Density functional theory calculation of structure and electronic properties in N-methane hydrate

Luo Qiang; Yang Heng; Guo Ping; Zhao Jian-Fei

doi:10.7498/aps.68.20182230

Abstract

As a clean and efficient unconventional energy source, natural gas hydrate has been highly valued and vigorously developed by many countries in recent years. In order to solve the problem that the existing hydrate structure symmetry is not high, which leads the theoretical research to be restricted, it is imperative to explore a new type of methane hydrate structure with high symmetry. Using the first-principles method which is based on the density functional theory (DFT), the structure and electronic properties of N-methane hydrate are calculated in the generalized gradient approximation (GGA) for Grimme dispersion correction. The obtained results are shown below. 1) The water cage structure of N-methane hydrate is a truncated octahedron (4⁶6⁸), which is composed of 8 regular hexagons and 6 squares, and the average length of the hexagons and the average length of the squares are both 2.723 Å. The average bond length of water molecules is optimized to be 1.056 Å, and the average bond angle of water molecules is 107.738°. The average bond length of methane molecules is 1.0973 Å. The average distance from methane molecules to water molecules is 4.2831 Å that is longer than the distance in the I- methane hydrate. So N-methane hydrate can accommodate larger volumes of gas molecules. The symmetric group is ${\rm{IM}}\bar 3{\rm{M}}$ for N-methane hydrate, which has a simple and strict periodic stable structure. 2) The lattice parameter of N-methane hydrate is 7.70 Å, and the density is 0.903 g/cm³, which is greater than I-, II- and H-type hydrate density. 3) The x-ray diffraction(XRD) pattern of N-methane hydrateis calculated and is close to that of of I-methane hydrate, while the water cage of N-methane hydrate is larger. 4) The interaction between methane molecules and the water cage is van der Waals force, and the formation energy of N- methane hydrate is –0.247 eV, which indicates that the N-methane hydrate is easy to form. Both the density of states and partial density of states indicate that the interaction between methane and water cage is weak, and it relies on molecular force. 5) In addition, N-methane hydrate is an insulator material with the energy gap greater than 5 eV.

Keywords:

Authors and contacts

1.
College of Science, Southwest Petroleum University, Chengdu 610500, China
2.
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China

Corresponding author: Luo Qiang, luoqiang@swpu.edu.cn ; Guo Ping, guopingswpi@vip.sina.com ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.51875091,61701455) and the Science and Technology Project of Sichuan Province, China (Grant No.2018JY0174).

