基于分子动力学模拟的轮胎橡胶催化热解制氢机理

doi:10.16085/j.issn.1000-6613.2021-1339

摘要/Abstract

摘要：

采用分子动力学模拟方法，选取Ni、ZSM-5以及Ni/ZSM-5催化剂，对轮胎橡胶热解制氢的机理进行探究，并同时与前人做过的实验研究进行对比验证模拟计算。文中利用Material Studio建立轮胎橡胶模型，DMol3模块对生成氢气路径进行过渡态搜索，CULP模块对其加入Ni催化剂的热解过程进行模拟。模拟结果表明，制氢催化效果顺序为Ni>Ni/ZSM-5>ZSM-5。催化热解大致分为两个阶段：①低温阶段长链裂解成单体化合物，单体主要是异戊二烯、苯乙烯以及1,3-丁二烯；②高温阶段自由基攻击单体生成小分子物质。加入Ni催化剂后降低了热解终止温度。催化剂的加入在低温阶段主要表现在加快热解进程，增加低温阶段时单体数量。在高温阶段主要表现在改变了气体产物分布，Ni的加入降低了轮胎热解温度，并且使氢比例增加。

关键词: 轮胎橡胶, 分子动力学, 催化热解, 制氢

Abstract:

In this study, molecular dynamics simulation method was used to study the mechanism of hydrogen production by catalytic fast pyrolysis of tire rubber over Ni, ZSM-5 and Ni/ZSM-5. At the same time, it was compared with the previous experimental studies to verify the simulation calculation. The model was established by Material Studio, the transition state of the hydrogen generation path was searched by DMol3 module, and the catalytic pyrolysis process of adding Ni was simulated by CULP module. The simulation results indicated that the energy barrier of hydrogen generation path decreased with the addition of three catalysts, and the order of catalytic effect was Ni>Ni/ZSM-5>ZSM-5. The catalytic fast processing was divided into two stages:①the low temperature stage was the long chains released monomer compounds, which was mainly isoprene, styrene and 1,3-butadiene; and ②the high temperature stage was that free radical attacked monomer compounds to form small molecular structure. The addition of the catalyst in the low temperature stage was mainly manifested in speeding up the pyrolysis process and increasing the number of monomers in the low temperature stage. The pyrolysis temperature was reduced and the proportion of H₂increased with the addition of Ni catalyst.

Key words: tire rubber, molecular dynamics, catalytic pyrolysis, hydrogen production

中图分类号:

TQ33

陶礼, 杨启容, 李昭莹, 亓昊, 王力伟, 马欣如. 基于分子动力学模拟的轮胎橡胶催化热解制氢机理[J]. 化工进展, 2022, 41(6): 3010-3021.

TAO Li, YANG Qirong, LI Zhaoying, QI Hao, WANG Liwei, MA Xinru. Mechanism of hydrogen production by catalytic pyrolysis of tire rubber based on molecular dynamics simulation[J]. Chemical Industry and Engineering Progress, 2022, 41(6): 3010-3021.

