structure of D, and there are 12 possible CO2 configurations. The Rietveld-refined structure obtained for D ⊃ 6CO2, with P1 (No. 1) symmetry, is shown in Figure 4 together with the CO2 density distribution determined by the GCMC method, while the Rietveld-refined pattern of D ⊃ 6CO2 is depicted in Figure 5, both of which, once again, indicate that our analysis is highly accurate; the crystallographic parameters are listed in Tables 1 and S6. Kanoh and co-workers38 have already reported the crystal structure of ELM-11 after the higher gate opening by CO2 at 195 K, which was predicted manually without performing any Rietveld analyses. The cell parameters determined by our strict structure-refinement method are different to those reported by Kanoh et al. (a = 1.584 nm, b = 1.111 nm, c = 2.026 nm, α = 89.14°, β = 105.25°, and γ = 91.85°);34 however, they are in approximate agreement when the lattice vectors are transformed by: a' = a – c, b' = b, and c' = a + c, using our lattice vectors, a, b, and c.

Figure 5. Rietveld refined XRPD pattern of D ⊃ 6CO2 at 195 K. The bottom panel shows the residual error.

Changes in the host framework structure. Figure 6 depicts the crystal structures of A, B ⊃ 2CO2, C ⊃ 3CO2, and D ⊃ 6CO2, where the most energetically stable CO2 configuration was chosen. The interlayer distance between the 2D grid frameworks of ELM-11 decreases from 0.6960 (the average value; see below for details) to 0.5685 nm at the higher gate closing, and from 0.5676 to 0.4427 nm at the lower gate closing, which means that the interlayer distance in D ⊃ 6CO2 shrinks by 36% through the closing of the two gates. The framework structure D is AB stacked, with two different interlayer distances (0.7031 and 0.6889 nm; average value is 0.6960 nm as mentioned above), while the framework structures A, B and C, are AA stacked, with unique interlayer distances. Moreover, the 2D grids of D are close to regular tetragonal; on the other hand, those of A, B and C are rhombic in shape. The dramatic change in the grid structure of D is attributed to the weakening of the interaction potential between the 2D grid layers (0.32 times weaker than in C) due to the widening of the interlayer separation. The framework structures of B and C are almost identical; however, the orientations of the BF4 anions are slightly different. That is, the small increase in cell volume and the change in the orientation of BF4 anions from B to C, lead to a small torusshaped expansion of the pore space within the host framework