FullText HTML

References

[1]	Holder G, Kamath V, Godbole S 1984 Annu. Rev. Energy 9 427
[2]	Max M, Lowrie A 1996 J. Petrol. Geol. 19 41 Google Scholar
[3]	Collett T S 2002 AAPG Bull. 86 1971
[4]	Kvamme B, Kuznetsova T, Sapate A, Qorbani K 2016 J. Nat. Gas Sci. Eng. 35 1594 Google Scholar
[5]	Zhao J, Chen X, Song Y, Zhu Z, Yang L, Tian Y, Wang J, Yang M, Zhang Y 2014 Energy Procedia 61 75 Google Scholar
[6]	Khlebnikov V, Antonov S, Mishin A, Bakulin D, Khamidullina I, 梁萌, Vinokurov V, Gushchin P A 2016 天然气工业 36 40 Google Scholar Khlebnikov V, Antonov S, Mishin A, Bakulin D, Khamidullina I, Liang M, Vinokurov V, Gushchin P A 2016 Nat. Gas Ind. 36 40 Google Scholar
[7]	Lim D, Ro H, Seo Y, Seo Y, Lee J, Kim S, Lee J , Lee H 2017 J. Chem. Thermodyn. 106 16 Google Scholar
[8]	Partoon B, Nashed O, Kassim Z, Sabil K, Sangwai J, Lal B 2016 Process Eng. 148 1220
[9]	Zhang L X, Yang L, Wang J Q, Zhao J F, Dong H S, Yang M J, Liu Y, Song Y C 2017 Chem. Eng. J. 308 40 Google Scholar
[10]	Castellani B, Rossetti G, Tupsakhare S, Rossi F, Nicolini A, Castaldi M 2016 J. Petrol. Sci. Eng. 147 515 Google Scholar
[11]	Michael K, Roland B, Edward B, Lewis R N 2004 J. Am. Chem. Soc. 126 9407 Google Scholar
[12]	Xu C G, Cai J, Lin F H, Chen Z Y, Li X S 2015 Energy 79 111 Google Scholar
[13]	Naeiji P, Varaminian F, Rahmati M 2017 J. Nat. Gas Sci. Eng. 44 122 Google Scholar
[14]	朱金龙, 赵予生, 靳常青 2019 物理学报 68 018203 Zhu J L, Zhao Y S, Jin C Q 2019 Acta Phys. Sin. 68 018203
[15]	Choudhary N, Kushwaha O S, Bhattacharjee G, Chakrabarty S, Kumara R 2017 Energt Procedia 105 5026 Google Scholar
[16]	Alavi S, Ohmura R 2016 J. Chem. Phys. 145 154708 Google Scholar
[17]	Huang Y, Yuan L, Su Y, Zhao J 2015 Mol. Simul. 41 1086 Google Scholar
[18]	Nguyen A H, Molinero V 2014 J. Chem. Phys. 140 3440
[19]	Yagasaki T, Matsumoto M, Andoh Y, Okazaki S, Tanaka H 2014 J. Phys. Chem. B 118 11797
[20]	Druart M L, Michel L, Van D H 2014 Fluid Phase Equilib. 381 108 Google Scholar
[21]	耿春宇, 丁丽颖, 韩清珍, 温浩 2008 物理化学学报 24 595 Google Scholar Geng C Y, Ding L Y, Han Q Z, Wen H 2008 Acta Phys. Chim. Sin. 24 595 Google Scholar
[22]	Lasich M, Ramjugernath D 2016 Philos. Mag. 96 15 Google Scholar
[23]	Zong X, Cheng G, Qiu N, Huang Q, He J, Du S, Li Y 2017 Chem. Lett. 46 1141 Google Scholar
[24]	Liu Y, Ojamäe L 2014 J. Phys. Chem. A 118 51
[25]	Zhang X, Qiu N, Huang Q, Zha X, He J, Li Y, Du S 2017 J. Mol. Struct. 1153 292
[26]	Waldron C J, English N J 2017 J. Chem. Phys. 147 024506 Google Scholar
[27]	Zquierdo-Ruiz F, Otero-de-la-Roza A, Contreras-García J, Menéndez B, Recio J M 2015 High Pressure Res. 35 49 Google Scholar
[28]	Liu C, Zhang Z, Guo G J 2016 RSC Adv. 6 106443 Google Scholar
[29]	Tang L, Shi R, Su Y, Zhao J 2015 J. Phys. Chem. A 119 10971 Google Scholar
[30]	郑朝阳, 赵纪军 2012 物理化学学报 28 1809 Google Scholar Zheng C Y, Zhao J J 2012 Acta Phys. Chim. Sin. 28 1809 Google Scholar
[31]	Huang Y, Zhu C, Wang L, Cao X, Su Y, Jiang X, Meng S, Zhao J, Zeng X C 2016 Sci. Adv. 2 e1501010 Google Scholar
[32]	曹潇潇 2016 博士学位论文(大连: 大连理工大学) Cao X X 2016 Ph. D. Dissertation (Dalian: Dalian University of Technology University) (in Chinese)
[33]	曹潇潇, 苏艳, 赵纪军, 刘昌岭, 周潘旺 2014 物理化学学报 30 1437 Google Scholar Cao X X, Su Y, Zhao J J, Liu C L, Zhou D W 2014 Acta Phys. Chim. Sin. 30 1437 Google Scholar
[34]	Nityananda R, Hohenberg P, Kohn W 2017 Resonance 22 809 Google Scholar
[35]	Kohn W, Sham L J 1965 Phys. Rev. 140 1133 Google Scholar
[36]	Huang Y Y, Zhu C Q, Wang L 2017 Chem. Phys. Lett. 2017 186 Google Scholar
[37]	Blöchl E 1994 Phys. Rev. B 50 17953 Google Scholar
[38]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[39]	罗强, 唐斌, 张智, 冉曾令 2013 物理学报 62 077101 Google Scholar Luo Q, Tang B, Zhang Z, Ran Z L 2013 Acta Phys. Sin. 62 077101 Google Scholar
[40]	Wang Z H, Li Y, Meng W J, Guo P, Luo Q, Ran Z L 2017 Appl. Ecol. Environ. Res. 15 861 Google Scholar
[41]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[42]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188 Google Scholar
[43]	Broyden C G 1970 J. Inst. Math. Applic. 6 76 Google Scholar
[44]	Fletcher R 1970 Comput. J. 13 317 Google Scholar
[45]	Goldfarb D 1970 Math. Comput. 24 23 Google Scholar
[46]	Shanno D F 1970 Math. Comput. 24 647 Google Scholar
[47]	Guo P, Qiu Y L, Li L L, Luo Q, Zhao J F, Pan Y K 2018 Chin. Phys. B 27 276
[48]	丁家祥, 史伶俐, 申小冬, 梁德青 2017 化工学报 68 4802 Ding J X, Shi L L, Sheng X D, Liang D Q 2017 J. Chem. Ind. Eng. 68 4802

