摩擦能量耗散的统计热力学初步研究
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摘要
摩擦是典型的非平衡态不可逆过程,摩擦中机械能到热能的转变是能质降低的能量耗散过程。运用分子动力学方法研究摩擦的能量耗散机制是揭开摩擦本质的有效途径,也是纳米摩擦学领域研究的难点。统计热力学中的熵函数是表征热力学系统不可逆过程演化方向的特征参量,将熵函数应用于摩擦学的研究中,可以实现摩擦过程中不同量纲影响因素的统一。本文的研究是在摩擦热力学体系下,结合有限元和分子动力学方法,对摩擦状态下的熵变做定性分析,以证明这一过程的能量耗散性。
本文先用有限元的方法对弹簧振子模型进行了瞬态动力学分析。从振子的位移、速度、动能和势能的角度详细分析了振子的运动规律,并从弹性波的角度来推导这一过程的能量耗散即熵增性质。把振子按动能值划分到不同的能量区间中,从统计分布角度初步分析了系统微观状态的变化。使用分子动力学的方法对金刚石晶体模型进行了研究。在模型上施加正压力和切向力来近似模拟摩擦作用力,观察其动态响应情况。对动能进行统计分布分析来研究系统微观状态数的变化和能量耗散过程。并分析了系统总动能、总势能和内能的变化规律。主要结论是:1.在外力作用下,弹簧振子的运动表现出了弹性波的特性。所有振子的位移随着时间的推移呈现周期性的波动,且在大的周期性运动中个体振子具有微小的振动,原因可能是原子间的相互作用。弹性波是能量传播的载体,从理论上可以近似证明弹性波的传播是熵增加的过程。2.对弹簧振子和金刚石原子的动能进行区间分布统计分析可知,一个动力学系统元素的能量状态分布都具有一定的规律性,样本空间越大,这种分布状态越稳定。从这种分布统计可以间接获取系统微观状态数的变化。根据统计热力学理论,系统微观状态数越多,熵值越大,机械能不断地转变成热能,导致了能量不可逆地耗散。
Friction is a typical nonequilibrium inreversible process. It is a energy dissipation process of energy quality degrading with mechanical energy change into heat in friction. It is a effective methods to study frictional energy dissipation mechanism with Molecular Dynamics method, which is hot point in nano-tribology. Entropy in statistical thermodynamics is a characteristic parameter to study the irreversible process direction in thermodynamical system. Entropy in tribology can unifies factors in different unit. Within tribo-thermodynamics, this paper give exploratory study to qualitative analysis of the entropy to testify energy dissipation with FE and Molecular Dynamics.
First we gave a transient analysis to 100 spring-oscillator model. The law of motion is obtained from dispalacement、velocity、kinetic energy and potential energy of oscillators. The oscillators are assigned to energy intervals according their kinetic energy and the change of entropy is concluded from the perspective of statistics. We studied diamond model with Molecular Dynamics and use nomal load and tangential force to simulate frictional effect. We also study the statistical distribution of kinetic energy to analyze change of microstatus of the system and its energy dissipation. We analyze total kinetic energy、total potential energy and internal energy of the system. The results shows that: (1)The 1-D spring-oscallitor model can be regarded as elastic medium approximately. The movement are elastic waves under the external force. Displacement of all atoms advance with time showing a cyclical fluctuations,and individual atoms moves in small vibration in the cyclical movement. It is may be due to the impact of the interaction between atoms. Elastic wave is a carrier of energy spreading. It is proved approximately in theory that the elastic wave of the movement is the process of entropy increasement. (2)From the analysis of kinetic energy statistical distribution for oscallitors and diamond atoms we know that the energy distribution of elements in dynamical system shows regularity. The bigger the sample space, the more stable of distributional status. The change of micro-status in system can be obtained indirectly from the distribution. The more the micro-status, the bigger the entropy of the system.
