Abstract
Thermal expansion, or more widely thermal deformation, is characterized by the changes of the dimensions of a body resulting from the temperature changes. Similar to the thermal conductivity, the thermal expansivity occurs due to anharmonicity of various modes of lattice vibrations [1, 2]. Any formulations concerning the thermal expansivity of solids are closely related to the main ideas of an equation of state for solids. According to the original Gruneisen assumption [1] the internal energy of a solid can be divided into a static and athermal portion. This assumption leads to an equation of state for the pressure which contains two terms: one of the terms corresponds to the static interaction (internal pressure) and the other represents the thermal pressure due to the expansivity of the lattice vibrations. Thus, the most widely used form of the equation of state for solids is
which corresponds to the usual Mie-Gruneisen approximation. In this equation Pi = -dUL/dV is the internal pressure, γ is the Gruneisen parameter, PT = Ut/V is the thermal pressure, and UT is the thermal energy. Differentiation of Eq. (3.1) with respect to temperature at constant volume yields
where α is the thermal expansion coefficient, and KT is the isothermal bulk modulus.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gruneisen E (1926) In: Handbuch der Physik, vol 10, p1, Geifer H, Scheel K (ed), Springer Berlin
Novikova SI (1974) Thermal Expansion of Solids (in Russian), Nauka Moscow
Girifalco LA (1973) Statistical Physics of Materials, Wiley Inerscience New York
Barron THK (1955) Phil Mag 46: 720
Barker RE Jr(1967) J Appl Phys 38: 4234
Warfield RW (1974) Makromol Chem 175: 3285
Shen M and Reese W (1975) In: Progress in Solid State Chemistry, vol 9, pp 241–268, McColdin, Samojai (ed), Pergamon Oxford
Shen M (1979) Polymer Eng Sci 19: 995
Wada Y, Itani A, Nishi T and Nagai S (1969) J Polym Sci part A-27: 201
Pastine DJ (1968) J Chem Phys 49: 3012
Wu CK, Jura G and Shen M (1972) J Appl Phys 43: 4348
Broadhurst MG and Mopsik FI (1970) J Chem Phys 52: 3634
Curro JG (1974) J Macromol Sci-Revs Macromol Chem C11(2): 321
Prigogine I, Trappeniers N and Mathot V (1953) Disc Faraday Soc N15: 93
Prigogine I, Bellemans A and Mathot V (1957) The Molecular Theory of Solutions, Wiley New York
Simha R (1980) J Macromol Sci Phys 18: 377
Simha R and Somcynscy T (1969) Macromolecules 2: 342
Olabisi O and Simha R (1975) Macromolecules 8: 206,211
Simha R (1979) J Polym Sci Polym Phys Ed 17: 1929
Ainbinder SB, Tjunina EL and Tsirule KI (1981) Mechanics of compos mater N3: 387
Simha R, Roe JM and Nanda VS (1972) J Appl Phys 43: 4312
Curro JG (1973) J Chem Phys 58: 374
Gibbons TG (1974) J Chem Phys 60: 1094
Shen M; Hansen WN and Romo PC (1969) J Chem Phys 51: 425
Volodin VP and Gudymov SYu (1984) Solid State Phys (FTT) 26: 1563
Devis GT, Eby RK and Colson JP (1970) J Appl Phys 41: 4316
Kijima T, Koga K, Imada K and Takayanagi M (1975) Polym J 7: 14
Engeln I, Meissner M and Pape UE (1985) Polymer 26: 364
Perepechko II (1980) Low temperature properties of polymers, Pergamon Oxford
Kato E (1980) J Chem Phys 73: 1020
Barron THK (1970) J Appl Phys 41: 5044
Lifshitz IM (1952) J Exp Theor Phys (JETF) 22: 475
Wakelin JH, Sutherland A and Beck LR (1960) J Polym Sci 42: 278
