. 1997 Mar-Apr;102(2):171–185. doi: 10.6028/jres.102.013

Table 1.

Correlation of Kauzmann temperatures T_K with Vogel-Fulcher T₀ to values for various substances

Substance	T_g^a	T_K	Ref.^b	T₀ (high)	T₀ (low)	Ref.	T_g/T₀	T_g/T_K	frag. m^c	(frag.)⁻¹ D	−logτ₀^d (−logη0) (−logD₀)	T_K/T₀
1-butene	58^a	48	¹	64(η)	[54(η)]	³¹	1.07	1.20				>0.88
2-methylpentane	78^a	58	²	59(η)	60+5 (η)	³², ³³	1.43	1.38	58			0.97
2-methylpentane	83			n-hex.
butyronitrile	100	81.2	³		58(τ_D)	³⁴	1.72	1.19	47	32	16	1.26↓
ethanol	95	71	⁴ ^b		70–75(τ_D)	³⁵	1.28	1.33			7	1.0
ethanol	90^a			80(τ_D)		³⁶	1.19			2.7	8.9	0.93↑
methanol	103	64±5	⁵, ⁶		60±15(τ_D)	^37(a)	1.71	1.61		12.4		1.06
methanol			⁹	66(D)		^37(b)				12.4	(7.1)	0.97
n-propanol	105	73	⁷	73.5(η)	73.5(τ_D)	³⁸	1.42	1.44	33		11.7	1.00↑
n-propanol	100^a				50.3(τ_D)	³⁶			40		12.4	1.45
toluene tol + 17% benzCl	126	96	⁸	103(η)	<108(τ_D)	^39(a)	>1.16	1.19		5.6	(3.5)	0.93
toluene tol + 17% benzCl	126			108(τ_D)	108(τ_D)	^39(b)	>1.16		107		13.0	~1.0
ethylene glycol (ethan diol)	153	115	⁹		109(τ_D)	⁴⁰	1.43	1.33		16	14.3	1.05
ethylene glycol (ethan diol)		119	¹⁰	125 (η)		⁴¹	1.22
1–3 prop. diol	154	109	¹⁰					1.41
1–3 prop. diol	145^a
1–2 prop diol (T_g=T_g(1·3)+18	172	109+18?	¹¹	109(η)	114(τ_H)	⁴²	1.57	1.41	52	17.8	14.6	1.11
1–2 prop diol (T_g=T_g(1·3)+18		(127)			122(τ_D)	⁴²			52	13.5	13.2	1.04
glycerol	193	135	¹² ^b		128(τ_H)	⁴²	1.51	1.43	53	19.5	15.6	1.04
	187				137(τ_H)	⁴⁴	1.41		53			0.99
					127(τ_D)	³⁸,⁹	1.52			12.7	14.6	1.07
					127(τ_D)	⁴⁵				8	33	1.07↓
				121(τ_D)		^45(b)						1.11
H₂SO₄·1H₂O	182	142	¹³ ^b	146(σ)		⁴⁶	1.25	1.28				0.97
H₂SO₄·2H₂O	169	131	¹³ ^b	120(σ)		⁴⁶	1.41	1.29				1.09
H₂SO₄·3H₂O	162	135	¹³ ^b	128(σ)		⁴⁶	1.27	1.20				1.05
H₂SO₄·3H₂O	155^a
H₂SO₄·4H₂O	157	133	¹³ ^b	136(η)		⁴⁶	1.15	1.18
H₂SO₄·4H₂O				136(σ)		⁴⁶						0.98
triphen.phosfite	205	166	¹⁴	183	186	³⁴	1.12	1.23	160	2.9	13.3	0.91
PMS (disiloxane)	165^a	137	^15(a)			⁴⁷		1.20
Salol	220^a	167	¹⁶		135(τ_H)	⁴⁸	1.63	1.31		38.7	24.5	1.24↓
Salol		157	¹⁷,⁴⁸		141(τ_D)	⁴⁸	1.56	1.40		33	23.3	1.11↓
orthoterphenyl and otp + 16% opp	244	200	¹⁸		184(τ_H)	^49(a)	1.33	1.22			17.7	1.09↓
					196(η)	¹⁷, ³²	1.26	1.26	81^c			1.04
					193(η)	⁵⁰
dibutyl phthallate1 (uncrystallizable)	179		¹⁹	151(η)	151(η)	⁵¹	1.18				(3.6)
dibutyl phthallate1 (uncrystallizable)					137(τ_D)	³², ^49(b)	1.30		69		14
m-toluidinc	187	151	¹⁴,^8(b)		153(τ_D)	^8(b)			79		13	1.00
m-toluidinc		157	^15(b)
propylene carbonate	156	125.8	²⁰		130(τ_D)	⁵²	1.20	1.23	104	2.9	13.1	0.97
propylene carbonate		128	^52b		132.3(τ_D)	³⁶						0.95
Ca(NO₃)₂·4H₂O	217	200	²¹	205(η)		⁵³		1.09				0.98
		204	²²		190(η)	⁵⁴	1.14					1.05
				201(σ)		⁵⁵	1.08					1.0
Cd(NO₃)₂·4H₂O	213	198	²¹			⁵⁶		1.08
fructose	286	210	¹⁴		206(τ_E)	⁵⁷	1.39	1.36			13.5	1.02
glucose	306	271^a	²³		231	⁵⁸	1.32	1.13				1.17
glucose					259(τ_D)	⁴³		1.18			12	1.05
mannitol	282	236	⁹, ²⁴
sorbitol (dulcitol)	266	236?	²⁴	212(η)		⁵⁹		1.13	93	8.6		1.11
sorbitol (dulcitol)		217	²⁴		224(τ_D)	⁹	1.19	1.23		7.8	14.3	1.05
sucrose	323	283	²⁵		290	⁵⁸	1.11	1.14		0.154		0.98
sucrose		287	¹⁴					1.125
trehalose	388		¹⁴			⁵⁷					13.5
phenolphtalein	363	310	¹⁴		274(τ_E)	⁵⁷	1.32	1.17			13.5	1.13
selenium	307	240±10	²⁶		251(η)	³²,⁶³	1.22	1.28	87^c			1.04
ZnCl₂	380	250±25	²⁷	260(η)		⁶⁰	1.46	1.52				0.96
					180(τ₁)	³²,⁶⁴			30^c		14	1.39
					236(τ_V)	³²,⁶⁵	1.61		42.5^c		14	1.06
Li acetate	401	381^e	²⁸	371(σ)		⁶¹	1.08	1.05^a			14	1.03
As₂S₃	455	265	²⁶		237(τ_h)	⁴⁴	1.82	1.93			18.7	1.00↓
La₂O·2B₂O₃	959	845	²⁹	864	850(η)	²⁹	1.12	1.13				0.99
CaAl₂Si₂O₈	1118	815	³⁰		805(η)	⁶²	1.39	1.37				1.01

