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Nikolaev V.F., Ismagilova G.I., Sultanova R.B.
C O NT RI B U T I O NS O F I NT E RM O L E C U L AR I NT E RA C T I O NS T O NO RM AL B O I L I N G P O I NT O F PU RE MO L E C UL AR L I Q U ID S
В статье «Вклады межмолекулярных взаимодействий в нормальные температуры кипения индивидуальных молекулярных жидкостей» предложен новый подход к анализу нормальных температур кипения индивидуальных веществ, отличающийся от известных аддитивно-групповых подходов использованием дескрипторов дисперсионного и электростатического межмолекулярного взаимодействий. Дескриптор дисперсионного взаимодействия рассчитывается на основе мольной рефракции и мольного объема веществ, а электростатический дескриптор - на основе дипольного момента и мольного объема веществ. Проанализированы нормальные температуры кипения органических веществ различных классов и оценены вклады дисперсионных, электростатических и специфических взаимодействий. Вклад в температуру кипения электростатических межмолекулярных взаимодействий находится в интервале, нижняя граница которого определяется электростатическим дескриптором, рассчитываемым с использованием квадрата молекулярного дипольного момента, а верхняя - с использованием суммы квадратов дипольных моментов полярных связей, входящих в молекулу.
Ключевые слова: нормальные температуры кипения, индивидуальные жидкости, электростатический вклад, дисперсионный вклад, дипольный момент, молекулярная рефракция, молярный объем.
1. Introduction. Normal boiling point is one of the most important identifying parameters of pure substance. This parameter is often used as a basic value for calculating the critical temperature needed to predict the substance properties basing on the principle of corresponding states.
The additive-group methods for the normal boiling point estimation, which mainly associate the boiling point with the molecular structure, and not with the character of interaction of mutual affinity molecules, are still widely spread [1-5]. These methods do not allow to assess the contributions of different types of universal and specific interactions to normal boiling point. So far the problems concerning the boiling points of molecular liquids and the nature of electrostatic interaction in liquids have been a point of discussion in the learned society [6].
Main components of intermolecular interactions are dispersion (London), orientation (dipole-dipole, dipole-quadrupole), induction (dipole-induced dipole, quadrupole - induced dipole), and specific interactions. For describing main contributions of universal interactions in the proposed model we used the data on dipole moments, molar refractions and molar volumes of substances. In the absence of the appropriate experimental data they may be calculated basing on the molecular structure and the known scalar (for molar refraction [7] and molar volume [8; 9]) and vector (for dipole moment [10]) additive schemes.
2. Database. Operability of the proposed model has been exemplified on normal boiling point analysis of the following classes of organic substances: n-alkanes, n-alcohols, n-carboxylic acids (section 4.1.), polar and non-polar derivatives of aromatic hydrocarbons of benzene and naphthalene series (section
4.2.), derivatives of cyclic and aliphatic hydrocarbons (halogenalkanes, nitriles, ketones, nitroalkanes) (section 4.3). In the present paper there have been used the literary data on boiling points, density, refractive index, and dipole moments, indicated in works [11-13].
3. Non-continuum model for describing the normal boiling point of pure molecular liquids In work [14] we have proposed a non-continuum model for predicting molar physicochemical properties of pure liquids and for assessing the contributions of different types of intermolecular interactions. Molar physicochemical properties of liquid F (molar enthalpy of evaporation, boiling point, molar surface tension [15], vapor pressure logarithm, etc.) may be represented as a sum of several contributions:
for substances with universal interactions
where FHhm is physicochemical property of hypothetical homomorph of a substance (dispersive contribution), i.e. the property of the same substance, but with «disconnected» electrostatic and specific interactions between their molecules, Felst - electrostatic contribution, which includes the contribution of orientation (dipole-dipole) interactions and the interactions of dipole-induced dipole, FSP - specific contribution due to the formation of hydrogen bonds between molecules.
