Abstract

Polymeric components are desirable in optical and photonic applications because of their light weight, high impact resistance, and/or ability to be formed into sophisticated shapes or gradient index (GRIN) optics. However, relatively large thermal effects in polymers can limit applications. We studied a selected series of amorphous polyimides in order to evaluate their potential application in components of optical devices. Several of these polyimides have thermo-optic coefficients (dn/dT) and volume coefficients of thermal expansion (VCTE) about 50% smaller than those of standard optical polymers, such as PMMA and polycarbonate. Surprisingly, these low dn/dT and VCTE values were found in amorphous polyimides which have sterically hindered, kinked linkages between phenyl rings. This suggests a different structural dependence than that found in previous studies, which showed that low thermal expansion in crystalline polyimides is correlated with a rigid linear backbone molecular structure. Thus, amorphous polyimides with favorable backbone structures represent a class of materials with improved thermo-optical stability for polymeric optical devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

R. Ishige, T. Masuda, Y. Kozaki, E. Fujiwara, T. Okada, and S. Ando, “Precise analysis of thermal volume expansion of crystal lattice for fully aromatic crystalline polyimides by X-ray diffraction method: relationship between molecular structure and linear/volumetric thermal expansion,” Macromolecules 50(5), 2112–2123 (2017).
[Crossref]

2016 (1)

H. Fein and M. Ponting, “Analytical study of thermal invariance of polymeric nanolayer gradient index optical components,” Proc. SPIE 9822, 98220X (2016).
[Crossref]

2015 (1)

2014 (3)

J.-C. Kim and J.-H. Chang, “Quarternary copolyimides with various monomer contents: thermal property and optical transparency,” Macromol. Res. 22(11), 1178–1182 (2014).
[Crossref]

Y. Terui and S. Ando, “Polarization dependence of thermo-optic coefficients in polyimide films originating from chain orientation and residual thermal stress,” J. Appl. Phys. 116(5), 053524 (2014).
[Crossref]

S. Neyertz and D. Brown, “The effect of structural isomerism on carbon dioxide sorption and plasticization at the interface of a glassy polymer membrane,” J. Membr. Sci. 460, 213–228 (2014).
[Crossref]

2013 (2)

M. Hasegawa, T. Ishigami, J. Ishii, K. Sugiura, and M. Fujii, “Solution-processable transparent polyimides with low coefficients of thermal expansion and self-orientation behavior induced by solution casting,” Eur. Polym. J. 49(11), 3657–3672 (2013).
[Crossref]

T. Kurosawa, T. Higashihara, and M. Ueda, “Polyimide memory: a pithy guideline for future applications,” Polym. Chem. 4(1), 16–30 (2013).
[Crossref]

2009 (2)

N. Sensui, J. Ishii, A. Takata, Y. Oami, M. Hasegawa, and R. Yokota, “Ultra-low CTE and improved toughness of PMDA/PDA polyimide-based molecular composites containing asymmetric BPDA-type polyimides,” High Perform. Polym. 21(6), 709–728 (2009).
[Crossref]

S. Shenogin, N. Raravikar, R. Ozisik, and P. Keblinski, “Using vibrational mode analysis for predicting the coefficient of thermal expansion of amorphous polymers,” J. Polym. Sci., B, Polym. Phys. 47(21), 2114–2121 (2009).
[Crossref]

2005 (1)

G. D. Barrera, J. A. O. Bruno, T. H. K. Barron, and N. L. Allan, “Negative thermal expansion,” J. Phys. Condens. Matter 17(4), R217–R252 (2005).
[Crossref]

2001 (1)

A. I. Slutsker, L. A. Laius, I. V. Gofman, V. L. Gilyarov, and Y. I. Polikarpov, “Mechanisms of reversible thermal deformation of oriented polymers,” Phys. Solid State 43(7), 1382–1388 (2001).
[Crossref]

1997 (1)

Y. Sato, Y. Yamasaki, S. Takishima, and H. Masuoka, “Precise measurement of the PVT of polypropylene and polycarbonate up to 330°C and 200 MPa,” J. Appl. Polym. Sci. 66(1), 141–150 (1997).
[Crossref]