Cited By

图 1 模型示意图　(a) N型甲烷水合物骨架模型; (b) 优化后的结构

Figure 1. Model diagram: (a) N-methane hydrate skeleton model; (b) optimized structure of N-methane hydrate.

DownLoad: Full-Size Img PowerPoint

图 2 N型甲烷水合物结构X射线衍射图

Figure 2. X-ray diffraction of N- methane hydrate structure.

DownLoad: Full-Size Img PowerPoint

图 3 甲烷分子态密度和分波态密度

Figure 3. Density of states and partial density of states in methane molecules.

DownLoad: Full-Size Img PowerPoint

图 4 水笼子的态密度及分波态密度

Figure 4. Density of state and partial density of state in water cage.

DownLoad: Full-Size Img PowerPoint

图 5 能带结构

Figure 5. Energy band structures.

DownLoad: Full-Size Img PowerPoint

表 1 平均晶格参数

Table 1. Average lattice parameters.

晶格参数	GGA	原始值	I型甲烷水合物^[47]
六边形边长/Å	2.7231	2.6804	2.7152
四边形边长/Å	2.7233	2.7656	/
水分子键长/Å	1.0056	0.994	0.993
水分子键角/(°)	107.738	109.406	106.629
甲烷分子键长/Å	1.0973	1.1178	1.0917
甲烷分子键角/(°)	109.471	109.454	109.471
甲烷分子到水分子距离/Å	4.2831	4.278	3.78115
氢键键长/Å	1.7293	1.7025	1.7128

DownLoad: CSV

表 2 GGA近似下的形成能

Table 2. Formation energy of GGA approximation

能量	GGA	I型甲烷水合物^[47]
∆E_form/eV	–0.247	–0.581
E_total/eV	–6074.782	–21186.729
E_cage/eV	–5634.720	–20976.902
E_CH4/eV	–219.784	–209.246

