Tunable Azacrown-Embedded Graphene Nanomeshes for Ion

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Tunable Azacrown-Embedded Graphene Nanomeshes for Ion Sensing and Separation Rohini Krishnakumar, and Rotti Srinivasamurthy Swathi ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b10528 • Publication Date (Web): 06 Dec 2016 Downloaded from http://pubs.acs.org on December 7, 2016

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ACS Applied Materials & Interfaces

Tunable Azacrown-Embedded Graphene Nanomeshes for Ion Sensing and Separation Rohini Krishnakumar and Rotti Srinivasamurthy Swathi* School of Chemistry, Indian Institute of Science Education and Research-Thiruvananthapuram, Kerala, India – 695016 E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT

Remarkable selectivity with which crown ethers served as macrocyclic hosts for various guest species has led to numerous investigations on structure-specific interactions. Successful fabrication of graphene nanomeshes has opened up a plethora of avenues for sensing and separation applications. Embedding crown ether backbones in graphene frameworks can therefore be an interesting strategy for exploring the advantages offered by crown ether backbones, yet having the properties of graphene-based materials. Motivated by the recent success in fabrication of crown ether-based graphene nanopores, herein we investigate their performance towards ion sensing and separation using electronic structure methods. The effect of topology and electronic properties of the nanopore are probed by considering a series of oxygenbased and nitrogen-based graphene crown ethers (crown-n; n=1-6). Our computations have revealed the excellent alkali ion binding properties of azacrown-based graphene nanomeshes over conventional oxygen crown-based graphene nanomeshes and normal crown ethers. Selectivity in ion transmission through the nanomeshes is demonstrated by employing graphene crown ethers [crown-n (n=4-6)]. To the best of our knowledge, this article is the first report on azacrown-based graphene nanomeshes and their possible applications in ion sensing and separation, an aspect that we hope will be demonstrated in experiments soon.

Keywords: crown ethers, azacrown, circumcoronene, circumcircumcoronene, graphene nanomeshes, ion sensing


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INTRODUCTION The discovery of crown ethers by Pedersen in 1967 has led to the emergence of new host-guest chemistry principles for the selective binding of cations.1-3 Demonstration of the remarkable selectivity with which the cations crowned the macrocyclic hosts resulted in the 1987 Nobel Prize for Pedersen, jointly with Cram and Lehn for their investigations of structure-specific interactions.4-6 Ion-dipole interactions between the cations and the negatively charged oxygen ends of the cyclic polyether rings drive the host-guest complex formation. Experiments performed in gas phase, and solution and crystalline phases have revealed the role of the size and the charge of the cation, size of the macrocyclic cavity, number of heteroatoms in the ring and the nature of the solvating medium in determining the stabilities of the complexes. 7-13 Gas phase investigations of these complexes using the techniques of mass spectrometry and the success in crystallization of the salt complexes, along with the availability of computational tools for probing the binding strengths have triggered numerous studies in this area of supramolecular chemistry. Thanks to a variety of techniques like collision-induced dissociation,14-15 infrared multiple photon dissociation spectroscopy,16 IR-UV double resonance spectroscopy,17 UV photodissociation spectroscopy, laser-induced fluorescence spectroscopy,18 and isothermal titration calorimetry,19 the complexes of crown ethers with various cations are well characterized. The binding efficiencies of crown ether-guest complexes are primarily dependent on the sizematching criteria. The efficiency is the highest when the size of the guest matches reasonably with the size of the cavity of the macrocyclic host. This has fuelled intense activity in the direction of employing crown ethers as components in photochemical and electrochemical molecular switching, amphiphiles in membranes, ionophores, ion sensing and transport.20 Early studies on crown ethers had oxygen atoms as the heteroatoms in the macrocycles. Subsequently,


