Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol

Experimental data on the thermal conductivity κ(T) of some simple alcohols have been compared, analyzed and generalized. The objects of investigation were methyl, protonated and deuterated ethyl, 1-propyl and 1-butyl alcohols in the thermodynamically equilibrium phase with a complete orientational o...

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Datum:	2011
1. Verfasser:	Korolyuk, O.A.
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spelling	irk-123456789-1185472017-05-31T03:03:50Z Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol Korolyuk, O.A. 8th International Conference on Cryocrystals and Quantum Crystals Experimental data on the thermal conductivity κ(T) of some simple alcohols have been compared, analyzed and generalized. The objects of investigation were methyl, protonated and deuterated ethyl, 1-propyl and 1-butyl alcohols in the thermodynamically equilibrium phase with a complete orientational order. The temperature interval was from 2 K to the melting point under the equilibrium vapor pressure. It is found that in the region above the temperature of the maximum thermal conductivity κ(T) deviates from the 1/Т law. This is because the total thermal conductivity has an extra contribution κII(T) of short-lived phonons in addition to κI(T) contributed by propagating phonons: κ(T) = κI(T) + κII(T). The contribution κI(T) is well described by the Debye–Peierls model allowing for the phonon–phonon processes and scattering of phonons by dislocations. At Т > 40 K the contribution κI(T) obeys the law A/Т and κII(T) is practically temperature-independent. It is shown that the Debye temperature ΘD of alcohol is dependent on the molecular mass as ΘD = 678М⁻⁰.⁴² K and the coefficient А characterizing the intensity of the phonon–phonon scattering increases with the molecular mass of the simple monoatomic alcohol by the law А = 0.85М⁰.⁸ W/m, which suggests a decreasing intensity of the phonon–phonon process. 2011 Article Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol / O.A. Korolyuk // Физика низких температур. — 2011. — Т. 37, № 5. — С. 526–530. — Бібліогр.: 29 назв. — англ. 0132-6414 PACS: 66.70.–f, 63.20.–e http://dspace.nbuv.gov.ua/handle/123456789/118547 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals
spellingShingle	8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals Korolyuk, O.A. Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol Физика низких температур
description	Experimental data on the thermal conductivity κ(T) of some simple alcohols have been compared, analyzed and generalized. The objects of investigation were methyl, protonated and deuterated ethyl, 1-propyl and 1-butyl alcohols in the thermodynamically equilibrium phase with a complete orientational order. The temperature interval was from 2 K to the melting point under the equilibrium vapor pressure. It is found that in the region above the temperature of the maximum thermal conductivity κ(T) deviates from the 1/Т law. This is because the total thermal conductivity has an extra contribution κII(T) of short-lived phonons in addition to κI(T) contributed by propagating phonons: κ(T) = κI(T) + κII(T). The contribution κI(T) is well described by the Debye–Peierls model allowing for the phonon–phonon processes and scattering of phonons by dislocations. At Т > 40 K the contribution κI(T) obeys the law A/Т and κII(T) is practically temperature-independent. It is shown that the Debye temperature ΘD of alcohol is dependent on the molecular mass as ΘD = 678М⁻⁰.⁴² K and the coefficient А characterizing the intensity of the phonon–phonon scattering increases with the molecular mass of the simple monoatomic alcohol by the law А = 0.85М⁰.⁸ W/m, which suggests a decreasing intensity of the phonon–phonon process.
format	Article
author	Korolyuk, O.A.
author_facet	Korolyuk, O.A.
author_sort	Korolyuk, O.A.
