Journal of Modern Physics, 2013, 4, 8-15 Published Online July 2013 (
Thermal Analysis of Thermophysical Data for Equilibrium
Pur e Fluids
Boris Sedunov
Computer and Information Systems Department, Russian New University (ROSNOU), Moscow, Russia
Received April 30, 2013; revised June 4, 2013; accepted July 4, 2013
Copyright © 2013 Boris Sedunov. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The thermal analysis of precise thermophysical data for pure fluids from electronic databases is developed to investigate
the molecular interaction mechanisms and parameters and the structural features of heterogeneities in fluids. The
method is based on the series expansion of thermophysical values by powers of the monomer fraction density. Unlike
the virial expansion by powers of the total density, the series expansion terms in this method directly reflect properties
of the corresponding cluster fractions. The internal energy had been selected among thermophysical properties as the
most informative for this method. The thermal analysis of its series expansion coefficients permits to estimate the tem-
perature dependence of the pair bond parameters, the clusters’ bond energies and equilibrium constants, the structural
transitions between dominating isomers of clusters. The application of method to different pure fluids, including noble
and molecular gases with van der Waals and polar molecular interactions, brings unknown clusters’ characteristics for
the fluids under investigation. The thermal analysis of the ordinary and heavy Water vapors points on no trivial isotopic
effects. The unpredictable growth of the pair bond energy with temperature in Alkanes points on existence in hydrocar-
bons of some unknown molecular interaction forces in addition to dispersion forces.
Keywords: Molecular Interaction; Cluster; Equilibrium Constant; Bond Energy; Structural Transition; Isotopic Effect
1. Introduction
In the thermal physics of fluids there are clearly seen two
different aspects:
The statistical behavior of many particle systems with
a supposed universal attraction-repulsion mechanism
leading to universal laws, such as the famous van der
Waals equation of state or the corresponding states
The particular features of interactions between mole-
cules with their unique quantum structure leading to a
diversity of specific for every fluid thermophysical pro-
perties and equations of state.
The steady growth of the experimental data precision
and growing requirements to the fine tuning of techno-
logical processes makes now the first aspect rather ex-
hausted and explains an enlarged attention to the indi-
vidual features of fluids, reflected in modern publications
The investigation of equilibrium molecular interac-
tions [2,3] in real gases, liquids and supercritical fluids
presents a very complex problem. The energies of mo-
lecular interactions are of the same order of magnitude as
the energies of thermal movements, therefore, the spec-
trum of bound states is not discrete, but rather continuous
[4]. For this reason the methods of spectroscopy, being
very informative at the chemical bonding investigations,
become not so effective as far as the molecular interac-
tions in fluids are concerned. So, there is a need in alter-
native methods to study molecular interactions in fluids.
The investigation of molecular interactions in local
equilibrium heterogeneities of fluids is very important for
better understanding of the fluids’ structures and for fur-
ther improvement of the technological processes. The he-
terogeneity of the fluids’ structure [5,6] is very essential
and should be taken into consideration for the molecular
interactions study because the fluids possess temporarily
existing local molecular agglomerations of different struc-
tures and sizes:
In real gases, in addition to the dominating fraction of
monomers [7], there are fractions of dimers, trimers,
tetramers and larger clusters [8-12]. The molecular clus-
ters are presented in different isomer configurations
[13], the number of which grows with the number of
particles in the cluster. The clusters in gases are the
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centers of nucleation [14-16] developing at a super
saturation into liquid drops or solid particles [17], like
in a fog.
In liquids there is a continuous net of molecules with
short intermolecular distances, interrupted by point va-
cancies [18] and pores of larger dimensions depend-
ing on density. The local number of the intermolecu-
lar bonds in the net may differ for different mole-
The supercritical fluids possess at subcritical densities
a fog-like and at supercritical densities a foam-like
structure with a superposition of clusters in pores and
pores in clusters [19,20].