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a variety of heteroatoms like nitrogen, sulphur and phosphorus were explored.21-27 Crown ethers with nitrogen atoms as the heteroatoms are referred to as the azacrowns. With the advent of carbon-based materials like fullerenes, carbon nanotubes and graphene, methods to tether/functionalize the carbon-based materials with crown ethers have evolved leading to numerous applications.28-34 Among the members of the carbon family, graphene has enjoyed an unprecedented status over the last decade due to its excellent electronic, mechanical, thermal, physical and chemical properties.35-37 Cutting graphene sheets into ribbons, and drilling pores through graphene to generate nanomeshes provides a further handle to control the properties of this two-dimensional honeycomb crystalline material. Successful fabrication and characterization of graphene nanomeshes38-44 down to the sub-nm size regime have opened up a plethora of applications45-52 in areas ranging from field effect transistors, gas sensors,53-55 catalysis56,57 to state-of-the-art DNA sequencing58 and protein translocation experiments. Design of graphene-based bioinspired artificial ion channels is yet another area of intense activity, motivated primarily by the objective to achieve high selectivities in ion passage through the nanopores.59-62 In spite of the fact that ion passage through crown ethers has been well studied for over half a century now, interesting applications towards artificial ion channels20 and energy storage63 are pursued with great interest only over the last few years. Besides, studies on ion passage through graphene nanopores have explored the advantages offered by the graphene-based membrane materials. It is then natural to think of integrating crown ethers with graphene nanopores as an even better strategy towards ion sensing and separation. In 2013, Maarouf and co-workers had studied the effect of doping by cations and anions within the pores of graphene nanomeshes.64 The authors had investigated the effect of cations on the electronic properties of crown ether-


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based graphene nanomeshes. Interestingly, in 2014, Guo and co-workers have succeeded in embedding crown ethers in graphene frameworks to exploit the advantages offered by crown ethers as well as graphene membranes.65 The authors further demonstrated that the crown etherbased graphene nanomeshes have a rather strong binding with the alkali metals than the normal crown ethers. To the best of our knowledge, these are the only two reports in the literature on crown ether embedded graphene networks. Herein, based on our electronic structure calculations, we propose that azacrown-based graphene nanomeshes can bind alkali metal ions even more strongly and are potential candidates for achieving the selective separation of the alkali ions. Recent experimental findings in fact are very encouraging, suggesting that the azacrown-based graphene nanomeshes will soon be fabricated and used for ion sensing.41, 66

COMPUTATIONAL METHODOLOGY All the computations reported in this manuscript are performed using density functional theory (DFT) with the hybrid functional B3LYP at B3LYP/6-311G(d,p) level.67 This functional has earlier been widely used for electronic structure calculations involving crown ethers.8, 12, 26, 27 Cohesive energies per atom (Ecoh/atom) of the nanoporous substrates are calculated to evaluate their structural stabilities. Cohesive energy is defined as the energy required to dissociate the system into its constituent isolated atomic species and is calculated using Ecoh/atom = - (Esystem- nCEC- nHEH- nNEN- nOEO) / M, where Esystem, EC, EH, EN and EO correspond to the energies of the nanoporous substrate, isolated carbon, hydrogen, nitrogen and oxygen atoms. nC, nH, nN and nO are the number of carbon, hydrogen, nitrogen and oxygen atoms, respectively, while M defines the total number of atoms as given by M=nC+nH+nN+nO.


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The interaction energies corresponding to the binding of alkali metal ions with GCEs are evaluated using Eint = Ecomplex - EGCE - Eion. where Ecomplex, EGCE and Eion correspond to the energies of the optimized geometries of the complex, the GCE and the alkali metal ion respectively. Frequency calculations are also performed along with geometry optimizations to confirm whether the structures indeed correspond to the energy minima. The energy barriers for the passage of the Na+ and K+ ions through the pores of GCEs are obtained as Ebarrier= Eint (transition state) - Eint (minimum energy configuration). The reported interaction energies are corrected for the basis set superposition errors using the counterpoise correction scheme.68 All the computations are implemented using the Gaussian-09

