The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion
The thermal conductivity of liquid CHCl₃, C₆H₆, and CCl₄ was measured by steady-state method under saturated vapour pressure in the temperature areas that correspond to pre-crystallization temperatures. Based on the obtained experimental results, we have investigated the isobaric thermal conductivit...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1171122017-05-20T03:03:41Z The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion Pursky, I.O. Konstantinov, V.A. Bulakh, V.V. 7th International Conference on Cryocrystals and Quantum Crystals The thermal conductivity of liquid CHCl₃, C₆H₆, and CCl₄ was measured by steady-state method under saturated vapour pressure in the temperature areas that correspond to pre-crystallization temperatures. Based on the obtained experimental results, we have investigated the isobaric thermal conductivity jump ΔΛp at crystal–liquid phase transition in CHCl₃, C₆H₆, and CCl₄. The contributions of the phonon–phonon and phonon–rotational interaction to the total thermal resistance, in solid and liquid state, are specified using modified method of reduced coordinates. A reduction in the thermal conductivity ΔΛp at crystal–liquid phase transition is explained by a combined effect of variations in positional distribution of molecules and in form of rotational molecular motion. 2009 Article The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion / I.O. Pursky, V.A. Konstantinov, V.V. Bulakh // Физика низких температур. — 2009. — Т. 35, № 4. — С. 401-404. — Бібліогр.: 6 назв. — англ. 0132-6414 PACS: 66.70.–f, 63.20.kk http://dspace.nbuv.gov.ua/handle/123456789/117112 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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English |
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7th International Conference on Cryocrystals and Quantum Crystals 7th International Conference on Cryocrystals and Quantum Crystals |
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7th International Conference on Cryocrystals and Quantum Crystals 7th International Conference on Cryocrystals and Quantum Crystals Pursky, I.O. Konstantinov, V.A. Bulakh, V.V. The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion Физика низких температур |
| description |
The thermal conductivity of liquid CHCl₃, C₆H₆, and CCl₄ was measured by steady-state method under saturated vapour pressure in the temperature areas that correspond to pre-crystallization temperatures. Based on the obtained experimental results, we have investigated the isobaric thermal conductivity jump ΔΛp at crystal–liquid phase transition in CHCl₃, C₆H₆, and CCl₄. The contributions of the phonon–phonon and phonon–rotational interaction to the total thermal resistance, in solid and liquid state, are specified using modified method of reduced coordinates. A reduction in the thermal conductivity ΔΛp at crystal–liquid phase transition is explained by a combined effect of variations in positional distribution of molecules and in form of rotational molecular motion. |
| format |
Article |
| author |
Pursky, I.O. Konstantinov, V.A. Bulakh, V.V. |
| author_facet |
Pursky, I.O. Konstantinov, V.A. Bulakh, V.V. |
| author_sort |
Pursky, I.O. |
| title |
The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion |
| title_short |
The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion |
| title_full |
The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion |
| title_fullStr |
The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion |
| title_full_unstemmed |
The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion |
| title_sort |
thermal conductivity jump at crystal-liquid phase transition in chcl₃, c₆h₆, and ccl₄: the action of rotational molecular motion |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2009 |
| topic_facet |
7th International Conference on Cryocrystals and Quantum Crystals |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117112 |
| citation_txt |
The thermal conductivity jump at crystal-liquid phase transition in CHCl₃, C₆H₆, and CCl₄: the action of rotational molecular motion / I.O. Pursky, V.A. Konstantinov, V.V. Bulakh // Физика низких температур. — 2009. — Т. 35, № 4. — С. 401-404. — Бібліогр.: 6 назв. — англ. |
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Физика низких температур |
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| fulltext |
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4, p. 401–404
The thermal conductivity jump at crystal–liquid phase
transition in CHCl3, C6H6, and CCl4: the action
of rotational molecular motion
I.O. Pursky1, V.A. Konstantinov2, and V.V. Bulakh1
1
T. Shevchenko National University of Kyiv, Faculty of Physics, 6 Glushkova Ave., Kyiv 03680, Ukraine
2
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 January 4, 2009
The thermal conductivity of liquid CHCl3, C6H6, and CCl4 was measured by steady-state method under
saturated vapour pressure in the temperature areas that correspond to pre-crystallization temperatures.
Based on the obtained experimental results, we have investigated the isobaric thermal conductivity jump
ΔΛp at crystal–liquid phase transition in CHCl3, C6H6, and CCl4. The contributions of the phonon–phonon
and phonon–rotational interaction to the total thermal resistance, in solid and liquid state, are specified us-
ing modified method of reduced coordinates. A reduction in the thermal conductivity ΔΛp at crystal–liquid
phase transition is explained by a combined effect of variations in positional distribution of molecules and in
form of rotational molecular motion.