DownLoad: CSV

[1]	Holder G, Kamath V, Godbole S 1984 Annu. Rev. Energy 9 427
[2]	Max M, Lowrie A 1996 J. Petrol. Geol. 19 41 Google Scholar
[3]	Collett T S 2002 AAPG Bull. 86 1971
[4]	Kvamme B, Kuznetsova T, Sapate A, Qorbani K 2016 J. Nat. Gas Sci. Eng. 35 1594 Google Scholar
[5]	Zhao J, Chen X, Song Y, Zhu Z, Yang L, Tian Y, Wang J, Yang M, Zhang Y 2014 Energy Procedia 61 75 Google Scholar
[6]	Khlebnikov V, Antonov S, Mishin A, Bakulin D, Khamidullina I, 梁萌, Vinokurov V, Gushchin P A 2016 天然气工业 36 40 Google Scholar Khlebnikov V, Antonov S, Mishin A, Bakulin D, Khamidullina I, Liang M, Vinokurov V, Gushchin P A 2016 Nat. Gas Ind. 36 40 Google Scholar
[7]	Lim D, Ro H, Seo Y, Seo Y, Lee J, Kim S, Lee J , Lee H 2017 J. Chem. Thermodyn. 106 16 Google Scholar
[8]	Partoon B, Nashed O, Kassim Z, Sabil K, Sangwai J, Lal B 2016 Process Eng. 148 1220
[9]	Zhang L X, Yang L, Wang J Q, Zhao J F, Dong H S, Yang M J, Liu Y, Song Y C 2017 Chem. Eng. J. 308 40 Google Scholar
[10]	Castellani B, Rossetti G, Tupsakhare S, Rossi F, Nicolini A, Castaldi M 2016 J. Petrol. Sci. Eng. 147 515 Google Scholar
[11]	Michael K, Roland B, Edward B, Lewis R N 2004 J. Am. Chem. Soc. 126 9407 Google Scholar
[12]	Xu C G, Cai J, Lin F H, Chen Z Y, Li X S 2015 Energy 79 111 Google Scholar
[13]	Naeiji P, Varaminian F, Rahmati M 2017 J. Nat. Gas Sci. Eng. 44 122 Google Scholar
[14]	朱金龙, 赵予生, 靳常青 2019 物理学报 68 018203 Zhu J L, Zhao Y S, Jin C Q 2019 Acta Phys. Sin. 68 018203
[15]	Choudhary N, Kushwaha O S, Bhattacharjee G, Chakrabarty S, Kumara R 2017 Energt Procedia 105 5026 Google Scholar
[16]	Alavi S, Ohmura R 2016 J. Chem. Phys. 145 154708 Google Scholar
[17]	Huang Y, Yuan L, Su Y, Zhao J 2015 Mol. Simul. 41 1086 Google Scholar
[18]	Nguyen A H, Molinero V 2014 J. Chem. Phys. 140 3440
[19]	Yagasaki T, Matsumoto M, Andoh Y, Okazaki S, Tanaka H 2014 J. Phys. Chem. B 118 11797
[20]	Druart M L, Michel L, Van D H 2014 Fluid Phase Equilib. 381 108 Google Scholar
[21]	耿春宇, 丁丽颖, 韩清珍, 温浩 2008 物理化学学报 24 595 Google Scholar Geng C Y, Ding L Y, Han Q Z, Wen H 2008 Acta Phys. Chim. Sin. 24 595 Google Scholar
[22]	Lasich M, Ramjugernath D 2016 Philos. Mag. 96 15 Google Scholar