suite of programs.69 Natural bond orbital (NBO) analysis is performed using NBO 6.070 to compute the partial charges on the alkali metal ions in the ion-substrate complexes. RESULTS AND DISCUSSION Driven by the recent experimental success in creating vacancies in graphene and in achieving substitutional doping of carbon atoms in graphene by boron, nitrogen, oxygen atoms etc. and keeping in mind our objective of designing crown ether-based graphene nanomeshes for ion sensing, we consider various graphene crown ethers (GCEs) with oxygen and nitrogen atoms as the heteroatoms. Initially, circumcoronene (C54H18) has been employed as the model system for graphene and the number of heteroatoms in the GCEs has been systematically varied from one to six. We employ density functional theory as the methodology for electronic structure


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calculations performed using the Gaussian 09 suite of programs70. All the computations reported herein are performed using the B3LYP functional68 with 6-311G(d,p) basis set (see the section on Computational Methodology). Figure 1 and Figure 2 shows the optimized geometries of the GCEs (crown-n; n=1-6) with oxygen and nitrogen atoms as the heteroatoms respectively. Crown-n (n=1-6) are generated by substitutional doping of carbon atoms with oxygen and nitrogen atoms and/or by removing one, two, three, four and six carbon atoms from circumcoronene. For instance, 9-crown-1 is obtained by substitutional doping of a carbon atom with a heteroatom and removing a carbon atom, while 10-crown-2 is generated by substitutional doping of two carbon atoms with heteroatoms. Substitutional doping of three carbon atoms with heteroatoms and removal of a carbon atom yield 12-crown-3. 14-crown-4, 16-crown-5 and 18crown-6 are generated by substitutional doping of four, five and six carbon atoms with heteroatoms and removing two, three and six carbon atoms respectively.

9-crown-1

10-crown-2

14-crown-4

16-crown-5

12-crown-3

18-crown-6


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Figure 1. The optimized geometries of O-based GCEs generated from circumcoronene (C54H18).

9-crown-1

14-crown-4

10-crown-2

16-crown-5

12-crown-3

18-crown-6

Figure 2. The optimized geometries of N-based GCEs generated from circumcoronene (C54H18). Cohesive energies are indicative of structural stability. A comparison of the computed cohesive energies (see the section on Computational Methodology) of various GCEs with O atoms and N atoms as shown in Figure 3 suggests a preference for N atoms over O atoms as the pore perimeter passivators. The electrostatic potential surfaces of GCEs (Figure S1 in Supporting Information) also reflect that the pores in N-based GCEs are associated with regions of higher electrostatic potential than the conventional O-based GCEs. Based on this, we hypothesize that azacrown-based graphene nanomeshes can be ideal candidates for binding alkali metal ions. Further, the number of heteroatoms in the pore perimeter can be used as a handle to tune pore sizes, enabling selectivity for the passage of the ions. Therefore, our objective in this work is to


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assess the role of the topological and the electronic properties of the nanopores in governing the performance of GCEs toward ion sensing. (a)

(b)

7.4 O-based N-based

7.68

Ecoh/atom (kcal/mol)

Ecoh/atom (kcal/mol)

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


7.3

7.2

7.1

7.0

C54H18-based GCEs

O-based N-based

7.66 7.64 7.62 7.60 7.58 7.56

C96H24-based GCEs

7.54

6.9 9-crown-1 10-crown-2 12-crown-3 14-crown-4 16-crown-5 18-crown-6

14-crown-4

GCEs

16-crown-5

18-crown-6

GCEs

Figure 3. Cohesive energies of O-based and N-based GCEs generated from (a) circumcoronene (C54H18) and (b) circumcircumcoronene (C96H24). The initial geometries for the complexes of Li+, Na+ and K+ with O and N-based GCEs are therefore generated by placing the ions at the centres of the GCEs and electronic structure calculations are performed. The optimized geometries of the complexes of the ions with the GCEs (n=1-6) and their interaction energies are reported in Figures S2-S3 in Supporting Information. The interaction strengths of the ions with the GCEs (Table 1) follow the order: Li+>Na+>K+. The binding strength of Li+ is highest with crown-4 among the O-based GCEs and with crown-5 among the N-based GCEs. However, Na+ and K+ have strong binding with crown-6 GCEs (O-based as well as N-based), as can be easily understood based on the size matching criteria. From the interaction energy values, it can be clearly seen that the alkali metal ions bind strongly to the azacrown-based graphene nanopores than the conventional crown ether-based nanopores. In the optimized geometries of the complexes of crown-n (n=1-6), some of the ions


