Acoustic rotational relaxation of hydrogen around normal temperture

Zhang Xiang-Qun; Wang Shu; Zhu Ming

doi:10.7498/aps.67.20172665

Abstract

Hydrogen is an important energy carrier, and it is widely used due to its extraordinary advantages, such as high heat, clean fuel, being large-scale and renewable. The detection of hydrogen is essential in practical application. Therefore, many researches have focused on monitoring the hydrogen concentration over the past years. Acoustic relaxation theory based on molecular relaxation process is a very promising method of detecting hydrogen gas. However, the existing acoustic relaxation models for gas detection are developed from the vibrational relaxation of gas molecules, and thus they are not applicable for hydrogen and its mixture. In this paper, we present a model for the rotational relaxation process of hydrogen. Firstly, the molecular relaxation process of hydrogen is different from those of other gases due to its large spacing of rotational energy-level and special molecular physical structure. Acoustic relaxation process of hydrogen is mostly determined by the molecular rotational relaxation. Hydrogen molecule is made up of one quarter of para-hydrogen and three quarters of ortho-hydrogen at normal temperature. There is three-rotational-level model for hydrogen rotational relaxation, such as rotational level in states with J=0, 2, 4 (J is rotational quantum-number) for para-hydrogen and J=1, 3, 5 for ortho-hydrogen. Secondly, we introduce effective specific heat into one-mode rotational relaxation at constant pressure, and then extend it to multi-mode rotational relaxation. Upon periodic perturbation of acoustic waves, the temperature and the number of molecules in each rotational level change periodically in the relaxation process. On the basis, we obtain the relaxation equations in a matrix form and calculate effective specific heat at constant pressure for rotational relaxation process. With the relationship between the complex wave number and the effective thermodynamics acoustic speed, we calculate the frequency-dependent acoustic speed and relaxation absorption, and then discuss the difference between the rotational relaxation and the vibrational relaxation. Thirdly, we compare the predicted acoustic speed and absorption spectrum with their corresponding experimental data and investigate the influences of rotational characteristics on absorption spectra in hydrogen and its mixtures. The simulation results show that acoustic speed and relaxation absorption curves calculated by the proposed model are in good agreement with their corresponding experimental data. The model is not only applicable to pure hydrogen gas but also can be used to obtain the acoustic relaxation spectra of gas mixtures with multiple vibrational modes. This model provides a theoretical foundation for the acoustic detecting of hydrogen gas mixtures.

Keywords:

acoustic relaxation /
rotational relaxation /
gas detection /
effective specific heat at constant pressure

Authors and contacts

1.
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China;
2.
School of Information Engineering, Xuchang University, Xuchang 461000, China

Corresponding author: Zhu Ming, zhuming@mail.hust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61571201, 61371139, 61461008), the Program for Key Scientific Research in Universities of Henan Province, China (Grant No. 15A510037), and the Program for Science and Technology Innovation Talents in Universities of Henan Province, China (Grant No. 18HASTIT022).

