Heat transfer in solid methyl alcohol

Thermal conductivity coefficient к(T) of two crystalline (orientationally-ordered and orientationally-disordered) phases of pure methanol (at temperatures from 2 K to Tm , Tm is the melting temperature), CH₃OH + 6.6 % H₂O glass from 2 K to Tg , Tg is the glass transition temperature and a supercoole...

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Hauptverfasser: Korolyuk, O.A., Krivchikov, A.I., Sharapova, I.V., Romantsova, O.O.
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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-117111
record_format dspace
spelling Korolyuk, O.A.
Krivchikov, A.I.
Sharapova, I.V.
Romantsova, O.O.
2017-05-19T19:26:01Z
2017-05-19T19:26:01Z
2009
Heat transfer in solid methyl alcohol / O.A. Korolyuk, A.I. Krivchikov, I.V. Sharapova, O.O. Romantsova // Физика низких температур. — 2009. — Т. 35, № 4. — С. 380-384. — Бібліогр.: 34 назв. — англ.
0132-6414
PACS: 66.70.–f, 63.20.–e, 63.50.–x
https://nasplib.isofts.kiev.ua/handle/123456789/117111
Thermal conductivity coefficient к(T) of two crystalline (orientationally-ordered and orientationally-disordered) phases of pure methanol (at temperatures from 2 K to Tm , Tm is the melting temperature), CH₃OH + 6.6 % H₂O glass from 2 K to Tg , Tg is the glass transition temperature and a supercooled liquid from Tg to 120 K has been measured under equilibrium vapor pressure. The dependence к(T) is described approximately as a sum of two contributions: кI(T) describing heat transport by acoustic phonons and кII(T) —by localized high-frequency excitations. The temperature dependences of the thermal conductivity of primary monoatomic alcohols CH₃OH, C₂H₅OH, and C₃H₇OH in the glass state have been compared. Different mechanisms of phonon scattering in the crystalline phases and glass have been analyzed. The кII(T) has been calculated within the Cahill–Pohl model. There is an anomaly of the thermal conductivity of the glass state near Tg (a smeared minimum in the к(T) — curve).
The authors are sincerely grateful to B.Ya. Gorodilov, Prof. V.G. Manzhelii and Prof. F.J. Bermejo for helpful discussions and interest in this study. The investigations is made on the competition terms for joint projects of NAS of Ukraine and Russian Foundation for Fundamental Research (Agreement N 9-2008, Subject: «Collective processes in metastable molecular solids»).
en
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
Физика низких температур
7th International Conference on Cryocrystals and Quantum Crystals
Heat transfer in solid methyl alcohol
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Heat transfer in solid methyl alcohol
spellingShingle Heat transfer in solid methyl alcohol
Korolyuk, O.A.
Krivchikov, A.I.
Sharapova, I.V.
Romantsova, O.O.
7th International Conference on Cryocrystals and Quantum Crystals
title_short Heat transfer in solid methyl alcohol
title_full Heat transfer in solid methyl alcohol
title_fullStr Heat transfer in solid methyl alcohol
title_full_unstemmed Heat transfer in solid methyl alcohol
title_sort heat transfer in solid methyl alcohol
author Korolyuk, O.A.
Krivchikov, A.I.
Sharapova, I.V.
Romantsova, O.O.
author_facet Korolyuk, O.A.
Krivchikov, A.I.
Sharapova, I.V.
Romantsova, O.O.
topic 7th International Conference on Cryocrystals and Quantum Crystals
topic_facet 7th International Conference on Cryocrystals and Quantum Crystals
publishDate 2009
language English
container_title Физика низких температур
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
format Article
description Thermal conductivity coefficient к(T) of two crystalline (orientationally-ordered and orientationally-disordered) phases of pure methanol (at temperatures from 2 K to Tm , Tm is the melting temperature), CH₃OH + 6.6 % H₂O glass from 2 K to Tg , Tg is the glass transition temperature and a supercooled liquid from Tg to 120 K has been measured under equilibrium vapor pressure. The dependence к(T) is described approximately as a sum of two contributions: кI(T) describing heat transport by acoustic phonons and кII(T) —by localized high-frequency excitations. The temperature dependences of the thermal conductivity of primary monoatomic alcohols CH₃OH, C₂H₅OH, and C₃H₇OH in the glass state have been compared. Different mechanisms of phonon scattering in the crystalline phases and glass have been analyzed. The кII(T) has been calculated within the Cahill–Pohl model. There is an anomaly of the thermal conductivity of the glass state near Tg (a smeared minimum in the к(T) — curve).