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are displaced vertically from the centers of the nanopores (see Table 2). In crown-4 and crown-5, Li+ binds within the pore, while Na+ and K+ are displaced vertically from the pore centers. Li+, Na+ and K+ are found to bind within the nanopores of crown-6. Owing to its small size in comparison with the size of the nanopore, in crown-6, Li+ is found to bind at horizontal offcenter positions at distances of 0.79 Å and 0.72 Å in the pores of O-based and N-based crown-6 GCEs respectively. Similar is the case with O-based crown-5 GCE wherein Li+ binds at a horizontal off-center position of 0.48 Å in the pore.

Table 1. The interaction energies (in kcal/mol) of the complexes of alkali metal ions with Obased and N-based GCEs (crown-n; n=1-6) generated from C54H18. Ions/

9-crown-1

10-crown-2

12-crown-3

14-crown-4

16-crown-5

18-crown-6

GCEs

O

N

O

N

O

N

O

N

O

N

O

N

Li+

-56.99

-70.61

-53.92

-68.75

-69.25

-109.01

-89.86

-133.37

-83.29

-135.98

-84.25

-124.36

Na+

-40.10

-49.31

-38.68

-47.71

-43.70

-69.05

-58.50

-86.89

-58.81

-101.06

-75.81

-114.73

K+

-29.17

-36.17

-30.01

-35.97

-30.62

-49.97

-40.62

-61.57

-41.21

-72.58

-62.51

-94.87


10

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Table 2. The positions of the metal ions from the centres of the pores of O-based and N-based GCEs generated from C54H18 (in Å). Ions/GCEs 12-crown-3 14-crown-4 16-crown-5

a

18-crown-6

O

N

O

N

O

N

O

N

Li+

1.04

0.97

0.00

0.00

0.00 (0.48)a 0.00 0.00 (0.79) 0.00 (0.72)

Na+

1.70

1.67

1.23

1.19

0.88

0.70 0.00

0.00

K+

2.23

2.15

1.89

1.85

1.69

1.59 0.00

0.00

Horizontal off-center distances

In view of the higher binding efficiencies of the alkali ions with crown-n (n=4-6) GCEs, they are chosen for further detailed studies on probing their interactions with the alkali ions. Some of the alkali ion-GCE complexes exhibited structural distortions when circumcoronene is used as the model system for graphene (Figures S2-S3 of Supporting Information). Therefore, we went on to build GCEs with circumcircumcoronene (C96H24) as the model system for graphene. The optimized geometries of the resultant O-based and N-based crown-n (n=4-6) GCEs are shown in Figure 4. As earlier, the cohesive energies (Figure 3) and the electrostatic potential analysis (Figure 5) reveal that the azacrown-based GCEs are robust over conventional O-based GCEs for ion binding. The binding strengths with alkali ions are further estimated by performing geometry optimizations of the complexes, the results of which are shown in Figure 6. From the geometries, it is clear that the structural distortions in the nanoporous substrates are now smaller when compared to the previous instance (with C54H18 as the model system). However, the trends in the interaction strengths with various ions are the same as earlier and the variation in interaction


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energies employing C54H18 and C96H24 as the model systems for graphene is small (see Figure 7). Again, a clear preference for azacrown-based graphene nanopores over conventional oxygenbased GCEs is evident from Figure 7. The binding positions of the ions in the complexes of Obased and N-based GCEs (crown-n; n=4-6) generated from C96H24 are summarized in Table 3. 14-crown-4

16-crown-5

18-crown-6

O-based

N-based

Figure 4. The optimized geometries of O-based and N-based crown-n (n=4-6) GCEs generated from circumcircumcoronene (C96H24).