title	Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol
title_short	Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol
title_full	Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol
title_fullStr	Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol
title_full_unstemmed	Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol
title_sort	thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2011
topic_facet	8th International Conference on Cryocrystals and Quantum Crystals
url	http://dspace.nbuv.gov.ua/handle/123456789/118547
citation_txt	Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol / O.A. Korolyuk // Физика низких температур. — 2011. — Т. 37, № 5. — С. 526–530. — Бібліогр.: 29 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT korolyukoa thermalconductivityofmolecularcrystalsofmonoatomicalcoholsfrommethanoltobutanol
first_indexed	2025-07-08T14:13:14Z
last_indexed	2025-07-08T14:13:14Z
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fulltext	© O.A. Korolyuk, 2011 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5, p. 526–530 Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol O.A. Korolyuk B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkov 61103, Ukraine E-mail: korolyuk@ilt.kharkov.ua Received December 10, 2010 Experimental data on the thermal conductivity κ(T) of some simple alcohols have been compared, analyzed and generalized. The objects of investigation were methyl, protonated and deuterated ethyl, 1-propyl and 1-butyl alcohols in the thermodynamically equilibrium phase with a complete orientational order. The temperature inter- val was from 2 K to the melting point under the equilibrium vapor pressure. It is found that in the region above the temperature of the maximum thermal conductivity κ(T) deviates from the 1/Т law. This is because the total ther- mal conductivity has an extra contribution κII(T) of short-lived phonons in addition to κI(T) contributed by propa- gating phonons: κ(T) = κI(T) + κII(T). The contribution κI(T) is well described by the Debye–Peierls model allow- ing for the phonon–phonon processes and scattering of phonons by dislocations. At Т > 40 K the contribution κI(T) obeys the law A/Т and κII(T) is practically temperature-independent. It is shown that the Debye temperature ΘD of alcohol is dependent on the molecular mass as ΘD = 678М –0.42 K and the coefficient А characterizing the intensity of the phonon–phonon scattering increases with the molecular mass of the simple monoatomic alcohol by the law А = 0.85М 0.8 W/m, which suggests a decreasing intensity of the phonon–phonon process. PACS: 66.70.–f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves; 63.20.–e Phonons in crystal lattices. Keywords: thermal conductivity, crystals, simple monoatomic alcohols, phonon–phonon scattering, orientational ordering. Introduction The temperature dependence of the thermal conductivity of simple dielectrically-perfect crystals with orientational degrees of freedom usually has the shape of bell. The ther- mal conductivity in the low-temperature region of the curve is determined by the grain-boundary scattering of phonons and obeys the law Т3 [1]. As the temperature rises, a maxi- mum of thermal conductivity appears in the curve, its height being dependent on the crystal quality. On further heating, the thermal conductivity decreases exponentially and finally changes to the law 1/Т (e.g., see [2–7]). This law is deter- mined by the processes of phonon–phonon scattering. In addition to acoustic phonon modes, molecular crys- tals with several molecules per unit cell also have localized short-wavelength vibrational modes which can cross the acoustic branches. This influences the temperature beha- vior of the thermal conductivity in the region above the temperature of the phonon maximum. It has been shown recently that localized short-wavelength vibrational modes are considerably important for the thermal conductivity of simple molecular orientationally-ordered hydrogen-bonded crystals under the equilibrium pressure [8]. The thermal conductivity investigated [8] in three simple monoatomic alcohols in the orientationally-ordered phase exhibited a deviation from the law A/Т in the high-temperature region (А is a coefficient characterizing the intensity of phonon– phonon scattering, which is dependent on the number of C atoms in the alcohol molecule). The law A/T cannot de- scribe the behavior of the isochoric thermal conductivity of cryocrystals [9]. Primary monoatomic alcohols are organic compounds consisting of a carbon skeleton with a hydroxyl group OH at its end. The alcohol molecule is “flexible” as to the bond length between the carbon skeleton and the hydroxyl group and the angle between the carbon skeleton and the OH group. Such flexibility is an additional source of low- energy intramolecular local vibrations in the alcohol crys- tal [10]. Simple monoatomic alcohols are very interesting objects to investigate, especially ethyl alcohol which exhi- bits rich polymorphism in the condensed phase [10–12]. Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 527 Fig. 1. The temperature dependences of the thermal conductivity of methyl [15], deuterated ethyl [19], and 1-butyl [16] alcohols in the orientationally-ordered phase. The dependence А/Т + С for the crystal 1-butanol at T > 40 K (black thick line) along with the dependence А/Т (red line) for coefficients А = 28.0 W/m and С = 0.32 W/(m⋅K) are illustrated in this picture. 1 10 100 0,1 1 Deuterated ethanol 1-butanol methanol T, K T 2 A T C/ + A T/ � � , W /( m K ) On cooling primary alcohols are readily supercooled and form glasses. The thermal conductivity in such glasses demonstrate rather unusual behavior. For example, at low temperatures it is dependent on the number of C atoms in the alcohol molecule [13]. On crystallization into the orien- tationally-ordered phase, the molecules of a monoatomic alcohol form a chain-like structure due to the H bonds. This study presents a detailed analysis of the thermal conductivity of molecular crystals of monoatomic orien- tationally-ordered alcohols in the series from methanol to 1-butanol including deuterated ethanol. The general regu- larities of the temperature dependence of the thermal con- ductivity have been revealed for molecular crystals of orientationally-ordered alcohols. It is shown that the coef- ficient А characterizing the intensity of phonon–phonon scattering increases almost linearly with the molecular mass of the simple monoatomic alcohol. Experiment and discussion The thermal conductivity of crystalline alcohols was measured under the equilibrium vapor pressure in the setup developed by [14] using the flat steady — state potenti- ometric method at temperatures from 2 K to the melting point Tm. The sample preparation is detailed elsewhere [8,15,16]. The deuterated C2D5OD alcohol (D purity was 99%, anhydrous) was supplied by Cambridge Isotope La- boratories, Inc. The concentration of hydrogen isotopic defects was 1%. The crystals of protonated and deuterated ethyl, 1-propyl and 1-butyl alcohols in completely orienta- tionally-ordered thermodynamically-equilibrium phase were obtained from the glass state by gradual heating through several successive metastable states. Each sample was long-annealed near Tm. The thermal conductivity was investigated for two methanol samples [15], one high qual- ity sample of hydrogenated ethanol [8] and some middle quality samples of hydrogenated ethanol [17], one sample of 1-propanol [18], one sample of 1-butanol [16], and four samples of deuterated ethanol [19]. The measured temperature dependences of the orienta- tionally-ordered crystals of methanol [15], deuterated etha- nol [19] and 1-butanol [16] are illustrated in the double logarithmic coordinates in Fig. 1. The curves have the bell- like shape typical of orientationally-ordered crystals. They have a distinct phonon-induced maximum of κ(T) at T = 14.2 K in deuterated ethanol, T = 17.1 K in methanol and T = 28 K in 1-butanol. Deuterated ethanol and 1-bu- tanol have close maximal thermal conductivities. The max- imal thermal conductivity of methanol is somewhat lower, which indicates a worse quality of the crystal. Below ph maxT the thermal conductivity of the alcohols is close to the qu- adratic temperature dependence which corresponds to the processes of phonon scattering at dislocations. Above ph maxT the thermal conductivity of the alcohols decreases with the temperature rise. This corresponds to the effective processes of phonon–phonon scattering [8,15]. In 1-butyl alcohol the thermal conductivity is the lowest at low tem- peratures and the highest at high temperatures. Above T = 40 К the thermal conductivity deviates obviously from the expected dependence 1/Т. It is seen that in this temper- ature region the heat transport is effected not only through the phonon–phonon mechanism of heat dissipation follow- ing the dependence 1/Т but is contributed by an additional mechanism independent of temperature. On this basis the temperature dependence of the thermal conductivity κ(T) can be presented as a sum [8] κ(T) = А/Т + С. (1) The first term А/Т characterizes the resistive processes of phonon–phonon scattering. The term С refers to the addi- tional mechanism of heat transport by localized short-wa- velength vibrational modes, or phonons whose mean free path is comparable with the phonon half-wavelength. The dependence А/Т + С for the crystal 1-butanol at T > 40 K (black thick line) along with the dependence А/Т (red line) for coefficients А = 28.0 W/m and С = 0.32 W/(m⋅K) are illustrated in Fig. 1. Table 1 carries the coefficients А and С of Eq. (1) for some simple alcohols along with their molar masses, spatial symmetry groups, melting temperatures Tm, Debye tempera- tures ΘD and the coefficients CD at Т3 derived from heat capacity data. ΘD of some crystals of simple monoatomic alcohols were calculated using the coefficient CD at Т3 ob- tained by the Spanish researchers investigating the heat ca- pacity of alcohols [12,20]. Coefficients A for 1-butanol and methanol were obtained with accuracy 3–4% and for deu- terated ethanol accuracy of coefficient A is 9%. O.A. Korolyuk 528 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 Fig. 2. The Debye temperature ΘD of simple monoatomic alco- hols as a function of the mass of the alcohol molecule. The line illustrates the dependence ΘD = 678М –0.42 K. 