issn 0132-6414
url https://nasplib.isofts.kiev.ua/handle/123456789/117111
citation_txt Heat transfer in solid methyl alcohol / O.A. Korolyuk, A.I. Krivchikov, I.V. Sharapova, O.O. Romantsova // Физика низких температур. — 2009. — Т. 35, № 4. — С. 380-384. — Бібліогр.: 34 назв. — англ.
work_keys_str_mv AT korolyukoa heattransferinsolidmethylalcohol
AT krivchikovai heattransferinsolidmethylalcohol
AT sharapovaiv heattransferinsolidmethylalcohol
AT romantsovaoo heattransferinsolidmethylalcohol
first_indexed 2025-11-25T12:21:14Z
last_indexed 2025-11-25T12:21:14Z
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fulltext Fizika Nizkikh Temperatur, 2009, v. 35, No. 4, p. 380–384 Heat transfer in solid methyl alcohol O.A. Korolyuk, A.I. Krivchikov, I.V. Sharapova, and O.O. Romantsova 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 January 26, 2009 Thermal conductivity coefficient �(T) of two crystalline (orientationally-ordered and orientational- ly-disordered) phases of pure methanol (at temperatures from 2 K to Tm , Tm is the melting temperature), CH3OH + 6.6 % H2O glass from 2 K to Tg , Tg is the glass transition temperature and a supercooled liquid from Tg to 120 K has been measured under equilibrium vapor pressure. The dependence �(T ) is described approximately as a sum of two contributions: �I(T) describing heat transport by acoustic phonons and �II(T) — by localized high-frequency excitations. The temperature dependences of the thermal conductivity of primary monoatomic alcohols CH3OH, C2H5OH, and C3H7OH in the glass state have been compared. Dif- ferent mechanisms of phonon scattering in the crystalline phases and glass have been analyzed. The �II(T) has been calculated within the Cahill–Pohl model. There is an anomaly of the thermal conductivity of the glass state near Tg (a smeared minimum in the �(T) — curve). PACS: 66.70.–f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves; 63.20.–e Phonons in crystal lattices; 63.50.–x Vibrational states in disordered systems. Keywords: heat transport, acoustic phonons, thermal conductivity, monoatomic alcohols. Introduction Methanol is a monoatomic primary alcohol. The single methyl group CH3 of the methanol molecule is bound to the hydroxyl group OH. Among the primary alcohols, methanol has the shortest and most mobile molecule, which makes it a suitable object for modeling the proper- ties of alcohols having more complex molecules [1–6]. The simple structure of the methanol molecule shows up most obviously in its properties [2–12]. In contrast to wa- ter ice which, under normal conditions, is an associated substance with strong tetragonally directed cooperative H bonds, monoatomic alcohols in the condensed state are viewed as associated objects with moderate H bonds and a chain-like structure [1,4]. The effects of the cooperative hydrogen bond in differ- ent properties of alcohols decreases as the number of car- bon atoms in the molecule increases. At varying tempera- ture and pressure, methanol displays more equilibrium phases than ethanol [4–6,13]. Polymorphism of the crys- talline phases of methanol is governed by its H bonds which are stronger than the dispersive molecular interac- tions and by its simpler molecular structure in comparison to ethanol. It is found in the previous studies [14–16] of thermal conductivity of alcohols (ethanol and isomers of propyl alcohol) in different polymorphous states that eth- anol has similar temperature dependence of thermal con- ductivity (especially at low temperatures) in the phases of a metastable orientationally disordered crystal and a glass (structurally disordered solid). In the propyl alcohols (1-propyl alcohol and 2-propyl alcohol) a strong isomeric effect in the temperature dependence of thermal conduc- tivity was observed. Under equilibrium vapor pressure and by lowering temperature, methanol crystallizes at Tm = 175.37 K into the orientationally disordered high-temperature state (�-phase). Upon the further decrease of temperature, a so- lid–solid transformation into the low-temperature ori- entationally-ordered state (�-phase) occurs at T�–� = = 