The local structures in fluids change with time, tem-
perature and density; the change of an average density
does not lead to a uniform change of intermolecular dis-
tances. The fluids’ models based on assumptions of the
uniform stretching are not productive for the molecular
interactions study. For example, widely used in practice
virial expansion of thermophysical values by powers of
the fluid density [13,21] silently supposes the uniform
distribution of the density in a volume. But the given in
thermophysical tables density averages the local densities
inherent to heterogeneities and is not a universal variable
for all local objects in a fluid. For this reason this type of
series expansion cannot lead to a correct picture of the
fluid structure. A more adequate variable is needed as ba-
sic for the method aimed at the fluids’ structural features
and molecular interaction mechanisms and parameters.
The goal of this paper is to describe the new method of
thermal analysis of the molecular interactions in pure
fluids based on the series expansions of precise equilib-
rium thermophysical data by powers of the monomer frac-
tion density [4,7,22]. This phenomenological approach is
capable to open significant details of the microscopic
structural features of fluids.
2. The Thermal Analysis of Precise
Thermophysical Data for Equilibrium
Pure Fluids
The bulk of the thermal analysis methods develop their
own experimental tools and procedures. But the thermal
analysis of thermophysical data, to be discussed here, uti-
lizes already existing experimental data. To provide valu-
able results we should select as precise data as possible
from the state of art level sources. The greatest precision
of thermophysical data is now achieved by the generali-
zation of experimental results of different research groups
from all over the World [23] and by their computer pro-
cessing with an account of thermodynamically driven cor-
relations between different thermophysical values [24].
These data accumulate collective efforts of researchers
during a long period of experimental and analytical in-
In modern science and technology a large attention is
paid to pure fluids, which thermophysical properties can
be determined very precisely. The purity of fluids insures
the reproducibility of technological processes and leads
to a high precision of thermophysical data. For this rea-
son our method utilizes precise electronic databases for
thermophysical properties of pure fluids. The method can
be extended also to mixtures provided the precision of
composition and thermophysical data for mixtures stays
at the same level as for pure fluids.
2.1. The Source of Experimental Data for New
Method of Thermal Analysis
Now, due to the joint computer processing of raw experi-
mental data from different sources, it is possible to im-
prove the resulting precision of the generalized data. This
process is named as the critical evaluation of experimen-
tal data [24,25]. The web site of the Thermodynamics
Research Center (TRC) of the US National Institute of
Standards and Technology (NIST) presents this sort of
scientific activity as [25]:
“Critical evaluation is a process of analyzing all avail-
able experimental data for a given property to arrive at
recommended values together with estimates of uncer-
tainty, providing a highly useful form of thermodynamic
data for our customers. The analysis is based on inter-
comparisons, interpolation, extrapolation, and correlation
of the original experimental data collected at TRC. Data
are evaluated for thermodynamic consistency using fun-
damental thermodynamic principles, including consisten-
cy checks between data and correlations for related pro-
perties. While automated as much as possible, this proc-
ess is overseen by experts with a great deal of experience
in the field of thermodynamic data.”
The thermodynamically driven correlations between
different thermophysical values are very important. For
example, the individual measurements of equilibrium
compressibility, heat capacities, sound speed, Joule-Thom-
son coefficient and some other thermophysical values in
a wide range of pressures and temperatures can be gener-
alized in a mutually correlated system of thermophysical
properties and presented in a form of an electronic data-
base, such as the NIST databases for thermophysical pro-
perties of pure fluids [26,27]. All initial data for this work
had been taken from the NIST Database: “Thermophy-
sical Properties of Fluid Systems” [26].
The extraction of the molecular interaction parameters
from thermophysical data is the inverse mathematical
problem that suffers from enlarged final errors even at
rather small initial errors. So, the regularization of ex-
perimental data leading to generalized data with mini-
mized errors is obligatory for this type of analysis.