We have proposed the following relation to describe the properties of molecular liquids only with universal intermolecular interactions:
where F - molar physicochemical properties of pure liquid,
(1)
for substances with specific interactions
(2)
F = F + F HHM ELST
F
HHM
A + B - molar physicochemical properties of hypothetical ho-
n2
momorph of substance, F = C • — - electrostatic contribution in the 1 ’ ELST V
molar physicochemical properties (the orientation contribution together with
dipole-induced dipole interaction contribution), // - dipole moment,
i2 -1^ M
mr = —----< — molar Lorentz-Lorenz refraction (n - refractive index at 293.15
<2+2^ d
Kfor the ZMine Na), d- density at 293.15 K M- molecular weight, A, B, C-coefficients derived from statistic data processing for substances having no specific interacting groups-COOH,-OH,-CONH2,-NH2, etc. For the specific interaction substances the contribution of electrostatic interactions F Q have not
ELS I
been singled out separately, since in the formation of hydrogen bonding a molecule in a liquid loses its individuality and the dipole moment, determined in the inert solvent, practically does not reflect the real behavior of a particular molecule among others.
3.1. Descriptors of the universal intermolecular interactions for pure liquids
3.1.1. The descriptor of electrostatic interactions. The previous analysis of evaporation enthalpies of homologous series of polar primary monosubstituted normal alkanes has demonstrated that besides dispersive contribution they include the contribution proportional to dipole moment square [16]. Square of dipole moment may be attributed to the presence of pure liquids of two types of electrostatic intermolecular interactions. The first type: dipole -induced dipole interaction, and the second - non-rotating dipole-dipole interaction. In paper [16] this contribution has been identified as the energy contribution of dipole-induced dipole interactions, which is proportional to the square of the dipole moment according to the relation: E= -f ti2 0.2/21*, where //i - dipole moment of molecule 1, a - the average polarizability of molecule 2, r -distance between the centers of molecules [17]. On the other hand, proportionality of electrostatic contributions to physicochemical properties of pure substances to the dipole square moment follows from the analysis of the experiment on the magnetic birefringence (Cotton-Mouton effect). This conclusion has been made on the basis of analysis [18; 19] of solvent effect on molar Cotton-Mouton constants of nitrobenzene mCNB in the process of their determination in series of aliphatic and aromatic solvents with different polarity and anisotropic polarizability. The explanation has been given on the basis of the relation that describes the dipole-dipole interaction energy between two nonrotating dipoles. There has been obtained a linear correlation relation (4), which confirmed the short-range order of orientation interactions of nitroben-
zene with the molecules of solvent S, as well as permissibility of using the dipole approximation in describing solvent effects:
(.cj,=„c,+a.^^A , (4)
NB-S
where (mCNB)S - molar Cotton-Mouton constant of nitrobenzene in solvent S, mCo - intercept, close in value to molar Cotton-Mouton constant of nitrobenzene in gas phase, jus - dipole moment, (Ahu)s - polarizability anisotropy of solvent molecule S relative to the direction of the dipole moment juS, SNB-S - the average distance between the molecule of nitrobenzene and solvent molecules of the first solvate layer, calculated from the molar volumes of nitrobenzene and solvent S. It is noteworthy that molar Cotton-Mouton constant of pure nitrobenzene conforms to the same dependence. It has been revealed that determinative contributions to (mCNB) S are the dipole-dipole orientation p,NB - M-S and quadrupole-dipole QNB - p,S interactions between nitrobenzene (NB) and the molecules of solvent (S). The presence of solvent polarizability anisotropy in the relation (4) is due to the fact that only solvent effects with participation of solvent molecules, which are anisotropic on polarizability, are «visible» in the magnetic birefringence. The established correlation (4) was the second reason for justifying the need to use in the non-continuous model the dipole moment square as a descriptor of electrostatic interactions in the analysis of properties of pure liquids, with the only difference that, in accordance with relation (5), the energy of interaction of two fixed dipoles requires the account of distance between the centers of molecules [17; 20]:
E = —|_i, ■ цДЗсоэе, cos02 -cos612)/r3 ’ (5)
where hi, jj.2- dipole moments of interacting molecules, r - distance between dipoles, 6i, 62 - angles defining the orientation of dipoles in the polar coordinate system, 0n - angle between the directions of dipoles.
In the case of analysis of electrostatic contributions to the physicochemical properties of pure liquids, when fj.i = u2, the proportionality E ~ |o,2 /r3 should be observed. Taking into account the proportionality of the cubed average distance r3 between directly contacting molecules of pure liquid toits molar volume V, the descriptor of electrostatic interactions in the final appearance has
taken the form (-L / V where V - molar volume of the substance, calculated from its molar mass M and density d ( at 293.15 K).
