By Yuxiao Lin A D ISS E R T ATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Materials Science and Engineering Doctor of Philosophy 2019 D issolved Li - PS s can di ffuse in the electrolyte , and precipitate as insulating Li 2 S on electrode surface s, leading to qui iv v ................................ ................................ ................................ ................ ................................ ................................ ................................ ................ ................................ ................................ ........... ................................ ................................ ................................ ................................ ................................ ..... ................................ ................... ................................ ............................... ................................ ................... ............ 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Schematics of the function (a) and structure [14] (b) of SEI on the anode. (Copyright from ) ................................ ................................ ................................ . Schematic of Li - PS shuttle in Li - S battery (Copyright fro m Journal of Power Sources 2014) ................................ ................................ ................................ ............................. ................................ ................................ ................................ ................................ ........ (Copyright from Journal of the Electrochemical Society 2015) ............................ ................................ ................................ ................................ ........................... (a) Convex hull of Li - S systems from DFT calculation by Yang ................................ ................................ ................................ ......... ................................ ................................ ................................ .......... .............................. ................................ ................ ..... ................................ ................................ ................................ ................................ .................. x ................................ ................................ ................................ ................................ .......... ................................ ................................ ................................ ... ................................ ................................ ....................... ........ ................................ ................................ ................................ ............ ........................ ................................ ................................ ................................ ............. ................................ ................................ ................................ .................. ................................ ................................ ................................ xi ................................ ................................ ................................ ................................ .................. ................................ ... ................................ ................................ .................... ................................ ................................ ... ................... ................................ ................................ ................................ ......................... ................................ ................................ ................................ ............................. .................. ................................ ................................ ................................ ........................... ................................ ................................ ... xii ................................ ................................ ................................ ................................ ..... ................................ ................................ ................................ ................................ ................ .. 1 1 1.1 1.1.1 2 3 4 Schematics of the function (a) and structure [14] (b) of SEI on the anode. (Copyright from ) The capacity, [15] 5 6 1.1.2 7 Schematic of Li - PS shuttle in Li - S battery (Copyright from Journal of Power Sources 2014) 8 9 10 1.2 [41] inve stigated the reduction product in an 11 12 the energy barrier provided by [54] 13 (Copyright from Journal of the Electrochemical S ociety 2015) 14 1.3 1.3.1 15 16 17 (a) Convex hull of Li - S systems from DFT calculation by Yang 1.3.2 18 [15] 19 1.3.3 The size of 20 arious carbon materials with different pore size had been used for the carbon matrix in S - C cathodes. Typical examples with smallest pore size included 3 nm mesopore carbon [71] , 0.5 nm micropore carbon [67] and 5 nm open rings in the walls of CNT [69] . if the nanopore size is small enough to block the transport of Li - PS solvation shell, while still allows the transport of Li ions in the electroly