本文先用有限元的方法对弹簧振子模型进行了瞬态动力学分析。从振子的位移、速度、动能和势能的角度详细分析了振子的运动规律,并从弹性波的角度来推导这一过程的能量耗散即熵增性质。把振子按动能值划分到不同的能量区间中,从统计分布角度初步分析了系统微观状态的变化。使用分子动力学的方法对金刚石晶体模型进行了研究。在模型上施加正压力和切向力来近似模拟摩擦作用力,观察其动态响应情况。对动能进行统计分布分析来研究系统微观状态数的变化和能量耗散过程。并分析了系统总动能、总势能和内能的变化规律。主要结论是:1.在外力作用下,弹簧振子的运动表现出了弹性波的特性。所有振子的位移随着时间的推移呈现周期性的波动,且在大的周期性运动中个体振子具有微小的振动,原因可能是原子间的相互作用。弹性波是能量传播的载体,从理论上可以近似证明弹性波的传播是熵增加的过程。2.对弹簧振子和金刚石原子的动能进行区间分布统计分析可知,一个动力学系统元素的能量状态分布都具有一定的规律性,样本空间越大,这种分布状态越稳定。从这种分布统计可以间接获取系统微观状态数的变化。根据统计热力学理论,系统微观状态数越多,熵值越大,机械能不断地转变成热能,导致了能量不可逆地耗散。
Friction is a typical nonequilibrium inreversible process. It is a energy dissipation process of energy quality degrading with mechanical energy change into heat in friction. It is a effective methods to study frictional energy dissipation mechanism with Molecular Dynamics method, which is hot point in nano-tribology. Entropy in statistical thermodynamics is a characteristic parameter to study the irreversible process direction in thermodynamical system. Entropy in tribology can unifies factors in different unit. Within tribo-thermodynamics, this paper give exploratory study to qualitative analysis of the entropy to testify energy dissipation with FE and Molecular Dynamics.
First we gave a transient analysis to 100 spring-oscillator model. The law of motion is obtained from dispalacement、velocity、kinetic energy and potential energy of oscillators. The oscillators are assigned to energy intervals according their kinetic energy and the change of entropy is concluded from the perspective of statistics. We studied diamond model with Molecular Dynamics and use nomal load and tangential force to simulate frictional effect. We also study the statistical distribution of kinetic energy to analyze change of microstatus of the system and its energy dissipation. We analyze total kinetic energy、total potential energy and internal energy of the system. The results shows that: (1)The 1-D spring-oscallitor model can be regarded as elastic medium approximately. The movement are elastic waves under the external force. Displacement of all atoms advance with time showing a cyclical fluctuations,and individual atoms moves in small vibration in the cyclical movement. It is may be due to the impact of the interaction between atoms. Elastic wave is a carrier of energy spreading. It is proved approximately in theory that the elastic wave of the movement is the process of entropy increasement. (2)From the analysis of kinetic energy statistical distribution for oscallitors and diamond atoms we know that the energy distribution of elements in dynamical system shows regularity. The bigger the sample space, the more stable of distributional status. The change of micro-status in system can be obtained indirectly from the distribution. The more the micro-status, the bigger the entropy of the system.
引文
[1] H.C.Meng, K.C.Ludema. Wear models and predictive equations:their form and content[J]. Wear, 1995, 181-183: 443-457.
[2] J.M.Dobromiski. Variables of fretting Process: are they 50 of them?[C]. ASTM 1159, 1992.
[3]国家自然科学基金委员会工程与材料科学部.机械与制造科学[M].北京:科学出版社, 2006.
[4] Czichos著,刘钟华等译.摩擦学-对摩擦、润滑和磨损科学技术的系统分析[M].北京:机械工业出版社, 1984.
[5]周仲荣主编.摩擦学发展前沿[M].北京:科学出版社, 2006.
[6] F.P.Bowden, D.Tabor . Friction and Lubrication of Solids[M]. Oxford, Oxford University Press, 1964.
[7] J.A.Greenwood, J.Williamson. Contact of nominally flat surfaces[C]. Process Royal Society., 1966, A295:300-319.
[8] J.N.Israelachvili. Adhesion, friction and lubrication of molecularly smooth surfaces. In: I.L.Singer, H.M.Pollock. Fundamental of Friction[M]. Kluwer Academic Publishers, 1991.
[9]张涛,王慧,胡元中.无磨损摩擦的原子理论[J].摩擦学学报, 2001, 21(5): 396-400.