Copyright © 2013 SciRes. JMP
2.2. The Basic Variable for the Thermophysical
Data Thermal Analysis
For thermal analysis of thermophysical data the mono-
mer fraction density (MFD), Dm, had been suggested [4,7]
as the basic variable. In a microscopic sense Dm means
the density of not bound particles that are temporarily
free from interactions with other particles. This definition
of the MFD can be applied only to small density real
gases or to local zones with temporarily reduced density
in denser fluids. Instead of the misleading microscopic
definition we use the phenomenological definition of the
Dm [7] as the reflection of the translational part Gtr of the
molar fluid’s Gibbs energy, G:
mq tr
The tr is determined [7] as the difference between
the total Gibbs energy and the Gibbs energy for internal
molecular movements intint . In this pheno-
menological approach the Gint is supposed to be inde-
pendent on the fluid density and all density dependent
part of G is ascribed to Gtr. In an equilibrium fluid the
Gibbs energy G for a mole of basic particles, named as
the Chemical potential, does not depend on the nature of
heterogeneities. It is the same for all basic particles, as
for free moving (monomers) and for included in clusters
and other agglomerations. It allows us to use Equation
(1) for all basic particles in the fluid. The defined so new
variable MFD inherits the uniformity of the Gibbs energy
and coincides with heterogeneous microscopic density of
no bound particles only in the local small density zones
of fluids.
The included in Equation (1) universal gas constant R
is specific for a database and a substance to be analyzed.
The electronic databases, like [26], reflect historic char-
acter of the thermophysical research. They are based on
experimental data received in different times, when the R
value could differ from its contemporary nominal value.
It makes the R values in the electronic databases different
for different substances. So, before processing the table
of data for some substance it is needed to estimate the
specific R value as the limit of P/TD ratio at zero P.
Equation (1) contains also the quantum volume Vq [28]
of basic particles, proportional to the third power of the
thermal de Broglie wavelength:
34 2.pMRT
It is not needed to find separately the Gint and Gtr val-
ues. For us it is essential that all pressure dependent part
of G is included in the Gtr. So, we can apply the well
known equation GPV to Gtr given by Equation (1)
just to come to the equation for Dm:
. (2)
The numerical integration of Equation (2) at a constant
T is a delicate procedure with small initial 1 and step
i 1
ii values. The initial value for m may
be found from initial values for pressure P1 and density
11 11m
1, 2, 3,n
[7]. At small pressures the Dm (P)
stays very close to the total molar density D (P), Figure
1. But at larger pressures there is a large divergence of
these values, due to a large contribution of clusters in the
total density.
The clusters in an equilibrium fluid are in some way
similar to chemical compounds in an equilibrium reac-
tion medium. According to the chemical equilibrium prin-
ciples the partial molar density Dn of the n-particle clus-
ter fraction should be proportional to the n-th power of
the monomer fraction density: nn
, with C1 = 1
Here Cn is an apparent equilibrium
constant, reflecting the PDT relations, but for clusters the
nature of the Cn is more complex than for chemical
compounds [4,7]: at high temperatures the Cn may be-
come negative. Just to distinguish the constants Cn from
equilibrium constants we will name the Cn as the PDT
constants. The name “constant” for Cn means that they are
constant only in isothermal conditions for all pressures,
but their change with temperature is great.
As we said, the local density of no bound particles
may be equal to Dm only for zones of fluid that are tem-
porarily free from interactions between particles. It
means that the molar number of not bound particles is
not equal to the product of Dm by the molar volume V.
We should subtract from the molar volume the volume of
fluid with active molecular interactions, Vint, belonging to
clusters. Then, the molar number of monomers becomes
equal to
NDVVintmm . And the contribution of the
monomer fraction in the total density becomes equal to
the product
1DVVintm. The negative part of
, may lead to negative terms in series
expansions of D or P by Dm. These negative terms have
been ascribed by the author to virtual clusters [4,7] that
0 10203040
D, D
, D
Pressure (bar)
Figure 1. Comparison of the Monomer Fraction Density, Dm
(thin line), with the total Density, D (thick line), and the
ideal gas Density, Dp = P/RT (dashed line), for Ammonia at
T = 350 K.
Copyright © 2013 SciRes. JMP
do not exist physically, but appear in series expansions of
P and D by Dm.
