Theoretical Study of Reactions Between Polysulfides and Ethylene Carbonate and Raman Spectra in Lithium-sulfur Battery†

doi:10.7503/cjcu20150144

Abstract

Abstract:

Two mechanisms of the reaction between polysulfides( $S 2 - n$ , n=2—4) and ethylene carbonate(EC) and Raman spectra of the reactants and main products were investigated by density functional theory(DFT) method. The results showed that the reaction of polysulfides attacking the ethyl carbon of EC is more favorable than that attacking the carbonyl carbon of EC in terms of the activation energies and Gibbs free energies. Sulfur groups in polysulfides display strong Raman signals, so that simulated Raman spectra of the products of the $S 2 - n$ +EC reaction significantly change after the reaction. The coordination effect of Li⁺ cation also influenced the simulated Raman spectra of reaction products. DFT results and Raman spectroscopic analysis provide a new insight on structural stability of polysulfides and EC electrolyte in the lithium sulfur battery.

Key words: Lithium sulfur battery, Density functional theory, Raman spectroscopy, Ethylene carbonate, Polysulfide

CLC Number:

O646

TrendMD:

PAN Wenbo, LI Mingxue, SU Yaqiong, WU Deyin, TIAN Zhongqun. Theoretical Study of Reactions Between Polysulfides and Ethylene Carbonate and Raman Spectra in Lithium-sulfur Battery^†[J]. Chem. J. Chinese Universities, 2015, 36(9): 1771.

Figures/Tables 13

Fig.1 Optimized configurations of ethylene carbonate(A) and its complex Li+(EC)(B)

Table 1 Comparison of theoretical and experimental geometrical parameters for EC and Li+(EC)

Parameter		EC				Li⁺(EC)
Parameter		6-311++G(d,p)	Expt.(crys)^[40]	Expt.(MW)^[35]	aug-cc-pVDZ^[24]	6-311++G(d,p)
Bond length/nm	C=O	0.1188	0.1203	0.1200	0.1203	0.1208
	C₃—O	0.1361	0.1342	0.1358	0.1370	0.1333
	C—O	0.1437	0.1457	0.1428	0.1440	0.1456
	C—C	0.1529	0.1522	0.1540	0.1520	0.1531
	C—H	0.1089	0.1091	0.1095	0.1090	0.1089
Bending angle/(°)	O=C—O	124.9	124.2		124.2	124.0
	C—O—C	109.4	108.7	109.5	108.4	109.3
	O—C—O	110.1	111.7	110.4	110.4	112.4
	C—C—O	102.6	102.2	102.4	102.5	102.6
	H—C—H	109.9	110.8		114.0	110.6
Dihedral angle/(°)	O=C—O—C	-171.7	-171.3	-171.5	170.6	179.9
	C—O—C—C	-20.0	-21.3	-20.2	22.9	-16.3
	O—C—C—O	23.5	24.8	23.9	27.2	19.1
	O—C—O—C	8.3	8.7	8.5	9.4	6.7

Table 2 Calculated frequencies, Raman activity(AR) and assignment of EC along with the reference dataa

