Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄
The isochoric thermal conductivity of solid n-hexane C₆H₁₄ has been investigated on three samples of different density in the temperature interval from 100 K to the onset of melting. In all the cases the isochoric thermal conductivity varied following a dependence which is weaker than Λ ∝ 1/Т. The r...
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nasplib_isofts_kiev_ua-123456789-1185492025-02-23T19:25:09Z Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ Konstantinov, V.A. Revyakin, V.P. Sagan, V.V. 8th International Conference on Cryocrystals and Quantum Crystals The isochoric thermal conductivity of solid n-hexane C₆H₁₄ has been investigated on three samples of different density in the temperature interval from 100 K to the onset of melting. In all the cases the isochoric thermal conductivity varied following a dependence which is weaker than Λ ∝ 1/Т. The results obtained are compared with the thermal conductivities of other representatives of n-alkanes. The contributions of low-frequency phonons and “diffuse modes” to the thermal conductivity are calculated. 2011 Article Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ / V.A. Konstantinov, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2011. — Т. 37, № 5. — С. 531-534. — Бібліогр.: 17 назв. — англ. 0132-6414 PACS: 66.70.–f https://nasplib.isofts.kiev.ua/handle/123456789/118549 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals |
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8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals Konstantinov, V.A. Revyakin, V.P. Sagan, V.V. Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ Физика низких температур |
| description |
The isochoric thermal conductivity of solid n-hexane C₆H₁₄ has been investigated on three samples of different density in the temperature interval from 100 K to the onset of melting. In all the cases the isochoric thermal conductivity varied following a dependence which is weaker than Λ ∝ 1/Т. The results obtained are compared with the thermal conductivities of other representatives of n-alkanes. The contributions of low-frequency phonons and “diffuse modes” to the thermal conductivity are calculated. |
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Article |
| author |
Konstantinov, V.A. Revyakin, V.P. Sagan, V.V. |
| author_facet |
Konstantinov, V.A. Revyakin, V.P. Sagan, V.V. |
| author_sort |
Konstantinov, V.A. |
| title |
Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ |
| title_short |
Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ |
| title_full |
Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ |
| title_fullStr |
Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ |
| title_full_unstemmed |
Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ |
| title_sort |
isochoric thermal conductivity of solid n-alkanes: hexane c₆h₁₄ |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2011 |
| topic_facet |
8th International Conference on Cryocrystals and Quantum Crystals |
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https://nasplib.isofts.kiev.ua/handle/123456789/118549 |
| citation_txt |
Isochoric thermal conductivity of solid n-alkanes: hexane C₆H₁₄ / V.A. Konstantinov, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2011. — Т. 37, № 5. — С. 531-534. — Бібліогр.: 17 назв. — англ. |
| series |
Физика низких температур |
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2025-11-24T15:46:57Z |
| last_indexed |
2025-11-24T15:46:57Z |
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1849687243259641856 |
| fulltext |
© V.A. Konstantinov, V.P. Revyakin, and V.V. Sagan, 2011
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5, p. 531–534
Isochoric thermal conductivity of solid n-alkanes:
hexane C6H14
V.A. Konstantinov, V.P. Revyakin, and V.V. Sagan
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: konstantinov@ilt.kharkov.ua
Received December 10, 2010
The isochoric thermal conductivity of solid n-hexane C6H14 has been investigated on three samples of differ-
ent density in the temperature interval from 100 K to the onset of melting. In all the cases the isochoric thermal
conductivity varied following a dependence which is weaker than Λ ∝ 1/Т. The results obtained are compared
with the thermal conductivities of other representatives of n-alkanes. The contributions of low-frequency pho-
nons and “diffuse modes” to the thermal conductivity are calculated.
PACS: 66.70.–f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves,
Keywords: n-alkanes, hexane, isochoric thermal conductivity, phonons, “diffusive” modes.
Introduction
Normal alkanes (n-paraffins) of the CnH2n+2 type form
a class of substances that are intermediate in changing –
over to long-chain polymers. N-alkanes have a compara-
tively simple structure and a molecular packing: in the so-
lid state the axes of all molecules are always parallel to one
another irrespective of a particular crystalline modification
[1]. Owing to their relative simplicity, normal alkanes are
naturally considered as the starting point for understanding
the structural and termophysical properties of more com-
plex long-chain compounds.