References

[1]	Melaina M W, Antonia O, Penev M 2013Blending Hydrogen Into Natural Gas Pipeline Networks: a Review of Key Issues (Golden, CO: National Renewable Energy Lab.) Report No. NREL/TP-5600-51995
[2]	Hanf S, Bgzi T, Keiner R, Frosch T, Popp J 2015 Anal. Chem. 87 982
[3]	Hbert T, Boon-Brett L, Black G, Banach U 2011 Sens. Actuators B: Chem. 157 329
[4]	Phillips S, Dain Y, Lueptow R M 2003 Meas. Sci. Technol. 14 70
[5]	Zhang K S, Zhang X Q, Tang W Y, Xiao Y Q, Jiang X Q 2018 Acta Acust. 43 399 (in Chinese) [张克声, 张向群, 唐文勇, 肖迎群, 蒋学勤 2018 声学学报 43 399]
[6]	Hauptmann P, Hoppe N, Pttmer A 2002 Meas. Sci. Technol. 13 R73
[7]	Hu J H, Zheng X F 2011 Practical Infrared Spectroscopy (Beijing: Science Press) pp1-20 (in Chinese) [胡皆汉, 郑学仿 2011 实用红外光谱学 (北京: 科学出版社) 第120页]
[8]	Du G, Zhu Z M, Gong X 2012 Acoustics Foundation (Nanjing: Nanjing University Press) pp295-310
[9]	Liu T, Wang S, Zhu M 2017 J. Acoust. Soc. Am. 141 1844
[10]	Hong J, Lee S, Seo J, Pyo S, Kim J, Lee T 2015 ACS Appl. Mater. Interfaces 7 3554
[11]	Minami Y, Yogi T, Sakai K 2011 J. Opt. 13 075708
[12]	Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[13]	Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[14]	Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[15]	Petculescu A G, Lueptow R M 2012 Sens. Actuators B: Chem. 169 121
[16]	Yan S, Wang S 2008 Acta Phys. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
[17]	Jia Y Q, Wang S, Zhu M, Zhang K S, Yuan F G 2012 Acta Phys. Sin. 61 095101 (in Chinese) [贾雅琼, 王殊, 朱明, 张克声, 袁飞阁 2012 61 095101]
[18]	Zhang K S, Wang S, Zhu M, Hu Y, Jia Y Q 2012 Acta Phys. Sin. 61 174301 (in Chinese) [张克声, 王殊, 朱明, 胡佚, 贾雅琼 2012 61 174301]
[19]	Zhang K S, Chen L K, Ou W H, Jiang X Q, Long F 2015 Acta Phys. Sin. 64 054302 (in Chinese) [张克声, 陈刘奎, 欧卫华, 蒋学勤, 龙飞 2015 64 054302]
[20]	Zhang K S, Zhu M, Tang W Y, Ou W H, Jiang X Q 2016 Acta Phys. Sin. 65 134302 (in Chinese) [张克声, 朱明, 唐文勇, 欧卫华, 蒋学勤 2016 65 134302]
[21]	Zhang K S, Wang S, Zhu M, Ding Y, Hu Y 2013 Chin. Phys. B 22 014305
[22]	Hu Y, Wang S, Zhu M, Zhang K S, Liu T, Xu D 2014 Sens. Actuators B: Chem. 203 1
[23]	Zhu M, Wang S, Wang S T, Xia D H 2008 Acta Phys. Sin. 57 5749 (in Chinese) [朱明, 王殊, 王菽韬, 夏东海 2008 57 5749]
[24]	Zhu M, Liu T, Wang S 2017 Meas. Sci. Technol. 28 085008
[25]	Rhodes Jr J E 1946 Phys. Rev. 70 932
[26]	Takayanagi K, Kishimoto T 1953 Prog. Theor. Phys. 9 578
[27]	Geide K 1963 Acta Acust. Acust. 13 31
[28]	Sluijter C G, Knaap H F P, Beenakker J J M 1964 Physica 30 745
[29]	Knaap H F P, Sluijter C G, Beenakker J J M 1965 Lw Temp. Phys. 1 1233
[30]	Winter T G, Hill G L 1967 J. Acoust. Soc. Am. 42 848
[31]	Behnen S W, Rothwell H L, Amme R C 1971 Chem. Phys. Lett. 8 318
[32]	Bauer H J, Bass H E 1972 J. Chem. Phys. 57 1763
[33]	Davison W D 1964 Proc. Roy. Soc. Ser. A 280 227
[34]	Montero S, Prez-Ros J 2014 J. Chem. Phys. 141 114301
[35]	Sears F W, Salinger G L 1976 Thermodynamics, Kinetic Theory and Statistical Thermodynamics (3rd Ed.) (Reading, Massachusetts: Addison_Wesley Pub. Co.) pp413-415
[36]	Li W 1989 Thermodynamics and Statistical Physics (Beijing: Beijing Institute of Technology Press) pp89- 120 (in Chinese) [李卫 1989 热力学与统计物理 (北京: 北京理工大学出版社) 第89120页]
[37]	Valley L M, Amme R C 1968 J. Acoust. Soc. Am. 44 1144
[38]	Minami Y, Yogi T, Sakai K 2009 J. Appl. Phys. 106 113519
[39]	Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) pp115-129
[40]	Herzfeld K F, Litovitz T H 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic) pp338-343
[41]	Stewart E S, Stewart J L, Hubbard J C 1945 Phys. Rev. 68 231
[42]	Raff L M, Winter T G 1968 J. Chem. Phys. 48 3992
[43]	Bhatia A B 1985 Ultrasonic Absorption (New York: Dover) pp87-101
[44]	Warren P M 1964 Physical Acoustics: Principles and Methods (Vol. 2) (London: Academic Press) pp160-180
[45]	Wan J K S, Ioffe M S, Depew M C 1996 Sens. Actuators. B: Chem. 32 233