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0.06 a.u.

-0.06 a.u.

Figure 5. Electrostatic potential surfaces of O-based and N-based GCEs [crown-n (n=4-6)] generated from circumcircumcoronene (C96H24). GCEs/Ions

Li+

Na+

K+

-90.69

-59.25

-41.36

-136.12

-89.17

-63.78

O

14crown-4

N


13


O

18crown-6

-82.73

-74.65

-127.20

-117.65

-61.84

N

-98.38

Figure 6. The optimized geometries of the complexes of alkali metal ions with crown-4 and crown-6 GCEs along with their interaction energies (in kcal/mol).

(a)

(b)

crown-4

-60 -80 -100 C54H18-O

-120

C54H18-N C96H24-O C96H24-N

-140 Li

+

+

Na

crown-6

-60

+

K

Eint (kcal/mol)

-40

Eint (kcal/mol)

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

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-80

-100

-120

C54H18-O C54H18-N C96H24-O

-140

C96H24-N

Li

Ions

+

+

Na

+

K

Ions

Figure 7. Comparison of the interaction energies of the alkali metal ions with (a) crown-4 and (b) crown-6 GCEs generated from circumcoronene (C54H18) and circumcircumcoronene (C96H24) model systems.


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Table 3. The positions of the metal ions from the centres of the pores of O-based and N-based GCEs generated from C96H24 (in Å). Ions/GCEs 14-crown-4 O

a

N

18-crown-6 O

N

Li+

0.00

0.00 0.00 (0.85)a 0.00 (0.76)

Na+

1.24

1.19

0.00

0.00

K+

1.90

1.84

0.00

0.00

Horizontal off-center distances

In order to assess the relative alkali ion binding strengths of GCEs over normal crown ethers, we have optimized the geometries of the complexes of Li+, Na+ and K+ with 12-crown-4 (C8O4H16) and 18-crown-6 (C12O6H24) at the same level of theory.6,

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A comparison of the

binding strengths of the ions with normal 12-crown-4, 18-crown-6 and the respective O-based and N-based GCEs is shown in Figure 8 (see also Figure S4 in Supporting Information). In contrast to the flexible nature of normal crown ethers, graphene-based crown ethers offer rigid host backbones for the complexation with the ions. Guo and co-workers had earlier reported a comparison of the alkali metal atom binding strengths with 18-crown-6 and crown-6 O-based GCE.69 Our current finding provides a thrust to this result by predicting that azacrown-based GCEs have even more binding affinities for alkali ions than the O-based GCEs. We performed the NBO analysis to monitor the variation of charges on the alkali metal ions in the ion-substrate complexes when compared to the bare ions (see Table S1 in Supporting Information). We found that the charges on the ions decrease on complexation indicating charge transfer from the GCEs to the alkali ions.


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(a)

(b) -60

-60

-80

-100

-120 Normal crown ether N-based GCE O-based GCE

-140

Eint (kcal/mol)

crown-4

-40

Eint (kcal/mol)

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

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crown-6

-80

-100

-120 Normal crown ether N-based GCE O-based GCE -140

+

Li

+

Na

+

K

Ions

+

Li

+

Na

+

K

Ions

Figure 8. Comparison of the interaction energies of the alkali metal ions with O-based and Nbased (a) crown-4 and (b) crown-6 GCEs generated from C96H24 and the normal crown ethers. We now analyze the passage of the ions through the nanopores of GCEs, with the objective of testing if one can attain selectivity in ion passage by employing crown-n (n=4-6) GCEs. The energetics for the transmission of the ions through the pores is analysed by performing single point energy scans. The ions are kept at various vertical positions from the centers of the GCEs in their optimized geometries in the [-10, 10] Å interval and single point calculations are performed to obtain the energy scans. A step size of 0.2 Å was employed in the calculations. Figure 9 shows the resultant scans obtained for the passage of Li+, Na+ and K+ through the pores of O-based and N-based crown-4 GCEs. The passage of Li+ through crown-4 GCEs is found to be barrierless, while that of Na+ and K+ is associated with an energy cost (see Table 4 for the numerical values of energy barriers). Thus, crown-4 GCEs allow the passage of Li+ through the pores while blocking Na+ and K+. It is interesting to note that the estimated barriers are not very sensitive to the size of the model systems used to represent graphene (see Table 4 and Figure S5 in Supporting Information). This is essentially due to the fact that the bottleneck in the process is


