Chapter 4. Development of Novel Solid-electrolyte Material
4.2 Ion Slippage through Li + -centered G-quadruplex
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To investigate structural stability and explore Li+ conduction behavior of solid-sate LiGQ structure, initial size and shape of bulk LiGQ unit cell were decided following the information of experiment XRD. 8 Li+-centered G-quartets were stacked into 48.04 Å × 48.04 Å × 30.4 Å sized hexagonal unit cell, maintaining the most stable stacking sequence. To relax the LiGQ structure, geometry optimization was carried out until the convergence criteria (1000 kJ nm mol-1 for the maximum energy change) were satisfied. Subsequently, the MD simulation under canonical ensemble (i.e., NVT) were performed to anneal the alkyl chain moieties, with position restraints (applying harmonic spring constant k = 100 kJ mol-1) on G-quartet atoms. The temperature of each system was maintained to 298 K for 1 ns with 1 fs time step. After the annealing, equilibration of the LiGQ was performed under the isothermal-isobaric ensemble (i.e., NPT), at 1 bar and 298 K with 1 fs time step until the unit cell length was converged.
Production run was performed under the NPT ensemble at 1 bar and 298 K, for 500 ps. In all MD simulations, the temperature and the pressure of each system were controlled by the Berendsen thermostat and barostat, 62 respectively. During the equilibration and production run, the trajectories were analyzed every 1 ps.
Density functional theory (DFT) calculations were conducted using the Cambridge Serial Total Energy Package (CASTEP) to investigate partial density of states (PDOS) of Li+ and single ion conducting moieties. 63 The spin-polarized calculations were performed using a generalized gradient approximation (GGA) with PBE functional. 64 The interactions between the core and the valence electrons were described using the on-the-fly generation (OTFG) ultrasoft pseudopotential; 64, 65 the energy cutoff was set to 517 eV. The Tkatchenko–Scheffler (TS) method for DFT-D correction was used to describe the van der Waals interaction. 66 The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm was applied to the geometry optimization. 67 The convergence threshold for the geometry optimization and SCF density convergence were 1×10−5 eV atom-1 and 1×10−6 eV atom-1, respectively.
The convergence precision of the geometry optimization for the maximum force, stress, and displacement were set to 0.03 eV Å-1, 0.05 GPa, and 0.001 Å, respectively. The Monkhorst–Pack k- point grid was set to 3 × 3 × 3. 68
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4.2.2 Results and Discussion
4.2.2.1 Self-assembly Structure of the LiGQ
The self-assembly procedure of the LiGQ, along with its chemical structure, is illustrated in Fig.
4.1b. The monomer was synthesized according to a previously reported method. 30 The bulky pan- shaped bithiophene on the C8 position of guanine, which is composed of π-conjugated aromatic rings and long lipophilic chains, induces a strong intra-/inter-quartet π–π stacking and lamellar stacking. 30 Furthermore, the octyl side chain on the N9 position hinders unwanted hydrogen bonding at the N3 position, 69 which could help form the LiGQ instead of ribbon-like polymorphs.
We have conducted molecular mechanics simulation to confirm the origin of quartet structure formation from the oligothiophene-substituted guanine derivative. In Fig. 4.2, the self-assembly structure made up of guanine and oligothiophene-substituted guanine derivative are compared. In Fig.
4.2a, we can observe all three possible self-assembly structure of guanine molecule can be freely constructed, since there are no substituents which may obstruct N3 hydrogen bond. But with introduction of C8 and N9 substituent, circumstance changes. First, when guanine derivative constructs quartet structure, there were no steric hindrance (Fig. 4.2b). Both C8 and N9 substituents lean towards outside of the quartet structure and do not disturb N3 hydrogen bond. Second, when guanine derivative forms ribbon A structure, the C8 substituent made strong steric hinderance with guanine part of adjacent molecule and interfered N3 hydrogen bond (Fig. 4.2c). Because of this, after optimization, ribbon A structure of guanine derivative was separated and could not be maintained. Finally, when guanine derivative forms ribbon B structure, the N9 substituent stretches out towards the vertical direction of ribbon structure and made small steric hinderance with adjacent molecule. However, it did not affect N3 hydrogen bond much, so ribbon B structure was able to maintain its structure. Additionally, we have calculated the formation energy of guanine derivative quartet and ribbon B structure, to compare thermodynamic preference of each structure. The formation energy is calculated as follows.