1994 (1)

M. T. Pottiger, J. C. Coburn, and J. R. Edman, “The effect of orientation on thermal expansion behavior in polyimide films,” J. Polym. Sci., B, Polym. Phys. 32(5), 825–837 (1994).
[Crossref]

1991 (1)

T. M. Tong, H. K. D. Hsuen, K. L. Saenger, and G. W. Su, “Thickness-direction coefficient of thermal expansion measurement of thin polymer films,” Rev. Sci. Instrum. 62(2), 422–430 (1991).
[Crossref]

1989 (1)

R. K. Jain and R. Simha, “Theoretical equation of state: thermal expansivity, compressibility, and the Tait relation,” Macromolecules 22(1), 464–468 (1989).
[Crossref]

1987 (1)

S. Numata, K. Fujisaki, and N. Kinjo, “Re-examination of the relationship between packing coefficient and thermal expansion coefficient for aromatic polyimides,” Polymer (Guildf.) 28(13), 2282–2288 (1987).
[Crossref]

1981 (1)

T. H. Jamieson, “Thermal effects in optical systems,” Opt. Eng. 20(2), 156–160 (1981).
[Crossref]

1969 (1)

Y. Wada, A. Itani, T. Nishi, and S. Nagai, “Grüneisen constant and thermal properties of crystalline and glassy polymers,” J. Polym. Sci 7(Part A-2), 201–208 (1969).

1967 (1)

R. E. Barker., “Grüneisen numbers for polymeric solids,” J. Appl. Phys. 38(11), 4234–4242 (1967).
[Crossref]

1965 (1)

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” JOSA 55(10), 1205–1209 (1965).
[Crossref]

Allan, N. L.

G. D. Barrera, J. A. O. Bruno, T. H. K. Barron, and N. L. Allan, “Negative thermal expansion,” J. Phys. Condens. Matter 17(4), R217–R252 (2005).
[Crossref]

Ando, S.

R. Ishige, T. Masuda, Y. Kozaki, E. Fujiwara, T. Okada, and S. Ando, “Precise analysis of thermal volume expansion of crystal lattice for fully aromatic crystalline polyimides by X-ray diffraction method: relationship between molecular structure and linear/volumetric thermal expansion,” Macromolecules 50(5), 2112–2123 (2017).
[Crossref]

Y. Terui and S. Ando, “Polarization dependence of thermo-optic coefficients in polyimide films originating from chain orientation and residual thermal stress,” J. Appl. Phys. 116(5), 053524 (2014).
[Crossref]

Barker, R. E.

R. E. Barker., “Grüneisen numbers for polymeric solids,” J. Appl. Phys. 38(11), 4234–4242 (1967).
[Crossref]

Barrera, G. D.

G. D. Barrera, J. A. O. Bruno, T. H. K. Barron, and N. L. Allan, “Negative thermal expansion,” J. Phys. Condens. Matter 17(4), R217–R252 (2005).
[Crossref]

Barron, T. H. K.

G. D. Barrera, J. A. O. Bruno, T. H. K. Barron, and N. L. Allan, “Negative thermal expansion,” J. Phys. Condens. Matter 17(4), R217–R252 (2005).
[Crossref]

Beadie, G.

Brindza, M.

Brown, D.

S. Neyertz and D. Brown, “The effect of structural isomerism on carbon dioxide sorption and plasticization at the interface of a glassy polymer membrane,” J. Membr. Sci. 460, 213–228 (2014).
[Crossref]

Bruno, J. A. O.

G. D. Barrera, J. A. O. Bruno, T. H. K. Barron, and N. L. Allan, “Negative thermal expansion,” J. Phys. Condens. Matter 17(4), R217–R252 (2005).
[Crossref]

Chang, J.-H.

J.-C. Kim and J.-H. Chang, “Quarternary copolyimides with various monomer contents: thermal property and optical transparency,” Macromol. Res. 22(11), 1178–1182 (2014).
[Crossref]

Coburn, J. C.