(see Figure S1), which is attributed to the increase in CO2 loading, from 2 to 3 mol-CO2/mol-MU. Free energy analyses. Figure 7a displays fictitious adsorption isotherms, Nkguest (k = B, C, and D), obtained from the GCMC simulations using the respective host framework structures, together with the experimental desorption isotherm. The newly determined atomic charges for C and D, which were used in the GCMC simulations, are tabulated in Tables S4 and S6. The fictitious adsorption isotherm, NDguest, passes through the green triangle on the experimental desorption isotherm in Figure 7a, just before the closing of the higher gate, which corresponds to the aforementioned D ⊃ 5.5CO2 structure. This observation suggests that the host framework structure of D ⊃ 5.5CO2 can be regarded to be the same as that of D ⊃ 6CO2. Moreover, the fictitious adsorption isotherms, NCguest and NBguest, also exactly pass through the points on the experimental isotherm corresponding to the C ⊃ 3CO2 and B ⊃ 2CO2 structures, which indicates that the host framework structures and the force fields used in the GCMC simulations are appropriate. It is also worth noting that there is a large difference between the fictitious adsorption isotherms, NBguest and NCguest, even though the two framework structures are similar, as mentioned above. This demonstrates the importance of strictly determining the host framework structure when performing precise free energy analyses. We integrated the fictitious adsorption isotherms, NDguest and NCguest, according to eqn. (4), and obtained the free energy change of host framework; ∆FDChost = −12.5 kJ/mol-MU. The absolute value of ∆FDChost is smaller than that of ∆FBAhost (−17.1 kJ/mol-MU),18 which suggests that the work required to shrink the framework structure during higher gate-closing is smaller than that required at the lower gate-closing pressure. We next calculated the change in osmotic free energy, ∆ΩAkOS (k = B, C, and D), according to eqn. (3), by assuming ∆FCAhost ≈ ∆FBAhost and ∆FDAhost ≈ ∆FDChost + ∆FBAhost, since the value of ∆FBChost is negligible. The free energy profiles obtained in this manner, which are shown in Figure 7b, clearly demonstrate that the most stable state is that of host framework D encapsulating CO2 over the higher gate-closing pressure, after which it switches to host framework A, without CO2, below the lower gate-closing pressure. It should be noted that the structural transition from C to B does not occur at the intercept of ∆ΩACOS and ∆ΩABOS at 1 kPa, but takes place continuously between the higher and lower gateclosing pressures, as indicated by the in-situ synchrotron XRPD data. In other words, the change in osmotic free energy over the range of the higher and lower gate-closing pressures is expected to occur at the dashed lines depicted in Figure 7b, which are lower than ∆ΩACOS and ∆ΩABOS. The ∆FDChost values at 200 and 205 K were also determined from free energy analyses in which fictitious adsorption isotherms at each temperature were calculated from the GCMC simulations using host framework structure D at 195 K. The temperature-dependence of ∆FDChost (195, 200 and 205 K) is shown in Figure 8, together with the ∆FBAhost values determined in the previous study.18 The free energy profiles, ∆ΩAkOS (k = B, C, and D), at 200 and 205 K are provided in Figures S2 and S3. ∆UDChost and ∆SDChost values were then determined from the intercept and slope of the temperature dependence of ∆FDChost, obtained by the least-squares fitting of eqn. (5). The absolute values of the thermodynamic quantities obtained in this manner for the closing of the higher gate (∆UDChost



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Page 18 of 24

Figure 6. Crystal structures of ELM-11 with different CO2 loadings at 195 K: Top views of (a) A, (b) B ⊃ 2CO2, (c) C ⊃ 3CO2, and (d) D ⊃ 6CO2; and side views of (e) A, (f) B ⊃ 2CO2, (g) C ⊃ 3CO2, and (h) D ⊃ 6CO2. The most energetically stable CO2 configuration was chosen.

= −16.0 kJ/mol-MU, and ∆SDChost = −18.0 J⋅K-1⋅mol-MU-1) are also smaller than those for the lower gate closing (∆UBAhost =−30.6 kJ/mol-MU and ∆SBAhost = −65.9 J⋅K-1⋅mol-MU-1).18

Figure 8. Temperature dependence of the Helmholz free energy change of the host, −∆FBAhost (black circles) and −∆FDChost (red triangles), obtained from the free energy analysis. The −∆FBAhost values are from ref. 18. The two lines are determined from the leastsquares fitting of eqn. (5).

Figure 7. (a) Fictitious adsorption isotherms for CO2 on frameworks B (blue line), C (green line), and D (red line) at 195 K obtained by GCMC simulations, and the experimental desorption isotherm at 195 K (gray line with circles). (b) Osmotic free energy changes for the B, C, and D state based on the A state. The colorcoding is the same as that for the fictitious adsorption isotherms. A dashed orange line shows an expected free energy change of the real system where the host framework structure gradually deforms from B to C.

Transition enthalpies and intrinsic thermal management capabilities. Transition enthalpies per mol of CO2, ∆HDCtrs / ∆NDCguest and ∆HBAtrs / ∆NBAguest, at the higher and lower gate closings were determined by substituting the thermodynamic quantities obtained from the GCMC simulations and the free energy analyses into eqn. (6); the thermodynamic quantities used are listed in Table 2. The molar integral heats of adsorption at each state, B ⊃ 2CO2, C ⊃ 3CO2, and D ⊃ 5.5CO2, are 40.8, 38.3, and 33.6 kJ/mol-CO2, respectively, which are above the average isosteric heat of adsorption of typical MOFs.42 The transition enthalpies were determined to be 21.9 kJ/mol-CO2 for the higher gate closing, and 25.5 kJ/mol-CO2 for the lower gate closing, which suggests that the both closings are endothermic processes, and that more heat is removed from the system for the lower gate closing than for the higher.


