Journal of Molecular Liquids 182 (2013) 32–38

Contents lists available at SciVerse ScienceDirect

Journal of Molecular Liquids

j ourna l homepage: www.e lsev ie r .com/ locate /mol l iq

On viscosity of selected normal and associated liquids

Oleg Prezhdo a, Andrzej Drogosz b, Valentina Zubkova c, Victor Prezhdo c,⁎a Department of Chemistry, University of Rochester, Rochester, NY 14627, USAb Institute of Physics, Jan Kochanowski University, 15 Swietokrzyska Str., 25-406 Kielce, Polandc Institute of Chemistry, Jan Kochanowski University, 15 Swietokrzyska Str., 25-406 Kielce, Poland

⁎ Corresponding author. Tel.: +48 41 3497025; fax: +E-mail address: victor@ujk.edu.pl (V. Prezhdo).

0167-7322/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.molliq.2013.03.004

a b s t r a c t

a r t i c l e i n f o

Article history:Received 6 January 2013Received in revised form 19 February 2013Accepted 6 March 2013Available online 21 March 2013

Keywords:ViscosityBenzene derivativesOrdinary liquidsAssociated liquidsHydrogen bond

The viscosity of 34 benzene derivatives was determined at 404, 445, and 457 K to establish the relationshipbetween the macroscopic properties of ordinary liquids, in particular viscosity, and the properties of mole-cules these liquids consist of. The nature of changes in viscosity in homologous and isologous series of com-pounds along with substituted compounds was explained on the basis of this dependence. The peculiaritiesof viscosity of associated compounds were determined and explained by hydrogen bonding.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Formulation of a rigorous and comprehensive theory of viscosity ofliquids, applicable to a wide range of substances, remains a challengingtask. A number of empirical and semi-empirical formulas are used inpractice, reflecting the dependence of viscosity of selected classes ofliquids and solutions on temperature and chemical composition [1].Early in the 20th century, Bachinski [2,3] suggested the followingexpression for the viscosity

η ¼ CVs−bB

; ð1Þ

where Vs is specific volume, and C and bB are constants. The majority oforganic liquids, with notable exception of alcohols and organic acids,are well described by Eq. (1). The equation is rooted in the notionthat the viscosity of liquids is determined by molecular interactions.

Considering that transfer of momentum between layers of a flowingliquid occurs due to temporary association of molecules of the liquid atthe interface between the layers, Andrade [4] developed the equation

η ¼ Aρ1=3 exp−CRT

: ð2Þ

48 41 3497062.

rights reserved.

Here, the constant А is proportional to the frequency of molecularvibrations, the constant С is proportional to the potential energy ofintermolecular interactions, and ρ is the density of the liquid.

Eq. (3) shown below was obtained on the basis of the microscopickinetic theory of Frenkel [5]. Calculations using this expression givegood agreement with experimental data. The form of the expressionthat is commonly used in modern practice is given by

η ¼ 8t03π

nkT exp−ΔEpkT

ð3Þ

where, t0 is the time that the particle spends in the transition state.Typical values of t0 are on the order of 10−13 s. n is the number ofmolecules in unit volume; Ep is the potential energy of intermolecularinteractions; T is temperature, and k is the Boltzmann constant.

A number of statistical–mechanical theories of viscosity of liquidshave been developed. For instance,monograph [6] discusses a practical-ly useful, approximate approach for calculating viscosity.

In addition to the expressions derived starting from the fundamen-tal chemical principles, a variety of empirical equations has been pro-posed. In 1835, Poiseuille determined experimentally an empiricalequation describing the temperature dependence of the viscosity ofwater. The Slotte temperature–viscosity relationship is described in[7]. The expression

η ¼ expCTa ; ð4Þ

proposed by Le Chatelier [8] forms the basis for a whole series of em-pirical formulas. In Eq. (4), C and a are certain constants, and T is

33O. Prezhdo et al. / Journal of Molecular Liquids 182 (2013) 32–38

absolute temperature. An interesting variant of the Le Chatelier formu-la is obtained in [9]

vþ 0:8ð Þ ¼ expCTa ; ð5Þ

where v is the kinematic viscosity, and 0.8 is an empirical coefficienthaving the kinematic viscosity units. This equation is widely used instudies of lubrication.

Numerous publications are dedicated to investigation of the rela-tionship between viscosity and molecular structure. A detailed accountof such studies is reported by Bondi [10], who discusses severalqualitative correlations. In particular, Bondi observes that increases inmolecular mass, degree of branching in molecular structure and extentof intermolecular association result in viscosity growth and greatersensitivity of viscosity to changes in temperature. Introduction ofdouble bonds into molecules of a liquid typically decreases liquidviscosity.