N-alkanes exhibit an extremely diverse dynamic behavior
both in the solid and liquid states. The melting temperature
increases in this series of compounds with the length of the
chain and its behavior is nonmonotonic: the n-alkanes with
an add number of carbon atoms (odd n-alkanes) melt at
comparatively lower temperatures than those with an even
number of C atoms (even n-alkanes). An interesting effect is
observed when the orthorhombic, monoclinic and triclinic
structures alternate with the even and odd members of the
series [1–3]. The even n-alkanes with n = 6 – 24 (n = the
number of C atoms) crystallize at low temperatures forming
a triclinic cell. Heptane (n = 7) and nonane (n = 9) have an
orthorhombic structure at low temperatures. Glass-like “ro-
tational” phases with hexagonal symmetry were found in
rather narrow temperature interval below the melting points
of odd n-alkanes starting with n = 9. The region of existence
of the “rotational” phase increases with the length of the
chain. Hexagonal modifications also occur in even n-alkanes
starting with n = 22 [1–4].
Short-chain (n ≤ 6) and “even” n-alkanes are the least
studied members of the series. Previously, thermal con-
ductivity was investigated only in “odd” n-alkanes with
n = 9–19 at constant pressure 30 MPa [5]. We have inves-
tigated the isochoric thermal conductivity of methane [6],
ethane [7] and propane [8]. Here we report the isochoric
thermal conductivity of solid n-hexane (C6H14) measured
on samples of various densities in the temperature interval
from 100 K to the onset of melting.
According to colorimetric data, n-hexane has only one
crystallographic modification and melts at Tm = 177.8 K
with the entropy of melting ΔSf /R = 8.85 [9]. The crystal
structure of n-hexane has been determined by the x-ray
method at 90 and 158 K [2,10]. It is triclinic, space group
Pī, with one molecule in the unit cell. On elastic neutron
scattering [11], the lattice mode peaks occur at 35, 55, 71
and 93 cm–1, which agree well with the Raman scattering
data [12] (53, 74 and 87 cm–1). It is found that in n-hexane
the lowest intramolecular modes are separated from the
lattice modes not so distinctly as in light n-alkanes. The
Debye temperature may be evaluated as the upper boun-
dary of the lattice modes (∼102 K).
Experimental
For a correct comparison with theory, the measurement
must be made at a constant density of the sample to ex-
clude the thermal expansion effect. Constant-volume in-
vestigations are possible for molecular solids having com-
paratively high compressibility coefficients. Using a high
pressure cell, it is possible to grow samples of sufficient
density which can be cooled then with practically invaria-
V.A. Konstantinov, V.P. Revyakin, and V.V. Sagan
532 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5
Fig. 1. The isochoric thermal conductivity of three solid n-hexane
samples of various densities: №1(■), №2 (▲) и №3 (●). Solid lines
are smoothed values of isochoric thermal conductivity. Dashed line
is the thermal conductivity under atmospheric (zero) pressure.
100 120 140 160 180 200
2
3
4
5
6
7
3
2
1
T, K
C H6 14
�
�
,
m
W
/c
m
K
Fig. 2. Isobaric thermal conductivity of some n-alkanes (this
study and [5,7,8]). Data for ethane, propane and hexane corres-
pond to zero pressure; thermal conductivity of “odd” n-alkanes
with n = 9–19 correspond to pressure 30 MPa.
40 80 120 160 200 240 280 320
2
4
6
8
T, K
C H19 40
C H17 36
C H15 32
C H13 28
C H11 24
C H9 20
C H6 14
C H2 6
C H3 8
�
�
,
m
W
/c
m
K
ble volume whereas the pressure in the cell decreases. As
samples of moderate densities are cooled the pressure in
the sell drops to zero at a certain characteristic temperature
T0 and the isochoric condition is then broken. At and be-
low T0 isochoric data turn to isobaric at zero pressure. On
further cooling, the sample can separate from the walls of
the cell or its continuity can be disturbed. In constant-
volume experiments melting occur in a certain temperature
interval, and its onset shifts towards higher temperatures as
the density of the samples increases. These measurements
were made by a steady – state flow heat method in a coaxi-
al geometry setup [13]. The samples were grown under
different pressures (40–120 MPa), the temperature gradient
over the measuring cell being about 1.5 K/cm. As the
growth was completed, the capillary was blocked by cool-
ing it with liquid nitrogen, and the samples were annealed
below melting temperatures for about two hours to remove
the density gradients. After the measurements the samples
were evaporated into a thin-wall vessel, and the samples
masses were determined through weighting. The molar
volumes of the samples were found from known volume of
the measuring cell and the sample mass. Purity of the
C6H14 used was no worse than 99.8%.
Results and discussion
The experimental results are shown in Fig. 1, which
carries the smoothed thermal conductivity of the solid
phase (solid lines) and the isobaric (P = 0, MPa) thermal
conductivity (dashed line). The thermal conductivities of
the samples grown under identical conditions (grown time,
pressure and temperature gradient over the measuring cell)
coincident within the experimental error, which is evidence
of the fine – disperse state of the samples (considerable
anisotropy of the thermal conductivity can be expected
along and across the plane of the layers). The molar vo-
lumes Vm of the samples, the temperatures T0 of the onset
of experimental condition V = const, and the temperatures
Tm of the onset of melting are given in Table 1. The
Bridgman coefficient ( ln / ln )Tg V= − ∂ Λ ∂ was calcu-
lated from experimental data to be 7.6 ± 0.6 at T = 178 K.