图/表 19

表1 橡胶主要成分分子式、单链及长链模型

天然

橡胶

顺-1,4-聚异戊二烯

单链

长链

丁苯

橡胶

苯乙烯 1,3-丁二烯

单链

长链

顺丁

橡胶

顺-1,4-聚丁二烯

单链

长链

图1 优化结构后轮胎橡胶模型

图2 Ni催化剂模型

图3 ZSM-5催化剂模型

图4 加入1∶1 Ni催化剂轮胎橡胶模型

图5 异戊二烯产生自由基的反应路径

图6 1,3-丁二烯产生自由基的反应路径

图7 苯乙烯产生自由基的反应路径

图8 H基攻击三种单体的反应路径

表2 加入Ni催化剂前后自由基生成能垒

催化前路径→ 催化后路径	反应式	催化前能垒E /kJ·mol^-1	催化后能垒E /kJ·mol^-1	差值（前-后）?E /kJ·mol^-1
1→25	CH₂CHC(CH₃)CH₂ $→$ CH₂ $C ·$ C(CH₃)CH₂+H·	496.983	489.913	7.070
2→26	CH₂CHC(CH₃)CH₂ $→$ CH₂CHC(CH₂·)CH₂+H·	563.528	471.695	91.833
3→27	CH₂CHC(CH₃)CH₂ $→$ CH₂CH $C ·$ CH₂+CH₃·	443.147	426.989	16.158
4→28	CH₂CHCHCH₂ $→$ CH₂CHCHCH·+H·	557.935	540.672	17.263
5→29	CH₂CHCHCH₂ $→$ CH₂CH $C ·$ CH₂+H·	472.465	422.380	50.085
6→30	CH₂CHCHCH₂ $→$ 2CH₂CH·	568.622	551.242	17.380
7→31	C₆H₅CHCH₂ $→$ C₆H₅CHCH·+H·	607.728	588.120	19.608
8→32	C₆H₅CHCH₂ $→$ C₆H₅ $C ·$ CH₂+H·	567.442	548.374	19.068
9→33	(1) C₆H₅CHCH₂ $→$ ·C₆H₄CHCH₂+H·	625.861	571.079	54.782
10→34	(2) C₆H₅CHCH₂ $→$ ·C₆H₄CHCH₂+H·	593.822	589.774	4.048
11→35	(3) C₆H₅CHCH₂ $→$ ·C₆H₄CHCH₂+H·	605.718	597.183	8.535
12→36	C₆H₅CHCH₂ $→$ C₆H₅·+CH₂CH·	575.395	555.164	20.231

表2 加入Ni催化剂前后自由基生成能垒

催化前路径→ 催化后路径	反应式	催化前能垒E /kJ·mol^-1	催化后能垒E /kJ·mol^-1	差值（前-后）?E /kJ·mol^-1
1→25	CH₂CHC(CH₃)CH₂ $→$ CH₂ $C ·$ C(CH₃)CH₂+H·	496.983	489.913	7.070
2→26	CH₂CHC(CH₃)CH₂ $→$ CH₂CHC(CH₂·)CH₂+H·	563.528	471.695	91.833
3→27	CH₂CHC(CH₃)CH₂ $→$ CH₂CH $C ·$ CH₂+CH₃·	443.147	426.989	16.158
4→28	CH₂CHCHCH₂ $→$ CH₂CHCHCH·+H·	557.935	540.672	17.263
5→29	CH₂CHCHCH₂ $→$ CH₂CH $C ·$ CH₂+H·	472.465	422.380	50.085
6→30	CH₂CHCHCH₂ $→$ 2CH₂CH·	568.622	551.242	17.380
7→31	C₆H₅CHCH₂ $→$ C₆H₅CHCH·+H·	607.728	588.120	19.608
8→32	C₆H₅CHCH₂ $→$ C₆H₅ $C ·$ CH₂+H·	567.442	548.374	19.068
9→33	(1) C₆H₅CHCH₂ $→$ ·C₆H₄CHCH₂+H·	625.861	571.079	54.782
10→34	(2) C₆H₅CHCH₂ $→$ ·C₆H₄CHCH₂+H·	593.822	589.774	4.048
11→35	(3) C₆H₅CHCH₂ $→$ ·C₆H₄CHCH₂+H·	605.718	597.183	8.535
12→36	C₆H₅CHCH₂ $→$ C₆H₅·+CH₂CH·	575.395	555.164	20.231

图9 催化后各路径吉布斯自由能变随温度变化

图10 催化后各路径焓变随温度变化

表3 加入Ni催化剂前后H基攻击单体能垒

催化前路径→ 催化后路径	反应式	催化前能垒E /kJ·mol^-1	催化后能垒E /kJ·mol^-1	差值（前-后）?E /kJ·mol^-1
13→37	CH₂CHC(CH₃)CH₂+H· $→$ CH₂ $C ·$ C(CH₃)CH₂+H₂	563.377	558.412	4.965
14→38	CH₂CHC(CH₃)CH₂+H· $→$ CH₂CHC(CH₂·)CH₂+H	562.737	466.852	95.885
15→39	CH₂CHC(CH₃)CH₂+H· $→$ CH₂CH $C ·$ CH₂+CH₄	465.693	534.293	-68.600
16→40	CH₂CHCHCH₂+H· $→$ CH₂CHCHCH·+H₂	555.528	548.718	6.810
17→41	CH₂CHCHCH₂+H· $→$ CH₂CH $C ·$ CH₂+H₂	470.745	424.791	45.954
18→42	CH₂CHCHCH₂+H· $→$ CH₂CH·+CH₂CH₂	560.811	552.665	8.146
19→43	C₆H₅CHCH₂+H· $→$ C₆H₅CHCH·+H₂	605.986	596.668	9.318
20→44	C₆H₅CHCH₂+H· $→$ C₆H₅ $C ·$ CH₂+H₂	559.744	550.074	9.670
21→45	(1) C₆H₅CHCH₂+H· $→$ ·C₆H₄CHCH₂+H₂	595.119	574.616	20.503
22→46	(2) C₆H₅CHCH₂+H· $→$ ·C₆H₄CHCH₂+H₂	594.249	585.621	8.628
23→47	(3) C₆H₅CHCH₂+H· $→$ ·C₆H₄CHCH₂+H₂	603.500	598.502	4.998
24→48	C₆H₅CHCH₂+H· $→$ C₆H₅·+CH₂CH₂	569.472	555.126	14.346

