Thermal Analysis of Thermophysical Data for Equilibrium Pure Fluids

doi:10.4236/jmp.2013.47A2002

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Journal of Modern Physics, 2013, 4, 8-15

http://dx.doi.org/10.4236/jmp.2013.47A2002 Published Online July 2013 (http://www.scirp.org/journal/jmp)

Thermal Analysis of Thermophysical Data for Equilibrium

Pur e Fluids

Boris Sedunov

Computer and Information Systems Department, Russian New University (ROSNOU), Moscow, Russia

Email: [email protected]

Received April 30, 2013; revised June 4, 2013; accepted July 4, 2013

permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

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

law;

 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

[1].

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

B. SEDUNOV 9

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-

cules.

 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-

vestigations.

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.

B. SEDUNOV

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

D VG

:tr

GG GG



lnRT

(1)

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

VhN

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)

DPDRTD

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

PP D

11 11m

:2DD PRTD





DCD

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

and



 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





–NDVVintmm . And the contribution of the

monomer fraction in the total density becomes equal to

the product





1DVVintm. The negative part of

intmm

,NDVV



, 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

0.5

1.5

0 10203040

D, D

, D

(mol/l)

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.

B. SEDUNOV 11

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]:

nnm

D nCD

nnm

RTCD

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

Energy

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

CC

,,UTPET.

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

energy.



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

Estimation

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



for

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

B. SEDUNOV

with different tangents of slope in the temperature ranges:

from 180 to 420 K and from 450 to 620 K.

2000

4000

6000

8000

10000

12000

250 300 350 400 450 500

(K)

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

enough.

Figure 3 shows that the bond energies E2 for dimers

1.5 2.5 3.5

ln (Ku4)

1000/T

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

vapor.

Dominating

isomer

Temperature

range (K)

Cluster bond

energy (K)

Attraction zone

volume (l/mol)3

3D tetramer 180 - 380 11600 2.0 × 10−13

Linear tetramer 440 - 620 6000 2.8 × 10−7

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-

tion.

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-

uid.

B. SEDUNOV 13



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

5.1

5.2

5.3

5.4

5.5

5.6

ln (K

)

1000/T

5.7

810

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

ml/mol.

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:







222

22 2

exp ;

exp1 .

CV ET

CV ET V





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

200

300

400

100 150 200 250

, C

, V

(ml/mol)

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

B. SEDUNOV

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

)

1000/T

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-

perature.

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;

1300

1500

1700

250 350 450 550 650

(K)

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

line).

250

300

350

100 200 300 400 500

E2(K)

T (K)

Figure 8. The typical for Alkanes growth of the pair bond

energy with temperature in Prop ane.

B. SEDUNOV

 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-

lecules;

 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-

ods.

The complex utilization of the new thermal analysis

method and spectroscopy methods may be very produc-

tive.

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