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the passage through the pores and the energy barriers are predominantly dictated by the atoms in the pore perimeter. (a)

(b)

(c)

Li+

Eint (kcal/mol)

-30

-60

O-based N-based

-90

-120

200

Na+

0

Eint (kcal/mol)

0

Eint (kcal/mol)

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


-20

-40 O-based N-based

-60

-80

K+

150

100

50

O-based N-based

0

-50

-100

-150

-10

-8

-6

-4

-2

0

2

4

6

8

10

-10

z (Å)

-8

-6

-4

-2

0

2

4

6

8

-8

10

-6

-4

-2

0

2

4

6

8

z (Å)

z (Å)

Figure 9. The energy scans for the passage of (a) Li+, (b) Na+ and (c) K+ through the nanopores of O-based and N-based crown-4 GCEs generated from C96H24. Table 4. Energy barriers (in kcal/mol) for the passage of the ions through the pores of O-based and N-based GCEs generated from C96H24. The results for ion passage through the pores of GCEs generated from C54H18 are given in parentheses. 14-crown-4

16-crown-5

18-crown-6

Ions/GCEs O

N

O

N

O

N

Li+

0.00 (0.00)

0.00 (0.00)

0.00 (0.00)

0.00 (0.00)

0.00 (0.00)

0.00 (0.00)

Na+

36.75 (36.09)

38.79 (38.55)

8.37 (8.58)

6.90 (6.87)

0.00 (0.00)

0.00 (0.00)

K+

192.23 (202.46)

227.00 (232.38)

88.61 (88.56)

96.98 (91.85)

0.00 (0.00)

0.00 (0.00)

As the passage of Li+ through crown-4 is found to be barrierless, we anticipate the same feature for its passage through crown-5. Therefore, the energy scans were performed for the passage of Na+ and K+ through O-based and N-based crown-5 GCEs, the results of which are shown in Figure 10 (see also Figure S6 in Supporting Information). The barrier for the passage of Na+ is found to be very small (Table 4). However, transmission of K+ through the pores of crown-5 GCEs involves a substantial energy cost. On similar lines, energy scans for the passage of Na+


17


and K+ through the pores of crown-6 GCEs are obtained and are shown in Figure 11 (see also Figure S7 in Supporting Information). Due to the large pore sizes, crown-6 GCEs allow the passage of all the three cations without an energy cost. (a)

(b) 0

K+

Na+ 50

Eint (kcal/mol)

Eint (kcal/mol)

-20 -40 -60 -80 O-based N-based

-100

25 0 -25 -50

O-based N-based

-75 -10

-8

-6

-4

-2

0

2

4

6

8

10

-8

-6

-4

-2

z (Å)

0

2

4

6

8

z (Å)

Figure 10. The energy scans for the passage of (a) Na+ and (b) K+ through the nanopores of Obased and N-based crown-5 GCEs generated from C96H24. (a)

(b)

0

0

-25

-50

-75 O-based N-based

-100

Eint (kcal/mol)

Na+

Eint (kcal/mol)

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

Page 18 of 33

K+

-20

-40

-60

-80

O-based N-based

-100

-125 -8

-6

-4

-2

0

2

4

6

8

-8

-6

z (Å)

-4

-2

0

2

4

6

8

z (Å)

Figure 11. The energy scans for the passage of (a) Na+ and (b) K+ through the nanopores of Obased and N-based crown-6 GCEs generated from C96H24. In cases where the energy barrier is non-zero, the nature of the energy scans reflects a doublewell potential. The two minima in the potential correspond to two equal energy configurations