𝐸𝑓𝑜𝑟= 𝐸𝑎𝑓𝑡𝑒𝑟− 𝐸𝑏𝑒𝑓𝑜𝑟𝑒 (4.2.2.1) where 𝐸𝑎𝑓𝑡𝑒𝑟 is energy of the optimized structure of quartet or ribbon structure, 𝐸𝑏𝑒𝑓𝑜𝑟𝑒 is sum of energy of molecular components that consists of quartet or ribbon structure. The results showed that quartet structure is more favorable than ribbon structure (-691 kJ/mol vs. -381 kJ/mol), with c.a. 310 kJ/mol difference in formation energy. In conclusion, N9 substituent and C8 substituent in guanine derivative prevent the formation of ribbon structure and facilitate the formation of quartet structure.
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Fig. 4.2 (a) Optimized structure of Li+ centered quartet, ribbon A and ribbon B, which are self-assembly structure made of guanine molecule. Orange, gray, white, blue, red, yellow colors represent lithium, carbon, hydrogen, nitrogen, oxygen and sulfur atoms, respectively. (b) Li+ centered quartet structure made of guanine derivative. Cyan color represents atoms of guanine part in quartet structure. (c) Two possible conformation of ribbon A structure made of guanine derivative. Conformations are classified with the position of first sulfur atom at C8 substituent. The one with sulfur atom on the opposite side of octyl-side chain (upper), and the other with sulfur atom on the same side of octyl-side chain (lower). (d) Ribbon B structure made of guanine derivative. Octyl side chains attached at N9 atom stretch toward vertical direction of ribbon structure and minimize steric hinderance. In (c) and (d), light green color represents atoms of guanine part in ribbon structure. Note that in (b), (c) and (d), hydrogen atoms are not shown for clarity.
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4.2.2.2 Stacking Sequence of the LiGQ
To identify the thermodynamically favorable stacking sequence of the LiGQ, we exploited molecular mechanics method. To hierarchically investigate the stacking sequence, we considered 3 variables (i.e., Polarity, rotation angle, and stacking distance) (Fig. 4.3a). First, the G-quartet’s polarity is determined by the direction of N-H···O=C hydrogen bonds. 70 If hydrogen bond direction is clockwise, the G-quartet has “Head” conformation (H), and if hydrogen bond direction is counterclockwise, it has
“Tail” conformation (T). In case of the polarity, two combinations of HH and HT are possibly suggested.
Second, the most favorable rotation angle is investigated by rotating the top G-quartet 10º at a time from 0º to 90º. Finally, the most stable stacking distance was examined by manipulating the distance between top and bottom G-quartet 0.2 Å at a time from 3.0 to 4.4 Å. Note that the distance between the G-quartets was determined to be equal to the distance between centroids of each G-quartet. Then, single point energy calculation was performed at each point. At each point, the formation energy 𝐸𝑓𝑜𝑟 of each structure is calculated as follows.
𝐸𝑓𝑜𝑟 = 𝐸𝑡𝑜𝑡− 8𝐸𝑔𝑢𝑎𝑛𝑖𝑛𝑒− 2𝐸𝐿𝑖+ (4.2.2.2) where 𝐸𝑡𝑜𝑡 is non-bonding energy of the total stacking system, 𝐸𝑔𝑢𝑎𝑛𝑖𝑛𝑒 is non-bonding energy of the guanine molecule and 𝐸𝐿𝑖+ is non-bonding energy of the Li+. Subsequently, the formation energy was compared by getting relative energy based on the lowest value among all 𝐸𝑓𝑜𝑟 values (Fig. 4.3b).
We found that the most stable stacking sequence is HH stacking, 80° rotation angle with 3.8 Å stacking distance (Fig. 4.3c).
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Figure 4.3. (a) Three variables that are considered to find the most stable stacking sequence of LiGQ. (b) Contour plot of relative formation energy, with every possible combination of variables. (c) The most stable stacking sequence found for LiGQ.