M. T. Pottiger, J. C. Coburn, and J. R. Edman, “The effect of orientation on thermal expansion behavior in polyimide films,” J. Polym. Sci., B, Polym. Phys. 32(5), 825–837 (1994).
[Crossref]

Edman, J. R.

M. T. Pottiger, J. C. Coburn, and J. R. Edman, “The effect of orientation on thermal expansion behavior in polyimide films,” J. Polym. Sci., B, Polym. Phys. 32(5), 825–837 (1994).
[Crossref]

Fein, H.

H. Fein and M. Ponting, “Analytical study of thermal invariance of polymeric nanolayer gradient index optical components,” Proc. SPIE 9822, 98220X (2016).
[Crossref]

Flynn, R. A.

Fujii, M.

M. Hasegawa, T. Ishigami, J. Ishii, K. Sugiura, and M. Fujii, “Solution-processable transparent polyimides with low coefficients of thermal expansion and self-orientation behavior induced by solution casting,” Eur. Polym. J. 49(11), 3657–3672 (2013).
[Crossref]

Fujisaki, K.

S. Numata, K. Fujisaki, and N. Kinjo, “Re-examination of the relationship between packing coefficient and thermal expansion coefficient for aromatic polyimides,” Polymer (Guildf.) 28(13), 2282–2288 (1987).
[Crossref]

Fujiwara, E.

R. Ishige, T. Masuda, Y. Kozaki, E. Fujiwara, T. Okada, and S. Ando, “Precise analysis of thermal volume expansion of crystal lattice for fully aromatic crystalline polyimides by X-ray diffraction method: relationship between molecular structure and linear/volumetric thermal expansion,” Macromolecules 50(5), 2112–2123 (2017).
[Crossref]

Gilyarov, V. L.

A. I. Slutsker, L. A. Laius, I. V. Gofman, V. L. Gilyarov, and Y. I. Polikarpov, “Mechanisms of reversible thermal deformation of oriented polymers,” Phys. Solid State 43(7), 1382–1388 (2001).
[Crossref]

Gofman, I. V.

A. I. Slutsker, L. A. Laius, I. V. Gofman, V. L. Gilyarov, and Y. I. Polikarpov, “Mechanisms of reversible thermal deformation of oriented polymers,” Phys. Solid State 43(7), 1382–1388 (2001).
[Crossref]

Hasegawa, M.

M. Hasegawa, T. Ishigami, J. Ishii, K. Sugiura, and M. Fujii, “Solution-processable transparent polyimides with low coefficients of thermal expansion and self-orientation behavior induced by solution casting,” Eur. Polym. J. 49(11), 3657–3672 (2013).
[Crossref]

N. Sensui, J. Ishii, A. Takata, Y. Oami, M. Hasegawa, and R. Yokota, “Ultra-low CTE and improved toughness of PMDA/PDA polyimide-based molecular composites containing asymmetric BPDA-type polyimides,” High Perform. Polym. 21(6), 709–728 (2009).
[Crossref]

Higashihara, T.

T. Kurosawa, T. Higashihara, and M. Ueda, “Polyimide memory: a pithy guideline for future applications,” Polym. Chem. 4(1), 16–30 (2013).
[Crossref]

Hsuen, H. K. D.

T. M. Tong, H. K. D. Hsuen, K. L. Saenger, and G. W. Su, “Thickness-direction coefficient of thermal expansion measurement of thin polymer films,” Rev. Sci. Instrum. 62(2), 422–430 (1991).
[Crossref]

Ishigami, T.

M. Hasegawa, T. Ishigami, J. Ishii, K. Sugiura, and M. Fujii, “Solution-processable transparent polyimides with low coefficients of thermal expansion and self-orientation behavior induced by solution casting,” Eur. Polym. J. 49(11), 3657–3672 (2013).
[Crossref]

Ishige, R.

R. Ishige, T. Masuda, Y. Kozaki, E. Fujiwara, T. Okada, and S. Ando, “Precise analysis of thermal volume expansion of crystal lattice for fully aromatic crystalline polyimides by X-ray diffraction method: relationship between molecular structure and linear/volumetric thermal expansion,” Macromolecules 50(5), 2112–2123 (2017).
[Crossref]

Ishii, J.