表3 加入Ni催化剂前后H基攻击单体能垒

催化前路径→ 催化后路径	反应式	催化前能垒E /kJ·mol^-1	催化后能垒E /kJ·mol^-1	差值（前-后）?E /kJ·mol^-1
13→37	CH₂CHC(CH₃)CH₂+H· $→$ CH₂ $C ·$ C(CH₃)CH₂+H₂	563.377	558.412	4.965
14→38	CH₂CHC(CH₃)CH₂+H· $→$ CH₂CHC(CH₂·)CH₂+H	562.737	466.852	95.885
15→39	CH₂CHC(CH₃)CH₂+H· $→$ CH₂CH $C ·$ CH₂+CH₄	465.693	534.293	-68.600
16→40	CH₂CHCHCH₂+H· $→$ CH₂CHCHCH·+H₂	555.528	548.718	6.810
17→41	CH₂CHCHCH₂+H· $→$ CH₂CH $C ·$ CH₂+H₂	470.745	424.791	45.954
18→42	CH₂CHCHCH₂+H· $→$ CH₂CH·+CH₂CH₂	560.811	552.665	8.146
19→43	C₆H₅CHCH₂+H· $→$ C₆H₅CHCH·+H₂	605.986	596.668	9.318
20→44	C₆H₅CHCH₂+H· $→$ C₆H₅ $C ·$ CH₂+H₂	559.744	550.074	9.670
21→45	(1) C₆H₅CHCH₂+H· $→$ ·C₆H₄CHCH₂+H₂	595.119	574.616	20.503
22→46	(2) C₆H₅CHCH₂+H· $→$ ·C₆H₄CHCH₂+H₂	594.249	585.621	8.628
23→47	(3) C₆H₅CHCH₂+H· $→$ ·C₆H₄CHCH₂+H₂	603.500	598.502	4.998
24→48	C₆H₅CHCH₂+H· $→$ C₆H₅·+CH₂CH₂	569.472	555.126	14.346

图11 催化后各路径吉布斯自由能变随温度变化

图12 催化后各路径焓变随温度变化

表4 加入ZSM-5、Ni/ZSM-5催化剂前后自由基生成能垒

路径	ZSM-5催化前能垒E/kJ·mol^-1	ZSM-5催化后能垒E/kJ·mol^-1	ZSM-5差值?E（前-后） /kJ·mol^-1	Ni/ZSM-5催化前能垒E/kJ·mol^-1	Ni/ZSM-5催化后能垒E/kJ·mol^-1	Ni/ZSM-5差值?E（前-后） /kJ·mol^-1
1	496.983	538.039	-41.056	496.983	514.535	-17.552
2	563.528	563.264	0.264	563.528	557.316	6.212
3	443.147	516.820	-73.673	443.147	501.211	-58.064
4	557.935	560.108	-2.173	557.935	554.662	3.273
5	472.465	483.454	-10.988	472.465	468.531	3.934
6	568.622	547.395	21.227	568.622	543.058	25.564
7	607.728	595.726	12.002	607.728	593.713	14.015
8	567.442	568.036	-0.594	567.442	560.853	6.589
9	625.861	585.312	40.549	625.861	577.266	48.595
10	593.822	586.593	7.229	593.822	586.341	7.481
11	605.718	595.927	9.791	605.718	595.153	10.565
12	575.395	573.566	1.829	575.395	567.689	7.706