The total density D and pressure P are the sums of par-
tial contributions [4,7]:
D nCD
Dn (3)
PRTD (4)
The divergence of D and Dm at large pressures, seen at
Figure 1, is due to contributions of clusters and ex-
plains why the virial expansion by D differs from the
series expansion by Dm.
2.3. The Series Expansion of the Potential
The isothermal series expansion terms of some thermo-
physical value by powers of Dm reflect contributions of
corresponding cluster fractions in this thermophysical
value. For our thermal analysis method the most infor-
mative thermophysical property is the potential energy U,
defined phenomenologically as the difference between
molar internal energy E at a given pressure P and its
value at zero pressure:
,0P ET
nMC D
The defined so potential energy is negative and includes
in its pressure dependence the microscopic changes of
both potential and kinetic energy [4].
Instead of the molar potential energy U we expand by
Dm the positive potential energy density W, equal to –UD.
The series expansion of W may be better understood in
comparison with the expansion for specific density
, where M is the molecular mass of basic
particles and nM is the cluster’s mass. For W we use in-
stead of nM the bond energy En of the n-particle cluster
and instead of the Cn, reflecting the PDT relations, the
equilibrium constant Cun for potential energy. Unlike the
PDT constant Cn, it does not contain the virtual part, be-
cause the monomers do not contribute to the potential
The equilibrium constant Cun has the same sense as the
spectroscopic equilibrium constant Csn. At the domina-
tion of only one isomer in the n-particle cluster fraction
unsn . In general, it differs from the spectroscopic
equilibrium constant due to different mechanics of the
cluster isomers’ contribution in energetic and spectro-
scopic characteristics.
2.4. The Parameters of Molecular Interactions in
Pure Fluids
The pair bond energ y, E2. It may be found from the
temperature dependence for the second coefficient
Ku2 of the W series expansion by Dm. It is the average
molar energy of the dimer fraction decomposition to
free moving particles. The energy of the dimer bound
state is the minimal energy of the pair interaction po-
tential plus the kinetic energy of the dimer’s internal
molecular movements. This energy may depend not
only on the distance between particles, but also on the
mutual orientation of particles. This effect is very im-
portant for polar gases, but also may influence the pair
bonding in the van der Waals gases, even in atomic
gases, due to the lack of rotational symmetry of their
electronic outer shells.
The bond energ y, En, for n-p article cluster fraction.
It may be found from the temperature dependence for
the n-th coefficient Kun of the W series expansion by
Dm. It is the average molar energy of the n-particle
cluster fraction decomposition to free moving parti-
cles. In the temperature range, where only one isomer
dominates, the En value may be close to a constant.
But in the temperature range, where two or more
isomers may coexist, the En depends on temperature.
The equilibrium constant Cun for the n-particle
cluster fraction. It may be found by division of the
n-order series expansion coefficient Kun for W by the
bond energy REn. The spectroscopic method can feel
the difference in spectrums of different isomers, there-
fore, the equilibrium constant Csn may be split on par-
tial isomers’ equilibrium constants, but the Cun is a
thermodynamic average for all isomers of the n-par-
ticle cluster fraction.
The pair attraction zone volume, V2. It may be
found by division of the equilibrium constant Cu2 by
the Boltzmann factor exp (E2/RT).
The cluster attraction zone volume, Vn. Its dimen-
sion is equal to 3 (n 1) and it may be found by divi-
sion of the equilibrium constant Cun by the Boltzmann
factor exp (En/RT).
The pair interaction excluded volume, Vex. It may
be found from values for the pair attraction zone vo-
lume V2 and the PDT constant C2:
22 2
exp 1
VV ERTC. (5)
2.5. The Method of the Cluster Bond Energies En
To estimate the cluster fractions’ bond energies we use
the temperature dependencies of series expansion coeffi-
cients Kun (T) for the potential energy density W. The ln
(Kun) plot versus reverse temperature 1000 T
some temperature ranges may have almost linear parts
corresponding to the dominating cluster isomers in the
n-particle cluster fraction. Figure 2 shows the depend-
ence of the ln (Ku4) for 4-particle cluster fraction in the
Methanol vapor from the reverse temperature, 1000/T. It
is seen that there are two almost linear parts of the graph
Copyright © 2013 SciRes. JMP
with different tangents of slope in the temperature ranges:
from 180 to 420 K and from 450 to 620 K.