[10] M.Weiss, F.J.Elmer. Dry friction in the Frenkel-Kontorova-Tomlinson model: dynamical properties[J]. Zeitschrift Fur Physik B, 1997, 104: 55-69.
[11] M.Hirano, K.Shinjo. Atomistic locking and friction[J]. Physical Review B, 41(17): 837-851.
[12]戴振东,王珉,薛群基著.摩擦体系热力学引论[M].北京:国防工业出版社, 2002.
[13] B.E.Klamecki. Wear-An entropy Production Model[J]. Wear, 1980, 58: 325-330.
[14] B.E.Klamecki. A Thermodynamic Model of Friction[J]. Wear, 1980, 63: 113-120.
[15] B.E.Klamecki. Energy Dissipation in Sliding[J]. Wear, 1982, 77: 115-128.
[16] B.E.Klamecki. An Entropy-based Model of Plastic Deformation Energy Dissipation in Sliding[J]. Wear, 1984, 96: 319-329.
[17] A.Zmitrowicz. A Thermodynamical Model of Contact, Friction and Wear, I. Governing Equations[J]. Wear, 1987, 114: 135-168.
[18] A.Zmitrowicz. A Thermodynamical Model of Contact, Friction and Wear, II. Constitutive Equations for Materials and Linearized Theories[J]. Wear, 1987,114: 169-198.
[19] A.Zmitrowicz. A Thermodynamical Model of Contact, Friction and Wear, III. ConstitutiveEquations for Friction, Wear and Frictional Heat[J]. Wear, 1987, 114: 199-221
[20] A.Zmitrowicz. Constitutive Modelling of Anisotropic Phenomena of Friction, Wear and Friction Heat. Gdansk, Instytut Maszyn Przeplywowych Pan, 1996.
[21] Lashkhi IL, Buyanovaski IA, Borenko LV. Use of concepts of solid state thermodynamics to explain the action of friction modifiers. Trenie I Iznos, 1986, 17(2):250-255.
[22] J.Hokikian著,王芷译.无序的科学[M].长沙:湖南科学技术出版社, 2007.
[23]龚昌得编.热力学与统计物理学[M].北京:人民教育出版社, 1982.冯端,冯少彤.溯源探幽-熵的世界[M].北京:科学出版社, 2005.
[24]冯端,冯少彤.溯源探幽-熵的世界[M].北京:科学出版社, 2005.
[25]黄明智.板成形过程熵产生分析[硕士学位论文].南京:南京航空航天大学, 2006.
[26]邹邦银编著.热力学与分子物理学[M].武汉:华中师范大学出版社, 2004.
[27]尚仰震著.热力学体系统计熵[M].成都:四川科学技术出版社, 1988.
[28] J.B.Sokoloff. Microscopic mechanisms for kinetic friction: Nearly frictionless sliding for small solids[J]. Physical Review B, 1995, 52(10): 7205-7214.
[29]黄昆著.固体物理学[M].北京:高等教育出版社, 1988.
[30] G.P.Ostermeyer. The mesoscopic particle approach[J]. Tribology Inernational, 2007, 49(6): 953-959.
[31]曾攀,杜婧,杨学贵.用于C-C共价键力能关系表征的等效C-C键合单元[J].固体力学学报, 2007, 28(4): 325-332.
[32]汤甦野著.熵-一个世纪之谜的解析[M].合肥:中国科学技术大学出版社, 2004.
[33]孙泽辉.纳米薄膜力学行为的分子动力学模拟研究[博士学位论文].长沙:中国科学技术大学, 2007.
[34]文玉华,朱如曾.分子动力学模拟的主要技术[J].力学进展, 2003, 33(1): 65-73.
[35]陆帅.碳纳米管摩擦性能的分子动力学模拟[硕士学位论文].南京:东南大学, 2006.
[36] W.F.Gunsteren, H.Berendsen. Algorithm for Brownian dynamics[J]. Molecular Physics, 1982, 45(3): 637-647.
[37]蒋开.超滑现象及超薄膜润滑机理的分子动力学研究[硕士学位论文].南京:东南大学, 2005.
[38]林梦海.量子化学计算方法与应用[M].北京:科学出版社, 2004.