Cited By

[1]	Melaina M W, Antonia O, Penev M 2013Blending Hydrogen Into Natural Gas Pipeline Networks: a Review of Key Issues (Golden, CO: National Renewable Energy Lab.) Report No. NREL/TP-5600-51995
[2]	Hanf S, Bgzi T, Keiner R, Frosch T, Popp J 2015 Anal. Chem. 87 982
[3]	Hbert T, Boon-Brett L, Black G, Banach U 2011 Sens. Actuators B: Chem. 157 329
[4]	Phillips S, Dain Y, Lueptow R M 2003 Meas. Sci. Technol. 14 70
[5]	Zhang K S, Zhang X Q, Tang W Y, Xiao Y Q, Jiang X Q 2018 Acta Acust. 43 399 (in Chinese) [张克声, 张向群, 唐文勇, 肖迎群, 蒋学勤 2018 声学学报 43 399]
[6]	Hauptmann P, Hoppe N, Pttmer A 2002 Meas. Sci. Technol. 13 R73
[7]	Hu J H, Zheng X F 2011 Practical Infrared Spectroscopy (Beijing: Science Press) pp1-20 (in Chinese) [胡皆汉, 郑学仿 2011 实用红外光谱学 (北京: 科学出版社) 第120页]
[8]	Du G, Zhu Z M, Gong X 2012 Acoustics Foundation (Nanjing: Nanjing University Press) pp295-310
[9]	Liu T, Wang S, Zhu M 2017 J. Acoust. Soc. Am. 141 1844
[10]	Hong J, Lee S, Seo J, Pyo S, Kim J, Lee T 2015 ACS Appl. Mater. Interfaces 7 3554
[11]	Minami Y, Yogi T, Sakai K 2011 J. Opt. 13 075708
[12]	Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[13]	Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[14]	Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[15]	Petculescu A G, Lueptow R M 2012 Sens. Actuators B: Chem. 169 121
[16]	Yan S, Wang S 2008 Acta Phys. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
[17]	Jia Y Q, Wang S, Zhu M, Zhang K S, Yuan F G 2012 Acta Phys. Sin. 61 095101 (in Chinese) [贾雅琼, 王殊, 朱明, 张克声, 袁飞阁 2012 61 095101]
[18]	Zhang K S, Wang S, Zhu M, Hu Y, Jia Y Q 2012 Acta Phys. Sin. 61 174301 (in Chinese) [张克声, 王殊, 朱明, 胡佚, 贾雅琼 2012 61 174301]
[19]	Zhang K S, Chen L K, Ou W H, Jiang X Q, Long F 2015 Acta Phys. Sin. 64 054302 (in Chinese) [张克声, 陈刘奎, 欧卫华, 蒋学勤, 龙飞 2015 64 054302]
[20]	Zhang K S, Zhu M, Tang W Y, Ou W H, Jiang X Q 2016 Acta Phys. Sin. 65 134302 (in Chinese) [张克声, 朱明, 唐文勇, 欧卫华, 蒋学勤 2016 65 134302]