250 300 350 400 450 500
T (K)
On differentiating the ln (Kun) by 1000 T
find the clusters’ bond energies En, expressed in kK. The
average bond energy in the Methanol vapor tetramers for
the low temperature zone, T < 420 K, may be estimated
as E4l = 11600 K, and for the high temperature zone, T >
450 K, E4h = 6000 K. The bond energy here is expressed
in K to provide its comparison with the system tempera-
ture T, Table 1.
Table 1 shows also the attraction zone volumes for
dominating isomers that differ more than million times. It
means that the freedom of movement of every particle,
attached to the central particle, in the dense 3D configu-
ration is limited by two orders of magnitude as compared
to their movements in the loose linear configuration.
It is seen that the bond energies for both temperature
zones are much larger than the maximal temperatures in
the zones. It gives a hope that the bond parameters in
clusters of polar gases may be found also by some spec-
troscopy method.
2.6 The Method to Study the Structural
Transition in Gaseous Clusters
The temperature dependence n shows changes of
the molecular cluster isomer structure with temperature.
Figure 3 shows estimations for bond energies in dimers,
trimers and tetramers for Methanol vapor in the tempe-
rature range 250 - 500 K, where the results are stable
Figure 3 shows that the bond energies E2 for dimers
1.5 2.5 3.5
ln (Ku4)
4.5 5.5
Figure 2. The ln (Ku4) dependence from the reverse tem-
perature for the tetramer fraction in the Methanol vapor.
Table 1. Bond parameters of tetramers in the Methanol
range (K)
Cluster bond
energy (K)
Attraction zone
volume (l/mol)3
3D tetramer 180 - 380 11600 2.0 × 1013
Linear tetramer 440 - 620 6000 2.8 × 107
Figure 3. Bond energies of dimers (thick line), trimers (thin
line) and tetramers (dashe d line) for Methanol vapor in the
temperature range 250 - 500 K.
and E3 for trimers in the Methanol vapor fall noticeably
in the temperature range 250 - 400 K. This fall may be
explained by loosening of the hydrogen bonds due to the
growth of the mutual molecular vibrations amplitude in
the clusters with temperature. The apparent growth of the
pair bond energy at T > 400 K needs a special investiga-
The dominating isomer configuration for trimers in the
range of temperature, where E3/E2 ratio does not exceed
2, is an open chain structure with two pair bonds. Only
lower T = 300 K E3/E2 ratio exceeds 2 that may be inter-
preted as the growing influence of trimers with a closed
triangular tightly bound structure.
But the most interesting is the E4 (T) dependence. It
clearly shows the structural transition in the tetramer
fraction from tightly bonded isomers at T < 380 K to
loosely bound isomers at T > 440 K. In the high tem-
perature range the E4/E2 ratio is around 3 - 4 that tells
about the loosely bound linear or ring isomer configura-
tion. But in the low temperature range the E4/E2 ratio is
near 6. It tells about the compact 3D isomer structure
with 6 hydrogen bonds.
This structural transition is not abrupt, but takes a
rather wide range of temperatures, 380 - 440 K, in which
both isomer modifications coexist. This type of structural
transitions can be named as the soft structural transition
[4]. The individual reaction of clusters on changing tem-
perature makes the transition zone between different
dominating isomers extended. The larger is the differ-
ence between the isomers’ bond energies, the narrower is
the transition zone. When the number of particles grows,
the transition zone becomes narrower. At macroscopic
sizes of clusters the transition zone vanishes and the soft
structural transition converts to the first order phase
transition with the strictly determined transition point.