M. Hasegawa, T. Ishigami, J. Ishii, K. Sugiura, and M. Fujii, “Solution-processable transparent polyimides with low coefficients of thermal expansion and self-orientation behavior induced by solution casting,” Eur. Polym. J. 49(11), 3657–3672 (2013).
[Crossref]

N. Sensui, J. Ishii, A. Takata, Y. Oami, M. Hasegawa, and R. Yokota, “Ultra-low CTE and improved toughness of PMDA/PDA polyimide-based molecular composites containing asymmetric BPDA-type polyimides,” High Perform. Polym. 21(6), 709–728 (2009).
[Crossref]

Itani, A.

Y. Wada, A. Itani, T. Nishi, and S. Nagai, “Grüneisen constant and thermal properties of crystalline and glassy polymers,” J. Polym. Sci 7(Part A-2), 201–208 (1969).

Jain, R. K.

R. K. Jain and R. Simha, “Theoretical equation of state: thermal expansivity, compressibility, and the Tait relation,” Macromolecules 22(1), 464–468 (1989).
[Crossref]

Jamieson, T. H.

T. H. Jamieson, “Thermal effects in optical systems,” Opt. Eng. 20(2), 156–160 (1981).
[Crossref]

Keblinski, P.

S. Shenogin, N. Raravikar, R. Ozisik, and P. Keblinski, “Using vibrational mode analysis for predicting the coefficient of thermal expansion of amorphous polymers,” J. Polym. Sci., B, Polym. Phys. 47(21), 2114–2121 (2009).
[Crossref]

Kim, J.-C.

J.-C. Kim and J.-H. Chang, “Quarternary copolyimides with various monomer contents: thermal property and optical transparency,” Macromol. Res. 22(11), 1178–1182 (2014).
[Crossref]

Kinjo, N.

S. Numata, K. Fujisaki, and N. Kinjo, “Re-examination of the relationship between packing coefficient and thermal expansion coefficient for aromatic polyimides,” Polymer (Guildf.) 28(13), 2282–2288 (1987).
[Crossref]

Kozaki, Y.

R. Ishige, T. Masuda, Y. Kozaki, E. Fujiwara, T. Okada, and S. Ando, “Precise analysis of thermal volume expansion of crystal lattice for fully aromatic crystalline polyimides by X-ray diffraction method: relationship between molecular structure and linear/volumetric thermal expansion,” Macromolecules 50(5), 2112–2123 (2017).
[Crossref]

Kurosawa, T.

T. Kurosawa, T. Higashihara, and M. Ueda, “Polyimide memory: a pithy guideline for future applications,” Polym. Chem. 4(1), 16–30 (2013).
[Crossref]

Laius, L. A.

A. I. Slutsker, L. A. Laius, I. V. Gofman, V. L. Gilyarov, and Y. I. Polikarpov, “Mechanisms of reversible thermal deformation of oriented polymers,” Phys. Solid State 43(7), 1382–1388 (2001).
[Crossref]

Malitson, I. H.

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” JOSA 55(10), 1205–1209 (1965).
[Crossref]

Masuda, T.

R. Ishige, T. Masuda, Y. Kozaki, E. Fujiwara, T. Okada, and S. Ando, “Precise analysis of thermal volume expansion of crystal lattice for fully aromatic crystalline polyimides by X-ray diffraction method: relationship between molecular structure and linear/volumetric thermal expansion,” Macromolecules 50(5), 2112–2123 (2017).
[Crossref]

Masuoka, H.

Y. Sato, Y. Yamasaki, S. Takishima, and H. Masuoka, “Precise measurement of the PVT of polypropylene and polycarbonate up to 330°C and 200 MPa,” J. Appl. Polym. Sci. 66(1), 141–150 (1997).
[Crossref]

Nagai, S.

Y. Wada, A. Itani, T. Nishi, and S. Nagai, “Grüneisen constant and thermal properties of crystalline and glassy polymers,” J. Polym. Sci 7(Part A-2), 201–208 (1969).