Mode^a	6-311++G(d,p)	Scaled	Expt.^[34]	aug-cc-pVDZ^[19]	10¹⁹A_R/(nm⁴·kg^-1)	PED(%)^b
ν₁(b)	3135	3031	3011	3205	46.6	νCH₂(100)
ν₂(a)	3123	3020	3004	3194	57.6	νCH₂(86)
ν₃(b)	3058	2957	3000	3112	18.3	νCH₂(100)
ν₄(a)	3054	2953	2990	3109	132.3	νCH₂(86)
ν₅(a)	1895	1860	1868	1898	10.4	ν(C=O) (86)
ν₆(a)	1529	1500	1570	1546	2.5	sciCH₂(99)
ν₇(b)	1521	1492	1480	1539	6.3	sciCH₂(98)
ν₈(b)	1400	1373	1421	1421	0.6	ωCH₂(81)
ν₉(a)	1386	1360	1386	1420	2.6	ωCH₂(87)
ν₁₀(a)	1245	1222	1223	1271	4.4	τCH₂(91)
ν₁₁(a)	1238	1214	1218	1267	4.6	τCH₂(79)
ν₁₂(a)	1154	1132	1157	1175	0.2	rockCH₂(95)
ν₁₃(b)	1115	1070	1125	1138	0.4	ν(C—O)(59)
						β(C=O)(12)
ν₁₄(a)	1090	1094	1090	1123	1.4	ν(C—O)(76)
						ν(C—C)(14)
ν₁₅(b)	1051	1031	1087	1079	0.1	ν(C—O)(72)
ν₁₆₍a)	964	946	960	991	4.5	ν(C—C)(62)
ν₁₇(a)	891	874	891	895	0.9	R breathing
ν₁₈(b)	889	872	881	919	8.3	rockCH₂(52)
ν₁₉(b)	772	758	768	779	0.3	β(C=O)(97)
ν₂₀(a)	718	704	715	719	3.7	νR(68)
ν₂₁(b)	691	678	673	673	1.6	τR(62)
ν₂₂(b)	523	513	527	527	0.3	γ(C=O)(70)
ν₂₃(a)	187	184	227	227	0.2	τR(97)
ν₂₄(b)	178	175	184	184	0.2	τR(97.3)

Fig.2 Optimized bond lengths(nm) and bond angles(°) of polysulfide anions

Table 3 Structure parameters and NBO charge distribution of polysulfide anions at the PCM-B3LYP/6-311++G(d,p) level

Species	Structure		Charge distribution
Species	Bond length/nm	Bending angle/(°)	S1	S2	S3	S4
$S 2 2 -$	0.2220		-1.00	-1.00
$S 3 2 -$	0.2151	110.5	-1.05	-0.34	-0.61
$S 4 2 -$	0.2127	111.4	-0.61	-0.39	-0.39	-0.61

Table 3 Structure parameters and NBO charge distribution of polysulfide anions at the PCM-B3LYP/6-311++G(d,p) level

Species	Structure		Charge distribution
Species	Bond length/nm	Bending angle/(°)	S1	S2	S3	S4
$S 2 2 -$	0.2220		-1.00	-1.00
$S 3 2 -$	0.2151	110.5	-1.05	-0.34	-0.61
$S 4 2 -$	0.2127	111.4	-0.61	-0.39	-0.39	-0.61

Fig.3 Reaction activation energies and Gibbs free energies(kJ/mol) for nucleophilic attack of S22- at the carbonyl and ethyl carbon atoms of EC calculated at the PCM-B3LYP/6-311++G(d,p) level

Table 4 Reaction activation energies, enthalpies and Gibbs free energies(kJ/mol) for nucleophilic attack of polysulfide anions S2-n(n=2—4) at the carbonyl and ethyl carbon atoms of EC calculated at the PCM-B3LYP/6-311++G(d,p) level

Species	Attacking ethyl carbon				Attacking carbonyl carbon
Species	ΔH_act,1	ΔG_act,1	ΔH_r,1	ΔG_r,1	ΔH_act,2	ΔG_act,2	ΔH_r,2	ΔG_r,2
$S 2 2 -$	40.9	77.4	-116.0	-85.4	71.3	112.5	68.8	103.3
$S 3 2 -$	53.7	93.3	-80.0	-43.5	116.6	163.5	116.2	156.6
$S 4 2 -$	62.4	100.9	-60.4	-24.9	135.6	187.3	141.0	178.2

Species	Attacking ethyl carbon				Attacking carbonyl carbon
Species	ΔH_act,1	ΔG_act,1	ΔH_r,1	ΔG_r,1	ΔH_act,2	ΔG_act,2	ΔH_r,2	ΔG_r,2
$S 2 2 -$	40.9	77.4	-116.0	-85.4	71.3	112.5	68.8	103.3
$S 3 2 -$	53.7	93.3	-80.0	-43.5	116.6	163.5	116.2	156.6
$S 4 2 -$	62.4	100.9	-60.4	-24.9	135.6	187.3	141.0	178.2