The dew point is an example of the precisely determin-
ed phase transition point for macroscopic drops of liq-
Copyright © 2013 SciRes. JMP
3. The Results of the Thermal Analysis for
Different Fluids
3.1 Thermal Analysis of the Pair Interaction
Parameters for Argon
Argon is the most investigated real gas. But different
publications give different estimations of the pair inter-
action bond energy. These estimations are mainly about
the depth of the atomic interaction potential well. Many
publications discuss the second virial coefficient B (T)
temperature dependence, but there is no information about
the dimer fraction equilibrium constant and its parame-
ters: the molar volume of the attraction zone and the ex-
cluded volume.
In our method the pair bond energy for atomic gases is
the molar energy of the dimer fraction dissociation to
free moving atoms. This energy can be found from the
tangent of slope for the ln (Ku2) versus 1000/T graph,
Figure 4. The found so E2 = 91.4 K in the temperature
range 100 - 250 K. The root mean square deviation from
the average value for E2 is near 1.5 K.
The range 100 - 250 K is representative enough and
includes the critical temperature. In this range the results
for E2 are the most stable, but out of this range there are
noticeable deviations of found by this method values
from the average value for E2. Near the triple point there
is a slight growth of the pair bond energy that may be
caused by the lack of rotational symmetry for the outer
electronic shell and over T = 250 K the influence of the
repulsion forces on the potential energy of the Argon real
gas becomes noticeable.
Having found the pair bond energy E2 we find the
equilibrium constant Cu2, Figure 5, simply dividing the
Ku2 values by RE2 [4]. The second coefficients of the
series expansions for P (Dm) and D (Dm) in accordance
with the system of Equations (3) and (4) [4,7] give the
PDT constant C2 (T), shown also at Figure 5. It is clearly
seen that between equilibrium constant Cu2 and PDT
constant C2 there is a large difference, caused by virtual
dimers [4,7,12].
= 91.4 K
ln (K
Figure 4. The pair bond energy for gaseous Argon as the
tangent of slope for the logarithmic dependence of the po-
tential energy density second series expansion coefficient
Ku2 by Dm versus reverse temperature.
Dividing Cu2 by
exp ET
2 we find the pair attract-
tion zone volume V2 that for Argon in the temperature
range 100 - 250 K is equal to 147.4 ml/mol. Deviations
from this average value in the temperature range under
investigation are very small and do not surpass 0.5
Then Equation (5) provides the excluded volume Vex =
37.4 ml/mol. Deviations from the average value for Vex
are by the order of magnitude lower than the deviations
of the V2 values and do not surpass 0.05 ml/mol. It tells
that the model of atomic interactions in Argon with con-
stant values for E2, V2 and Vex has a good precision in the
100 - 250 K temperature range.
Both volumes are seen at Figure 5. So, we came to the
full picture of pair interactions in Argon for the tem-
perature range 100 - 250 K.
It is useful to write the full system of equations and
parameters, Table 2, for molecular interactions in Argon
in the temperature range 100 - 250 K:
22 2
exp ;
exp1 .
Similar systems of equations and pair interaction pa-
rameters have been found for many investigated pure real
gases with the van der Waals interactions and their zones
of stability for the pair bond energy have proven to be
wide enough. But in polar gases, like in the Water vapor,
this zone of stability is narrow due to high temperature
dependence of the hydrogen bond energy at low tem-
peratures, how it will be seen from the next section.
100 150 200 250
, C
, V
, V
Temp era ture ( K)
Figure 5. The full picture of the volume interaction pa-
rameters for dimers in Argon in the temperature range 100
- 250 K: equilibrium constant Cu2 (thick solid line), PDT
constant C2 (thin solid line), pair attraction zone volume V2
(thick dashed line), excluded volume Vex (thin dashed line).
Table 2. The pair interaction parameters for Argon in the
temperature range 100 - 250 K.
Pair bond energyPair attraction
zone volume Excluded volume
E2 (K) V2 (ml/mol) Vex (ml/mol)
91.4 147.4 37.4
Copyright © 2013 SciRes. JMP
3.2. Thermal Analysis of Isotopic Effects in
Water Vapors
It is very interesting to see how the molecular interaction
parameters feel the difference in masses of atoms for the
same chemical structure of molecules. Investigation of
the ordinary and heavy Water vapors discovers the high
sensitivity of the clusters’ characteristics to the mass of
hydrogen atoms, Figure 6.