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for the ions to bind on either side of the GCEs. The higher energy configuration corresponds to a transition state geometry wherein the ion becomes planar with the GCE. Thus, the energy barriers for the passage of the ions through the pores are obtained as the differences in energies of the transition state and the minimum energy geometries (see the section on Computational Methodology). However, estimation of energy barriers using this approach has a limitation. This does not take into account the relaxation in the geometry of the nanopore as a result of its interaction with the incoming ion. Therefore, we went on to obtain optimized geometries of the transition states (by keeping the ions in the pore centres) in all the cases where the barriers were found to be non-zero. The transition state geometries were confirmed by the presence of an imaginary frequency. Subsequently, energy barriers were estimated as the differences in the energies of the complexes in the transition states and the minimum energy geometries. The transition state geometries were optimized only for the GCEs generated from C54H18 to save the computational time. We find that the barriers in all the cases have now dropped down (see Table 5), as we have allowed for the relaxation of the nanopore which is evident from the increase in the pore size in the transition state geometries. Such a relaxation in the geometries of the nanopores of O-based and N-based 14-crown-4 GCEs after incorporation of Na+ and K+ within the nanopores can be seen clearly from Figure 12.

Table 5. Energy barriersa (in kcal/mol) for the passage of the ions through the pores of O-based and N-based GCEs generated from C54H18. Ions

14-crown-4

/GCEs O Na+

N

23.97 24.20

16-crown-5 O

N

3.92

2.42


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K+

a

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88.20 113.67 41.38 41.46

barriers computed after taking into account the relaxation in the pore geometries due to the ions.

3.78

3.83

(a)

4.01

4.54

4.08

4.48

(b)

(c)

Figure 12. The geometries of nanopores (diagonal distances in Å) in (a) pristine O-based and Nbased crown-4 GCEs, (b) transition states of the complexes with Na+ and (c) transition states of the complexes with K+. The effect of solvation is studied using Polarizable Continuum Model (PCM) which is a widely used implicit-solvation model. Water is used as the solvent for the calculations. The solvent effects are probed to evaluate the alkali metal ion binding with the N-based crown-4 and crown-6 GCEs. The optimised geometries of the complexes along with their interaction energies in water are given in Figure 13. The interaction energies are found to decrease significantly on going from the gas phase to the solvent medium. This arises due to the coordination of water


20

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molecules around the cations, which neutralises the charge on the cations, thereby retarding the interaction between cations and the substrates. Further, passage of the ions through the pores in solvent medium is also studied by computing the energy scans in solvent medium. Figure 14 and Figure 15 show a comparison of the energy scans in gas phase and in solvent medium for the crown-4 and crown-6 N-based GCEs. Interestingly, we find that the selectivity of ion transmission through the pores is more or less retained on moving to the solvent medium, despite changes in the values of the interaction energies.

GCEs/Ions

Li+

Na+

-32.50

-17.78

K+

14-crown-4

-12.42

18-crown-6

-22.02

-26.24

-24.84

Figure 13. The optimized geometries of the complexes of alkali metal ions with crown-4 and crown-6 N-based GCEs along with their interaction energies in water (in kcal/mol).


21


(a)

(b) 180

250 200

+

Li + Na + K

60

+

Eint (kcal/mol)

Eint (kcal/mol)

120

0 -60

Li + Na + K

150 100 50 0

-120

-50 -12 -10 -8

-6

-4

-2

0

2

4

6

8

-6

10 12

-4

-2

z (Å)

0

2

4

6

z (Å)

Figure 14. The energy scans for the passage of Li+, Na+ and K+ through the nanopores of Nbased crown-4 GCEs generated from C54H18 in the (a) gas phase and in the (b) water medium. (a)

(b) 0

0

-20

Eint (kcal/mol)

Eint (kcal/mol)