表5 加入ZSM-5、Ni/ZSM-5催化剂前后H基攻击单体能垒

路径	ZSM-5催化前能垒E/kJ·mol^-1	ZSM-5催化后能垒E/kJ·mol^-1	ZSM-5差值?E（前-后） /kJ·mol^-1	Ni/ZSM-5催化前能垒E /kJ·mol^-1	Ni/ZSM-5催化后能垒E /kJ·mol^-1	Ni/ZSM-5差值?E（前-后） /kJ·mol^-1
13	563.377	551.610	11.767	563.377	512.982	50.395
14	562.737	485.404	77.333	562.737	563.570	-0.833
15	465.693	429.513	36.180	465.693	431.711	33.982
16	555.528	561.711	-6.183	555.528	553.184	2.344
17	470.745	458.099	12.646	470.745	441.238	29.507
18	560.811	537.675	23.136	560.811	546.240	14.571
19	605.986	599.984	6.002	605.986	606.070	-0.084
20	559.744	579.891	-20.147	559.744	550.765	8.979
21	595.119	598.029	-2.910	595.119	590.540	4.579
22	594.249	588.556	5.693	594.249	586.053	8.196
23	603.500	602.583	0.917	603.500	598.740	4.760
24	569.472	585.647	-16.175	569.472	567.295	2.177