Fig.4 Simulated Raman spectra of EC(A) and products Ⅱ(B) and Ⅲ(C) calculated at the PCM-B3LYP/6-311++G(d,p) level

Fig.5 Reaction activation energies and Gibbs free energies(kJ/mol) for nucleophilic attack of S22- at the carbonyl and ethyl carbon atoms of Li+EC calculated at the PCM-B3LYP/6-311++G(d,p) level

Table 5 Reaction activation energies, enthalpies and Gibbs free energies(kJ/mol) for nucleophilic attack of polysulfides anions S2-n(n=2—4) at the carbonyl and ethyl carbon atoms of Li+(EC) calculated at the PCM-B3LYP/6-311++G(d,p) level

Species	Attacking ethyl carbon				Attacking carbonyl carbon
Species	ΔH_act,1	ΔG_act,1	ΔH_r,1	ΔG_r,1	ΔH_act,2	ΔH_r,2	ΔG_act,2	ΔG_r,2
$S 2 2 -$	21.8	61.1	-168.0	-112.5	28.9	-41.2	78.7	53.1
$S 3 2 -$	34.3	78.5	-131.6	-81.7	77.7	203.1	132.6	62.5
$S 4 2 -$	42.8	86.7	-256.1	-57.5	114.2	41.2	165.8	91.5

Species	Attacking ethyl carbon				Attacking carbonyl carbon
Species	ΔH_act,1	ΔG_act,1	ΔH_r,1	ΔG_r,1	ΔH_act,2	ΔH_r,2	ΔG_act,2	ΔG_r,2
$S 2 2 -$	21.8	61.1	-168.0	-112.5	28.9	-41.2	78.7	53.1
$S 3 2 -$	34.3	78.5	-131.6	-81.7	77.7	203.1	132.6	62.5
$S 4 2 -$	42.8	86.7	-256.1	-57.5	114.2	41.2	165.8	91.5

Fig.6 Simulated Raman spectra of Li+(EC)(A) and products Ⅴ(B) and Ⅵ(C) calculated at the PCM-B3LYP/6-311++G(d,p) level

Fig.7 Optimized structures(A1—A3) and simulated Raman spectra(B1—B3) of isomerization products calculated at the PCM-B3LYP/6-311++G(d,p) level(A1), (B1) Ring-Li+(EC)S22-; (A2), (B2) ring-Li+(EC)S32-; (A3), (B3) ring-Li+(EC)S42-.

Table 6 Enthalpies and Gibbs free energies for isomerization products calculated at the PCM-B3LYP/6-311++G(d,p) level

Reaction	ΔH/(kJ·mol^-1)	ΔS/(J·mol^-1·K^-1)	ΔG/(kJ·mol^-1)
Li⁺(EC) $S 2 2 -$ →ring-Li⁺(EC) $S 2 2 -$	-18.1	-17.8	-12.8
Li⁺(EC) $S 3 2 -$ →ring-Li⁺(EC) $S 3 2 -$	-18.6	-26.5	-10.7
Li⁺(EC) $S 4 2 -$ →ring-Li⁺(EC) $S 4 2 -$	-14.3	-37.9	-3.0

Table 6 Enthalpies and Gibbs free energies for isomerization products calculated at the PCM-B3LYP/6-311++G(d,p) level

Reaction	ΔH/(kJ·mol^-1)	ΔS/(J·mol^-1·K^-1)	ΔG/(kJ·mol^-1)
Li⁺(EC) $S 2 2 -$ →ring-Li⁺(EC) $S 2 2 -$	-18.1	-17.8	-12.8
Li⁺(EC) $S 3 2 -$ →ring-Li⁺(EC) $S 3 2 -$	-18.6	-26.5	-10.7
Li⁺(EC) $S 4 2 -$ →ring-Li⁺(EC) $S 4 2 -$	-14.3	-37.9	-3.0

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