157.4 K [13]. Their space groups are P212121 for �-phase and Cmcm �-phase [13]. Unlike the situation in ethanol and propanol, fast cooling of the liquid phase hin- ders the glass transition in methanol. It proceeds more prominently when vapor is condensed onto a cold sub- strate below Tg = 103.4 K [8,17]. Poor glass-forming ability of this substance is caused by the structure of its liquid and crystalline phases which consist of zigzag chains of alternating H-bonded molecules. The glass © O.A. Korolyuk, A.I. Krivchikov, I.V. Sharapova, and O.O. Romantsova, 2009 phase of methanol can be obtained by adding a small quantity of water (~6.5 mol.% H2O) to it [18]. The glass transition in methanol with water admixture occurs in rather wide temperature interval Tg = 100–120 K [19]. In this study the thermal conductivity has been mea- sured, for the first time, on pure methanol in different states — equilibrium crystalline phases from 2 to 175 K, glass from 2 K to Tg, and supercooled liquid from Tg to 120 K of methanol with water admixture. The measure- ments were made under equilibrium vapor pressure using the method of steady-state linear heat flow. Experiment and discussion The thermal conductivity of different phases of solid methanol was measured under equilibrium vapor pressure in a set-up described earlier [20] using the steady-state potentiometric method. The container for the sample [20] was a stainless steel tube. Two copper wires 1 mm in di- ameter were placed across the container perpendicular to its axis, which permitted measurement of the average temperature in the isothermal planes across the sample. At the outer surface of the container, copper sockets were soldered to the wires to hold temperature sensors. The liq- uid methanol sample was admitted into the container of the measuring cell under 4He gas. The helium gas was used to improve the heat exchange between the sample and the container. The container with the sample was vac- uum-tight closed by a copper cap with an indium O-ring. A heater was mounted on the container cap to generate a downward heat flow along the sample. The thermal conductivity of pure methanol and its so- lution with distilled water was measured. According to chromatographic analysis, the water content in the pure methanol was less than 0.2% H2O. The water-methanol solution contained 6.6 mol.% H2O. The samples in the glass and crystalline phases (� and �) were prepared using the techniques applied to ethanol [14,15]. The measurements were performed at gradually decreasing temperature. After reaching the lowest tem- perature point the measurement was continued at increas- ing temperature. Crystalline sample was grown in the measuring container during slow cooling the liquid slightly below Tm. Thermal conductivity was measured on crystalline samples of pure methanol and methanol with 6.6 % H2O. The water impurity had practically no ef- fect on the magnitude of the thermal conductivity of methanol. The glass-state sample of methanol with H2O admix- ture was created by very fast (above 50 K·min–1) cooling the liquid to the temperature of liquid N2 (boiling at nor- mal pressure). By heating above Tg the glass sample transformed into a supercooled liquid. Upon the further increase of temperature, above T � 121 K the supercooled liquid crystallized spontaneously, thermal conductivity of the sample increasing abruptly. The experimental temperature dependence of the ther- mal conductivity �(T) measured on methanol crystals (�- and �-phases), glass, and the supercooled liquid methanol with 6.6 % H2O are shown in Fig. 1 along with the temperatures of glass (Tg) and orientational phase (T�–�) transitions. The dependence �(T) of the crystalline sample exhibits some interesting features. The thermal conductivity of the �-phase (orientationally disordered crystal) is independ- ent of temperature (see Fig. 1,b). This agrees with the fact that methanol glass has many structural features in com- mon with the �-phase crystal [2,8,7]. In the orientati- Heat transfer in solid methyl alcohol Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 381 