[39] M.S.Daw, M.I.Baskes. Embeded atom method derivation and application to impurities, surface, and other defects in metals[J]. Physical Review B, 1984, 29(12):8486-8495.
[40] M.W.Finnis, J.E.Sinclair. A simple empirical n-body potential for transition-metals[J].Philosophic Magazine A, 1984, 50(1): 45-55.
[41] G.J.Ackland, V.Vitek Many-body potentials and atom-scale relaxations in noble-metal alloys[J]. Physical Review. B,1990,41(15): 10324-10333.
[42]温诗铸著.纳米摩擦学[M].北京:清华大学出版社,1998.
[43] J.Tersoff. New Empirical Model for the Structural Properties of Silicon[J]. Physical Review Letters, 1986, 56(6): 632-636.
[44] J.Tersoff. New empirical approach for the structure and energy of covalent systems[J]. Physical Review B, 1988, 37(12): 6991-7000.
[45] J.Tersoff. Modeling solid-state chemistry: interatomic potentials for multicomponent systems[J]. Physical Review B, 1989, 39(8): 5566-5568.
[46] G.C.Abell. Empirical chemical pseudopotential theory of molecular and metallic bonding[J]. Physical Review B, 1985, 31(10): 6185-6196.
[47] Stephen C. Harvey, Robert K.-Z. Tan, Thomas E. Cheatham III. "The flying ice cube: velocity rescaling in molecular dynamics leads to violation of energy equipartition.", J. Comput. Chem., 1998, 19, 726-740.
[2] J.M.Dobromiski. Variables of fretting Process: are they 50 of them?[C]. ASTM 1159, 1992.
[3]国家自然科学基金委员会工程与材料科学部.机械与制造科学[M].北京:科学出版社, 2006.
[4] Czichos著,刘钟华等译.摩擦学-对摩擦、润滑和磨损科学技术的系统分析[M].北京:机械工业出版社, 1984.
[5]周仲荣主编.摩擦学发展前沿[M].北京:科学出版社, 2006.
[6] F.P.Bowden, D.Tabor . Friction and Lubrication of Solids[M]. Oxford, Oxford University Press, 1964.
[7] J.A.Greenwood, J.Williamson. Contact of nominally flat surfaces[C]. Process Royal Society., 1966, A295:300-319.
[8] J.N.Israelachvili. Adhesion, friction and lubrication of molecularly smooth surfaces. In: I.L.Singer, H.M.Pollock. Fundamental of Friction[M]. Kluwer Academic Publishers, 1991.
[9]张涛,王慧,胡元中.无磨损摩擦的原子理论[J].摩擦学学报, 2001, 21(5): 396-400.
[10] M.Weiss, F.J.Elmer. Dry friction in the Frenkel-Kontorova-Tomlinson model: dynamical properties[J]. Zeitschrift Fur Physik B, 1997, 104: 55-69.
[11] M.Hirano, K.Shinjo. Atomistic locking and friction[J]. Physical Review B, 41(17): 837-851.
[12]戴振东,王珉,薛群基著.摩擦体系热力学引论[M].北京:国防工业出版社, 2002.
[13] B.E.Klamecki. Wear-An entropy Production Model[J]. Wear, 1980, 58: 325-330.
[14] B.E.Klamecki. A Thermodynamic Model of Friction[J]. Wear, 1980, 63: 113-120.
[15] B.E.Klamecki. Energy Dissipation in Sliding[J]. Wear, 1982, 77: 115-128.
[16] B.E.Klamecki. An Entropy-based Model of Plastic Deformation Energy Dissipation in Sliding[J]. Wear, 1984, 96: 319-329.
[17] A.Zmitrowicz. A Thermodynamical Model of Contact, Friction and Wear, I. Governing Equations[J]. Wear, 1987, 114: 135-168.
[18] A.Zmitrowicz. A Thermodynamical Model of Contact, Friction and Wear, II. Constitutive Equations for Materials and Linearized Theories[J]. Wear, 1987,114: 169-198.