Thus, if the orientation (dipole-dipole) interactions are considered neither as rotating dipole interactions, described by the Keezom relation [17], nor as
dipole-continual medium interactions with dielectric permeability s (Kirkwood [21], Botcher [22]), but as the interactions of non-rotating dipoles of directly contacting molecules, then in the molar physicochemical properties of pure liquids there should be present the contribution which is proportional to /V. This ensures the possibility for the contributions of dipole-induced dipole and non-rotating dipole-dipole interactions to be described with the help of a single descriptorn2 / v. The value of the electrostatic descriptor |.i2/vfor nonassociated liquids can be indirectly assessed from the static permeability s and the refractive index n (e.g. 293.15 K and D-line Na) of liquids basing on the Jatkar relation [23]:
(є — n2) • V = 47iNc
kT
|i2 kT V " 4ttM
(s-n2)~(s-n2)
(6)
(7)
3.1.2. The dispersion interaction descriptor. The mathematic form of the empirical dispersion (London) interaction descriptor MR2/Vused by us [24] is consistent with the known correlations of the dispersion contribution to the different physicochemical properties of a solute A with bulk polarizability ((n2 -1) /(n2 + 2))s of variable solvents S, [25], as well as with the linear correlation of solvation enthalpies of different polar and non-polar solutes Ai in a single solvent S on the molecular refraction of the solute MRAi [26]. With the aim of simplifying the use of the model, the ionization potential J, present in the London equation for the paired dispersion interactions [17], has been excluded from the dispersion interaction descriptor, though, as it will be shown below, in some cases the inclusion of this characteristic turns out to be quite necessary. The analysis of the properties of pure substances can be considered as an analysis with simultaneous or co-ordination change of the solute and the solvent (Ai = Si). For the reasons given the dispersion interaction descriptor for pure liquid takes up the following form:
MR-(n2 -l)I(n2 +2) = ((n2 -ї)І(п2 +2)f ■M/d =
= MR2-d/M =MF?/V
The relation coefficients with dispersive and electrostatic members B / C in the equation (3 ) when analyzing different molar physicochemical properties of a single group of substances, whose molecules participate only in universal (Van der Waals) interactions, has remained almost stable.
4. Results and discussion
4.1. Normal boiling points of n-alkanes, primary n-alcohols and n-carboxylic acids. In our research, owing to the widening range of substances to be analyzed, and, thus, extending the interval for normal boiling points Tb (K), the exponent of the dispersion interaction descriptor has been empirically specified and the free term A, previously present in the model (3), has been excluded. The exclusion of free term from the model actually means that in the absence of the forces of universal interaction between molecules, when MR —» 0 n jj. 0, the boiling point Tb in extreme case has to tend to the temperature of absolute zero 0 K. Thus, the modified variant of non-continuous model for boiling temperatures has taken up the following form. (8):
T (K)= B-b
r o\n MR
V
2
tt ’ (8)
where B, C and n - parameters of the model obtained from the joint statistical data processing T (K) MR2 j±f_for a series of substances without specific inte-
b V ’ V
racting groups.
In order to check up the efficiency of the dispersion descriptor data on the normal boiling points of normal hydrocarbons (Fig. 1) has been analyzed. Fig. 1 illustrates the points for primary n-alcohols and n-carboxylic acids, which are lying on their own smooth lines, but above the line of n-alkanes. In
the limit when ME?_______> all three lines merge into one. It also follows from
V
Fig. 1 that the contributions of hydroxyl and carboxyl groups to the boiling point are not constant and decrease with the alkyl chain lengthening, which is only natural, the direct contacts between two identical functional groups, as well as the formation of hydrogen bonds becoming sterically less probable.
c
Fig. 1. Normal boiling points of n-alkanes, primary n-alcohols and n-carboxylic acids from the dispersion descriptor (Notations I - n-alkanes C4 - C30, O - 1-alcohols CVC20, A - 1-carboxylic acid, x -water).
Dependence of Tb for n-alkanes is described by relation (9):
Tb = 130.98-(MR2/V)0'436934 (r 0.9996, s 2.22) (9).