PACS: 66.70.–f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves;
63.20.kk Phonon interactions with other quasiparticles.
Keywords: thermal conductivity, phonon–phonon and phonon–rotational scattering, thermal resistance.
1. Introduction
In studies of correlation between the melting and
thermophysical properties, the structural peculiarities of
substances must be taken into account. It should be noted,
that the varied processes tending to general increase
of entropy at phase transition to liquid state are not in-
dependent of one another. A direct separation of these
processes is rather complicated problem. Therefore, a
simplified approach, where entropy raise processes are
considered independently, is often used in practice. In this
approximation the total entropy of melting can be treated
as sum of components corresponding to different types of
disordering processes.
Simple molecular crystals are characterized by both
translational and orientational degrees of freedom. De-
pending on a specific crystal and temperature the form of
orientational motion can vary from librations at small an-
gles to nearly free rotation. As a result of melting, in all
types of crystals the translational (positional) disordering
occurs. The orientational disordering at melting can oc-
cur, as a rule, in simple molecular crystals formed from
low-symmetry molecules.
The present paper gives an account of studies of iso-
baric thermal conductivity jump at crystal–liquid phase
transition in CHCl3, C6H6, and CCl4. We focused our at-
tention on the role of translation-orientational disorder-
ing processes at melting. To elucidate the issue, how dif-
ferent forms of thermal molecular motion affect the
Λp-jump at melting, in present study the contributions of
the phonon–phonon and phonon–rotational interaction to
the total thermal resistance, at pre and above melting tem-
peratures, are separated using modified method of re-
duced coordinates.
2. Experimental technique
The isobaric thermal conductivity of liquid CHCl3,
C6H6, and CCl4 was measured using the steady-state
method at pre-crystallization temperatures. The measure-
© I.O. Pursky, V.A. Konstantinov, and V.V. Bulakh, 2009
ments were carried out on coaxial-geometry setup (Fig. 1)
under atmospheric pressure. The measurement cell was
produced from copper, with a length of 175 mm and an in-
side diameter of 11 mm, which made it possible to elimi-
nate the axial heat flow. The inner measuring cylinder
was 10 mm in diameter and produced from stainless steel.
The liquid samples were between the outer and the inner
cylinder. The temperature sensors were platinum resis-
tance thermometers, which were mounted on the surface
of measuring cell and in the channel of the inner cylinder.
The heat fluxes due to thermal radiation were reduced
substantially with the aid of a radiation shield, on which
the temperature field of the measuring cell was repro-
duced. The measurements were made on the two samples
of each substance of 99.9% purity; the uncertainty in
thermal conductivity measurement did not exceed 3%.
3. Results and discussion
Figure 2 shows the experimental results for three sub-
stances. The Λp of liquid CHCl3, C6H6 and CCl4 de-
creases with temperature rises. The p-data for solid
CHCl3, C6H6 and CCl4, at pre-melting temperatures
(Fig. 2), were taken from [1]. The thermal conductivity
jump was calculated at pre and above melting tempera-
tures as = solid – liquid. The p-jump at phase tran-
sition essentially depends on the substance. Our results
show that:
ΔΛ CCl4
W (m K= ⋅0 007. / ),
ΔΛ C H6 6
W (m K)= ⋅0103. / ,
ΔΛ CHCl3
W (m K)= ⋅011. / .
402 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
I.O. Pursky, V.A. Konstantinov, and V.V. Bulakh
1
2
3
5
6
7
8
10
11
14
4
9
12
13
Fig. 1. The schematic of the measuring cell: 1 — external cop-
per cylinder; 2 — stainless steel tube pressed in copper cylin-
der; 3 — inner cylinder; 4 — inner cylinder plug; 5 — internal
heater; 6 — internal heater copper base used to equalization of
the axial heat flow; 7 — internal platinum thermometer; 8 —
high-heat conducting powder; 9 — external platinum ther-
mometer; 10 — channel of substance pressure feed; 11, 12 —
bridgman seals; 13 — service duct; 14 — fluoroplastic cen-
tring ring.