[21]	Zhang K S, Wang S, Zhu M, Ding Y, Hu Y 2013 Chin. Phys. B 22 014305
[22]	Hu Y, Wang S, Zhu M, Zhang K S, Liu T, Xu D 2014 Sens. Actuators B: Chem. 203 1
[23]	Zhu M, Wang S, Wang S T, Xia D H 2008 Acta Phys. Sin. 57 5749 (in Chinese) [朱明, 王殊, 王菽韬, 夏东海 2008 57 5749]
[24]	Zhu M, Liu T, Wang S 2017 Meas. Sci. Technol. 28 085008
[25]	Rhodes Jr J E 1946 Phys. Rev. 70 932
[26]	Takayanagi K, Kishimoto T 1953 Prog. Theor. Phys. 9 578
[27]	Geide K 1963 Acta Acust. Acust. 13 31
[28]	Sluijter C G, Knaap H F P, Beenakker J J M 1964 Physica 30 745
[29]	Knaap H F P, Sluijter C G, Beenakker J J M 1965 Lw Temp. Phys. 1 1233
[30]	Winter T G, Hill G L 1967 J. Acoust. Soc. Am. 42 848
[31]	Behnen S W, Rothwell H L, Amme R C 1971 Chem. Phys. Lett. 8 318
[32]	Bauer H J, Bass H E 1972 J. Chem. Phys. 57 1763
[33]	Davison W D 1964 Proc. Roy. Soc. Ser. A 280 227
[34]	Montero S, Prez-Ros J 2014 J. Chem. Phys. 141 114301
[35]	Sears F W, Salinger G L 1976 Thermodynamics, Kinetic Theory and Statistical Thermodynamics (3rd Ed.) (Reading, Massachusetts: Addison_Wesley Pub. Co.) pp413-415
[36]	Li W 1989 Thermodynamics and Statistical Physics (Beijing: Beijing Institute of Technology Press) pp89- 120 (in Chinese) [李卫 1989 热力学与统计物理 (北京: 北京理工大学出版社) 第89120页]
[37]	Valley L M, Amme R C 1968 J. Acoust. Soc. Am. 44 1144
[38]	Minami Y, Yogi T, Sakai K 2009 J. Appl. Phys. 106 113519
[39]	Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) pp115-129
[40]	Herzfeld K F, Litovitz T H 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic) pp338-343
[41]	Stewart E S, Stewart J L, Hubbard J C 1945 Phys. Rev. 68 231
[42]	Raff L M, Winter T G 1968 J. Chem. Phys. 48 3992
[43]	Bhatia A B 1985 Ultrasonic Absorption (New York: Dover) pp87-101
[44]	Warren P M 1964 Physical Acoustics: Principles and Methods (Vol. 2) (London: Academic Press) pp160-180
[45]	Wan J K S, Ioffe M S, Depew M C 1996 Sens. Actuators. B: Chem. 32 233