表6 低温阶段热解情况

不同比例（橡胶∶催化剂）	1100K时热解情况	1500K时热解情况
1∶0
5∶1
3∶1
1∶1

图 13 2800K未加催化剂热解模型

参考文献 28

1	张立民, 李志学. 我国新能源经济发展现状分析[J]. 现代商业, 2021(7): 25-27.
	ZHANG Limin, LI Zhixue. Analysis of the present situation of the development of new energy economy in China[J]. Modern Business, 2021 (7): 25-27.
2	LI G, ZHANG K, YANG B, et al. Life cycle analysis of a coal to hydrogen process based on ash agglomerating fluidized bed gasification[J]. Energy, 2019, 174: 638-646.
3	TOUILI S, ALAMI MERROUNI A, HASSOUANI Y EL, et al. Analysis of the yield and production cost of large-scale electrolytic hydrogen from different solar technologies and under several Moroccan climate zones[J]. International Journal of Hydrogen Energy, 2020, 45(51): 26785-26799.
4	LI W C, REN X S, DING S M, et al. A multi-criterion decision making for sustainability assessment of hydrogen production technologies based on objective grey relational analysis[J]. International Journal of Hydrogen Energy, 2020, 45(59): 34385-34395.
5	郭博文, 罗聃, 周红军. 可再生能源电解制氢技术及催化剂的研究进展[J]. 化工进展, 2021, 40(6): 2933-2951.
	GUO Bowen, LUO Dan, ZHOU Hongjun. Recent advances in renewable energy electrolysis hydrogen production technology and related electrocatalysts[J]. Chemical Industry and Engineering Progress, 2021, 40(6): 2933-2951.
6	国家统计局. 2019年7—12月我国合成橡胶、轮胎和汽车产量[J]. 橡胶科技, 2020, 18(3): 178.
	National Bureau of Statistics. Output of synthetic rubber, tires and cars in China from July to December 2019[J]. Rubber Science and Technology, 2020, 18(3): 178.
7	CHOI G G, OH S J, KIM J S, et al. Non-catalytic pyrolysis of scrap tires using a newly developed two-stage pyrolyzer for the production of a pyrolysis oil with a low sulfur content[J]. Applied Energy, 2016, 170: 140-147.
8	狄伟强. 废轮胎热解炭特性及其对废轮胎催化性能研究[D]. 大连: 大连理工大学, 2019.
	DI Weiqiang. Study on the characteristics of waste tire pyrolysis char and its catalytic pyrolysis effect on waste tires[D]. Dalian: Dalian University of Technology, 2019.
9	LI W P, WEI M M, LIU Y Q, et al. Catalysts evaluation for production of hydrogen gas and carbon nanotubes from the pyrolysis-catalysis of waste tyres[J]. International Journal of Hydrogen Energy, 2019, 44(36): 19563-19572.
10	Williams P T, Brindle A J.Catalytic pyrolysis of tyres: influence of catalyst temperature[J]. Fuel, 2002, 81(18): 2425-2434.
11	YU J, LIU S, CARDOSO A, et al. Catalytic pyrolysis of rubbers and vulcanized rubbers using modified zeolites and mesoporous catalysts with Zn and Cu[J]. Energy, 2019, 188: 116117.
12	李秉繁, 刘刚, 陈雷. 基于分子动力学模拟的CH₄溶解对原油分子间作用的影响机制研究[J]. 化工学报, 2021, 72(3): 1253-1263.
	LI Bingfan, LIU Gang, CHEN Lei. Study on the influence mechanism of CH₄ dissolution on the intermolecular interaction between crude oil molecules based on molecular dynamics simulation[J]. CIESC Journal, 2021, 72(3): 1253-1263.
13	LIU Y L, DING J X, HAN K L. Molecular dynamics simulation of the high-temperature pyrolysis of methylcyclohexane[J]. Fuel, 2018, 217: 185-192.
14	魏鑫. 天然橡胶热解气相产物生成机理研究[D]. 青岛: 青岛大学, 2019.
	WEI Xin. Study on the formation mechanism of gas phase products of natural rubber pyrolysis[D]. Qingdao: Qingdao University, 2019.
15	YANG Q R, YU S P, ZHONG H W, et al. Gas products generation mechanism during co-pyrolysis of styrene-butadiene rubber and natural rubber[J]. Journal of Hazardous Materials, 2021, 401: 123302.
16	于双鹏, 杨启容, 陶礼, 等. 基于分子动力学模拟的轮胎橡胶气相热解产物反应机理[J]. 化工进展, 2021, 40(6): 3119-3131.
	YU Shuangpeng, YANG Qirong, TAO Li, et al. Gas phase pyrolysis products of tire rubber based on molecular dynamics simulation[J]. Chemical Industry and Engineering Progress, 2021, 40(6): 3119-3131.
17	潘旗. 基于分子动力学模拟的变压器油纸绝缘老化特性基础研究[D]. 徐州: 中国矿业大学, 2020.
	PAN Qi. Basic research on aging characteristics of transformer oil paper insulation based on molecular dynamics simulation[D]. Xuzhou: China University of Mining and Technology, 2020.
18	HU S D, SUN W G, FU J, et al. Initiation mechanisms and kinetic analysis of the isothermal decomposition of poly(α-methylstyrene): a ReaxFF molecular dynamics study[J]. RSC Advances, 2018, 8(7): 3423-3432.
19	KWON H, LELE A, ZHU J Q, et al. ReaxFF-based molecular dynamics study of bio-derived polycyclic alkanes as potential alternative jet fuels[J]. Fuel, 2020, 279: 118548.
20	张贻亮. 原子-键电负性均衡方法及其在理论化学中的应用[D]. 长春: 吉林大学, 2002.
	ZHANG Yiliang. Atom-bond electronegativity equalization method and its application in theoretical chemistry[D]. Changchun: Jilin University, 2002.
21	ZHENG M, WANG Z, LI X X, et al. Initial reaction mechanisms of cellulose pyrolysis revealed by ReaxFF molecular dynamics[J]. Fuel, 2016, 177: 130-141.
22	杜鸟锋, 甯红波, 李泽荣, 等. 1,3-丁二烯热裂解的动力学计算与模型研究[J]. 物理化学学报, 2016, 32(2): 453-464.
	DU Niaofeng, NING Hongbo, LI Zerong, et al. Kinetic calculation and modeling study of 1,3-butadiene pyrolysis[J]. Acta Physico-Chimica Sinica, 2016, 32(2): 453-464.
23	徐宗平, 郭庆民. 废轮胎热解回收中的废气综合利用[J]. 中国轮胎资源综合利用, 2018(11): 36-39.
	XU Zongping, GUO Qingmin. The comprehensive utilization of waste gas in waste tire pyrolysis recycling[J]. China Tire Resources Recycling, 2018(11): 36-39.
24	张会亮, 范晓旭, 刘彦丰, 等. 块状废轮胎固定床热解特性实验研究[J]. 可再生能源, 2015, 33(1): 149-153.
	ZHANG Huiliang, FAN Xiaoxu, LIU Yanfeng, et al. Experimental study on pyrolysis of blocky tires in a fixed-bed reactor[J]. Renewable Energy Resources, 2015, 33(1): 149-153.
25	张冰, 付琦, 梁畅. 废轮胎橡胶热解技术研究进展[J]. 橡塑技术与装备, 2018, 44(15): 19-23.
	ZHANG Bing, FU Qi, LIANG Chang. Research progress on waste tire rubber pyrolysis technology[J]. China Rubber/Plastics Technology and Equipment, 2018, 44(15): 19-23.
26	ELBABA I F, WILLIAMS P T. Two stage pyrolysis-catalytic gasification of waste tyres: influence of process parameters[J]. Applied Catalysis B: Environmental, 2012, 125: 136-143.
27	ELBABA I F, WU C F, WILLIAMS P T. Hydrogen production from the pyrolysis-gasification of waste tyres with a nickel/cerium catalyst[J]. International Journal of Hydrogen Energy, 2011, 36(11): 6628-6637.
28	ZHANG Y S, WU C F, NAHIL M A, et al. Pyrolysis-catalytic reforming/gasification of waste tires for production of carbon nanotubes and hydrogen[J]. Energy & Fuels, 2015, 29(5): 3328-3334.