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Figure 9 Schematic diagrams for six operations to evaluate the intrinsic thermal management capabilities of ELM-11. Table 2. Thermodynamic quantities associated with the two gate closings obtained from the GCMC simulations and the free energy analysis. Lower gate-closing (i = B, k = A)

Higher gate-closing (i = D, k = C) 5.55

N iguest

mol-CO2/mol-MU

2.00

N kguest

mol-CO2/mol-MU

0

2.97

ΔN ikguest

mol-CO2/mol-MU

−2.00

−2.59

Qi int

kJ/mol-CO2

40.8

33.6

Q

kJ/mol-CO2

0

38.3

int k

ΔN

guest ik

Qi

int

kJ/mol-MU

−81.4

−86.8

N kguest (Qkint − Qi int )

kJ/mol-MU

0

14.1

− ΔU ikhost

kJ/mol-MU

30.6

16.0

− ΔH iktrs

kJ/mol-CO2

−25.5

−21.9

/ ΔN ikguest

In order to evaluate the intrinsic thermal management capability of ELM-11, we calculated the total endothermic heat associated with guest desorption, and the exothermic heat removed from the system when host shrinkage is taken into account, for the following three cases as illustrated in Figure 9. Case 1 starts from the B ⊃ 2CO2 state; all guest molecules are desorbed until the system transforms into A at the lower gateclosing pressure. Case 2 starts from the D ⊃ 5.5CO2 state; guest molecules are desorbed until the system transforms to the C ⊃ 3CO2 state at the higher gate-closing pressure. Case 3 starts from the D ⊃ 5.5CO2 state; all guest molecules are desorbed until the system transforms into A, while passing through C and B as the gas pressure is decreased from that for higher gate closing to that for lower gate closing. The results of this study are listed in Table 3. The details of these calculations for case 3 are provided in the Supporting Information. The total endothermic guest-desorption heat, Qik−, was determined to be −81.4 kJ/molMU for case 1, −86.8 kJ/mol-MU for case 2, and −200.4 kJ/molMU for case 3; however, considering the exothermic heat resulting from the shrinkage of host framework, Qik+, the net heat, Q'ik, removed from the system is reduced to −50.8 kJ/mol-MU for case 1, −56.7 kJ/mol-MU for case 2, and −139.7 kJ/mol-MU

for case 3. We subsequently evaluated the thermal management capability, eik, according to eqn. (12) and obtained values of 37.6% for case 1 and 34.7% for case 2, which demonstrates either gate-closing can be chosen, leading to almost the same thermal management capability at a desired operating gas pressure for a separation process. It is also worth mentioning that the exothermic heat due to shrinkage of the host in case 2 is about half of that calculated for case 1; however, the exothermic heat resulting from changes in host–guest interactions upon host shrinkage negates this disadvantage, resulting in a comparable thermal management capability for case 2 when compared to that of case 1. The thermal management capability for case 3 (30.3%) is slightly inferior to those of cases 1 and 2; however, it should be still effective, suggesting that flexible MOFs that exhibit multi-gate openings/closings are promising materials for the development of an intrinsically thermally managed system for CCS applications. Although the heat caused by gate-opening cannot be precisely treated by the thermodynamic model because it comes from a spontaneous transition through a metastable state;35, 40 we can estimate the thermal management capabilities of the adsorption process for the following three cases as depicted in Figure 9. Case 1' starts from the A state; CO2 molecules are adsorbed until the system transforms into B ⊃ 2CO2 at the lower gate-opening pressure. Case 2' starts from the C ⊃ 3CO2 state; CO2 molecules are adsorbed until the system transforms into D ⊃ 5.7CO2 at the higher gate-opening pressure. Case 3' starts from the A state; the CO2 molecules are adsorbed until the system transforms into D ⊃ 5.7CO2, while passing through states B and C as the gas pressure increases from that of the lower gate opening to that of the higher gate opening. Note that the amounts adsorbed by the two states, B ⊃ 2CO2 and C ⊃ 3CO2, at the corresponding gate-opening pressures, are only slightly larger than those at the corresponding gate-closing pressures, and that the intrinsic thermal management capabilities were calculated by bypassing the equilibrium gate-closings, as described in Figure S5. The intrinsic adsorption thermal management capabilities obtained in this manner are 37.5% for case 1', 33.3% for case 2', and 29.6% for case 3', which are almost