te solvents, the concentration of Li - PS inside the nanopore may change. More ideally at the sub - nano level, when only the Li ions are allowed to transport through the pore, while the solvent molecules and are kept out, there will be no solvent inside the s ub - nano pore to solvate the generated Li - PS. However, what is the ideal pore size? Although some previous computational models have compared the sizes of PS, electrolyte solvent, and pore in carbon matrix [63] [91] , the optimum pore size has not been determined. In this thesis, we will comput ationally design the idea l sized CNT. CNT has a more controlled size and morphology compared to other type s of carbon matrix materials. In addition , CNTs offer many advantages as the cathode for Li - S batteries, such as high thermal and electrical conductivities [92] [93] , good mechanical properties [94] , high surface area [95] . Their hollow space inside could also provide room for storage of sulfur . In one inspiring expe riment by Fujimori [70] , the 1D sulfur chain was encapsulated into CNT with 2nm diameter through the opened caps. DFT calculation supported weak interactions between S and CNT, leaving a possibility for S to react with Li. Sulfer can be evaporated into the CNT if there are opening on the CNT. These opening can then be used to selectively allow Li + ion diffusion but not electrolyte diffusion . The opening structures in CNT could be tuned by the oxidation process. Furthermo re, the open rings in the walls of the CNTs could increase its size with the level of oxidation [96] , change its size and chemistry with the oxidants [97] and temperature [98] , and even destroy the CNT structure under a very strong oxidation condition [99] . These 21 experiments suggested the feasibility to control the size of open rings in CNTs by controlling the oxidation processing conditions. The remaining design ques tions : a) what is the optimum pore size that can selectively allow Li transport and completely block the electrolyte solvent, and b) what is the relationship between the created pore size and the oxidation condition in CNT. Few similar simulations can be f ound in carbon systems that are related to the current work. For example, by calculating the transport energy barrier as a function of the pore size from DFT calculation, Zhang et al. successfully predicted that the selective transportation provided by the pore structure in graphdiyne and rhombic - graphyne enabled H 2 separation and purification from different gas mixtures [100 ] . With the aid of MD simulation, Jiao et al. [101] and Song et al. [102] also investigated how gas transportation will be affected by the defects in graphene oxides membranes and coal. Thus, an integrated model that can determine the optimum pore s ize using DFT and further predict the oxidation processing conditions to create the optimum pore size using (MD) method will be developed in this thesis. 1.4 1.4.1 22 23 1.4.2 24 25 1.5 26 Using 27 28 2 2.1 2.2 29 30 electrical insulating property of single SEI component. 31 2.3 2.3.1 32 By aligning the Fermi level ( f ), work function ( ) and band gap ( E g ) of the lithium an ode and SEI to the electron tunneling barrier ( t ) can be 33 34 2.3.2 35 2.4 2.4.1 36 37 38 2.4.2 As stated in 2.1.1, the electronic tunneling barrier and probability could be further derived according to Equation (2.1) and (2.2). In our model, the electronic tunneling barrier was constant since both the work function and band gap are converged for the same SEI component. Thus, the electronic tunneling probability was a function that only depends on the thickness of SEI. Thus, the critical thickness of SEI, d* , that blocks electron tunneling could be estimated from Equation (2.2) assuming a very small t unneling probability T = e - 40 . The d* values of each SEI component were listed in Table 2.1, and the order was LiF > Li 3 PO 4 > Li 2 CO 3 in both GGA and HSE06 methods. The d * here ranged from 2.0~3.0 nm in GGA calculation and 1.6~2.1 in HSE06 calculation, due to the underestimation of band gaps in GGA calculation. Nevertheless, both results were still consistent with both the TEM images by Shim [163] and predicted thickness by Li [51] . In the design of coating layers for anode materials, there were alw ays questions about what the coating materials should be and what thickness was sufficient. Based on the calculation, a ~2 nm LiF could totally block the electronic tunneling. Li 3 PO 4 was also an excellent electrical insulating material, and ~2 nm Li 3 PO 4 can also block electron tunneling. The thickness of Li 2 CO 3 required to block electron tunneling was ~3 nm. 39 40 41 42 2.4.3 LiF was chosen to further investigate the influence of stress on the tunneling barrier. The calculated work function of 10 layers LiF slab model is shown in Figure 2.5a. It can be seen 43 that the change in work function due to stress is quite small. If we ju st consider the 10% volume change of graphite, the work function can be treated as a constant in this range. However, the band gap values are greatly influenced by deformation. The general trend shown in Figure 2. 