Multiple scientists proposed empirical rules relating structuralcharacteristics of molecules to viscosity [11–17]. At the same time, itremains challenging to relate molecular structure to viscosity in adirect way, for instance, to predict viscosity values based on the substit-uents present in the molecule. Therefore, the approach advocated inthe current work relies on comparison of compounds that differ fromeach other in only one structural or any other integral feature[18–20]. The general idea is justified andwidely used for determinationof macroscopic physical properties. The macroscopic properties areultimately determined, under the same thermodynamic conditions(р and Т), by the characteristics of microscopic particles constitutingthe substance, in particular, particle size (VM), shape (Φ), mass (m),polarizability (α), dipole moment (μ), etc. Taking this into account,one can obtain useful insights into the macroscopic properties by con-sidering a series of compounds that are similar in most respects anddiffer only in one or few characteristics [21–23]. Simultaneous varia-tions in manymicroscopic properties make such analysis more difficultand applicable to a relatively narrow range of compounds, withoutshowing clear physical reasons for the changes in the macroscopicproperties. The current work presents an analysis of viscosity of a seriesof benzene derivatives on the basis of the microscopic properties of themolecules constituting the liquid.

2. Experimental section

2.1. Materials

The nitrobenzene, 2-nitrophenol, 3-nitrophenol, 4-nitrophenol,2-nitroanisole, 3-nitroanisole, 4-nitroanisole, 2-hydroxybenzaldehyde,3-hydroxybenzaldehyde, 4-hydroxy-benzaldehyde, acetophenone, 2-hy-droxyacetophenone, 3-hyd-roxyacetophenone, 4-hydroxyacetophenone,2-methoxyaceto-phenone, 3-methoxyacetophenone, 4-methoxyaceto-phenone, ethyl benzoate, 2-methylphenol, 3-methylphenol, 4-methyl-phenol, 2-methoxytoluene, 3-methoxytoluene, 4-methoxy-toluene, phe-nol, and anisole were of high purity grade reagents produced by Merck.Eight other compounds: 2-methoxy-benzaldehyde, 3-methoxybenz-aldehyde, 4-methoxybenzalde-hyde, 2-hydroxyethyl benzoate, 3-hy-droxyethyl benzoate, 4-hydroxyethyl benzoate, 2-methoxyethyl benzo-ate and 4-methoxyethyl benzoate (Table 1) were synthesized andpurified according to the techniques described in literature [24]. Thecomposition formulas of the associated liquids under study arepresented in Table 2. The identification of the synthesized compoundswas carried out with the IR and NMR spectroscopy [25]. All sampleswere degassed by heating and cooling just before use. The purity gradeand viscosities of pure components are given in Table 1, showing goodagreement with the literature data [26,27]. The densities of compoundsunder study are given in Ref. [28].

2.2. Measurement

Both literature data on viscosity of liquids and the results of ownmeasurements are presented in Table 1. The viscosity measurementsof the compounds under study were made using a U-tube Ostwaldviscometer. The viscometer was connected with a glass stopper withtwo openings for thermometer and pycnometer. A plug was insertedin the thin section of the thermostat. The laboratory thermostatHuber with control unit МPС-Е and heat capacity of 473 K was usedto maintain the constant temperature [29]. All measurements werecarried out using the same viscometer with the water efflux timeequal to 131 s. In the vast majority of cases, tx was determined fortwo or more samples of the same substance. The divergence betweensingle measurements of tx was ± 0.5 s at most. The dx values were de-termined at the same time [28]. In most cases, the obtained values of ηxare in good agreement with the literature data (Table 1). The effluxtime t was measured at 404, 445, and 457 K for 34 compounds(Table 1). The viscosity was determined according to Eq. (6):

ηx ¼ ηadxtxdata

; ð6Þ

where ηa is the viscosity coefficient for water at 20 °С, da is density andta is the efflux time for water at 20 °С; ηx, dx and tx are the values for thecompound under study, correspondingly.

The viscometer was calibrated with spectroscopic grade 1-butanoland doubly distilled water at the experimental temperature. Anelectronic digital stopwatch with accuracy of ±0.01 s was used forthe efflux time measurements. The temperature of the samples wascontrolled with an external thermostat. The uncertainty in dynamicviscosities was about ±3 × 10−3 mPa·s. The kinematic viscosity canbe obtained from the ratio of the dynamic viscosity and the densityof a substance.