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 M, g/mol � D , K Table 1. The molar mass M, melting temperature Tm, Debye temperature ΘD, coefficient CD at Т3 obtained from heat capacity data for alcohols [12,20], spatial symmetry groups of orientationally-ordered crystals and the coefficients А and С for 1-butanol (this study), deuterated ethanol [19], methanol, protonated ethanol and 1-propanol [8] * — extrapolation As the mass of the alcohol molecule increases, the coef- ficient С has nonmonotonic dependence, the coefficient А increases, which points to a reduction of the phonon– phonon scattering intensity. The second temperature-independent contribution in Eq. (1) can be described by the phenomenological Cahill– Pohl model [26], which assumes that in the approximation of the Debye phonon spectrum of the isotropic medium (the difference in the polarizations of the phonon modes is disregarded) the shortest lifetime of each vibration is equal to its half-period τ = π/ω [26]. Traditionally, the temperature dependence of thermal conductivity is described quite accurately by the Debye– Peierls model of an isotropic solid. Using this model the expression κ(T) = κI(T) + κII(T) can be obtained conceiv- ing the effective κ(T) as a sum of the contribution κI(T) of the phonons inducing resistive scattering and κII(T) of the phonons whose mean free path is equal to the phonon half- wavelength (the so-called localized short-wavelength vi- brational modes in the Cahill–Pohl model). The thermal conductivity of the methanol–1-butanol se- ries of alcohols in the orientationally-ordered phase was thus separated into two constituents κI(T) and κII(T). The component κII was calculated within the Cahill–Pohl mod- el by Eq. (3) of Ref. 8 for the whole temperature interval. The contribution κII is rather insignificant at low tempera- tures but it increases with a rising temperatures and be- comes determining at high temperatures. It accounts for the high-energy excitations that are thermally activated above 40 K. κII(T) of deuterated ethanol and 1-butanol was calcu- lated using the ΘD data of Table 1 and sound velocities v obtained from the ΘD data allowing for the density ρ: ρ = 1213 kg/m3 [25], v = 1795 m/s in deuterated ethanol and ρ = 1318.5 kg/m3 [23], v = 1704 m/s in 1-butanol. The dependence of the Debye temperature ΘD of some monoatomic alcohols on the molecular mass is shown in Fig. 2 in the double logarithmic coordinates. Unfortunate- ly, there are no direct data on the Debye temperature of methanol. ΘD = 106 K was estimated [15] from the longi- tudinal sound velocity [27]. Nevertheless, the ΘD values obtained for other alcohols fall quite accurately on the de- pendence ΘD = 678М –0.42 K, which makes it possible to extrapolate ΘD = 158 K for methanol. The dependence of ΘD on the mass of the molecule agrees with the depen- dence ΘD ~ M –1/2 in [10]. The decrease in ΘD with the increasing molecular mass indicates that the frequency interval of the acoustic modes reduces. In the investigated series of alcohols the region of acoustic frequencies was the largest in the methanol crystal and the smallest in 1-bu- tanol. This refers to the effective spectrum of vibrational states in the Debye model. As the number of C atoms in the alcohol molecule increases, the crossing of the local and acoustic modes occurring in alcohols with a small number of C atoms in the molecule [10] shifts gradually beyond the acoustic frequency region because the acoustic region reduces. This is one of the factors suppressing the intensity of phonon–phonon scattering when the mass of the alcohol molecule increases. The phonon contribution κI was obtained as a differ- ence between the measured total thermal conductivity κ(T) and the component κII. At high temperatures κI(T) obeys the law 1/Т. The component κI was then compared with the value calculated within the Debye–Peierls relaxation mod- el using Eq. (2) of Ref. 8 allowing for the resistive U-pro- Alcohol M, g/mol А, W/m С, W/(m⋅K) Space groups Tm, K CD, mJ/(mol⋅K4) ΘD, K Methanol 32.04 14.2 0.24±0.01 P212121 orthorhombic [21] 175.37 [21] 158 * 106 [15] Ethanol-Н 46.07 16.9 0.16±0.01 Pc monoclinic [24] 159 [11] 0.766 [12] 136 Ethanol-D 52.11 20.1 0.18±0.01 Pc monoclinic [25] 159 [12] 0.906 [12] 129 1-Propanol 60.09 21.6 0.10±0.01 P21/m monoclinic [22] 148 [12] 1.10 [12] 121 1-Butanol 74.12 28.0 0.32±0.01 triclinic [23] 183.5 [23] 1.40 [20] 112 [20] Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 529 Fig. 3. The coefficient А as a function of the molar mass of sim- ple alcohols: experiment (○), literature