[19] A.Zmitrowicz. A Thermodynamical Model of Contact, Friction and Wear, III. ConstitutiveEquations for Friction, Wear and Frictional Heat[J]. Wear, 1987, 114: 199-221
[20] A.Zmitrowicz. Constitutive Modelling of Anisotropic Phenomena of Friction, Wear and Friction Heat. Gdansk, Instytut Maszyn Przeplywowych Pan, 1996.
[21] Lashkhi IL, Buyanovaski IA, Borenko LV. Use of concepts of solid state thermodynamics to explain the action of friction modifiers. Trenie I Iznos, 1986, 17(2):250-255.
[22] J.Hokikian著,王芷译.无序的科学[M].长沙:湖南科学技术出版社, 2007.
[23]龚昌得编.热力学与统计物理学[M].北京:人民教育出版社, 1982.冯端,冯少彤.溯源探幽-熵的世界[M].北京:科学出版社, 2005.
[24]冯端,冯少彤.溯源探幽-熵的世界[M].北京:科学出版社, 2005.
[25]黄明智.板成形过程熵产生分析[硕士学位论文].南京:南京航空航天大学, 2006.
[26]邹邦银编著.热力学与分子物理学[M].武汉:华中师范大学出版社, 2004.
[27]尚仰震著.热力学体系统计熵[M].成都:四川科学技术出版社, 1988.
[28] J.B.Sokoloff. Microscopic mechanisms for kinetic friction: Nearly frictionless sliding for small solids[J]. Physical Review B, 1995, 52(10): 7205-7214.
[29]黄昆著.固体物理学[M].北京:高等教育出版社, 1988.
[30] G.P.Ostermeyer. The mesoscopic particle approach[J]. Tribology Inernational, 2007, 49(6): 953-959.
[31]曾攀,杜婧,杨学贵.用于C-C共价键力能关系表征的等效C-C键合单元[J].固体力学学报, 2007, 28(4): 325-332.
[32]汤甦野著.熵-一个世纪之谜的解析[M].合肥:中国科学技术大学出版社, 2004.
[33]孙泽辉.纳米薄膜力学行为的分子动力学模拟研究[博士学位论文].长沙:中国科学技术大学, 2007.
[34]文玉华,朱如曾.分子动力学模拟的主要技术[J].力学进展, 2003, 33(1): 65-73.
[35]陆帅.碳纳米管摩擦性能的分子动力学模拟[硕士学位论文].南京:东南大学, 2006.
[36] W.F.Gunsteren, H.Berendsen. Algorithm for Brownian dynamics[J]. Molecular Physics, 1982, 45(3): 637-647.
[37]蒋开.超滑现象及超薄膜润滑机理的分子动力学研究[硕士学位论文].南京:东南大学, 2005.
[38]林梦海.量子化学计算方法与应用[M].北京:科学出版社, 2004.
[39] M.S.Daw, M.I.Baskes. Embeded atom method derivation and application to impurities, surface, and other defects in metals[J]. Physical Review B, 1984, 29(12):8486-8495.
[40] M.W.Finnis, J.E.Sinclair. A simple empirical n-body potential for transition-metals[J].Philosophic Magazine A, 1984, 50(1): 45-55.
[41] G.J.Ackland, V.Vitek Many-body potentials and atom-scale relaxations in noble-metal alloys[J]. Physical Review. B,1990,41(15): 10324-10333.
[42]温诗铸著.纳米摩擦学[M].北京:清华大学出版社,1998.
[43] J.Tersoff. New Empirical Model for the Structural Properties of Silicon[J]. Physical Review Letters, 1986, 56(6): 632-636.
[44] J.Tersoff. New empirical approach for the structure and energy of covalent systems[J]. Physical Review B, 1988, 37(12): 6991-7000.
[45] J.Tersoff. Modeling solid-state chemistry: interatomic potentials for multicomponent systems[J]. Physical Review B, 1989, 39(8): 5566-5568.
[46] G.C.Abell. Empirical chemical pseudopotential theory of molecular and metallic bonding[J]. Physical Review B, 1985, 31(10): 6185-6196.
[47] Stephen C. Harvey, Robert K.-Z. Tan, Thomas E. Cheatham III. "The flying ice cube: velocity rescaling in molecular dynamics leads to violation of energy equipartition.", J. Comput. Chem., 1998, 19, 726-740.
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