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4.2.2.3 Specification of the Anion Position in the LiGQ
Since we have found the stacking sequence without considering anion effects, we investigated the anion position in the LiGQ using molecular dynamics. Referring to Forman et al., 70 we assumed that anion position in the LiGQ crystal is likely to be close to -NH2 groups, forming hydrogen bonds with the G-quartet. To elucidate the anion position in the LiGQ, we have constructed two systems. First case is a trapped anion system where OTf- anions are trapped by hydrogen bonds with the G-quartet and second case is a free anion system where OTf- anions are freely distributed in the alkyl chain region (Fig. 4.4a). After relaxation of each system, the OTf- anions in the trapped anion system maintained their initial position (Fig. 4.4b). In contrary, the OTf- anions in the free anion systems are dispersed mainly in the alkyl chain region and some of the anions have formed hydrogen bonds with -NH2 groups locating at the boundary of the G-quartet. From this result, we expect that the OTf- tend to form hydrogen bonds with the G-quartet rather than wandering in the alkyl chain region. We have also calculated non-bonding energy per quartet, which clearly demonstrated that the trapped anion system forms thermodynamically favorable structure than the free anion system (Fig. 4.4c). Finally, we have applied an electric field with strength of 2 V nm-1 to relaxed systems of trapped anion and free anion, and then analyzed the mean square displacement (MSD) of Li+ and OTf- ions to compare conduction behavior of two different cases. From the MSD calculations, Li+ transference numbers were obtained for each system. The calculated tLi+ was about 0.68 for the free anion system and 0.91 for the trapped anion system, respectively, indicating that the anion trapping crucially affects the single-ion conducting characteristics of the LiGQ (Fig. 4.4d).
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Figure 4.4. (a) Initially constructed systems to elucidate position of anions. In “Trapped anion” system, all anions are bound to G-quartet at initial structure while “Free anion” system is not. (b) Anion position after relaxation procedure. Anions tend to form hydrogen bond with G-quartets. (c) Non-bonding energy per G-quartet. Trapped anion system is thermodynamically more favorable than free anion system. (d) Mean square displacement of Li+ and OTf- for “Trapped anion” and “Free anion” systems.
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4.2.2.4 Effect of Li salts on Structural stability of the LiGQ
The structural stability of the LiGQ upon addition of Li salts was investigated by molecular dynamics. Starting from the relaxed structure of the trapped anion system, we have removed the Li+ and OTf- ions. And then, we have relaxed the ion-less GQ crystal structure to monitor whether the GQ crystal can maintain its structure in the absence of ions (Fig. 4.5a). To confirm the structure stability of the LiGQ and GQ, hydrogen bond length distribution of inner hydrogen bond (HBI) and outer hydrogen bond (HBo) of each G-quartet was analyzed. The LiGQ maintained stable hydrogen bond distance, about 2.3 Å for HBI and 2.1 Å for HBo. In the GQ case, both HBI and HBo are distributed over broad range of distance and hydrogen bonds were not preserved (Fig. 4.5b and 4.5c). Thus, we can infer that the Li+ and OTf- ions play a viable role in the structural stability of the LiGQ.
Figure 4.5. (a) Relaxed structure of LiGQ with and without Li salts, respectively. (b) Inner hydrogen bond distribution of G-quartet for the last 100 ps of trajectory. (c) Outer hydrogen bond distribution of G-quartet for the last 100 ps of trajectory.
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4.2.2.5 Directional Single Li
+conduction Behavior of the LiGQ
The single-ion conduction behavior of the LiGQ were investigated by applying an electric field of 2 V nm-1 and analyzing the MSD of Li+ and OTf- ions (Fig. 4.6). From the Li+ number density contour plot, we confirmed that Li ions are mainly distributed at the central molecular tube channel inside LiGQ.
This result designates the single-ion conduction characteristics of LiGQ. Additionally, to ascertain uni- directional movement of Li+ ions at LiGQ, we varied the direction of electric field θ to 0°, 30°, and 60°, respectively (Fig. 4.7a). The Li+ moves much faster than the OTf- under same strength of electric field (Fig. 4.7b). In addition, tLi+ was calculated to be ~0.91, fulfilling a key requirement of a single-ion conductor. The MSD of the Li+ was analyzed in terms of movement direction (along x, y and z axis).
The majority of the MSD comes from the z-axis component, which is parallel to LiGQ channel. In addition, no extra movement in x- or y- direction occurred while varying direction of the electric field (Fig. 4.7c). This result exhibits the Li+ slippage behavior at LiGQ, which is enabled by confined Li+ conduction along the channel, leading to the directional single-ion conduction.
Fig. 4.6. Contour plot of Li+ number density of the LiGQ under an electric field. Red bar indicates the 2D number density of Li+ projected to the yz-plane.