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Table 3. The intrinsic thermal management capabilities of ELM-11 on the desorption process. Case 1

Case 2

Case 3

B ⊃ 2CO2 → A

D ⊃ 5.5CO2 → C ⊃ 3CO2

D ⊃ 5.5CO2 → A

Internal energy change of host, − ΔU host

kJ/mol-MU

30.6 (30.6)

16.0 (16.0)

46.6 (46.6)

Exothermic heat by the remaining guest

kJ/mol-MU

0 (0)

14.1 (14.6)

14.1 (14.6)

Total exothermic heat caused by host shrinkage, Qik+

kJ/mol-MU

30.6 (30.6)

30.1 (30.6)

60.7 (61.2)

Endothermic heat by guest desorption, Qik−

kJ/mol-MU

−81.4 (−74.0)

−86.8 (−69.8)

−200.4 (−163.9)

Net heat, Q'ik

kJ/mol-MU

−50.8 (−43.4)

−56.7 (−39.2)

−139.7 (−102.7)

Thermal management capability, eik = − Qik+ / Qik−

%

37.6 (41.3)

34.7 (43.8)

30.3 (37.3)

ik

The values in parentheses are those predicted at 298 K.

the same as those for the corresponding desorption cases (see Table S7). These results indicate that the intrinsic thermal management of the adsorption process (the endothermic heats from host expansion and the changes in host-guest interactions upon host expansion) is as effective as it is for the desorption process. Toward the application of flexible MOFs to CCS. We focused on the two-step gate desorption of CO2 on ELM-11 at 195 K because this low temperature is suitable for the structural analysis using in-situ synchrotron XRPD, which is required for precise free energy analyses; however, our results should be also applicable to the system at moderate temperatures because it has been reported that the two-step gate adsorption/desorption isotherms of CO2 on ELM-11 up to 298 K are analogous to that at 195 K.34 We also previously found that the change of the unit cell volume of B between 195 and 298 K is only 2%.18 Hence, we assessed the CO2 separation characteristics of ELM-11 at 298 K, including the intrinsic thermal management capability and the CO2 selectivities for CO2/N2 and CO2/CH4 mixtures, using the B, C, and D structures at 195 K. We calculated the fictitious adsorption isotherms for CO2 on B, C, and D at 298 K by GCMC simulations and evaluated the intrinsic thermal management capability of ELM-11 at 298 K. The results for the three cases, which are the same settings at 195 K, are listed in Table 3. The thermal management capability of ELM-11 at 298 K is 41% for case 1, 44% for case 2, and 37% for case 3, which are surprisingly improved compared to those determined at 195 K. This is because of a decrease in the endothermic heat by CO2 desorption at 298 K: −9.1% for case 1, −20% for case 2, and −18% for case 3. These results suggest that the intrinsic thermal management capability of flexible MOFs is effective at the moderate temperatures relevant to CCS. We then conducted GCMC simulations for the adsorption of CO2/N2 (10:90) and CO2/CH4 (50:50) mixtures on ELM-11 at 298 K by using the RASPA43 software (see Supporting Information for details); the existence of structure C was omitted for the sake of simplicity. Figure 10a shows the resulting total and component adsorption isotherms for the CO2/N2 (10:90) mixture on B and D and the CO2 selectivity at 298 K. We assumed that the lower and higher gate closings occur when the partial pressure of CO2 becomes equal to the lower gate-closing pressure of 62 kPa18 and the higher gate-closing pressure of 1.3 MPa32 for the case of the pure CO2 adsorption at 298 K. The selectivity of CO2 over N2 at the lower gate-closing pressure (structure B) is extremely high and reaches 432. On the other hand, the CO2 selectivity at the higher gate-closing pressure (structure D) is 47