3. Results and discussion

3.1. Viscosity of ordinary liquids

The dependence of viscosity (η) on molecular mass follows fromthe data for η of isotopic compounds, which differ from each othermainly in the mass of molecules. As additional measurements showed[29], the viscosity of such compounds, e.g. methane and deuteratedmethane at 90.1 K, increases proportionally to

ffiffiffiffiffim

p. The dependence

ηð Þp;T;xh ¼ constffiffiffiffiffim

p; ð7Þ

where хh are all other properties of molecules except form, is in goodagreement with many viscosity formulas derived from kinetic or sta-tistic theories by Fischer [30], G.M. Panchenkov [31], Ya.I. Frenkel [5],

etc. For instance, in the Panchenkov theory, ρ4=3

M5=6 ¼ m1=3N4=3

N5=6 , where ρ isthe density equal to N′ m, and M = Nm; N′ is the number of mole-cules per unit volume, and N is Avogadro's number. In the Frenkeltheory the oscillation frequency is proportional to the inverse squareroot of mass, νe 1ffiffiffi

mp .

The value of the reduced property η=ffiffiffiffiffim

pin homo-isologous ranks

of the first type does not change with variation in vM i.е.

ηffiffiffiffiffim

p� �

p;T;xh

¼ const ð8Þ

where хh are all of the other properties of molecules except for massand size. It follows from the formula that viscosity does not dependon the size of the molecules. In most empirical and theoretically de-rived formulas of viscosity, the specific or molar volume along withthe length of molecules is taken into consideration, what should

Table 1The viscosity of substituted benzene.

Compound Purity mass fraction ηexp × 103/mPa⋅s ηmethoxy–ηhydroxy ηmeta–ηorto(para) ηlit × 103/mPa⋅s (T K) [26,27]

404 K 457 K 404 K 457 K 404 K 457 K

C6H5NO2 0.995 549 396 – – – – 704 (373)0.995 o-754 497 – – – – 708 (409)

C6H4(OH)NO2 0.995 m-1874 973 – – +1120 +476 464 (458)0.995 p-2797 1334 – – +2043 +837 2941 (402)

1365 (454)0.99 o-838 548 +84 +51 – – 911 (397)

C6H4(OCH3)NO2 515 (458)0.99 m-756 496 −1118 −477 −82 −52 –

0.99 p-901 568 −1896 −766 +63 +20 1550 (404)0.99 o-615 – – – – – 567 (406)

C6H4(OH)CHO 0.99 m-1926 – – – +1311 – –

0.99 p-2314 – – – +1699 – –

C6H5COCH3 0.995 420 329 – – – – –

0.99 o-701 465 – – – – 601(405)C6H4(OH)COCH3 0.99 m-2263 1174 – – +1562 +709 2916 (403)

1254 (452)p-3576 1770 – – +2875 +1305

0.99 o-609 412 −92 −53 - - -C6H4(OCH3)COCH3 0.99 m-682 445 −1581 −729 +73 +33 –

0.99 p-775 471 −2801 −1299 +166 −59 –

C6H5COC2H5 0.995 507 351 – – – – –

0.99 o-617 414 – – – – –

C6H4(OH)COOC2H5 0.99 m-2453 1110 – – +1836 +796 –

0.99 p-4044 1492 – – +3427 +1078 –

C6H4(OCH3)COOC2H5 0.99 o-682 443 +65 +29 – – –

0.99 p-802 493 −3242 −999 +120 +50 –

0.99 o-649 443 – – – – –

(445 K) 600 (408)C6H4(OH)CH3 0.99 m-694 458 – – +45 +15 638 (413)

(445 K) 442 (445)0.99 p-732 487 – – +83 +54 466 (448)

(445 K)0.99 o-376 287 −273 −156 – – 381 (398)

(445 K) 267 (444)C6H4(OCH3)CH3 0.99 m-350 269 −344 −189 −26 −18 341 (403)

(445 K) 246 (448)0.99 p-354 271 −378 −216 −22 −16 363 (398)

(445 K) 244 (449)C6H5OH 0.99 725 – – – – – 770 (398)C6H5OCH3 0.99 409 −316 – – – 419 (373)

34 O. Prezhdo et al. / Journal of Molecular Liquids 182 (2013) 32–38

show the contrary. However, the formulas, in which the length ofmolecules can be found (for example, in polymer homology), do notconsider changes in length along with changes in mass and polariz-ability of the molecules [32] for the compounds under study. On theother hand, the molar volume (or specific volume Vs) is equal toV = NVM + Vf, i.е. it is equal to the sum of molecular volumes(NVM) and the free volume of a liquid (Vf), which is determined bydistance between the molecules. The analysis of the derivations onthe basis of formulas with V or Vs [33] shows that these values appear,when the mechanism of viscous flow is considered, as the result oftaking into account the distances between the molecules and their

Table 2Values of z for associated compounds.