Kobajashi J and Keller A (1970) Polymer 11: 114
Baughman RH (1973) J Chem Phys 58: 2976
Kan KN (1975) Theoretical Questions of Thermal Expansion of Polymers (in Russian), Izd LGU Leningrad
Chen FC, Choy CL and Young K (1980) J Polym Sci Polym Phys Ed 18: 2312
Chen FC, Choy CL, Wong SP and Young K (1981) J Polym Sci Polym Phys Ed 19: 971
Barron RM, Barron THK, Mummery PM and Sharkey M (1988) Can J Chem 66: 718
Broadhurst MG and Mopsik FI (1971) J Chem Phys 54: 4239
Dadobaev G and Slutzker AI (1981) Solid State Physics (FTT) N7: 1936; (1982) Vysokomol Soyed A2+: 30; (1983) A25: 8
Frenkel Yal (1950) Introduction to the Theory of Metals, (in Russian) GITTL Moscow-Leningrad
Choy CL and Nakafuku C (1988) J Polym Sci Polym Phys Ed 26: 921
White GK, Smith TF and Birch JA (1976) J Chem Phys 65: 554
Godovsky YuK (1982) Colloid Polym Science 60: 461
Godovsky YuK (1986) Adv Polym Sci 76: 30
Godovsky YuK (1987) Progr Colloid Polym Science 75: 70
Shen M and Croucher M (1975) J Macromol Sci C12: 287
Thile JL and Cohen RE (1980) Rubber Chem Technol 53: 313
Godovsky YuK (1976) Thermophysical Methods of Polymers Characterization (in Russian), Khimiya Moscow
Mead WT, Desper CR and Porter RS (1979) J Polym Sci Polym Phys Ed 17: 859
Capiati NJ and Porter RS (1977) J Polym Sci Polym Phys Ed 15: 1427
Choy CL, Chen FC and Young K (1981) J Polym Sci Polym Phys Ed 19: 395
Choy CL, Ito M and Porter RS (1983) J Polym Sci Polym Phys Ed 21: 1427
Wolf F-P and Karl V-H (1980) Angew Makromol Chem 92: 89
Wolf F-P and Karl V-H (1981) Colloid Polym Science 259: 29
Wolf F-P and Karl V-H (1981) Makromol Chem 182: 1787
Hellwege K-H, Hannig J and Knappe W (1963) Kolloid Z Z Polym 188: 121
Wang L-H, Choy CL and Porter RS (1982) J Polym Sci Polym Phys Ed 20: 633
Wang L-H, Choy CL and Porter RS (1983) J Polym Sci Polym Phys Ed 21: 657
Choy CL, Chen FC and Ong EL (1979) Polymer 20: 1191
Kardos JL et al (1979) Polym Eng Sci 19: 1000
Shermergor TD (1977) Theory of Elasticity of Microheterogeneous Solids (in Russian), Nauka Moscow
Holliday L and Robinson JD (1973) J Mater Sci 8: 301
Holliday L and Robinson JD (1977) In: Polymer Engineering Composites, chap 6, Richardson MOW (ed), Applied Science Publishers London
Pinheiro MFF and Rosenberg HM (1980) J Polym Sci Polym Phys Ed 18: 217
Fahmy AH and Ragai AN (1970) J Appl Phys 41: 5112
Rogers KF, Phillips LN, Kingston-Lee DM, Yates B, Overy MJ, Sergent JP and McCalla BA (1977) J Mater Sci 12: 718
Yate B, Overy MJ, Sergent JP, McCalla BA, Kingston-Lee DM, Phillips LN and Rogers KF (1978) J Mater Sci 13: 433
Ishikawa T, Koyama K and Kobayaski S (1978) J Composite Mater 12: 153
Stife JR and Prevo KM (1979) J Composite Mater 13: 264
Tompkins SS (1987) Intern J Thermophysics 8(1): 119
Bowles DE and Tompkins SS (1989) J Composite Mater 23: 270
Vyshvanjuk VI, Alypov VT and Vishnevskii ZN (1982) Mekhanika Compo-sizionnych Materialov N6: 1102
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag
About this chapter
Cite this chapter
Godovsky, Y.K. (1992). Thermal Expansion. In: Thermophysical Properties of Polymers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51670-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-51670-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-51672-6
Online ISBN: 978-3-642-51670-2
eBook Packages: Springer Book Archive