[1]	谢璐垚, 陈崧哲, 王来军, 张平. 用于SO₂去极化电解制氢的铂基催化剂[J]. 化工进展, 2023, 42(S1): 299-309.
[2]	王家庆, 宋广伟, 李强, 郭帅成, DAI Qingli. 橡胶混凝土界面改性方法及性能提升路径[J]. 化工进展, 2023, 42(S1): 328-343.
[3]	张亚娟, 徐惠, 胡贝, 史星伟. 化学镀法制备NiCoP/rGO/NF高效电解水析氢催化剂[J]. 化工进展, 2023, 42(8): 4275-4282.
[4]	王蕴青, 杨国锐, 延卫. 过渡金属磷化物的改性方法及其在电化学析氢中的应用[J]. 化工进展, 2023, 42(7): 3532-3549.
[5]	符淑瑢, 王丽娜, 王东伟, 刘蕊, 张晓慧, 马占伟. 析氧助催化剂增强光阳极光电催化分解水性能研究进展[J]. 化工进展, 2023, 42(5): 2353-2370.
[6]	郑云武, 裴涛, 李冬华, 王继大, 李继容, 郑志锋. 金属氧化物活化P/HZSM-5催化生物质热解气重整制备富烃生物油[J]. 化工进展, 2023, 42(3): 1353-1364.
[7]	赵毅, 杨臻, 王佳, 李静雯, 郑煜. 沥青胶结料自愈合行为分子动力学模拟研究进展[J]. 化工进展, 2023, 42(2): 803-813.
[8]	李攀, 王彪, 徐骏浩, 王贤华, 胡俊豪, 宋建德, 白净, 常春. 生物质热解催化剂积炭问题的研究进展[J]. 化工进展, 2023, 42(1): 236-246.
[9]	肖周荣, 李国柱, 王涖, 张香文, 谷建民, 王德松. 液体碳氢燃料蒸汽重整制氢催化剂研究进展[J]. 化工进展, 2022, 41(S1): 97-107.
[10]	孙宪航, 任铸, 张国军, 孙媛, 范开峰, 黄维秋. 超临界CO₂作用下甲苯在活性炭中的脱附机理[J]. 化工进展, 2022, 41(S1): 631-636.
[11]	胡兵, 徐立军, 何山, 苏昕, 汪继伟. 碳达峰与碳中和目标下PEM电解水制氢研究进展[J]. 化工进展, 2022, 41(9): 4595-4604.
[12]	李玉峰, 王绍庆, 张安东, 毕冬梅, 李志合, 高亮, 万震. 催化型多孔陶瓷球制备及催化玉米秸秆热解[J]. 化工进展, 2022, 41(7): 3597-3607.
[13]	闫鹏, 程易. 用于分布式制氢的甲烷蒸汽重整膜反应器的数值模拟[J]. 化工进展, 2022, 41(7): 3446-3454.
[14]	张雷, 王海英, 韩洪晶, 陈彦广, 王程昊. 木质素催化热解用催化剂的研究进展[J]. 化工进展, 2022, 41(5): 2429-2440.
[15]	张轩, 樊昕晔, 吴振宇, 郑丽君. 氢能供应链成本分析及建议[J]. 化工进展, 2022, 41(5): 2364-2371.