T_g value based on the onset C_p from adiabatic calorimetry, which is several degrees lower than scanning calorimetry or DTA-based values because of the much longer time scale. T_g/T_K values are based on 10 K/min DSC or DTA data for T_g.

Indicates that the assessment of T_K will not be found in the calorimetry paper cited, but rather in one of the authors articles, or students’ thesis.

C. A. Angell and W. Sichina, Ann. N.Y. Acad. Sci. Vol. 279 (1976) p. 53.
E. J. Sare, Ph. D. thesis, Purdue Univ. (1970).
D. L. Smith, Ph. D. thesis, Purdue Univ. (1983).

Many values of m, defined as the slope of a Fig. 6 type plot at T_g/T = 1, are compiled in R. Bohmer, K. L. Ngai, C. A. Angell, and D. J. Plazek, J. Chem. Phys. 99 (5), 4201–4209 (1993). Where the m value is used to obtain T₀ via Ref. 32, the superscript c is attached to the m value. Such T₀ values are associated with −logτ₀ of 14 by assignment.

−logτ₀ is the value of τ₀ which is the best fit value for the T₀ value cited. If −logτ₀ is numerically larger than the physical value of 14 (phonons), then the T₀ value should be weighted up, and therfore T_K/T₀ should be weighted down. Where this is an important effect, the value of T_K/T₀ is tagged ↑ or ↓ to indicate the need for adjustment. For viscosity, the equivalent value of −log(η₀/P) is 3.5 and for diffusivity −log(D₀/m²s⁻¹) is 7.55. For cases in which T₀ is obtained from an m value via Ref. 32, the value of −logτ₀ is 14 by assignment.