Figure 10. The total and each component adsorption isotherm for (a) CO2/N2 (10:90) and (b) CO2/CH4 (50:50) mixtures on B and D, and CO2 selectivity at 298 K. The existence of structure C was omitted for the sake of simplicity.

and ten times smaller than that of the structure B; however, it is still higher compared to the conventional adsorbents (generally below 30).44 The high CO2 selectivity stems from the overwhelmingly high affinity of the B and D structures for CO2 over N2, which indicates that ELM-11 is particularly useful for CO2 separation. However, it should be noted that the lower and higher gate-closing pressures of ELM-11 for the CO2/N2 (10:90) mixture is unfortunately too high because post-combustion CO2 capture is considered to operate below ca. 0.1 MPa.3 Figure 10b shows the total and component adsorption isotherms for the CO2/CH4 (50:50) mixture on B and D and the CO2 selectivity at 298 K. The lower and higher gate-closing


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pressures were set in the same way as those for the adsorption of the CO2/N2 (10:90) mixture at 298 K. The selectivity of CO2 over CH4 is again unusually high. The B and D structures achieve CO2 selectivities of 135 at the lower gate-closing pressure and 16 at the higher gate-closing pressure, both of which are also surpass the records for general adsorbents (ca. 10).45 The lower gate-closing pressure of 0.12 MPa is below 0.5 MPa, the pressure at which CO2 capture from landfill gas [CO2/CH4 (50:50) mixture] is supposed operate.3 Moreover, the CO2 selectivity reaches 150 at 0.5 MPa, which suggests that ELM-11 is a promising porous material for CO2 capture from landfill gas. On the other hand, the higher gate-closing pressure is unfortunately over 0.5 MPa and hence, the higher gate closing cannot be utilized to capture CO2. In light of the aforementioned examples, it is unfortunately evident that multi-gate adsorption of ELM-11 for CO2 is not available for CCS at moderate temperatures, and consequently the further exploration and development of flexible MOFs is required in order to apply the intrinsic thermal management mechanism based on multi-gate openings/closings to CCS. Our free energy analysis provides insight into the relationship between the gating pressure and the thermodynamic quantities related to the host framework. For example, the attachment of flexible side chains to the linkers of a flexible MOF would increase ∆Shost because the configurational entropy is increased after gate opening. This causes a decrease in ∆Fhost, which results in the shift of the gating pressure to lower values (note that this would also improve the intrinsic thermal management capability. Supporting Information for more detail). On the other hand, if functional groups that enhance the host-host interaction are attached to the linkers of a flexible MOF, ∆Uhost would increase, which shifts the gating pressure to higher pressures while also enhancing the intrinsic thermal management capability. Note that the thermodynamic quantities ∆Shost and ∆Uhost are actually correlated to each other; consequently it may be difficult to change them independently; however, this speculation should be still useful when designing new flexible MOFs for CCS.