Associatedcompound

Metameric ether(ester)

Temperature,K

ηassocηmetam

z byEq. (15)

n-C3H7COOH CH3COOC2H5 293 3.80 1.95n-C4H9COOH C2H5COOC2H5 293 4.23 2.05

323 3.28 1.81n-C5H11COOH n-C3H7COOC2H5 293 4.79 2.18

323 3.68 1.92n-C6H13COOH n-C4H9COOC2H5 323 3.76 1.92n-C7H15COOH n-C5H11COOC2H5 323 4.01 2.00n-C4H9OH C2H5OC2H5 293 12.78 3.57n-C5H11OH n-C3H7OC2H5 293 11.64 3.41n-C6H13OH n-C3H7OC3H7-n 293 12.68 3.55

changes with the temperature, i.e. Vf not VM. In other words, theseformulas testify to the fact proved by Bachinski that viscosity dependson free volume of a liquid [34,35], or else the accessible volume [36].However, the dependence (8) does not mean that the size of mole-cules does not influence viscosity at all. The change in molecularsize can show some opposite influences that mutually compensateeach other. For example, if we believe that η depends, on the onehand, on the number of molecules in contact layers, proportional to1/VM

2/3, and, on the other hand, on the number of collisions betweenmolecules, proportional to VM

2/3, the viscosity ceteris paribus may notdepend on the size of molecules.

Taking into consideration the independence of η from VM, theviscosity value in homo-isologous series of the second type should reg-ularly vary with polarizability of molecules (α). If we take into accountthe influence of small differences in molecular mass and consider thechange in volume for η=

ffiffiffiffiffim

prather than η, we will see that η increases

in these series proportionally to α3/2 (Fig. 1) i.е.

ηffiffiffiffiffim

p� �

p;T;Φ;μ¼ const MRDð Þ3=2; ð9Þ

whereMRD is a molecular refraction. Characteristically, the slope of theline is the same for all series of the halogen derivatives. The depen-dence (9) should reflect the influence of dispersion forces on viscosity,which are proportional to α2 (according to London) or α3/2 (accordingto Slater and Kirkwood) [37].

Fig. 1. The dependence ofη⋅103ffiffiffiffiffi

Mp on the molecular refraction MRD

3/2 at 298 K for C2H5J

(●), n-C5H11Br (×), n-C8H17Cl (○), n-C3H7J ( ), n-C6H13Br ( ), n-C4H9Br (★),

n-C7H15Cl (□),n-C6H13J ( ), n-C9H19Br (■),n-C5H11J (☆), and n-C8H17Br ( ). The typ-

ing compounds are homo-isologous of second type.Fig. 3. The dependence of

η⋅103ffiffiffiffiffiM

p on the molecular refraction MRD3/2 at 323 K (unbroken

line) and 343 K (broken line) for n-CnH2n + 1COOH, where n = 3 (●), n = 4 (×), n =

5 (○), n = 6 ( ), n = 7 ( ), n = 8 (★), n = 9 (□), n = 11 ( ), n = 15 (■), and

n = 17 (☆).

35O. Prezhdo et al. / Journal of Molecular Liquids 182 (2013) 32–38

It follows from Fig. 2 that the viscosity in isoperiodic serieschanges regularly with changes in the dipole moment of the mole-cules and increases in a linear way according to:

ηð Þp;T;Φ;m;α ¼ Aþ const μ: ð10Þ

In this case, the value of constant A almost coincides with thevalue of η for the appropriate member of the series with μ equal tozero, e.g. a hydrocarbon. The value of the constant decreases with ris-ing temperature (Fig. 2) due to decrease of the role of orientationforces. We do not expect a strictly linear relationship in the com-pounds under study because their molecules show some variationsin mass, polarizability, and shape. Only the members of the seriescontaining ОН– and СООН– (except for compounds with intramolec-ular hydrogen bonding) deviate from the dependence (10). The influ-ence of dipole orientation on η of liquids has been mentioned widely[27,38]. The orientation is expected to influence the value of the con-stant В in the formula for changes of viscosity with temperature [27]:η = AeB/T. The constant can be considered as the activation energy ofviscous flow [39]. However, if the value of В were equal to the energyof interaction of a pair of molecules in the equilibrium position, amore substantial increase in η would be expected with rise in μ.

The data for heteromorphous compounds (Fig. 2) show a regularchange in η with the shape of molecules. Thus, the tertiary com-pounds, independently of the functional group, possess a greatervalue of η than the corresponding linear compounds. At 293–298 Kthe differences are 10–20%. It may be suggested that other factors,such as mass, polarizability and dipole moment, are also differentfor primary, secondary, and tertiary amines, pointing to a sharp

Fig. 2. The dependence of η × 103/mPa⋅s on the dipole moment μ × 1030/C⋅m at 298 K(unbroken line) and 404 K (broken line) for C6H5C3H7-n (●), C6H4(OCH3)CH3-o (×),C6H4(OCH3)CH3-m (○), C6H4(OCH3)CH3-p (■), C6H5OC2H5 ( ), C6H5N(CH3)2 (★),C6H5COCH3 (□), C6H4(OH)CHO-o ( ), C6H4(OH)CHO-p (■), C6H5NO2 (☆), and C6H5-

CH2CH2OH ( ). The typing compounds are isoperiodic compounds.

decrease in viscosity during transition to tertiary, more symmetricalcompounds [34,40]. The cyclic shape facilitates a sharp rise in viscos-ity in comparison to the linear shape. The differences are by a factor of2–4 at 298 K [34]. The ratio of ηcyclic/ηlinear grows with increase in thenumber of carbon atoms in the ring and chain. A similar effect is seenwith surface tension.