Table 1. Molar volumes Vm of samples, temperatures T0 of the
onset of experimental condition V = const, and temperatures Tm
of the onset of melting.
Number of sample Vm, cm3/mole T0, K Tm, K
1 95.6 116 235
2 96.7 142 210
3 97.3 166 192
The isochoric thermal conductivity of all solid n-hexane
samples decreases with increasing temperature following a
dependences weaker than Λ ∝ 1/T. A similar behavior was
observed previously in the low-temperature phase of
ethane [7] and in propane [8]. It was noted previously that
the thermal conductivity of long-chain odd n-alkanes
(C9H20–C19H40) has some features in common [5]. As the
“rotational” phase melts, the thermal conductivity changes
by about 35% and is independent of the chain length. The
jump of the thermal conductivity on changing to the low
temperature ordered phase decreases with the increasing
length of the chain and makes ∼85% for n-undecane and
∼40% for n-nonadecane. The absolute value of thermal
conductivity increases in the “rotational” phase with the
increasing chain length.
The isobaric thermal conductivity of some n-alkanes is
shown in Fig. 2 (data of this study and [5,7,8] along with the
thermal conductivities of the liquid phases of these com-
pounds measured immediately after melting [5,14]. Data for
ethane, propane and hexane correspond to zero pressure;
thermal conductivity of “odd” n-alkanes with n = 9–19 was
studied at constant pressure 30 MPa. Some information
about structure and thermo physical properties of n-alkanes
discussed is also available in Table 2. As noted above, the
Isochoric thermal conductivity of solid n-alkanes: hexane C6H14
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 533
isobaric thermal conductivity exhibits closely similar beha-
vior in short and long-chain n-alkanes. On the transition
from the ordered phase to a liquid the thermal conductivity
of the n-alkanes starting with propane changes nearly twice
and is independent of the total entropy of transitions and the
chain length. Such change is much smaller in the case of
spherical and elliptic molecules: for example, ΔΛ/ΛL is only
20–30% in methane and ethane. This can be related to the
higher degree of orientational ordering in solid long-chain n-
alkanes as compared to spherical molecules.
Table 2. The structure of n-alkanes [2,5,10], the temperature Tα–β and the entropy ΔSα–β/R of the transition to the “rotational” phase,
the temperature Tm and the melting entropy ΔSm/R [NIST Standard Reference Data: http://webbook.nist.gov/chemistry/form-ser.html], a
complete change of the entropy and variations of thermal conductivity Λα/ΛL during the ordered phase – liquid transition [5,7,8,14].
The deviation of the isochoric thermal conductivity
from the dependence Λ∝1/T in the orientationally-ordered
phases of molecular crystals can be explained proceeding
from the concept of the “lower limit to thermal conductivi-
ty” [15,16]. In this case the thermal conductivity can be
calculated within the model in which heat is transported by
both low-frequency phonons and “diffuse” modes. In sim-
ple Debye model the thermal conductivity can be described
by the following expression
3 / 4
2
0
e( ) 3 ( )
(e -1)
D T x
B x
D
T xT nk l x dx
Θ⎛ ⎞
Λ = ⎜ ⎟Θ⎝ ⎠
∫v (1)
where 2 1/3 ( / )(6 ) ,D Bh k nΘ = πv n is the number of
atoms (molecules) per unit volume, v is polarization – ave-
raged sound velocity, h is Planck constant l(x) is phonon
mean-free path. For T ≥ ΘD the phonon mean-free path can
be found as
2 2
2 2 2
1( )
B
hl x
CT k T x
=
v , (2)
where C is a coefficient. Since the mean-free path of the
phonons cannot be smaller than the half wavelength l(x) =
= aλ/2, where a ≈ 1, the “diffusivity edge” *Θ is
* 2 / ,Bh ak CTΘ = v (3)
The modes whose mean-free path is aλ/2 are denoted as
“diffuse” modes. It is assumed, that * DΘ ≤ Θ otherwise
* .DΘ = Θ The thermal conductivity integral can be sub-
divided into two parts describing the contributions to ther-
mal conductivity from low-frequency phonons Λph and
high-frequency “diffuse” modes Λdif:
Λ = Λph + Λdif (4)
*3 / 4
ph 2
0
e( ) 3 ( )
(e 1)
T x
B x
D
T xT nk l x dx
Θ⎡ ⎤⎛ ⎞ ⎢ ⎥Λ = ⋅ ⋅⎜ ⎟Θ ⎢ ⎥−⎝ ⎠ ⎣ ⎦
∫v (5)
*
3 / 4
dif 2
/
e( ) 3
2 (e 1)
D T x
B x
D BT
T h xT nk dx
k xT
Θ
Θ
⎡ ⎤⎛ ⎞ ⎢ ⎥Λ = ⋅ α ⋅⎜ ⎟ ⎢ ⎥Θ −⎝ ⎠ ⎣ ⎦
∫
vv
(6)
The lower limit to thermal conductivity Λmin is reached if
all vibrating modes have “diffusive” character: l(λ) = aλ/2
and it can be written as
2 /1/3 3
2/3
min 2
0
e3
6 (e 1)
D T x
B x
D
T xn k dx
Θ⎛ ⎞π⎛ ⎞Λ = α ⎜ ⎟⎜ ⎟ Θ⎝ ⎠ −⎝ ⎠
∫v . (7)
The least-square fitting to the smoothed thermal con-
ductivity was performed for the highest-density sample
with Vm = 95.6 сm3/mole. Unfortunately, no experimental
data on the sound velocity in solid n-hexane are available
presently. We therefore used value v = 2.4×103 m/s for
liquid n-hexane immediately after melting [17] and varied
the parameters C and α. The best agreement with the expe-
rimental was achieved with C = 6.8 10–10 сm/K and α =
= 1.86. These coefficients C and α are closed to those of
ethane and propane (see Table 3).