Neyertz, S.

S. Neyertz and D. Brown, “The effect of structural isomerism on carbon dioxide sorption and plasticization at the interface of a glassy polymer membrane,” J. Membr. Sci. 460, 213–228 (2014).
[Crossref]

Nishi, T.

Y. Wada, A. Itani, T. Nishi, and S. Nagai, “Grüneisen constant and thermal properties of crystalline and glassy polymers,” J. Polym. Sci 7(Part A-2), 201–208 (1969).

Numata, S.

S. Numata, K. Fujisaki, and N. Kinjo, “Re-examination of the relationship between packing coefficient and thermal expansion coefficient for aromatic polyimides,” Polymer (Guildf.) 28(13), 2282–2288 (1987).
[Crossref]

Oami, Y.

N. Sensui, J. Ishii, A. Takata, Y. Oami, M. Hasegawa, and R. Yokota, “Ultra-low CTE and improved toughness of PMDA/PDA polyimide-based molecular composites containing asymmetric BPDA-type polyimides,” High Perform. Polym. 21(6), 709–728 (2009).
[Crossref]

Okada, T.

R. Ishige, T. Masuda, Y. Kozaki, E. Fujiwara, T. Okada, and S. Ando, “Precise analysis of thermal volume expansion of crystal lattice for fully aromatic crystalline polyimides by X-ray diffraction method: relationship between molecular structure and linear/volumetric thermal expansion,” Macromolecules 50(5), 2112–2123 (2017).
[Crossref]

Ozisik, R.

S. Shenogin, N. Raravikar, R. Ozisik, and P. Keblinski, “Using vibrational mode analysis for predicting the coefficient of thermal expansion of amorphous polymers,” J. Polym. Sci., B, Polym. Phys. 47(21), 2114–2121 (2009).
[Crossref]

Polikarpov, Y. I.

A. I. Slutsker, L. A. Laius, I. V. Gofman, V. L. Gilyarov, and Y. I. Polikarpov, “Mechanisms of reversible thermal deformation of oriented polymers,” Phys. Solid State 43(7), 1382–1388 (2001).
[Crossref]

Ponting, M.

H. Fein and M. Ponting, “Analytical study of thermal invariance of polymeric nanolayer gradient index optical components,” Proc. SPIE 9822, 98220X (2016).
[Crossref]

Pottiger, M. T.

M. T. Pottiger, J. C. Coburn, and J. R. Edman, “The effect of orientation on thermal expansion behavior in polyimide films,” J. Polym. Sci., B, Polym. Phys. 32(5), 825–837 (1994).
[Crossref]

Raravikar, N.

S. Shenogin, N. Raravikar, R. Ozisik, and P. Keblinski, “Using vibrational mode analysis for predicting the coefficient of thermal expansion of amorphous polymers,” J. Polym. Sci., B, Polym. Phys. 47(21), 2114–2121 (2009).
[Crossref]

Rosenberg, A.

Saenger, K. L.

T. M. Tong, H. K. D. Hsuen, K. L. Saenger, and G. W. Su, “Thickness-direction coefficient of thermal expansion measurement of thin polymer films,” Rev. Sci. Instrum. 62(2), 422–430 (1991).
[Crossref]

Sato, Y.

Y. Sato, Y. Yamasaki, S. Takishima, and H. Masuoka, “Precise measurement of the PVT of polypropylene and polycarbonate up to 330°C and 200 MPa,” J. Appl. Polym. Sci. 66(1), 141–150 (1997).
[Crossref]

Sensui, N.

N. Sensui, J. Ishii, A. Takata, Y. Oami, M. Hasegawa, and R. Yokota, “Ultra-low CTE and improved toughness of PMDA/PDA polyimide-based molecular composites containing asymmetric BPDA-type polyimides,” High Perform. Polym. 21(6), 709–728 (2009).
[Crossref]

Shenogin, S.