The aforementioned dependences allow us to explain the natureof changes of η in series of compounds that differ in several molecularconstants. Molecules of the members of homologous series, beginningfrom the third or fourth member, differ only in mass, polarizability,and size. According to Eqs. (7), (8), and (9), in different homologousseries (see, for example Figs. 1, 3) η

ffiffiffiffiffim

pincreases proportionally to

α3/2 or (MRD)3/2. In this case, Eq. (9) holds at different temperatures,and the slope of the line decreases with increasing temperature. Atthe same temperature, the value of the constant may vary a littlewith change in functional groups. At low temperatures in some ho-mologous series [41] (Fig. 4), η

ffiffiffiffiffim

pincreases proportionally to α2. A

careful examination of the η data for these compounds reveals someadditional factors. Comparison of several dependencies (9) explainsthe changes in nature of η with variation in the number п of carbonatoms in the hydrocarbon chain. For two neighboring members ofthe homologous series the dependence is:

η nþ1ð Þηn

¼ M nþ1ð ÞMn

� �1=2 MRD nþ1ð ÞMRD nð Þ

!3=2

: ð11Þ

Fig. 4. The dependence ofη⋅103ffiffiffiffiffi

Mp on the molecular refraction MRD

2 at 293 K (unbroken

line) and MRD3/2 at 353 K (broken line) for n-CnH2n, where n = 9 (●), n = 10 (×),

n = 11 (○), n = 12 (■), n = 13 ( ), n = 15 (★), and n = 17 (□).

36 O. Prezhdo et al. / Journal of Molecular Liquids 182 (2013) 32–38

Since M(n + 1)/Mn, and MRD(n + 1)/MRD(n) are always greater thanone, η should always increase along the series, unlike, for instance, thechange in density in these series. Herewith, a relative increase of η de-creases with rise in п. For example, for normal hydrocarbons the ratiosare η(n = 6)/η(n = 5) = 1.35 аnd η(n = 11)/η(n = 10) = 1.28. BothM(n + 1)/Mn and MRD(n + 1)/MRD(n) approach one when п approachesinfinity.

The change of η in homologous series has been explained, as arule, by variations in the mass of molecules. For instance, theGartenmeister formula gives η = const M2, and the Dunstan andThole equations are lnη = AM + В or ln η = A ln M + В [27]. How-ever, these formulas do not fully account for the dependence on mass,because α also grows with т in these series. Hence, the equations for ηimplicitly capture the changes of polarizability with mass. Since themass of molecules is additive, the aforementioned formulas wereused for construction of different additive schemes for viscosity. Tak-ing the additivity of MRD, and putting the values M = A + 14n andMRD = А′ + 4.6n into Eq. (11) leads to

ηnþ1

η¼ Aþ 14 nþ 1ð Þ

Aþ 14n

� �1=2 A′ þ 4:6 nþ 1ð ÞA′ þ 4:6n

" #3=2:

This relation shows that it is fundamentally impossible to constructa proper and widely applicable additive model, because the differencein η and ln η for neighboringmembers of the homologous series cannotremain constant with changes in п and in the nature of the functionalgroup (A and А′).

With alkyl group substituted to sulfur, oxygen, selenium, or nitro-gen, the properties of the molecules in the series change in the sameway, except for minor variations in the dipole moment. Hence, thechange of η during formation of ethers can be compared with the cor-responding change during appropriate lengthening of the hydrocarbonchain, namely:

ηCnH2nþ1XH−ηCnH2nþ1XR

ηCnH2nþ1XH−ηCnH2nXH

≈1: ð12Þ

This relationship holds, for example, with thiols:

103 ηn�C4H9SH� ηn�C4H9SC4H9�n

ηn�C4H9SH� ηn�C3H7SH

!¼ 551

596¼ 0:92:

Fig. 5. The dependence ofη⋅103ffiffiffiffiffi

Mp on the molecular refraction MRD

3/2 at 293 K (unbroken

line), at 353 K (broken line), and at 393 K (dotted line) for C6H5X, where X = F (●), Cl

(×), Br (○), and J (■).