10 100 0.01 0.1 1 60 80 100 120 140 160 180 0.1 0.2 0.3 0.4 0.5 crystal glass supercooled liquid T, K a �, W ·m K – 1 – 1 �, W ·m K – 1 – 1 T, K b �II g �II g �I g �I g �II c �II c �I c �I c Tg Tg T� �– T� �– Fig. 1. Temperature dependence of the thermal conductivity in the �- and �-phases (�) of pure methanol and glass (�) and in the supercooled liquid (�) of methanol with 6.6 % H2O. Ther- mal conductivity of the sample after crystallization from the supercooled liquid at T = 121 K (�). Dashed straight lines are Tg and T�–�. Theoretical calculation of contributions of ther- mal conductivity for �-phase and the glass state: �I(T ) (solid lines) refers to the propagating acoustic phonons; �II(T ) (dot lines) accounts for the localized short-wavelength modes. So- lid lines are the sum � � �� � I II j j , where j = c or g for �-phase and the glass state respectively. The results are presented on double logarithmic scale in a wide interval of temperatures (a) and in the usual scale in the interval T > 60 K (b). onally ordered �-phase, �(T) increases at lowering tem- perature, passes through a broad maximum and then decreases, i.e., the curve has a bell-like shape, typical for an orientationally ordered molecular crystal. Thermal conductivity of the glass sample is distinctly different: �(T) increases with temperature, has a small kink near T = 7 K, goes through a smeared maximum at T � 55 K, then decreases down to a broad minimum and starts to in- crease again (in the supercooled liquid state). The highest value of d�(T)/dT is observed below 4 K. The broad mini- mum in the �(T) curve is an anomalous feature of the ther- mal conductivity of glass [21] (see Fig. 1,b). Thermal conductivity of methanol–H2O sample crystallized at T > 121 K coincides, within the experimental error, with �(T) of the sample prepared by crystallizing the pure methanol at T � Òm . The behavior of �(T) of the methanol glass is similar to that of the glasses of ethanol and 1-propanol [14,15] (see Fig. 2). In comparison with other alcohols, �(T) of metha- nol glass increases most rapidly with temperature up to a broad maximum. The highest values of �(T) in methanol are close to those in ethanol and 1-propanol. It is espe- cially interesting that the anomaly in the �(T) curve shows up in the interval 50–120 K. The anomalous behavior of the thermal conductivity can be approximately described by the dependence �(T) = aT –1 + b + cT (a = 2.25 W·m–1; b = 0.125 W·m–1K–1; c = 0.00043 W·m–1K–2) but its ori- gin is not yet fully understood. The results of this study furnish convincing evidence that the anomaly of �(T) is a typical characteristic of the curve describing thermal conductivity of glass state of a solid alcohol. The temperature dependence of the thermal conductiv- ity of the orientationally-ordered phase and glass state can be interpreted assuming that �(T) consists of two components [22–29]: �(T) = �I(T) + �II(T) . (1) The component �I(T) refers to the propagating phon- ons whose mean free path is longer than the phonon half-wavelength. The phonons are the main heat-transferring particles. The component �II(T) accounts for the localized short-wavelength vibrational modes, or phonons with the mean free path equal to the phonon half-wavelength. This approximation was used before to interpret �(T ) of etha- nol glasses [14] and isomers of propanol [15]. The contribution �I(T) can be calculated within the Debye–Peierls time-relaxation model. In the �I(T) case of the orientationally-ordered crystalline phase (at the tem- perature to the right of the phonon maximum) the phonon–rotational and phonon–phonon scattering mech- anisms dominate. They are effectively described by the Umklapp processes. The total inverse relaxation time (rate) of phonons is assumed to obey the Matthiesen rule and, therefore, can be expressed as a sum of rates repre- senting different processes leading to phonon scattering. For an ordered crystal, it is expected that the dominant mechanisms able to scatter heat-carrying phonons will concern anharmonic Umklapp processes with the rate �U �1, and scattering by dislocations � ��dis 1 . Relevant expressions for the scattering processes are given by: �U �1(�,T) = B� 2 T exp [–EU/T] , (2) �dis �1 (� ,T) = Ddis� , (3) where � is the phonon frequency, B is the frequency-fac- tor, EU is activation energy for the U-processes, and Ddis is the dislocation scattering strength. The temperature dependence of the contribution �I(T) to the thermal conductivity of glass can be described phenomenologically using the soft potential model (SPM) [30] which portrays phonon scattering as mainly caused by low-energy excitations of a strongly anharmon- ic ensemble of particles. The scattering rate of acoustic phonons in a disordered system �G �1 is given by a sum of three terms describing scattering by the tunnel states, classical relaxors and soft quasiharmonic vibrations, and reads: � G B C k T T W � �� � � � � �� � � � � � � � � � � 1 3 4 1 4 2 1 tanh ln / /� � 0 � � � � �� � � � � � � � � � � � 1 6 2 3 � W . (4) Here �0 is the inverse of an attempt frequency and is of the order of 10–13 s, which account, made of the sound wave frequencies (10–100 GH), yields a logarithmic factor ln–1/4 (1/ �0) � 0.7. The most relevant parameters are: the dimensionless C parameter and the characteristic en- ergy W. 382 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 O.A. Korolyuk, A.I. Krivchikov, I.V. Sharapova, and O.O. Romantsova 1 10 100 0.1 Methanol Ethanol 1-Propanol T, K �, W ·m K – 1 – 1 Fig. 2. Temperature dependences of the thermal conductivity of pure 1-propanol [16] (�), ethanol [14,15] (�), and metha- nol with 6.6 % H2O in glass state (this work) (�). The component �II(T ) refers to the heat transfer by lo- calized harmonic short-wavelength vibrational modes, or by acoustic phonons with the mean free path equal to the phonon half-wavelength. The simplest description of �II(T ) is provided by the phenomenological Cahill–Pohl model [31] which was proposed to interpret the thermal conductivity of amorphous solids at high temperatures. The model accounts adequately for the features of the isochoric high-temperature thermal conductivity of mo- lecular crystals in the orientationally-ordered phase [32]. According to the model, the thermal conductivity is: � � �II � � � � � � � � � � �� �6 1 1 3 2 3 2 3 2 0 / / ( ) B i i x x n T x e e dx � �/T i �� � � � �� � � !� , (5) where kB is the Boltzmann constant, n is the number of at- oms per unit volume; summation is over three vibrational modes with the sound velocities vi , i is the index of sum- mation over the phonon mode polarizations, �i is the Debye temperature for each polarization, x = ��/(kBT). In the Debye approximation for the phonon spectrum of an isotropic solid (the difference between the polarizations of the phonon modes is disregarded) �II(T ) becomes: � " � ## � � � � � � � � � � � � 3 1 36 1 1 3 1 3 2 2 3 2 F N M T x e A B x x / / ( )� � e dx T 0 �/ � , (6) where " is the density, Ì is the molar mass, NA is the Avo- gadro number, � is the averaged Debye temperature, F is the dimensionless fitting parameter allowing effectively for the intensity of the heat transfer by localized excita- tions, including the rotational ones. Note that in the orientationally disordered phase �(T) is determined by lo- calized states of different origin. The thermal conductivity of methanol was calculated using: Ì = 32.04 g/mol; " = 1015 kg/m3 [13]; the mean sound velocity v = 1400 m/s was calculated using the data for the longitudinal sound velocity [33]; � = 106 K was calculated from the v-value. Table 1 gives the fitting parameters obtained by com- paring experimental results and calculated curves. Table 1. Parameters obtained by fitting theoretical and experi- mental data B, s/K EU , K Ddis C W, K F �-phase 5.3·10 –16 18 4.6·10 –3 — — 4.8 $ 0.2 �-phase 0 — 0 — — 7.0 $ 0.2 glass 0 — 0 2.9·10 –3 5 2.9 $ 0.2 The curves in Fig. 1 are the dependences �I(T), �II(T), and �(T) calculated for �-phase and the glass state. At temperatures near and to the left of the �(T) maximum, the thermal conductivity of the �-phase of solid methanol is mainly determined by �I(T). Above the maximum and up to T�–� , the share of �II(T) increases with temperature. No �I(T) is observed in the �-phase. Similar behavior of �I(T) and �II(T) contributions to the total thermal conduc- tivity is observed in the glass state of methanol with water admixture: �I(T) determines the thermal conductivity at temperatures to the left of the kink at Ò < 7 K. At Ò > 10 K the component �II(T) starts to increase rapidly with tem- perature. The theoretical curve offered by this model is inadequate to explain the smeared minimum of �(T) near T = 80 K in the glass state. The division of �(T) into two components permits a satisfactory description of thermal conductivities in a substance capable of developing dif- ferent molecular structures with different degrees of ori- entational and translational ordering. McGaughey and Kaviany [28] accept it as a universal theoretical tool. The behavior and magnitude of the contribution �II(T) to the thermal conductivity of an orientationally ordered crystal � II c is similar to that in the glass state � II g , which prompts the conclusion that the contribution �II is practically inde- pendent of the substance state (glass or orientational- ly-ordered crystal). When the �-� phase transition oc- curs, it is accompanied with a volume jump %V/V � 4% [7]. However, there is no jump (within the experimental error) of the thermal conductivity (see Fig. 1,b). The rea- son may be that in the region below T�–� the thermal con- ductivity is determined not by the phonon contribution �I sensitive to volume variations but by the contribution �II from localized vibrational modes, and �II is only slightly sensitive to changes in the volume [34]. The contribution �II referring to the heat transport by localized states is in- dependent of the molecular structure of methanol and is determined primary by the increasing intensity of rotation of the methyl and hydroxyl groups of the molecule and their cooperative rotational hopping of the molecules at increasing temperature. The coupling of acoustic phon- ons and localized excitations becomes most efficient above 10 K and increases with temperature [18,19]. Summing, the thermal conductivity of methanol has been measured for the first time on samples in different states – equilibrium crystalline phases (from 2 K to Tm), glass state (from 2 K to Tg) and supercooled liquid (from Tg to 120 K) of methanol with water admixture. It is shown that in the solid states the thermal conductivity �(T) is a sum of two contributions: �I(T) corresponds to propagating phonons which are the main heat-transport- ing particles and are dependent on the translational and orientational ordering of molecules. The component �II(T) accounts for the heat transport by localized excita- tions. �II is almost independent of the methanol state (glass or an orientationally-ordered crystal). An anoma- lous feature has been detected in the thermal conductivity Heat transfer in solid methyl alcohol Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 383 of the methanol glass: a smeared minimum in the curve �(T) near the glass transition temperature. This behavior of �(T) is similar to that encountered in ethanol glass and two isomers of propanol [21]. The new results and a detailed analysis of the thermal conductivity of monoatomic alcohols both in the me- tastable states and in thermodynamically equilibrium phases are planned to be published in a subsequent paper. The authors are sincerely grateful to B.Ya. Gorodilov, Prof. V.G. Manzhelii and Prof. F.J. Bermejo for helpful discussions and interest in this study. The investigations is made on the competition terms for joint projects of NAS of Ukraine and Russian Foundation for Fundamen- tal Research (Agreement N 9-2008, Subject: «Collective processes in metastable molecular solids»). 1. D.C. Steytler, J.C. Dore, and D.C. Montague, J. Non Cryst. Solids 74, 303 (1985). 2. T. Doba, K.U. Ingold, A.H. Reddoch, W. Siebrand, and T.A. Wildman, J. Chem. Phys. 86, 6622 (1987). 3. J.M. Brown, L.J. Slutsky, K.A. Nelson, and L.-T. Cheng, Science 241, 4861, 65 (1988). 4. B.H. Torrie, S.-X. 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