S. Shenogin, N. Raravikar, R. Ozisik, and P. Keblinski, “Using vibrational mode analysis for predicting the coefficient of thermal expansion of amorphous polymers,” J. Polym. Sci., B, Polym. Phys. 47(21), 2114–2121 (2009).
[Crossref]

Shirk, J. S.

Simha, R.

R. K. Jain and R. Simha, “Theoretical equation of state: thermal expansivity, compressibility, and the Tait relation,” Macromolecules 22(1), 464–468 (1989).
[Crossref]

Slutsker, A. I.

A. I. Slutsker, L. A. Laius, I. V. Gofman, V. L. Gilyarov, and Y. I. Polikarpov, “Mechanisms of reversible thermal deformation of oriented polymers,” Phys. Solid State 43(7), 1382–1388 (2001).
[Crossref]

Su, G. W.

T. M. Tong, H. K. D. Hsuen, K. L. Saenger, and G. W. Su, “Thickness-direction coefficient of thermal expansion measurement of thin polymer films,” Rev. Sci. Instrum. 62(2), 422–430 (1991).
[Crossref]

Sugiura, K.

M. Hasegawa, T. Ishigami, J. Ishii, K. Sugiura, and M. Fujii, “Solution-processable transparent polyimides with low coefficients of thermal expansion and self-orientation behavior induced by solution casting,” Eur. Polym. J. 49(11), 3657–3672 (2013).
[Crossref]

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[Crossref]

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[Crossref]

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Appl. Opt. (1)

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[Crossref]

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[Crossref]

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Y. Terui and S. Ando, “Polarization dependence of thermo-optic coefficients in polyimide films originating from chain orientation and residual thermal stress,” J. Appl. Phys. 116(5), 053524 (2014).
[Crossref]

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[Crossref]

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[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Molecular structures of the monomers in this study.
Fig. 2
Fig. 2 Schematic representation of polyimide synthesis reactions.
Fig. 3
Fig. 3 Measured refractive index, n( T ), for mBAPS-BTDA. Solid circles: TE polarization. Open circles: TM polarization. The lines are linear least-squares fits to the data.
Fig. 4
Fig. 4 Lorentz-Lorenz function, L( T ), calculated from the data in Fig. 3 (circles), and the corresponding change in volume, ΔV/ V 0 (triangles), for mBAPS-BTDA. The lines are the respective linear least-squares fits.
Fig. 5
Fig. 5 The VCTE ( β ) vs. 1/ m * , where m * is the monomer molecular weight. The solid points are color coded to identify the dianhydride component of the amorphous polyimides studied here. The black open points are data for the crystalline polyimides previously reported by Ishige et al. [8], along with a corresponding least squares linear fit (black line).

Tables (4)

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Table 1 Average Refractive Index at 632.8 and 25°C for Polyimides in This Study

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Table 2 dn/dT (ppm/°C) at 632.8 for Polyimides in This Study, between 25 and 105°C

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Table 3 VCTE ( β ) (ppm/°C) for the Polyimides in This Study, between 25 and 105°C

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Table 4 ( 1/f )( df/dT ) (ppm/°C) for Polyimides in This Study, between 25 and 105°C

Equations (13)

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n a v e = ( 2 n T E 2 + n T M 2 ) / 3 .
L( T )= n 2 ( T )1 n 2 ( T )+2 =( 4π 3 N A α M )ρ( T ),
β= 1 V( T 0 ) ( ΔV ΔT ),
ρ( T 1 )= ρ( T 0 ) 1+βΔT ,
βΔT= ΔV V( T 0 ) = L( T 0 ) L( T 1 ) 1.
1 f =( n1 )( 1 R 1 1 R 2 ).
d( 1 f ) dT =( 1 R 1 1 R 2 )( dn dT ( n1 )( β/3 ) ).
1 f ( df dT )=( β/3 )( 1 n1 )( dn dT ).
dn dT = ( n 2 1 )( n 2 +2 ) 6n β.
1 f ( d f d T ) = ( n 3 + n 2 + 4 n + 2 n 4 + n 2 2 ) ( d n d T ) .
βγ C v,inter K,
C v,inter = 3 k B ρ m * ,
β3 k B ργK( 1 m * ).