Since the ionization potentials of n-alkanes, «-alcohols and «-carboxylic acids are close (10.80 eV (butane), 10.19 eV (n-decane), 10.95 eV (methanol), 10.30 eV (n-butanol), 10.66 eV (acetic acid), 10.22 eV (n-butane acid) [27]), then using the dependence (9), it is possible to estimate the boiling point THhm of hypothetical homomorph of alcohols and carboxilic acids (Table 1). Table 1 also shows the contributions determined by specific interactions ATsp. On assuming the probability of pair contact of functional groups to be proportional to the product of shares held by these groups on the molecular surface, we can use the approximating relation ATsp = ex (V p)4 3. Indeed, for 1-alcohols (with the inclusion of water) there has been obtained the relation ATsp = 50 287.2/(V+ 36.3032)4/s(r 0.9977, s 3.1) and for carboxylic acids ATsp = 194 946.0/(V+155.204)4/3(r 0.9991, s 1.05).
Table 1. Normal boiling point THhm of hypothetical homomorphs and specific contributions ATSP for 1-alcohols and n-carboxylic acids
Substance thhm, K ATsp, k Substance THHM, K (dispersion) ATsp, k
Water 130 243 1-Dodekanol 510 21
Methanol 183 155 1-Eykozanol 635 7
Ethanol 234 118 Formic acid 198 176
1-Propanol 276 95 Acetic acid 238 153
1-Butanol 312 79 Propanoic acid 277 137
1-Pentanol 344 67 Butyric acid 311 125
1-Hexanol 373 58 Pentanoic acid 343 116
1-Heptanol 399 50 Hexanoic acid 371 107
1-Octanol 422 45 Heptanoic acid 398 98
1-Nonanol 445 41 Octanoic acid 422 90
1-Dekanol 467 35 Dekanoic acid 462 81
1-Undekanol 486 30 Undekanoic acid 478 75
It is noteworthy that the boiling point of the hypothetical homomorph of water (with «disabled» electrostatic and specific interactions) should be 130K, i.e. by 243 degrees lower than its experimental value.
4.2. Boiling points of aromatic hydrocarbons and their derivatives.
The class of aromatic hydrocarbons owing to the substantial anizomery of benzene and naphtalene fragments, as well as the lower ionization potential J of molecules (benzene 9.21 eV, toluene 9.20 eV, p-chlorotoluene 7.95 eV, p-dihlorbenzene 8.95 eV, iodbenzene 9.10 eV [27]), as compared to the class of aliphatic hydrocarbons and cycloalkanes, has been developed separately.
Evidently, falling out of the obtained dependence (Fig. 2) are the points corresponding to the substances with specific interactions caused by intermole-cular hydrogen bonds (aniline, phenol, 1-naphthylamine).
600-
550-
500-
S 450-
400-
350-
1-Naphtylcarbonitrile, 1-Naphthylamine#
DiiodobenzenesO
Nitrobenzene
Dibromobenzenes _ n
D n
Chlorobromobenzenes va O ,
Dl,..,., Aniline □ V^Benzonitrile • • cff^Iodobenzene
, D \7 >^Diethylbenzenes Bromofluorobenzenes VDichlorobenzenes
□ Oir
V q/eromobenzene Xylenes Chlorobenzene rToluene ■Trifluoromethylbenzene _ -r rDifluorobenzenes >* Fluorobenzene Benzene
350
400
450
Tb,calc’K
500
550
600
Fig. 2. Compliance of experimental boiling points Tb, exp of aromatic hydrocarbons (Table 2) with one polar substituent (■) and the boiling point Tb calc, calculated (line) with the use of models (10). Points outside the line correspond to ortho-«o», meta- «V», and para-« » substituted dihalogenbenzenes and substances with specific («•») interactions (aniline, phenol, 1-naphthylamine).
For benzene, its mono-substituted polar derivatives and 1-naphtalencarbnitrile the dependence has been obtained:
Tb = 142.596 (MR2 / V)
0.445628
+
487.445-/V (r 0.998, s 3.46) (10).
In the correlation (10) there has been used the data for substances listed in Table 2. In Fig.2 it is seen that benzene and its mono-substituted derivatives of different polarity are lying on the same line. Two groups of substances have been excluded in obtaining the relation (10). The first group - substances with specific interactions: aniline, phenol, 1-naphthylamine, the second group - substances with substantial quadrupole moment, which is not taken into account in model (8), namely, para-, meta- and orto-disubstituted benzenes.