Similarly with the Methanol vapor, the change of tan-
gent of slope for the ordinary Water vapor graph in the
temperature range 340 - 380 K points on the change of
the dominating isomer from the loosely bound tetramer
at high temperatures to the tightly bound type at lower
temperatures. But for the heavy Water vapor the domi-
nating type of isomers in the tetramer fraction stays un-
changed in all temperature range under investigation. It
looks like the tightly bound clusters in the heavy Water
vapor cannot exist even near the triple point. It would be
interesting to investigate the equilibrium D2O vapor at tem-
peratures lower the triple point. The clearly seen coin-
cidence of the bond energies for loosely bound tetramers
in both cases tells that in the linear configuration the bond
energy is not sensitive to the masses of Hydrogen atoms.
But larger mass of Hydrogen isotop, Deuterium, for some
unknown reason prevents tetramers in D2O vapor from
bonding into more dense 3D configuration.
For dimers we see an opposite picture: at T < 380 K
the pair bond energies in the ordinary and heavy Water
are almost equal, but at higher temperatures the pair bond
energy in D2O is near 10% higher than in H2O, Figure 7.
At T < 380 K the bond energies in both cases fall with
temperature, reflecting the fact of the mutual vibration
amplitude growth with temperature. But at T > 380 K the
bond energies in both cases grow with temperature. If the
pair bond energy fall with temperature may be under-
stood on the chemical physics basis, the growth of the
pair bond energies in the Water vapors with temperature
1.5 2 2.5
ln (K
3 3.5
Figure 6. The isotopic effect for tetramers in H2O (thick line)
and D2O (thin line) expressed by the fourth series expansion
coefficient Ku4 in a logarithmic scale versus reverse tem-
is a challenging problem for researchers. The same cha-
racter of the pair bond energy behavior has been noticed
in Methanol, Figure 3, and Alkanes.
3.3. Thermal Analysis of Pair Molecular
Interactions in Alkanes
In Hydrocarbons the growth with temperature of the pair
interaction bond energy, found by this method, is seen in
all investigated real gases, including the Alkanes. Figure
8 shows the typical for Alkanes growth of the pair bond
energy with temperature in Propane.
This growth of the pair bond energy is very significant
and stimulates thinking about some new type of molecu-
lar interaction forces in no polar gases in addition to well
known dispersion forces. These new forces may be ther-
mally activated attractions between no polar Hydrogen
containing molecules.
4. Summary and Conclusions
The utilization of the monomer fraction density as an ar-
gument for series expansions of the thermophysical val-
ues instead of the total density has been put into the basis
of the new thermal analysis method aimed at the extrac-
tion from the precise electronic databases the molecular
interaction parameters:
The thermal analysis of the internal energy of real
gases permits to find the clusters’ bond energies and
equilibrium constants for the cluster fractions;
250 350 450 550 650
T (K)
Figure 7. The isotopic effect in the Water vapor dimers.
Pair bond energy E2 in K: in H2O (thick line) and D2O (thin
100 200 300 400 500
T (K)
Figure 8. The typical for Alkanes growth of the pair bond
energy with temperature in Prop ane.
Copyright © 2013 SciRes. JMP
Copyright © 2013 SciRes. JMP
The thermal analysis of the clusters’ bond energies
permits to discover the soft structural transitions be-
tween dominating isomers of clusters, the width of
the transition zone falling with the growth of the iso-
mers’ bond energy difference;
The thermal analysis of the pair bond energies in
many gases discovers the growth of the bond energy
at lowering the temperature that may be connected
with the limited rotation of interacting atoms or mo-
In no polar molecules, containing Hydrogen, as in Al-
kanes, the new thermal analysis method discovers the
pair bond energy growth with temperature that points
to a possible presence of the thermally activated in-
termolecular forces;
Large values of bond energies for polar molecular
clusters open possibilities for alternative methods of
their investigation, including the spectroscopic meth-
The complex utilization of the new thermal analysis
method and spectroscopy methods may be very produc-
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