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

Page 22 of 33

-40 -60

Na + K

-80

+

-100

-5 -10 -15

Na + K

+

-20 -25

-120 -10

-8

-6

-4

-2

0

2

4

6

8

10

-30 -6

z (Å)

-4

-2

0

2

4

6

z (Å)

Figure 15. The energy scans for the passage of Na+ and K+ through the nanopores of N-based crown-6 GCEs generated from C54H18 in the (a) gas phase and in the (b) water medium. Thus, from the computed energy barriers, it is clear that crown-4 GCEs allow the free passage of only Li+ ion, while crown-6 GCEs allow the passage of all the three ions (Li+, Na+ and K+). Crown-5 GCEs allow the free passage of Li+. However, a tiny barrier exists (2-4 kcal/mol) for the transmission of Na+, while large barrier (~40 kcal/mol) is found for the passage of K+. The


22

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tiny barrier in case of Na+ can be surmounted easily if the incoming ion has some energy. Thus, we see that crown-5 GCEs can in principle allow the passage of Li+ and Na+, while blocking K+.

CONCLUSIONS Overall, our computations employing circumcoronene and circumcircumcoronene as the model systems for graphene have revealed that azacrown-based graphene nanopores can be excellent receptors in comparison with oxygen-based graphene crown ethers and normal crown ethers for alkali metal ions. Further, by employing crown-n (n=4-6) O-based and N-based GCEs, we have shown that, it is possible to obtain selectivity in the passage of the ions through the pores. Crown-6 GCEs allow the passage of all the ions, while crown-4 GCEs allow the passage of only Li+ ion. Crown-5 GCEs can transmit Li+ and Na+ ions through the pores. With the successful fabrication of oxygen-based graphene crown ethers two years ago, we believe that azacrownbased graphene nanopores will soon become a reality and will be used for ion sensing.

SUPPORTING INFORMATION The electrostatic potential surfaces of the GCEs generated from C54H18, optimized geometries and interaction energies of the alkali metal ion complexes with various GCEs generated from C54H18 are given in Supporting Information. A comparison of the binding strengths of the ions with the GCEs and the normal crown ethers, the energy scans for the ion passage through the pores of GCEs generated from C54H18 are also given in Supporting Information. The NBO charges of the alkali ions in the complexes of the ions with the O-based and N-based crown-4 and crown-6 GCEs are also given in Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.


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Page 24 of 33

ACKNOWLEDGMENTS The authors acknowledge IISER-TVM for computational facilities. RK thanks IISER-TVM for financial support. Authors also thank P. Sravan Kumar, Indian Institute of Science, Bangalore for help with the NBO calculations. REFERENCES 1. Pedersen, C. J., Cyclic Polyethers and their Complexes with Metal Salts. J. Am. Chem. Soc. 1967, 89, 7017-7036. 2. Pedersen, C. J., The Discovery of Crown Ethers. Science 1988, 241, 536-540. 3. Pedersen, C. J.; Frensdorff, H. K., Macrocyclic Polyethers and Their Complexes. Angew. Chem. Int. Ed. 1972, 11, 16-25. 4. Gokel, G. W.; Leevy, W. M.; Weber, M. E., Crown Ethers: Sensors for Ions and Molecular Scaffolds for Materials and Biological Models. Chem. Rev. 2004, 104, 2723-2750. 5. Maleknia, S.; Brodbelt, J., Gas-phase Selectivities of Crown Ethers for Alkali Metal Ion Complexation. J. Am. Chem. Soc. 1992, 114, 4295-4298. 6. Glendening, E. D.; Feller, D.; Thompson, M. A., An ab Initio Investigation of the Structure and Alkali Metal Cation Selectivity of 18-Crown-6. J. Am. Chem. Soc. 1994, 116, 10657-10669. 7. Martínez-Haya, B.; Hurtado, P.; Hortal, A. R.; Hamad, S.; D. Steill, J.; Oomens, J., Emergence of Symmetry and Chirality in Crown Ether Complexes with Alkali Metal Cations. J. Phys. Chem. A 2010, 114, 7048-7054.


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