5 a is that the band gap value (computed wit h GGA method) increases as the stress changes from tension side to the compression side. What is more, under each loading condition, the changes of band gap values are almost linear with respect to the strain (or the ratio between stress and s, / E ), as shown in the four trend line s in Figure 2. 5a . According to recent research [166] , for ionic crystals where anions are localized, when lattice parameter increases, all bandwidths will shrink and energy states in both valence band and conduction band will increase. However, the shift of more localized valence band wi ll be faster than that of the conduction band. Therefore, the band gap will shrink. This suggests that the distance between anions rather than the distance between anions and cations is the most important parameter, as the electrons are donated to anions. This motivates us to propose a new structure parameter, , called normalized average anion distance: (2.6), where and r are the equilibrium distance between the nearest anions in the perfect structure and defo rmed structure of LiF, respectively. When calculating the distance between anions, all the 12 nearest anions were included in the sum. is computed from dimensionless for all four loading conditions. For a simpler representation, which demonstrates the connection with straa in in diffa erent direction, k and n were used to represent the ratio between the deformed lattice and the original lattice in specific directions in the strain tensor. The band gap value as a function of is shown in Figure 2. 5b , where value higher than 1 represents tension while less than 1 represents compression. Figure 2.5b clearly shows the band gap value decreases linearly with increasing 44 value of and all four loading conditions follow the same function. When the deformation is very large, the band gap values deviate from the linear relationship slightly. In these cases, some 2 nd or 3 rd nearest neighbor anions become very close to the center anion under large de formation, and should be included in the calculation. Nevertheless, the normalized anions distance is a newly proposed parameter to unify the lattice deformation in different loading conditions and the band gap decreases linearly with increasing . The refore, the electronic tunneling barrier will decrease under tension and increase under compression. To further evaluate the effect of the stress on electron tunneling, we estimated the capacity loss of an SEI covered graphite which undergoes 10% volume e xpansion due to lithiation. First, the SEI formed on graphite is considered stress free. This is reasonable, as suggested by some recent research that the organic part of SEI is formed before lithiation while the inorganic part of SEI is formed simultaneou sly with lithiation [139] [167] . It indicates an SEI film is almost stress - free perpendicu lar to the particle surface because the organic SEI layer is much softer compared with the inorganic layer. The inorganic layer of SEI will experience biaxial stress in the other two directions due to the volume expansion of the anode. Due to the 10% volum e expansion of graphite, the overall thickness of SEI is reduced by 2.1% due to Poisson's ratio. If we only assume that the SEI should grow back to its original thickness in order to block the electrons tunneling, it will lead to 2.1% more irreversible cap acity loss. However, the relationship between the band gap and sheds new insight. According to it, the 10% volume expansion of graphite will lead to a 2.0 % increase in . Thus, the band gap will decrease from 8.51 eV to 8.17 eV, leading to 0.34 eV reduc tion in the tunneling barrier. To achieve the same electronic tunneling probability, the thickness of SEI should increase by another 4.5%, leading to 11.0 % more irreversible capacity loss. 45 2.5 An electron tunneling model based on DFT calculations from a single component was made to characterize the electrical insulating mechanism of SEI. This simple model can provide a quantified prediction for the tunneling barrier, the critical thickness to block electron tunneling (2~3nm), and the irreversible capacity loss due to SEI formation. The agreement between the model and experiment suggests the initial irreversible capacity loss is likely due to the self - limiting electron tunneling property of the SEI. Furthermore, how electronic tunneling barrier and probability change under stress under different t ypes of loading conditions are also investigated. It was shown that the band gap decreases linearly with increasing value of while the work function stays the same, where is a new parameter to characterize the average distance between anions. That means the electron tunneling barrier decreases under tension and increases under compression. 