Unpublished data (Sichina and Angell) suggest this estimate of T_K is too high, that ΔC_p passes through a maximum and T_K retreats to ~ 360 K.

σ: T₀ value from conductivity.
η: T₀ value from viscosity measurements.
τ_D: T₀ value from dielectric relaxation measurements.
τ_E: T₀ value from tensile stress relaxation measurements and assignment τ0 = 10^–13.5 s.
τ_H: T₀ value from ac heat capacity measurements.
τ_L: T₀ value from longitudinal relaxation time from digital correlation spectroscopy.
τ_h: T₀ value from Sherer-Hodge T_g analysis Ref. 44.
τ_V: T₀ value from volume relaxation activation energy at T_g and Ref. 32.

References to Table

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D. R. Douslin and H. M. Huffmann, J. Am. Chem. Soc. 68, 1704 (1946).

M. Oguni, H. Hikawa, and H. Suga, Thermochim. Acta 158, 143 (1990).

⁴

O. Haida, H. Suga and S. Seki, J. Chem. Thermodyn. 9, 1113 (1979).

⁵

M. Sugisaki, H. Suga and S. Seki, Bull. Chem. Soc. Jpn. 41, 2586, 2591 (1968).

⁶

E. J. Sare, unpublished work.

⁷

J. F. Counsell, E. B. Lees, and J. F. Martin, J. Chem. Soc. (A), 1819 (1968) (Analysis by D. L. Smith).

⁸

(a) C. Alba, L. E. Busse, and C. A. Angell, J. Chem. Phys. 92, 617–624 (1990).

(b) C. Alba-Simionesco, A. Vessal, J. Fan, and C. A. Angell, J. Chem. Phys. (in press).

⁹

C. A. Angell and D. L. Smith, J. Phys. Chem. 86, 3845 (1982).

¹⁰

K. Takeda, O. Yamanamuro, I. Tsukushi, and T. Matsui, Fluid Phase Equilibria (in press); private communication.

¹¹

D. L. Smith, unpublished work.

¹²

G. E. Gibson and W. F. Giauque, J. Am. Chem. Soc. 45, 93 (1923).

¹³

J. E. Kunzler and W. F. Gianque, J. Am. Chem. Soc. 74, 797 (1952).

¹⁴

J. Fan, Ph.D. thesis, Arizona State Univ. (1995).

¹⁵

(a) H. Fujimori, M. Mizukami, and M. Oguni (to be published).

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¹⁶

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¹⁷

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¹⁸

S. S. Chang and A. B. Bestul, J. Chem. Phys. 56, 503 (1972); R. J. Greet and D. Turnbull, J. Chem. Phys. 47, 2185 (1967).

¹⁹

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²⁰

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²¹

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²²

X. Yu and L. Heppler et al., J. Chem. Thermodyn. 25, 191 (1992).

²³

W. Kauzmann, Chem. Rev. 43, 219 (1948).

²⁴

W. Sichina and C. A. Angell, unpublished work.

²⁵

Cited in Ref. 58.

²⁶

S. S. Chang and A. B. Bestul, J. Chem. Thermodyn. 6, 325 (1974).

²⁷

C. A. Angell, E. Williams, K. J. Rao, and J. C. Tucker, J. Phys. Chem. 81, 238 (1977).

²⁸

Chap. 1 in Glass: Structure by Spectroscopy, J. Wong and C. A. Angell, eds., Marcel Dekker, New York, New York (1976).

²⁹

C. A. Angell, C. A. Scamehorn, D. L. List, and J. Kieffer, eds., Proceedings of the XVth International Congress on Glass, O.V. Mazurin, Leningrad, NAVKA (1989) p. 204.

³⁰

P. Richet, Geochim. Cosmochim. Acta. 48, 471 (1984).

³¹

Y. Takeda, O. Yamamuro, and H. Suga, J. Phys. Chem. Sol. 52, 607 (1991); M. Oguni (private communication).

³²

T₀ obtained from the slope of the T_g-scaled Arrhenius plot, called fragility m, and its relation to T₀ and T_g. T₀ = T_g (1 – 16/m) for relaxation times, which presumes logτ₀ = 14, and T₀ = T_g (1 – 17/m) for viscosity. See Roland Böhmer and C. A. Angell, Phys. Rev. B. 45, 10091 (1992). Many values of m are collected in R. Böhmer, K. L. Ngai, C. A. Angell and D. J. Plazek, J. Chem. Phys. 99, 4201 (1993).