Table 3. The average sound velocity v, and the fitting parame-
ters C and α.
Substance v×10–5 cm/s C×109 cm/K α
C2H6 1.42 1.06 1.84
C3H8 1.95 1.1 2.64
C6H14 2.4 0.68 1.86
Substance Structure Tα–β, K ΔSα–β/R Tm, K ΔSm/R ΔSα–L/R Λα/ΛL
C2H6 P21/n, z = 2 89.8 2.74 90.3 0.77 3.6 1.3
C3H8 P21/n, z = 4 - - 85.5 4.95 4.95 2.2
C6H14 Pī, z = 1 - - 177.8 8.85 8.85 1.9
C9H20 Pī, z = 1 217.2 3.48 219.7 8.47 12.0 2.4
C11H24 Pbcn, z = 4 236.6 2.9 247.6 10.8 13.7 2.4
C13H28 Pbcn, z = 4 255.0 3.6 267.8 12.8 16.4 2.3
C15H32 Pbcn, z = 4 270.9 4.1 283.1 14.7 18.8 2.1
C17H36 Pbcn, z = 4 284.3 4.8 295.1 16.4 21.2 2.0
C19H40 Pbcn, z = 4 296.0 5.6 304.0 18.8 24.3 2.0
V.A. Konstantinov, V.P. Revyakin, and V.V. Sagan
534 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5
Fig. 3. The curve fitted to the smoothed experimental thermal
conductivity of sample №1 and the calculated contributions to
thermal conductivity from low-frequency phonons Λph and “dif-
fuse” modes Λdif. The dash–and–dot line is for the lower limit of
the lattice thermal conductivity Λmin.
100 120 140 160 180 200
0
1
2
3
4
5
6
�min
�dif
�ph
�
T, K
�
�
,
m
W
/c
m
K
The smoothed values of thermal conductivity (dark
squares), the fitting curve (solid line) and the contributions
of low-frequency phonons Λph and diffuse modes Λdif
(dashed lines) are shown in Fig. 3. Here as dot-dashed line is
also shown the lower limit to thermal conductivity, calcu-
lated according to Eg. (7). It is seen that the “diffuse” beha-
vior of the vibrational modes becomes evident at T > 130 K.
Up to T = 200 K the contribution of “diffuse” modes is
smaller than of phonons, which agrees well with the large
jump of thermal conductivity observed on melting.
Conclusion
The isochoric thermal conductivity of solid n-hexane
C6H14 has been investigated on three samples of different
density in the temperature interval from 100 K to the onset
of melting. In all the cases the isochoric thermal conductiv-
ity varied following a dependence which is weaker than
Λ ∝ 1/Т. The isobaric thermal conductivity exhibits closely
similar behavior in short and long-chain n-alkanes. On the
transition from the ordered phase to a liquid the thermal
conductivity of the n-alkanes starting with propane
changes nearly twice and is independent of the total entro-
py of transitions and the chain length. Such change is much
smaller in the case of spherical and elliptic molecules. This
can be related to the higher degree of orientational ordering
in solid n-alkanes as compared to spherical molecules. The
contributions of low-frequency phonons Λph and “diffuse
modes” Λdif to the thermal conductivity are calculated.
Unlike crystals consisting of the globular-shape molecules
Λph is smaller than Λdif, which agrees well with the large
jump of thermal conductivity observed on melting.
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