In isologous series, the members differ from each other substantial-ly in mass, and a little in polarizability and molecular size. Theaforementioned dependences show that the influence of α on η cannotbe compensated by the influence of vM. That is why the approximateproportionality of viscosity to the mass of molecules in isologous seriesdoes not reflect its real dependence on the latter. As in homologous se-ries, in isologous series

ηffiffiffiffiffim

p� �

p;T;μ¼ const MRDð Þ3=2:

(Figs. 1, 5). As before, fluorine derivatives of the lipid series andОН- and СООН-containing compounds do not obey this dependence:they exhibit slightly decreased and highly increased values ofη=

ffiffiffiffiffim

pMRDð Þ3=2, respectively.

The members of a series involving RХ substituents, where X are dif-ferent functional groups, and R-alkyl, aryl, etc., differ to a greater orlesser extent in all molecular constants. According to Eqs. (7)–(10),the viscosity in the series of molecules having the same shape obeysthe dependence:

ηffiffiffiffiffim

pMRDð Þ3=2

� �p;T;Φ

¼ Aþ const μ ð13Þ

at constants p and T (Fig. 6). Herewith, the value of А is close tothe value of η=

ffiffiffiffiffim

pMRDð Þ3=2 for an appropriate member of the series,

e.g. hydrocarbon, with μ equal to zero. Sharp divergence skewed tohigher values of η=

ffiffiffiffiffim

pMRDð Þ3=2 is shown only by ОН-, СООН- and

NH2 (aromatic) containing compounds. Small deviations from the line-ar dependence for othermembers of the series can be causedmainly bydifference in molecular shape.

In contrast to other substitutedmembers of the series, all molecularproperties of the members of the series of metamer compounds arevery similar. That is why metameric ethers and esters only slightly(up to 10%) differ in viscosity. The difference in the values of η formetamers can be caused by screening of the polar group: metamerswith a less screened polar group have a greater value of η. Only ОН-and СООН-containing metamers, in contrast to those containing SН-and СОSН-groups, have a sharply increased viscosity in comparisonto their metamer ethers.

Fig. 6. The dependence ofη⋅105

MRDð Þ3=2M1=2on the dipole moment μ × 1030/C⋅m at 298 K

for C6H5X, where X = CH3 (●), OCH3 (×), F (○), Br (■), Cl ( ), J ( ), N(CH3)2 (★),

COOC2H5 (□), COCH3 ( ), CN (&), NC (☆), NO2 ( ), NH2 (), and OH (*).

37O. Prezhdo et al. / Journal of Molecular Liquids 182 (2013) 32–38

3.2. Viscosity of associated liquids

As mentioned previously, ОН- and СООН-containing members ofa series show deviations from the regularity in the change of η, deter-mined for this series. In isoperiodic series of such type, the com-pounds have a value of η 5–8 times higher than that calculated fromthe dipole moment of their molecules. In case of cyclic oxides andnormal alcohols, ηcyclic/ηlinear is much less than one, instead of beinggreater than one. Thus, η of ethylene oxide at 235 K is almost 10times less than that of ethanol. The formation of ethers, especiallymethyl ethers, leads to a sharp decrease in η, explaining deviationsfrom the regularity (12). For alcohols and acids at 293 K the decreaseis by a factor of 3–8, for phenols at 404 and 457 K the decrease is by afactor of 2–6. In isologous series, alcohols have a greater value ofη=

ffiffiffiffiffim

pMRDð Þ3=2 than thiols. The substituted compounds also show

increased values of η=ffiffiffiffiffim

pMRDð Þ3=2 in comparison to those calculated

on the basis of the molecular dipole moment. The difference is by fac-tor of 5–10. The viscosity of alcohols and acids exceeds the viscosity oftheir metamer ethers by a factor of 11–17 and 4–5, respectively. Thesame effect is observed with substituted phenols. Thus, η of meta-and para-hydroxyacetophenone at 404 K is 3–5 times higher than ηof the metameric meta- and para-methoxybenzaldehydes (Table 1).

The anomalous behavior of ОН- and СООН-containing compoundsis explained by the fact that they are associated and consist of complexstructures formed due to hydrogen bonding [42], rather than singlemolecules. The effect of dimerization and higher order association ofОН- and СООН-containing molecules on viscosity is confirmed by thebehavior of compounds with intramolecular hydrogen bond, such asortho-nitrophenol, ortho-hydoxybenzaldehyde, ortho-hydroxy-aceto-phenone, and ethyl salicylate. TheseОН-containing compounds behavein the ordinary way, since they are devoid of the tendency to formintermolecular complexes due to formation of intramolecular hydrogenbond. Thus, the aforementioned ortho-hydroxy-compounds (Fig. 2) inisoperiodic series have the value of η appropriate to their dipolemoment. Their methyl ethers (Table 1), as a rule, have a higher valueof η than the initial phenol. They obey the dependence (7); thereforeat 131 °С