³³

A. C. Ling and J. E. Willard, J. Phys. Chem. 72, 1918 (1968); m = 58; also see Fig. 6 of Ref. 8. The value T₀ = 59 K is reported for viscosity fits of the unbranched isomer hexane, by O. G. Lewis, J. Chem. Phys. 43, 2693 (1965).

³⁴

B. Schiener, A. Loidl, R. V. Chamberlin, and R. Böhmer, J. Mol. Liq. 69, 243 (1996).

³⁵

D. L. Smith and C. A. Angell, unpublished data on ethanol-methanol mixtures.

³⁶

F. Stickel, E. W. Fischer, R. Richert, J. Chem. Phys. 104, 2043 (1996).

³⁷

(a) D. L. Denney and R. H. Cole, J. Chem. Phys. 23, 1767 (1955) and D. L. Smith and C. A. Angell, unpublished data on ethanol-methanol mixtures.

(b) N. Karger, T. Vardag, and H.-D. Lüdemann, J. Chem. Phys. 93, 3437 (1990).

³⁸

D. W. Davidson and R. H. Cole, J. Chem. Phys. 19, 1484 (1951).

³⁹

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⁴⁰

B. Schiener and R. Böhmer, J. Non-Cryst. Sol. 182, 180 (1995).

⁴¹

From data tabulated in Ref. 9.

⁴²

N. O. Birge, Phys. Rev. B 34, 1631 (1986).

⁴³

S. Matsuoko, G. Williams, G. E. Johnson, E. W. Anderson, and T. Furukawa, Macromolecules 18, 2652 (1985).

⁴⁴

I. M. Hodge, J. Non-Cryst. Sol. 169, 211 (1994); Table 2.

⁴⁵

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(b) H. Z. Cummins et al., Phys. Rev. Lett. 73, 2935 (1994).

⁴⁶

E. J. Sare, Ph. D. thesis, Purdue University (1970).

⁴⁷

Fujimori and M. Oguni (private communication).

⁴⁸

P. K. Dixon, Phys. Rev. B. 42, 8179 (1990).

⁴⁹

(a) P. K. Dixon and S. R. Nagel, Phys. Rev. Lett. 61, 341 (1988) (o-terphenyl + 9 %; o-phenylphenol, m = 81).

(b) T₀ = T_g(1 – 16/m), see Ref. 32.

⁵⁰

G. Williams and P. J. Hains, Faraday Symp. Chem. Soc. No. 6, 14 (1972).

⁵¹

A. J. Barlow, J. Lamb, and A. J. Matheson, Proc. Roy. Soc. A 292, 322 (1966).

⁵²

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⁵³

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⁵⁴

J. H. Ambrus, C. T. Moynihan, and P. B. Macedo, J. Electrochem Soc. 119, 192 (1972).

⁵⁵

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⁵⁶

C. T. Moynihan, C. R. Smalley, C. A. Angell, and E. J. Sare, J. Phys. Chem. 73(6), 2287 (1969).

⁵⁷

E. Sanchez and C. A. Angell (to be published).

⁵⁸

A. B. Bestul and S. S. Chang, in Proceedings III International Congress on Glass, Venezia, 1953, A. Garzanti, ed., Nello Stabilimento Grafico Di Roma Della, Rome (1954) p. 26.

⁵⁹

C. A. Angell, R. Stell, and W. J. Sichina, J. Phys. Chem. 86, 1540 (1982).

⁶⁰

A. J. Easteal and C. A. Angell, J. Chem. Phys. 56, 4231 (1972).

⁶¹

C. A. Angell and W. Sichina, Ann. N.Y. Acad. Sci. Vol. 279 (1976) p. 53, for fragility (D) and Ref. 32.

⁶²

P. Richet and Y. Bottinga, Earth Plan. Sci. Lett. 67, 415 (1984).

⁶³

M. Tatsumisago, B. L. Halfpap, J. L. Green, S. M. Lindsay, and C. A. Angell, Phys. Rev. Lett. 64, 1549 (1990).

⁶⁴

G. Fytas, G. N. Papatheodorou and E. A. Pavlatou, see Ref. 32.

⁶⁵

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