Basing on the obtained dependence (10) for aniline, phenol and 1-naphthylamine the boiling points of their hypothetical homomorphs (dispersive contribution) and specific interaction contributions have been calculated (Table
3).
Table 2. Boiling points of hypothetical homomorphs THhm of monosubstituted derivatives of benzene and
naphthalene, and the contribution ATelst of electrostatic interactions
Substance H, D mr2/v (x2/V Tb, K thhmj k (dispersion) AIelstj k (dipole)
Benzene 0 7.715 0 353.3 354 0
Fluorobenzene 1.47 7.273 0.023 358.3 345 11
Trifluoromethylbenzene 2.56 7.695 0.0533 375.5 354 26.0
Toluene 0.34 9.094 0.0011 383.8 381.4 0.5
Chlorobenzene 1.60 9.553 0.0252 404.8 390 12
Bromobenzene 1.52 10.98 0.022 429.2 415 11
Iodobenzene 1.38 13.76 0.0171 461.6 459 8
Benzonitrile 3.90 9.732 0.1483 464.3 393 72
Nitrobenzene 3.98 10.57 0.1549 484.2 408 76
1 -Naphthalencarbnitrile 4.15 17.44 0.1249 572.2 510 61
Table 3. Boiling points of hypothetical homomorphs THhm of mono-substituted aromatic hydrocarbons
and contributions ATSP of specific interactions
Substance mr2/v Tb, K THHM, K (dispersion contribution) ATsp, K*
Aniline 10.270 457.3 403 55
Phenol 9.054 455.0 381 74
1 -Naphthylamine 17.810 574.0 515 59
*Note: ATsp -Tb- THHM
Deviation from the straight line (Fig. 2) of the points corresponding to dihalogensubstituted benzenes (difluorobenzenes, dichlorobenzenes, dibromo-benzenes, chlorobromobenzenes, fluorobromobenzenes) grows normally in the series of o-isomer, m-isomer, ^-isomer. The latter is consistent with the increase of quadrupole moment in this series. Botcher was the first to pay atten-
tion at the necessity of taking into account the quadrupole contributions into the boiling points [22].
It is seen from Table. 4 that the total electrostatic contribution for dihalo-gensubstituted benzenes, as a rule, decreases in the series of ATelst (ortho) > ATelst (para) > ATELST(meta). For dialkylsubstituted benzenes such regularities have not been revealed.
4.3. Normal boiling points of aliphatic and cyclic hydrocarbon derivatives. These classes of organic substances turned out to be quite similar when subjected to the joint analysis of boiling points on universal interaction descriptors discussed in section 3.1. For calculating the experiment with model (8), data has been used for non-polar alkans, alkenes, alkynes, cycloalkans, cycloalkenes, as well as for their polar derivative with one polar group or bond (halogensubsti-tuted derivatives, nitroderivatives, nitriles, ketones).
The following equation has been obtained (Fig.3):
Tb = 129.726-(MR2 / vf436641 + 685.02-ff V(r 0.9938, s 8.3) (11)
Table 4. Boiling points THhm of hypothetical homomorph of positional isomers of disubstituted benzenes and contributions ATelst of electrostatic dipole and quadrupole interactions
Substance H, D mr2/v l_i2/V Tb, K THHM, K , 1) w "o J rp w h <1 w **; i , 2 ^ J £3 O .« a ft h & < w W 1? § S W H H s <
1,2-Difluorobenzene 2.38 6.790 0.0576 367.2 335 28 4 32
1,3- Difluorobenzene 1.58 6.778 0.0253 356.2 335 12 9 21
1,4- Difluorobenzene 0 6.854 0 361.7 336 0 25 25
1,2-Dichlorobenzene 2.33 11.490 0.0482 453.2 423 23 7 30
1,3- Dichlorobenzene 1.48 11.450 0.0192 446.2 423 9 14 23
1,4- Dichlorobenzene 0 11.12 0 447.5 417 0 30 30
1,2-Chlorobromobenzene 2.13 12.93 0.039 477.2 446 19 12 31
1,3-Chlorobromobenzene 1.51 12.91 0.0194 469 446 9 14 23
1,4-Chlorobromobenzene 0 12.9 ~0 469.2 446 0 23 23
1,2-Bromofluorobenzene 2.27 9.853 0.0502 429.7 395 24 10 34
1,3-Bromofluorobenzene 1.14 9.711 0.0127 423.2 393 6 24 30
1,4-Bromofluorobenzene 0 9.62 0 426.7 391 0 36 36
1,2-Dibromobenzene 2.03 14.5 0.0347 498.2 469 17 12 29
1,3-Dibromobenzene 1.46 14.46 0.0176 491.5 469 9 14 23
1,4-Dibromobenzene 0 14.45 0 493.6 469 0 25 25