ηo�C6H4 CHOð ÞOH � ηo�C6H4 CHOð ÞOCH3

ηo�C6H4 CHOð ÞOH � ηo�C6H4 COCH3ð ÞOH≈0:3:

The compounds under study behave in a normalway even in compar-ison to metameric ethers: ortho-hydroxyacetophenone possesses thesame viscosity as metameric ortho-methoxy-benzaldehyde (Table 1).The lack of intermolecular association for the ortho-hydroxycompoundsand its existence for meta- and para-isomers explain the sharp decreaseof η for the former in comparison to the latter. The decrease is by a factorof 2.5–5 at 404 and 457 K. The ortho-isomers usually have a greater valueof η than their isomers. Cresols constitute an exception, because intramo-lecular hydrogen bond cannot form in the ortho-isomer.

The anomalously high value of η for the associated compounds,causes the aforementioned deviations, is explained by the breaking ofhydrogen bonds in viscous flow and hence by an increased value ofwork needed for cavity formation due to “structural energy of activa-tion” [43]. However, a noticeable resistance of hydrogen bonds evenat high temperatures raises doubts about the viewpoint that a singlemolecule is a structural unit of the viscous flow for the associated com-pounds. In acids the complexes are resistant even in pairs, in phenolsand alcohols they are resistant in liquid state in a wide temperaturerange [44]. The anomalously high value of η for the associated com-pounds can be explained on the basis of their macro-properties,which are determined not by the properties of their molecules but bythe properties of molecular complexes being a unit of their viscousflow. Taking into consideration the fact that the mass of the complexis equal to zт (z is the number of molecules in the complex), and the

polarizability of the complex approximately matches zα or z(МRD)1/3,then for the associated compound

ηassoc� �

p;T;Φ ¼ zmð Þ1=2 zαð Þ3=2 Aþ constμcompl

: ð14Þ

Since z ≥ 2 and the dipolemoment ofmolecules in a complex eitherincreases (for alcohols and phenols O–H⋯O type) or decreases (for acids

due to formation of cyclic dimers ), it follows

from Eq. (14) that the value of η for the associated compounds shouldsharply increase in comparison with that calculated on the basis ofproperties of single molecules. Neglecting the difference in the dipolemoments of the molecules in the complex and in metamericnon-associated compounds, the value of z can be approximately calcu-lated from the relation:

ηassocηmetam:eth:

¼ zmð Þ1=2m1=2

zαð Þ3=2α3=2

Aþ const μcompl

Aþ const μmolecð Þ ≈z2;

on its basis

z≈ ηassocηmetam:eth:

� �1=2: ð15Þ

In accordance with the X-ray, electronographic, and other data[45,46], the value of z nears 2 for acids and 3–4 for alcohols (Table 2).

It also follows from Eq. (14) that the associated compounds obeythe same dependences as ordinary liquids when the value of z re-mains unchanged. Since the viscosity varies in homologous series ofalcohols and acids (Fig. 3) in the same way as in the series of theirethers, the lengthening of the hydrocarbon chain, at least from thefifth member, should not change the value of z. The value of z doesnot change either during transition from an acyclic alcohol to the cor-responding cyclic one.

4. Conclusions

The determined dependences between the viscosity of ordinary liq-uids and the properties of the molecules they consist of (polarizability,dipole moment, shape) allowed us to analyze and predict the viscosityvalues in series of compounds. The nature of changes in viscosity in ho-mologous and isologous series along with those for the series ofsubstituted hydrocarbons was explained on the basis of the establisheddependences. The peculiarities of viscosity were clarified for the com-pounds, which were associated inter- and intramolecularly throughthe formation of hydrogen bonds. The intermolecular hydrogen bondin associated liquids leads to increase in viscosity in comparison withordinary liquids.

Acknowledgments

OVP acknowledges financial support of the USA Department ofEnergy, grant no. DE-SC0006527.

References

[1] M.I. Ojovan, W.E. Lee, Journal of Applied Physics 95 (2004) 3803–3810.[2] E. Hatschek, The Viscosity of Liquids, Van Nostrand, New York, 1928.[3] A. Bachinski, Selected writings. Ed.AS USSR, Moscow, 1960 (Rus).[4] A.E. Andrade, Philosophical Magazine 17 (1934) 497–504.[5] Ya.I. Frenkel, Kinetic Theory of Liquids, Dover, NY, 1955.[6] C.A. Croxton, Progress in Liquid Physics, Wiley, Chichester, Eng. and New York,

1978.[7] M.A. Barber, Journal of Infectious Diseases 5 (1908) 379–382.[8] P. Lasareff, Nature 120 (1927) 281–283.[9] C. Walther, Erdoll and Teer 7 (1931) 382–384.