0.10
0.14
0.18
0.22
0.26
185 190 195 200 205 210 215 220 225
Tm
Solid Phase [1] Liquid Phase
CHCl3
Pressure 0.1 MPa
0.12
0.16
0.20
0.24
0.28
245 255 265 275 285 295
T, K
T, K
Tm
Tm
Solid Phase [1] Liquid Phase
C H6 6
Pressure 0.1 MPa
Pressure 0.1 MPa
b
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
225 230 235 240 245 250 255 260 265
T, K
Solid Phase (I ) [1]b
Liquid Phase
cCCl4
a
Λ
p
,
W
/(
m
·K
)
Λ
p
,
W
/(
m
·K
)
Λ
p
,
W
/(
m
·K
)
Fig. 2. T-dependence of isobaric thermal conductivity Λp in
solid [1] and liquid CHCl3 (a), C6H6 (b), and CCl4 (c) at
crystal–liquid phase transition. Tm is the melting temperature.
A reduction (Fig. 2) in the thermal conductivity at
crystal–liquid phase transition is usually connected with
jump-like volume changes resulting from variation in the
positional distribution of molecules and variations in the
rotational molecular motion.
At pre-melting temperatures investigated substances
differ essentially in nature of rotational molecular mo-
tion. Chloroform remains to be orientationally ordered
until the melting temperature is reached [2] (the reorien-
tation frequencies do not exceed 104 s–1, and entropy
of melting is Sf/R = 5.4). In solid benzene the melt-
ing-caused change in the entropy of melting is Sf/R =
= 4.22, which is much lager that Timmermans criterion
for orientationally disordered phases. The frequency of
molecular reorientations at 85 K is 104 s–1 [3]. On a fur-
ther rise of temperature it increases considerably, reach-
ing 1011 s–1 near melting temperature. The basic fre-
quency of the benzene molecule oscillations about sixfold
axis at 273 K is 1.05 1012 s–1 [4]. It is clear from these
data that solid benzene is a crystal where, provided that
the temperature grows, the transition from libration of
molecules to hindered rotation takes place only about one
axis, or in other words solid C6H6 is partially disordered
crystal. Because of low entropy of melting Sf/R = 1.21
[3], the high-temperature phase of carbon tetrachloride
may be classified as plastic. According to experimental
data [5], the character of the molecular motion in the plas-
tic phase of CCl4 is close to that in liquid state.
To understand of how different forms of thermal mo-
lecular motion affect the Λp-jump at crystal–liquid phase
transition the contributions of the phonon–phonon and
phonon–rotational interaction to the total thermal resis-
tance, in solid and liquid state, are separated using modi-
fied method of reduced coordinates [1]. Under the as-
sumption that the contributions of the phonon–phonon
Wpp and phonon–rotation Wpr interactions to the total
thermal resistance Wp = 1/Λp are additive, we separate the
phonon–rotation component. It is important to note that,
in this case, there is no necessity to engage that or another
approximate model of heat transfer. Suggesting that
the thermal resistance of molecular crystals resulting
from phonon–phonon scattering Wpp, when being ex-
pressed in terms of reduced coordinates (W* = W/Wmol,
T* = T/Tmol), is identical to that for solidified inert gases
at the same reduced volume V* = V/Vmol, one can extract
the phonon–phonon Wpp, and phonon–rotational Wpr,
components of the thermal resistance. As a rule, the re-
duction parameters are Tmol = ε/kB, Λ mol = k B / /σ ε μ2 ,
and Vmol = Nσ3, where σ and ε are the parameters of
Lennard–Jones potential, μ is the molar weight, and N is
the total number of particles.
Here, we used the temperatures Tcr and the molar vol-
umes Vcr of CHCl3, C6H6, and CCl4 and the solidified in-
ert gases Kr and Xe at their critical points [6] as the reduc-
tion parameters Tmol and Vmol (see Table 1). Such a
choice of critical coordinates is explained by the fact that,
in the case of simple molecular substances, the critical pa-
rameters Tcr and Vcr are proportional to and 3, respec-
tively. However, the determination accuracy of critical
parameters is much higher than the accuracy of binomial
potential parameters.
Table 1. Reduction parameters and molar weights for Kr, Xe,
CHCl3, C6H6, and CCl4
Substance
Tcr,
K
Vcr,
cm
3
/mole
μ,
g/mole
Wmol,
(m·K)/W
Kr 209.4 92.01 83.8 8.06
Xe 289.7 119.4 131.3 10
CHCl3 536.6 238.8 119.4 10.9
C6H6 562 260 78 9.43
CCl4 556.4 257 153.8 13.2
Figure 3 shows the results of our thermal resistance
components calculations. In all cases, the values of
phonon–phonon component Wpp at pre-crystallization
temperatures exceed the corresponding values of Wpp at
pre-melting temperatures. The distinctions Wpp of
phonon–phonon thermal resistance in liquid and solid
state are proportional to variations in positional distribu-
tion of the molecules resulting from melting. The values
of phonon–rotational thermal resistance Wpr in CHCl3
and C6H6 at pre-crystallization temperatures are more
than respective values Wpr at pre-melting temperatures.