1,2-Diiodobenzene 1.7 20.17 0.0223 559.2 544 11 4 15
1,3-Diiodobenzene 1.1 20.74 0.0091 558.2 551 4 3 7
1,4-Diiodobenzene 0 20.17 0 558.2 544 0 14 14
1,2-Xylene 0.58 10.63 0.0028 417.6 409 1 7 8
1,3-Xylene 0.37 10.53 0.0011 412.3 407 0.5 4.6 5.1
1,4-Xylene 0 10.52 0 411.5 407 0 4.6 4.6
1,2-Diethylbenzene 0.62 13.35 0.0025 456.6 453 1.2 2.8 4.0
1,3-Diethylbenzene 0.4 13.23 0.001 454.3 451 0.5 3.0 3.5
1,4-Diethylbenzene 0.24 13.23 0.0004 456.9 451 0.2 6.0 6.2
*Note: ATelst (quadrupole) = Tb - 142.596-(MR2/V)a445628 - 487.445-(i2/V
Fig. 3. Conformance of experimental and calculated by (11) boiling points of organic substances of aliphatic and cyclic series and their derivatives with single polar bond or polar group: n-alkanes C4-C30, hydrocyanic acid, nitriles C2-C3, C6, C11, fluoroalkanes C1-C6, chloroalkanes C1-C10, bromoalkanes C1-C12, iodoalkanes C1-C10, cycloalkanes C3-C6 and their derivatives, nitroalkanes C6,C11, ketones C3-C8.
One can see that the universal interaction contributions are well described by the relation (11). At the same time the electrostatic contribution calculated as ATelst = 685.02-ju/V for a number of polar substances can attain substantial values (nitrocyclohexane -74° cyclohexankarbnitrile -75° cyclo-hexanone -58 ° cycloheptanone ~54°). Contributions to the boiling point of specific interactions ATsp = Tb - THhm make up for cyclohexanecarbonic acid ~102° cyclohexanol ~37° cycloheptanol -32° cyclohexylamine -11°. Since in model (8) dipole approximation has been used for describing electrostatic interactions between directly contacting polar molecules, it is more accurate, as well as in the case of substituted benzenes, to describe boiling points of substances with single local polar group or bond in the molecule. If a molecule includes several polar groups (bonds) located in different parts of the molecule, the molecular dipole moment ceases to be an effective parameter for describing the interactions of directly contacting molecules and contributions of separate bond (group) dipoles should be taken into account. Thus, the electrostatic con-
tribution can be in the interval, the lower boundary of which is calculated basing on the square of molecular dipole moment and the upper one - on the basis of the sum of the squares of dipoles of the most polar bonds or groups.
5. Conclusions. This normal boiling point correlation of non-electrolytes on characteristics of polarity and polarizability of molecules in conjunction with the observed deviations is a conclusive evidence of short-rang electrostatic (orientation and polarization) interactions in liquids.
The given universal interaction descriptors MR2 /V and |a2/vcan be used to describe the other molar physicochemical properties of pure liquids. In analyzing physicochemical properties determined at T = 293.15 or 298.15 K, one can use the relation (3), in which free term A is included, and the exponent of dispersion descriptor is equal or close to 1. The difference between exponents of dispersion descriptor in equations (3) and (8) is due to the fact that substances with the properties determined at one temperature, in terms of the principle of corresponding states, are at different temperatures as related to their critical points.
An important conclusion coming from mathematic form of electrostatic descriptor is that the contribution of polar groups into normal boiling points, as well as the contributions of specific interactions are not additive and depend on the molar volume of the molecule. These facts should be taken into account when improving additive-group methods of estimation of normal boiling points and other physicochemical properties of pure liquids.
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