46 3 3.1 3.2 47 48 49 50 3.3 3.3.1 51 52 3.3.2 53 54 55 3.4 3.4.1 3.4.2 56 57 58 59 3.4.3 60 61 Implicit Model Explicit Model Cluster Model Combined Model Fully solvated Dmol3 - 0.80 [+0.01] - 2.27 [+0.08] - 2.16 [+0.03] VASP Min - 1.91 [+0.02] - 2.05 62 63 3.4.4 3.5 64 65 4 4.1 4.2 66 67 4.3 68 69 4.4 4.4.1 70 4.4.2 71 Solution N(Li 2 S 4 ) : N(DME) Density (g/cm 3 ) c S (mol/L) D (DME) (10 - 10 m 2 /s) D (Li 2 S 4 ) (10 - 10 m 2 /s) Pure DME 0:300 0.88 0 23.1 - 1.9 m 14:280 0.94 1.9 19.1 5.6 4.9 m 39:299 1.01 4.9 13.0 5.0 8.7 m 60:240 1.10 8.7 6.9 2.7 15.4 m 100:200 1.24 15.4 2.5 0.6 72 4.5 73 4.5.1 74 75 4.5.2 76 77 78 4.5.3 79 80 4.6 81 82 the analytical model. Symbol Description Category Value Total pore volume in the cathode region Function of p - (sep) Pore volume in separator Measured constant 2.5 mm 3 Pore volume in the cathode Function of p - The volume of dense cathode materials without any porosity Measured constant 5.3 mm 3 Porosity Variable - Utilization percentage of S in the first plateau Function of p - Mass of utilized S in the first plateau Function of p - T he t otal mass of S in the cathode Measured constant 6.5 mg Practical capacity in the first plateau Function of p - Theoretical capacity in the first plateau Calculated constant 420 mAh/g g The p arameter to include extra PS into the bulk electrolyte Matching constant 1.8 The s aturated concentration of PS in the electrolyte solvent in terms of S Measured constant 8 mol/L The m olar mass of S Constant 32 g/mol The p ractical concentration of PS due to the saturation limit Function of p - The s urface area of carbon matrix per gram Function of p - Empirical constant to describe the relationship between and Empirical constant 1 Constant to match the BET measured surface area of carbon matrix with 70 % porosity Matching constant 300 m 2 /g Effective surface area Function of p - k The r atio between the mass of non - utilized S and its covering surface area Fitting parameter 1.27 × 10 5 m 2 /g 2 R Tunneling resistance caused by the deposited Li 2 S 2 /Li 2 S layer Function of p - C The p arameter to describe the relationship between tunneling resistance and layer thickness. Later combined to - B The p arameter to describe the relationship between tunneling resistance and layer thickness. Later combined to - d T he t hickness of Li 2 S 2 /Li 2 S layer Function of p - Q Total capacity in the discharging curve Variable - b The p arameter to describe the relationship between thickens and total capacity. Later combined to - Mass of carbon matrix in the cathode Measured constant 3.3 mg I Discharging current, later combined to Measured constant - Parameters to describe the relationship between discharging voltage and capacity Fitting parameter 1.9 × 10 - 3 (m 2 ·g)/mAh Parameters to describe the relationship between discharging voltage and capacity Fitting parameter 0.050 V 83 5 5.1 5.2 84 85 5.3 86 5.4 5.4.1 87 88 89 5.4.2 90 91 Structure T/K Method G(T) Partially - solvated Li 2 S 4 Li 2 S 4 ·2DOL 10Li 2 S 4 ·20DOL 0 - 22.443 - - - - - - - 1.44 [+0.03] E V - 23.883 0 - 22.443 - - - - - - - 1.30 Cl V - 23.743 0 - 43754.542 0.244 0 0 0 0 0 - 1.43 [+0.081] Cl D - 43755.726 300 - 43754.542 0.375 - 0.219 0.038 - 0.369 0.038 - 0.530 - 1.43 [+0.08] Cl D - 43756.635 92 93 94 95 5.5 96 97 98 6 6.1 99 6.2 100 101 102 6.3 103 104 6.4 6.4.1 105 106 107 108 6.4.2 109 6.4.3 110 111 112 O:C ratio T (K) Periodic CNT length (Å) 10ps 50ps 100ps 200ps 500ps 1000ps 1:6 800 24.6 12 12 12 12 11 11 1:6 800 49.2 12 12 15 15 15 Destruct at 670 ps 1:6 800 73.8 14 14 18 14 Destruct at 390 ps 1:6 1000 24.6 12 14 14 14 14 14 1:3 800 24.6 11 11 11 Destruct at 220ps 1:3 1000 24.6 10 14 12 Destruct at 150ps 1:3 1000 49.2 17 18 Destruct at 55 ps 1:3 1000 73.8 14 14 14 20 Destruct at 250 ps 1:3 1300 24.6 10 Destruct at 50ps 113 6.5 114 7 7.1 7.2 115 116 117 7.3 118 Electrolyte composition Density (Experimentnal) (g/cm 3 ) Viscosity (m Pa/s) Ionic Conductivity (mS/cm) Freezing point ( °C ) +25 °C - 70 °C +25 °C - 70 °C 1m 1.03 0.22 30.57 8.93 1.37 - 88 2m 1.20 2.66 614.38 2.20 0.19 - 91 5m 1.39 14.99 106680 3.02 0.01 - 102 5m - 1 - 1 1.32 3.88 768.70 2.71 0.36 - 103 5m - 1 - 4 1.33 1.24 351.43 1.48 0.60 - 104 5m - 1 - 8 1.33 0.03 5.35 0.53 0.25 - 107 119 120 7.4 7.4.1 121 7.4.2 122 Electrolyte composition N(Li): N(EA): N(DCM ) CN N(free EA) : N(Li) Calculated Density (g/cm 3 ) D (Li + ) Li - O (EA) Li - O(TFSI) Li - N(TFSI) + 25 °C - 70 °C 0m (pure EA) 0:100:0 / / / / 0.89 / / 0.15m 6:100:0 4.5 1.1 0.7 62 0.9 / / 1m 30:360:0 3.5 1.9 1.4 8.5 1.03 3.0 0.3 2m 60:330:0 2.9 2.4 1.7 2.6 1.20 0.9 0.1 5m 120:270:0 1.7 2.9 2.2 0.6 1.45 0.4 ~0.03 5m - 1 - 1 40:90:220 1.6 2.9 2.1 0.7 1.39 3.0 0.3 5m - 1 - 4 8:18:176 1.7 3.2 2.4 0.6 1.37 6.8 2.0 5m - 1 - 8 8:18:352 1 2.8 1.7 1.3 1.27 8.3 3.1 Comparison N(Li): N(EC): N(DCM) CN N(free EA) : N(Li) Calculated Density (g/cm 3 ) D (Li + ) Li - O (EA) Li - O(TFSI) Li - N(TFSI) + 25 °C - 70 °C LiTFSI / / 4 2 1.25 / / 0.15m (EC) 6:100:0 5.3 0.1 0.1 62 1.30 / / 123 7.5 7.5.1 LUMO (eV) HOMO (eV) LiTFSI - 5.87 - 5.26 Li + ·(DCM) - 1.23 - 1.08 Li + ·(EA) - 2.07 - 1.78 Li + ·(2EA) - 3.77 - 2.84 Li + ·(3EA) - 4.78 - 3.84 Li + ·(4EA) - 5.57 - 4.76 7.5.2 124 125 7.5.3 126 127 128 7.5.4 129 LUMO (eV) HOMO (eV) DCM - 1.57 - 7.42 EA - 0.98 - 6.37 Li + ·(EA) - 5.95 - 11.71 Li + ·(2EA) - 5.30 - 10.87 TFSI - 2.89 - 3.20 LiTFSI - 2.17 - 7.63 (Li 2 TFSI) + - 2.88 - 8.40 7.6 130 131 8 132 133 134 135 136 137 138 139 140 141 142 143 144 1 45 146 147 148 149 150 151 152 153 154 155