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Fig. 4.7. (a) Schematic depicting direction of applied electric field E relative to Li channel direction (along z-axis). (b) MSD of Li+ and OTf- under 2 V nm-1 strength of electric field applied to LiGQ along z-axis (when θ = 0°). (c) MSD of Li+ in x, y and z direction, with varying direction θ of applied electric field. Li+ movement is dominant in the z-direction that is parallel to the direction of Li channel.
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4.2.2.6 Theoretical Elucidation of Li
+Slippage Phenomena at LiGQ
Considering that the ion–dipole interaction is weaker than the ion–ion interaction71, 72, we expect that the intermolecular interaction of Li+ (ion) with G-quartet (dipole) in the LiGQ could be weaker than those of traditional single-ion conductors bearing negatively charged moieties (Nafion with sulfonates, garnet with oxygen sublattices and others), eventually facilitating the transport kinetics of Li+. We theoretically investigated the interactions between Li+ and various ion-conducting moieties using a density functional theory method. Along with the G-quartet, some representative ion-conducting moieties6, such as sulfonate (−SO3−) of Nafion, bis(trifluoromethane)sulfonimide (−TFSI−) of polyanions and phosphorous oxynitride (−PON) of LiPON, were chosen as control systems. Their chemical structures and Li+ binding states are schematically depicted in Fig. 4.8a. The partial density of state (PDOS) for the Li+-bound ion-conducting moieties showed that the PDOS of Li+ was distributed at the range between -45~-42 eV, but that of GQ, Nafion, TFSI, and PON were distributed above -28 eV energy levels (Fig. 4.8b). The PDOS of Li+ and ion-conducting moieties do not overlap in the bonding region below the Fermi level. Moreover, the atomic charges of Li+ and ion-conducting moieties remained almost unchanged after Li+ binding (Table 4.1), which indicates that chemical bonds are not formed between them.73-76
Based on the aforementioned understanding of the physical bonding feature, we calculated the binding energies of Li+ with ion-conducting moieties using the molecular mechanics scheme with the AMBER force field. The binding energies (EMM) were deconvoluted into electrostatic (Eele) and van der Waals (EvdW) energies. These binding energies were normalized by the number of oxygen atoms that coordinate with Li+ because they can seriously affect the ion–ion or ion–dipole interaction between Li+ and ion-conducting moieties. Fig. 4.8c shows that EMM strongly depends on Eele in all ion-conducting moieties examined herein. The EMM of the LiGQ was lower than those of the other ion-conducting moieties by a significant gap of 100–150 kJ mol−1. Furthermore, the LiGQ showed a longer binding distance and smaller average partial charge of oxygen atoms, demonstrating the weak binding of Li+ to the G-quartet via ion–dipole interaction (Table 4.2).
According to the bond strength-coordination number fluctuation (BSCNF) model,77, 78 the mean residence time of an ion placed in a potential well is proportional to the product of ion binding energy and ion coordination number. We assume that Li+ in the LiGQ may have a lower mean residence time than those of other single-ion conductors owing to its weak binding strength with G-quartets.
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Fig. 4.8. (a) Schematic representation of the chemical structures and Li+ binding states of the LiGQ and conventional single-ion conductors. (b) PDOS of the ion-conducting moieties and Li+. Colored and uncolored areas represent PDOS of ion conducting moieties and Li+, respectively. (c) Li+ binding energy (expressed as EMM, Eele, and EvdW) calculated using AMBER force field. The binding energy is normalized by the number of oxygen atoms coordinating with Li+.
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Table 4.1. Charge distribution upon Li+ binding with single-ion conducting moieties. Amount of charges on Li+ and single-ion conducting moieties before and after Li+ binding is shown. Amount of charges are expressed as a unit of elementary charge (1 e-).
Table 4.2. The average binding distance of Li+−oxygen atoms and the average partial charge of oxygen atoms, in which oxygen atoms coordinate with Li+ in each binding moiety.
System Before After
Li+ Moiety Li+ Moiety
LiGQ 1.000 0.080 0.960 0.000
Li-Nafion 1.000 -0.990 0.980 -0.990
Li-TFSI 1.000 -1.000 0.980 -1.000
LiPON 1.000 -1.000 0.9 -0.902
Conducting moiety Distance (Å ) Charge (e-)
LiGQ 2.142 -0.573
Li-Nafion 1.975 -0.663
Li-TFSI 1.867 -0.586
LiPON 1.968 -0.650
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