data for N2 (Ú) [4]. Theory of phonon–phonon scattering: molecular crystals [7] (see Eq. (2)) (Δ); atomic crystals [29] (see Eq. (3)) (■); solid line — dependence А = 0.85М 0.8 W/m. 30 40 50 60 70 80 90 N2 CH OH3 C H OH2 5 C D OH2 5 C H OH3 7 A M= 0.85 W/m 0.8 C H OH4 9 10 100 M, g/mol A , W /m cesses of phonon scattering and also allowing for scatter- ing by dislocations. The relaxation rate of phonons causing resistive scattering 1 I −τ is assumed to obey the Matthiesen rule and, therefore, can be written as a sum of rates representing different processes 1:i −τ 1 1 I ( , ) ( , ).i i T T− −τ ω = τ ω∑ For an ordered crystal, the dominant mechanisms able to scatter heat-carrying phonons will concern anharmonic Umklapp processes with a rate 1,U −τ and scattering by dis- locations 1 dis.−τ Relevant expressions for all the scattering processes are given by 1 2 1 dis dis( , ) exp( / ), ( , ) ,U UT B T E T T D− −τ ω = ω − τ ω = ω where B is the frequency factor, EU is the activation energy for the U-processes, and Ddis is the dislocation scattering strength. It is found that the Debye–Peierls model de- scribes the phonon component κI(T) of the investigated alcohols quite accurately. At high temperatures the intensity of the phonon–pho- non processes in crystals is characterized by the coefficient А of Eq. (1) which can be estimated proceeding from the theory of phonon–phonon scattering. Knowing the melting temperature the coefficient А of molecular crystals can be calculated by Slack’s [28] formula as [7] 1/32 22 , 6 B D m AT N A M κ Θ ρ⎛ ⎞ = ⎜ ⎟ π⎝ ⎠ (2) where NA is the Avogadro constant. The coefficient А for cubic atomic crystals with n > 2 atoms per unit cell can be calculated by Slack’s equation [29]: 1/37 3 2 2/3 3 10 ,D A M MA Nn ⎛ ⎞⋅ Θ = ⎜ ⎟ργ ⎝ ⎠ (3) where γ is the Grüneisen constant equal to γ = 2.5 for the investigated crystals with n = 4 for methanol, ethanol and 1-butanol [21–23], and n = 6 for 1-propanol [24]. The de- pendence of the coefficient А upon the mass of a simple monoatomic alcohol molecule is illustrated in Fig. 3 in the double logarithmic coordinates (experimental results and calculation by Eqs. (2), (3)). It is seen that the coefficient А increases almost linearly with the molar mass of simple alcohols and falls quite well on the dependence А = = 0.85М 0.8 W/m. The theory of phonon–phonon processes does not describe the behavior of the coefficient А particu- larly in the case of low molar masses. The discrepancy between theory and experiment reduces as the molar mass increases. Equation (2) describes the experimental results more accurately than Eq. (3). The growth of the coefficient with the mass of the alcohol molecule implies that at high temperatures the thermal conductivity increases with the mass of the alcohol molecule. Hence, the intensity of pho- non–phonon scattering decreases. For comparison, Fig. 3 carries the coefficient A obtained from the thermal conduc- tivity data for nitrogen [4] in the orientationally-ordered phase. This value cannot be described by the above А-vs- mass dependence. Conclusions The data on the thermal conductivity of a series of sim- ple monoatomic alcohols from methanol to 1-butanol in the crystalline phase with a complete orientational order under equilibrium pressure have been analyzed. It is found that above the temperature of the maximum thermal con- ductivity κ(T) deviates from the expected law 1/Т, which follows from anharmonic interactions of acoustic excita- tions. The deviation is due to the contribution κII(T) of short-lived phonons, which appear in the total thermal conductivity in addition to the contribution κI(T) of propa- gating phonons: κ(T) = κI(T) + κII(T). The additional κII(T) is due to localized short-wavelength vibrational modes in the Cahill–Pohl model. It is shown that the Debye tempera- ture ΘD is dependent on the mass of the alcohol molecule as ΘD = 678М –0.42 K and the coefficient А characterizing the intensity of phonon–phonon scattering increases with the molar mass of the simple monoatomic alcohol follow- ing the law А = 0.85М 0.8 W/m, which corresponds to a decrease in the intensity of the phonon–phonon scattering. This behavior is due to the fact that in alcohol crystals with an orientational order acoustic phonons modes are hybri- dized with localized short-wavelength vibrational modes. The author is grateful to A.I. Krivchikov and I.V. Sha- rapova for the helpful and fruitful discussion and assis- tance in the preparation of the paper. O.A. Korolyuk 530 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 1. O.A. Korolyuk, A.I. Krivchikov, and B.Ya. Gorodilov, J. Low Temp. Phys. 122, 203 (2001). 2. R. Berman, Thermal Conduction in Solids, Clarendon press, Oxford (1976). 3. L.A. Koloskova, I.N. Krupskii, V.G. Manzhelii, and B.Ya. 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Thermal conductivity of molecular crystals of monoatomic alcohols: from methanol to butanol

Institution

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