[23]	Zong X, Cheng G, Qiu N, Huang Q, He J, Du S, Li Y 2017 Chem. Lett. 46 1141 Google Scholar
[24]	Liu Y, Ojamäe L 2014 J. Phys. Chem. A 118 51
[25]	Zhang X, Qiu N, Huang Q, Zha X, He J, Li Y, Du S 2017 J. Mol. Struct. 1153 292
[26]	Waldron C J, English N J 2017 J. Chem. Phys. 147 024506 Google Scholar
[27]	Zquierdo-Ruiz F, Otero-de-la-Roza A, Contreras-García J, Menéndez B, Recio J M 2015 High Pressure Res. 35 49 Google Scholar
[28]	Liu C, Zhang Z, Guo G J 2016 RSC Adv. 6 106443 Google Scholar
[29]	Tang L, Shi R, Su Y, Zhao J 2015 J. Phys. Chem. A 119 10971 Google Scholar
[30]	郑朝阳, 赵纪军 2012 物理化学学报 28 1809 Google Scholar Zheng C Y, Zhao J J 2012 Acta Phys. Chim. Sin. 28 1809 Google Scholar
[31]	Huang Y, Zhu C, Wang L, Cao X, Su Y, Jiang X, Meng S, Zhao J, Zeng X C 2016 Sci. Adv. 2 e1501010 Google Scholar
[32]	曹潇潇 2016 博士学位论文(大连: 大连理工大学) Cao X X 2016 Ph. D. Dissertation (Dalian: Dalian University of Technology University) (in Chinese)
[33]	曹潇潇, 苏艳, 赵纪军, 刘昌岭, 周潘旺 2014 物理化学学报 30 1437 Google Scholar Cao X X, Su Y, Zhao J J, Liu C L, Zhou D W 2014 Acta Phys. Chim. Sin. 30 1437 Google Scholar
[34]	Nityananda R, Hohenberg P, Kohn W 2017 Resonance 22 809 Google Scholar
[35]	Kohn W, Sham L J 1965 Phys. Rev. 140 1133 Google Scholar
[36]	Huang Y Y, Zhu C Q, Wang L 2017 Chem. Phys. Lett. 2017 186 Google Scholar
[37]	Blöchl E 1994 Phys. Rev. B 50 17953 Google Scholar
[38]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[39]	罗强, 唐斌, 张智, 冉曾令 2013 物理学报 62 077101 Google Scholar Luo Q, Tang B, Zhang Z, Ran Z L 2013 Acta Phys. Sin. 62 077101 Google Scholar
[40]	Wang Z H, Li Y, Meng W J, Guo P, Luo Q, Ran Z L 2017 Appl. Ecol. Environ. Res. 15 861 Google Scholar
[41]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[42]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188 Google Scholar
[43]	Broyden C G 1970 J. Inst. Math. Applic. 6 76 Google Scholar
[44]	Fletcher R 1970 Comput. J. 13 317 Google Scholar
[45]	Goldfarb D 1970 Math. Comput. 24 23 Google Scholar
[46]	Shanno D F 1970 Math. Comput. 24 647 Google Scholar
[47]	Guo P, Qiu Y L, Li L L, Luo Q, Zhao J F, Pan Y K 2018 Chin. Phys. B 27 276
[48]	丁家祥, 史伶俐, 申小冬, 梁德青 2017 化工学报 68 4802 Ding J X, Shi L L, Sheng X D, Liang D Q 2017 J. Chem. Ind. Eng. 68 4802