38 O. Prezhdo et al. / Journal of Molecular Liquids 182 (2013) 32–38

[10] A. Bondi, Annals of the New York Academy of Sciences 53 (1951) 870–905.[11] H. Mark, R. Simha, Nature 145 (1940) 571–573.[12] H.T. Leo, Transactions of the Faraday Society 62 (1966) 328–335.[13] H. Münstedt, Soft Matter 7 (2011) 2273–2283.[14] M. Eszterle, Zuckerindustrie 115 (1990) 263–267.[15] Liquid Crystals 33 (2006) 67–73.[16] R.L. Rowley, J.F. Ely, Molecular Physics 75 (1992) 713–730.[17] A.S. Meijer, A.S. de Wijn, M.F.E. Peters, N.J. Dam, W. van de Water, Journal of

Chemical Physics 133 (164315) (2010) 9.[18] L.L. Lee, Molecular Thermodynamics of Nonideal Fluids, Butterworth, London,

1988.[19] J.M. Prausnitz, G.D. Edmundo, Molecular Thermodynamics of Fluid-Phase Equilibrium,

Prentice Hall, New Jersey, 1975.[20] B.E. Poling, J.M. Prausnitz, J.P. O'Connell, The Properties of Gases and Liquids, 5th

ed. McGraw-Hill, New York, 2001.[21] K. Rajagopal, S. Chenthilnath, Journal of Chemical & Engineering Data 55 (2010)

1060–1063.[22] J. Restolho, A.P. Serro, J.L. Mata, B. Saramago, Journal of Chemical & Engineering

Data 54 (2009) 950–955.[23] A.A. Silva, R.A. Reis, M.L.L. Paredes, Journal of Chemical & Engineering Data 54

(2009) 2067–2072.[24] S. Warren, P. Wyatt, Organic Synthesis: The Disconnection Approach, Wiley, San

Francisco, 2009.[25] R.M. Silverstein, F.X. Webster, D.J. Kiemle, Spektroskopowe metody identyfikacji

związków organicznych, PWN, Warszawa, 2012.[26] C. Yaws, The Yaws' Handbook of Physical Properties for Hydrocarbons and

Chemicals, Gulf Publishing Company, Houston, 2005.[27] T.K. Ghosh, D.S. Viswanath, N.V.K. Dutt, K.Y. Rani, H.H.L. Prasad, Viscosity of

Liquids, Springer-Verlag Gmbh, Munich, 2010.

[28] O. Prezhdo, A. Drogosz, V. Zubkova, V. Prezhdo, Fluid Phase Equilibria 342 (2013)23–30.

[29] Huber Catalogue, , 2012/13.[30] I.Z. Fischer, Statistical Theory of Liquids, Univ. of Chicago Press, Chicago, 1965.[31] G.M. Panchenkov, Russian Journal of Physical Chemistry 34 (1960) 1883–1884.[32] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, New York,

1995.[33] K.J. Laidler, M.C. King, Journal of Physical Chemistry 87 (1983) 2657–2664.[34] I.G. Murgulescu, M. Serban, Revue Roumaine de Chimie 24 (1979) 1417–1422.[35] A.A. Askadskii, Computational Materials Science of Polymers, Cambridge Interna-

tional Science Publishing, Cambridge, 2003.[36] M. Prezhdo, L. Loginova, V. Zubkova, V. Prezhdo, Fluid Phase Equilibria 321 (2012)

44–48.[37] E. Silla, A. Arnau, I. Tunon, in: G. Wypych (Ed.), Handbook of Solvents, ChemTec

Publ., William Andrew Publ, Toronto–N.Y, 2001, pp. 7–36.[38] K.I. Brenkert, Elementary Theoretical Fluid Mechanics, John Wiley & Sons, Inc.,

New York, 1960.[39] J.-P. Hsu, S.-H. Lin, Journal of Chemical Physics 118 (2003) 172–178.[40] F.M. Gacino, T. Regueira, L. Lugo, M.J.P. Comunas, J. Fernandez, Journal of Chemical

& Engineering Data 56 (2011) 4984–4999.[41] F. Gutmann, L.M. Simmons, Journal of Applied Physics 23 (1952) 977–982.[42] M. Yasmin, M. Gupta, J.P. Shukla, Journal of Molecular Liquids 160 (2011) 22–29.[43] J.D. Ferry, Viscoelastic Properties of Polymers, John Wiley & Sons, Inc., New York,

N.Y., 1961[44] G.A. Jeffrey, An Introduction to Hydrogen Bonding (Topics in Physical Chemistry),

Oxford University Press, Oxford, 1997.[45] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, 1931.[46] R.K. Bansal, A Textbook of Organic Chemistry, New Age International Publisher,

Delhi, 2005.