[1]	Xiong Feng, Peng Zhi-Min, Ding Yan-Jun, Du Yan-Jun. Experimental study of nonlinear phenomenon of NO ultraviolet broadband absorption spectroscopy. Acta Physica Sinica, 2022, 71(20): 203302. doi: 10.7498/aps.71.20220975
[2]	Wen Ping. β-relaxation in glass forming systems. Acta Physica Sinica, 2017, 66(17): 176407. doi: 10.7498/aps.66.176407
[3]	Sun Qi-Cheng, Liu Chuan-Qi, Gordon G D Zhou. Relaxation of granular elasticity. Acta Physica Sinica, 2015, 64(23): 236101. doi: 10.7498/aps.64.236101
[4]	Zhang Ke-Sheng, Chen Liu-Kui, Ou Wei-Hua, Jiang Xue-Qin, Long Fei. A theory for monitoring combustion of natural gas based on the maximum point in sound absorption spectrum. Acta Physica Sinica, 2015, 64(5): 054302. doi: 10.7498/aps.64.054302
[5]	Xu Xue-Mei, Li Ben-Rong, Yang Bing-Chu, Jiang Li, Yin Lin-Zi, Ding Yi-Peng, Cao Can. Gas measurement system of NO and NO2 based on photoacoustic spectroscopy. Acta Physica Sinica, 2013, 62(20): 200704. doi: 10.7498/aps.62.200704
[6]	Zhang Ke-Sheng, Wang Shu, Zhu Ming, Hu Yi, Jia Ya-Qiong. Analytical model for acoustic multi-relaxation spectrum in gas mixtures. Acta Physica Sinica, 2012, 61(17): 174301. doi: 10.7498/aps.61.174301
[7]	Jia Ya-Qiong, Wang Shu, Zhu Ming, Zhang Ke-Sheng, Yuan Fei-Ge. The analytic model between effective heat capacity and relaxation time in gas acoustic relaxation process. Acta Physica Sinica, 2012, 61(9): 095101. doi: 10.7498/aps.61.095101
[8]	Zhu Ming, Wang Shu, Wang Shu-Tao, Xia Dong-Hai. An acoustic gas concentration measurement algorithm for carbon monoxide in mixtures based on molecular multi-relaxation model. Acta Physica Sinica, 2008, 57(9): 5749-5755. doi: 10.7498/aps.57.5749
[9]	Yan Shu, Wang Shu. Reconstruction algorithm of relaxation attenuation spectrum in polyatomic gas. Acta Physica Sinica, 2008, 57(7): 4282-4291. doi: 10.7498/aps.57.4282
[10]	Tian Jian-Hui, Han Xu, Liu Gui-Rong, Long Shu-Yao, Qin Jin-Qi. Investigation of the SiC nano-bar relaxation characteristics. Acta Physica Sinica, 2007, 56(2): 643-648. doi: 10.7498/aps.56.643
[11]	Wu Yu, Jiao Zhong-Xing, Lei Liang, Wen Jin-Hui, Lai Tian-Shu, Lin Wei-Zhu. Electron spin relaxation and momentum relaxation in semiconductor quantum wells. Acta Physica Sinica, 2006, 55(6): 2961-2965. doi: 10.7498/aps.55.2961
[12]	GAO WEN-BIN, R. DOPHEIDE, H. ZACHARIAS. A STUDY ON ROTATIONAL RELAXATION OF GAS PHASE C2H2 BY RAMAN UV OPTICAL DOUBLE RESONANCE. Acta Physica Sinica, 1992, 41(3): 400-407. doi: 10.7498/aps.41.400
[13]	LI JING-DE, LI JIA-BAO, FU SHI-LIU, SHEN WEN-BIN. THE FREE AND RANDOM DIELECTRIC RELAXATIONS. Acta Physica Sinica, 1992, 41(1): 155-161. doi: 10.7498/aps.41.155
[14]	ZHANG BAO-ZHENG, LI YU-XING, LIN MEI-RONG, CHEN WEN-JU. THEORETICAL STUDY OF MULTIPHONON RADIATIONLESS RELAXATION RATE. Acta Physica Sinica, 1990, 39(2): 261-269. doi: 10.7498/aps.39.261
[15]	DING E-JIANG, HUANG ZU-QIA. A KIND OF RELAXATION OF RAREFIED GASES IN INFINITE SPACE WITH SPHERICAL SYMMETRY. Acta Physica Sinica, 1985, 34(3): 289-297. doi: 10.7498/aps.34.289
[16]	XIA JIAN-BAI. RELAXATION EFFECTS OF THE (111) SURFACE OF Si AND GaAs. Acta Physica Sinica, 1984, 33(2): 143-153. doi: 10.7498/aps.33.143
[17]	LI JING-DE. THE PYROELECTRIC RELAXATION EFFECT. Acta Physica Sinica, 1984, 33(11): 1563-1568. doi: 10.7498/aps.33.1563
[18]	ZHU YONG, ZHANG DAO-FAN. RELAXATION BEHAVIORS OF THE DEPOLARIZATION CURRENT AND THE APPARENT DIELECTRIC CONSTANT OF α-LiIO₃ SINGLE CRYSTALS. Acta Physica Sinica, 1980, 29(4): 454-460. doi: 10.7498/aps.29.454
[19]	ZHANG KAI-MING, YE LING. A PRELIMINARY STUDY ON THE RELAXATION OF Si(111) SURFACE ATOMS. Acta Physica Sinica, 1980, 29(1): 122-126. doi: 10.7498/aps.29.122
[20]	MA BEN-KUN. SPIN-LATTICE RELAXATION. Acta Physica Sinica, 1965, 21(7): 1419-1436. doi: 10.7498/aps.21.1419

Catalog

Vol. 67, Issue 9 - 2018-05-05

Metrics

Abstract views: 6595
PDF Downloads: 110
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