[1]	Song Qing-Gong, Zhao Jun-Pu, Gu Wei-Feng, Zhen Dan-Dan, Guo Yan-Rui, Li Ze-Peng. Ductile and electronic properties of La-doped gamma-TiAl systems based on density functional theory. Acta Physica Sinica, 2017, 66(6): 066103. doi: 10.7498/aps.66.066103
[2]	Wen Jun-Qing, Zhang Jian-Min, Yao Pan, Zhou Hong, Wang Jun-Fei. A density functional theory study of small bimetallic PdnAl (n =18) clusters. Acta Physica Sinica, 2014, 63(11): 113101. doi: 10.7498/aps.63.113101
[3]	Wen Jun-Qing, Xia Tao, Wang Jun-Fei. A density functional theory study of small bimetallic PtnAl (n=18) clusters. Acta Physica Sinica, 2014, 63(2): 023103. doi: 10.7498/aps.63.023103
[4]	Ruan Wen, Xie An-Dong, Yu Xiao-Guang, Wu Dong-Lan. Geometric structure and electronic characteristics of NaBn (n=19) clusters. Acta Physica Sinica, 2012, 61(4): 043102. doi: 10.7498/aps.61.043102
[5]	Ge Gui-Xian, Yan Hong-Xia, Jing Qun, Zhang Jian-Jun. Density functional theory study on the structure and electronicproperties of Aun Sc3 (n =1—7) clusters. Acta Physica Sinica, 2011, 60(3): 033101. doi: 10.7498/aps.60.033101
[6]	Zhang Zhi-Long, Chen Yu-Hong, Ren Bao-Xing, Zhang Cai-Rong, Du Rui, Wang Wei-Chao. Density functional theory study on the structure and properties of (HMgN3)n(n=15) clusters. Acta Physica Sinica, 2011, 60(12): 123601. doi: 10.7498/aps.60.123601
[7]	Ge Gui-Xian, Jing Qun, Cao Hai-Bin, Yang Zeng-Qiang, Tang Guang-Hui, Yan Hong-Xia. The study on structures and properties of Run and Run Au(n=112) clusters by density functional theory. Acta Physica Sinica, 2011, 60(10): 103102. doi: 10.7498/aps.60.103102
[8]	Zhang Xiu-Rong, Li Yang, Yang Xing. Theoretical study on structural and electronic properties of WnNim(n+m=8) clusters. Acta Physica Sinica, 2011, 60(10): 103601. doi: 10.7498/aps.60.103601
[9]	Jin Rong, Chen Xiao-Hong. Structure and properties of ZrnPd clusters by density-functional theory. Acta Physica Sinica, 2010, 59(10): 6955-6962. doi: 10.7498/aps.59.6955
[10]	Sun Jian-Min, Zhao Gao-Feng, Wang Xian-Wei, Yang Wen, Liu Yan, Wang Yuan-Xu. Study of structural and electronic properties of Cu-adsorbed (SiO2)n(n=1—8) clusters with the DFT. Acta Physica Sinica, 2010, 59(11): 7830-7837. doi: 10.7498/aps.59.7830
[11]	Gao Hong, Zhu Wei-Hua, Tang Chun-Mei, Geng Fang-Fang, Yao Chang-Da, Xu Yun-Ling, Deng Kai-Ming. Density functional calculation on the geometric structure and electronic properties of the endohedral fullerene N2@C60. Acta Physica Sinica, 2010, 59(3): 1707-1711. doi: 10.7498/aps.59.1707
[12]	Liu Li-Ren, Lei Xue-Ling, Chen Hang, Zhu Heng-Jiang. Geometry and electronic properties of Bn(n=2—15) clusters. Acta Physica Sinica, 2009, 58(8): 5355-5361. doi: 10.7498/aps.58.5355
[13]	Li Xi-Bo, Wang Hong-Yan, Luo Jiang-Shan, Wu Wei-Dong, Tang Yong-Jian. Density functional theory study of the geometry, stability and electronic properties of ScnO(n=1—9) clusters. Acta Physica Sinica, 2009, 58(9): 6134-6140. doi: 10.7498/aps.58.6134
[14]	Chen Yu-Hong, Kang Long, Zhang Cai-Rong, Luo Yong-Chun, Pu Zhong-Sheng. Density functional theory study of the structures and properties of (Li3N)n(n=1—5) clusters. Acta Physica Sinica, 2008, 57(7): 4174-4181. doi: 10.7498/aps.57.4174
[15]	Chen Yu-Hong, Kang Long, Zhang Cai-Rong, Luo Yong-Chun, Yuan Li-Hua, Li Yan-Long. Density functional theory study on the structures and properties of (Ca3N2)n(n=1—4) clusters. Acta Physica Sinica, 2008, 57(10): 6265-6270. doi: 10.7498/aps.57.6265
[16]	Ge Gui-Xian, Luo You-Hua. Density functional theory study of the structure and electronic properties of MgnOn(n=2—8) clusters. Acta Physica Sinica, 2008, 57(8): 4851-4856. doi: 10.7498/aps.57.4851
[17]	Li Xi-Bo, Luo Jiang-Shan, Guo Yun-Dong, Wu Wei-Dong, Wang Hong-Yan, Tang Yong-Jian. Density functional theory study of the stability, electronic and magnetic properties of Scn, Yn and Lan (n＝2—10) clusters. Acta Physica Sinica, 2008, 57(8): 4857-4865. doi: 10.7498/aps.57.4857
[18]	Wang Qing-Lin, Ge Gui-Xian, Zhao Wen-Jie, Lei　Xue-Ling, Yan Yu-Li, Yang Zhi, Luo You-Hua. Density functional theory study on the structure and properties of CoBen(n=1—12) clusters. Acta Physica Sinica, 2007, 56(6): 3219-3226. doi: 10.7498/aps.56.3219
[19]	Chen Yu-Hong, Zhang Cai-Rong, Ma Jun. Density functional theory study on the structure and properties of MgmBn(m=1,2;n=1—4) clusters. Acta Physica Sinica, 2006, 55(1): 171-178. doi: 10.7498/aps.55.171
[20]	Tan Ming-Qiu, Tao Xiang-Ming, Xu Xiao-Jun, Cai Jian-Qiu. Density functional theory study on the electronic structure of UAl3 a nd USn3. Acta Physica Sinica, 2003, 52(12): 3142-3149. doi: 10.7498/aps.52.3142

Catalog

Vol. 68, Issue 16 - 2019-08-20

Metrics

Abstract views: 11496
PDF Downloads: 109
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板