The enhancement Wpr of phonon–rotational compo-
nents can be attributed to additional scattering of phonons
on collective rotational excitations, the density of which
increases resulting from intense growth of the processes
of orientational disordering at crystal–liquid phase transi-
tion; so that Wpr is proportional to growth of orien-
tational disordering processes at melting. In the case of
CCl4, the phonon–rotational thermal resistance decreases
at phase transition in liquid state. In our opinion, the later
results from the disappearance of the correlation in
orientational molecular motion and transition of the
CCl4-molecules to hindered rotation. This is in good
agreement with the data cited in [5] indicating that the
character of the molecular motion in CCl4 at pre-melting
temperatures is close to that in liquid state. It is interest-
ing to compare the relationship between Wpp and Wpr in
solid and liquid zone of melting. At pre-melting tempera-
tures, the phonon–rotational thermal resistance Wpr com-
prises 55% for CHCl3, 5% for C6H6 and 50% for CCl4 of
the phonon–phonon thermal resistance Wpp. As a conse-
The thermal conductivity jump at crystal–liquid phase transition
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 403
quence of melting, the change in magnitude of relation-
ship between Wpp and Wpr occurs, and at pre-crystalliza-
tion temperatures, phonon–rotational thermal resistance
comprises 35% for CHCl3, 45% for C6H6, and 17% for
CCl4 of the phonon–phonon thermal resistance.
4. Conclusion
The isobaric thermal conductivity jump at crystal–li-
quid phase transition has been investigated in CHCl3,
C6H6 and CCl4. It is shown that the reduction in the ther-
mal conductivity p at melting derives from the com-
bined effect of variations in positional distribution of
molecules and in the form of rotational molecular motion.
It was found that the melting of investigated crystals in-
volves an increase of phonon–phonon thermal resistance
due to the disordering processes in traslational subsys-
tem. The action of rotational molecular motion at melting
is dissimilar depending on the substance. For example, in
orientationally-ordered crystalline CHCl3 and partially
orientationally-disordered crystalline C6H6, as a result of
melting, theincrease of phonon–rotational thermal resis-
tance occurs, whereas in orientationally-disordered crys-
talline CCl4 during the process of melting one observes
the decrease of phonon–rotational thermal resistance.
The reason is the disappearance of the correlation in
orientational molecular motion and transition of
CCl4-molecules to localized hindered rotation accompa-
nied by the negative jump of orientational entropy at
melting.
1. O.I. Pursky, N.N. Zholonko, and V.A. Konstantinov, Fiz.
Nizk. Temp. 29, 1021 (2003) [Low Temp. Phys. 29, 771
(2003)].
2. H.S. Gytowsky and D.N. McCall, J. Chem. Phys. 32, 548
(1966).
3. A.R. Ubbelohde, Melting and Crystal Structure, Clarendon
Press, Oxford (1965).
4. N.G. Parsonage and L.A.K. Staveley, Disorder in Crystals,
Clarendon Press, Oxford (1978).
5. D.E. O’Reilly, E.M. Peterson, and C.R. Scheie, J. Chem.
Phys. 60, 1603 (1974).
6. Table of Physical Values. Reference Book, I.K. Kikoin (ed.),
Atomizdat, Moscow (1976) (in Russian).
404 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
I.O. Pursky, V.A. Konstantinov, and V.V. Bulakh
1
2
3
4
5
6
7
8
9
185 190 195 200 205 210 215 220 225
Solid Phase [1]
Liquid Phase
— W = 1/p pΛ
— Wpp
— Wpr
0
2
4
6
8
10
12
14
245 255 265 275 285 295
0
2
4
6
8
10
12
14
16
225 230 235 240 245 250 255 260 265
CHCl3
Pressure 0.1 MPa
Tm
— W = 1/p pΛ
— Wpp
— Wpr
— W = 1/p pΛ
— Wpp
— Wpr
Solid Phase [1]
Liquid Phase
Tm
C H6 6
Pressure 0.1 MPa
b
Solid Phase (I ) [1]b
Liquid Phase
Tm
Pressure 0.1 MPa
cCCl4
a
W
,
(m
·K
)/
W
W
,
(m
·K
)/
W
W
,
(m
·K
)/
W
T, K
T, K
T, K
Fig. 3. Phonon–phonon Wpp and phonon–rotational Wpr com-
ponents of the total thermal resistance W in CHCl3 (a), C6H6
(b), and CCl4 (c), calculated for the solid and liquid phases.
The solid line shows the sum of thermal resistances Wpp and
Wpr .
|