is for the desorption process. Moreover, we predict that the thermal management capabilities of ELM-11 at 298 K are surprisingly improved compared with those at 195 K. These results suggest that flexible MOFs that exhibit multiple gate openings/closings are promising materials for the development of an intrinsically thermally managed system for CCS. The findings in the present study should be also applicable to other adsorption systems such as gas storage and adsorption heat pump. We also predict that ELM-11 has an extremely high CO2 selectivity for both CO2/N2 (10:90) and CO2/CH4 (50:50) mixtures at 298 K, which is a crucial factor for CCS applications, in addition to intrinsic thermal management capability. The gateclosing pressures of ELM-11 do not necessarily match the operating pressures used in CCS; however, our speculations about the modification of host-framework linkers in order to tune the gating pressure should be useful when designing new flexible MOFs for CCS. It is worth noting that only flexible MOFs exhibiting sharp gate-openings/closings, such as ELM-11, are insufficient for CO2 separation using PSA because pure N2 or CH4 cannot be obtained from the adsorption process. In particular, flexible MOFs can no longer adsorb CO2 when the partial pressure of CO2 in the adsorption tower becomes lower than the gate-opening pressure, which results in the immediate breakthrough of CO2 before the intrinsic breakpoint is reached. We have therefore come to the conclusion that a game-changing CCS adsorbent is a combination of a flexible MOF whose lower gate-closing pressure is slightly higher than the desired desorption pressure and a minimum amount of a conventional adsorbent exhibiting a type I CO2-adsorption isotherm. Such a mixture should have excellent characteristics; namely CO2 selectivity, regenerability, CO2 working capacity, and adsorption-tower thermal management, which are required for the development of a highly efficient PSA system.

CONCLUSIONS

Details of GCMC simulations; derivation of eqn. (6); atomic coordinates and Mulliken charges of C ⊃ 3CO2; lattice parameters of B ⊃ 2CO2; atomic coordinates and Mulliken charges of D ⊃ 6CO2; snapshots of frameworks B and C; fictitious adsorption isotherms and free energy profiles at 200 and 205 K; intrinsic thermal management capability for case 3; illustration of a scheme to estimate the net heat released to the system at gate opening; intrinsic thermal management capability during the adsorption process; The relationship between the intrinsic thermal management capability and the thermodynamic properties of the host framework. The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org.

We successfully determined the crystal structures of ELM-11, C ⊃ 3CO2 and D ⊃ 6CO2, associated with the closing of the higher gate at 195 K, by combining GCMC simulations with the Rietveld method using in-situ synchrotron XRPD data. We then performed free energy analyses for the two-step gate-desorption isotherm of CO2 on ELM-11 at 195 K with the aid of GCMC simulations using the three framework structures of ELM-11, namely B, C and D. These analyses provided the accurate thermodynamic quantities required for the evaluation of the intrinsic thermal management capability of ELM-11 thanks to our strict structural refinement method. We derived thermodynamic formulae to evaluate the net heat removed from the system during the desorption process under adiabatic conditions, which is the sum of the endothermic heat associated with guest desorption, the exothermic heat generated by host shrinkage, and the exothermic heat of the guest molecules that remain in the host framework due to changes in hostguest interactions upon shrinkage of the host. We found that the last contribution is significant during the closing of the higher gate, which results in almost identical thermal management capabilities of ELM-11 for the higher and lower gate closings at 195 K. We also obtained results indicating that the intrinsic thermal management of the adsorption process is as effective as it

ASSOCIATED CONTENT Supporting Information

AUTHOR INFORMATION Corresponding Author E-mail: [email protected] E-mail: [email protected]

Notes The authors declare no competing financial interests.



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ACKNOWLEDGMENT This work was financially supported by a Grant-in-Aid for JSPS Fellows no. 15J05846, a Grant-in-Aid for Scientific Research (B) no. 17H03097, and JST CREST Grant Number JPMJCR1324, Japan. Computation time for the DFT calculation was provided by the Super Computer System, Institute for Chemical Research, Kyoto University. The synchrotron radiation experiments were performed at the BL02B2 beamline of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2015B1543, 2016A1481, 2016A1614, and 2016B1683). We thank Dr. Shogo Kawaguchi for great help of the synchrotron radiation experiments, and Dr. Hiroshi Kajiro, Prof. Hirofumi Kanoh and Dr. Atsushi Kondo for fruitful discussions.

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