Indian Journal of ChemistryVol. 20A, October 1981, pp. 963-968

.Status of Models for Flow Behaviour of Organic Liquids

NURUL ISLAM· & M. mRAHTMDepartment of Chemistry. Aligarh Muslim University. Aligarh 202001

Received 30 October 1980; revised 6 February 1981; accepted 23 March 1981

The densities and viscosities of several organic liquids have been measured. The applicability of two-parameteras well as three-parameter equations to viscosities of these liquids has been examined. The Hildebrand equation hasbeen found to be inadequate not only for non-associated and nonpolar liquids at low temperatures but also in any tem-perature range of study.

MUCH interest has been shown in the study ofviscous behaviour of organic liquids as itfurnishes information on the intermolecular

mteract.ons and consequently the structure of theorganic liquids. Such structural informations areprovided in terms of several empirical equationsbased on several models=s, which are essentiallybased on the consideration of either temperatureor volume change. Hildebrand" modified Batschi-nski's equation- for the viscosity of non-associatedliquids and suggested Eq. (I), assuming fluidity,.pC= 1I')), to be a linear function of the ratio of inter-molecular volume to the volume, Vo,

rP = B(V-Vo)/Vo ...(1)where B is a constant whose value depends upon thecapacity of the molecules to absorb momentum be-cause of their mass, flexibility or inertia of rotation..Extrapolation of molarvolume to rP=O yields' Vowhile the slope gives the ratio BIVo' The Vo hence-forth is denoted by VB, the Hildebrand volume.Apart from its success", Eq. (1) was inapplicable?in a number of cases especially in the vicinity ofmelting points. .

Even though Hildebrands explained the cause' offailure of Eq. (1) at temperatures close to the freezingpoint, Eicher and Zwolinski's observation? raised aquestion which- was far more important than merelyone of fitting experimental data in equations byintroducing the adjustable, non-operative parameters.The basic question is whether a very simple equation,based upon 'the concept of molecular chaos implicitin the van der Waals' equation, is adequate, orwhether it is necessary to imagine the presence of'solid-like' structures. Our objective in studyingfluidity and density has been to compare the validityof different concepts of the liquid state.

In the present paper densities and viscosities ofeighteen organic liquids-from very simple, non-polar. non-associated to highly associated liquids-were measured. A comparison between the Arrhe-nius and Hildebrand equations in explaining thetemperature dependence of viscosities of organicliquids has been made.

Materials and MethodsAcetone, n-octane, acetic anhydride, pyridine,

bromo benzene, nitrobenzene, n-valeric acid, isopro-pyl alcohol, m-toluidin~, o-toluidine, aniline, amylalcohol, dioxane, phenol and glycol, all of reagentgrade (BDH), and toluene and carbon tetrachlorideof AR grade (BDB) were purified by standardmethods and redistilled before use. Purified quino-line (Riedel) was used as the reference liquid for thedetermination of viscosities of different liquids.

Densities were measured using a dilatometer ofapproximately 5.6 ml capacity with graduated stemof 0.0 I ml divisions. Cannon- Ubbelohdew viscometerwas used for the viscosity measurements (accuracy ±0.1 %). These measurements were made over thetemperature range 303 to 363 K in a thermo statedbath of ± O.l°C thermal stability .

Results and DiscussionThe plots of log') versus 1IT for the majority of

organic liquids under investigation, except ethyleneglycol, phenol and aniline and to some extent quino-line, m-toluidine and o-toluidine, follow the Arrhe-nius equation over the experimental range of tempe-rature (Fig. 1). The plots of In') versus liT for glycol,phenol and aniline show deviation from the Arrhe-nius behaviour in the low temperature region, attri-butable to the presence of association in these liquids.

The plots of log (fluidity) against the reciprocalof free volume, 1/(V-vo)where vois the molar volumeextrapolated to zero degree absolute without chang-ing the phase, are linear for only those liquids whichfollow Arrhenius equation (Fig. 2), e.g. the plots forliquids showing non-Arrhenius behaviour likeglycol, phenol, aniline, m-toluidine, o-toluidine andquinoline show deviations from the linear behaviour(figure not shown) suggesting the superiority ofDoolittle equation over that of the Arrhenius inidentical temperature intervals. Consequently thetemperature dependence of rP for such liquids wasexamined in terms of the Vogel-Tammann-Fulcher(VTF) equation,

963

INDIAN J. CHEM., VOL. 20A, OCTOBER 1981

1·0

'XIV

xv

0·5

III11

-0·5... ~ ... I..

. .

~.

27 30 33

Fig. 1 - Plots of log '1 versus l/T for (I) acetone, (II) n-octane, (III) toluene, (IV) acetic anhydride, (V) pyridine, (VI) carbontetrachloride, (VII) bromo benzene, (VIII) dioxane, (IX) isopropyl alcohol, (X) nitrobenzene, (XI) n-valeric acid, (XII)

m-toluidine, (XIII) quinoline, (XIV) o-toluidine and (XV) amyl alcohol.

°i03

0·01560~

x

'f55XI

of}

E

5·0

0;04, ,0·030XII 0'025

I 5'00·035

ro~I

4j·~":.O:-::2------:0'-:.0:-::2-::-5---:'-. :"':V""II-"":',X,..,...--.:0....,.O'""3""O------...,0"".0""3-:=-S-----...,0"".0'""'4'='0--'20

0:0<4 -6 O'.OS II.V. VI 0·0610 Y(V-Vo); m-3mol

Fig. 2 - Plots of In 4> versus l/(V-Vo) for (I) amyl alcohol, (II) isopropyl alcohol, (UI) nitrobenzene, (IV) n-valeric acid,(V) acetone, (VI) pyridine, (VII) toluene, (VIII) bromo benzene, (IX) carbon tetrachloride, (X) dioxane, (XI) acetic anhydride

and (XII) n-octane.

964

ISLAM & IBRAHIM : FLOW BEHAVIOUR OF ORGANIC LIQUIDS

TABLE 1 - LEAST SQUARES FITTFD PARAMETERS OF EQ. (2) AND DOOLITTLE EQUATION'"

LiquidEq. (2)

A k'

Quinoline 4923.9 1163.0o-Toluidine 14010.0 1433.3m-Toluidine 15096.0 1386.3Aniline ]3902.0 ]412.2Phenol 54729.0 1874.3Glycol 38758.0 1860.8

*t/> = A' exp r-Bo/(V-Vo)]

Doolittle equation

To(K) A' Bo Vo

68.6 2715.8 78.20 101.1667.4 5018.3 91.23 90.1972.2 5101.4 90.63 90.7070.6 4830.0 74.22 17.1374.1 572.19 21.02 82.5985.9 410.18 13.07 52.83

rP = A exp [- k'/( T-To)] ...(2)in which A and k' stand for the pre-exponential andexponential parameters, respectively. The significantparameter, To, known as the zero mobility tempera-ture was obtained by the least-squares fit. The plotsof In rP versus 1/(T-To) arc linear (Fig. 3) for liquids

.0 ~o3-5 4·0 4·5 5·0

10-3/(T-"t;, )Fig. 3 - Plots of In", 'versus 1/(T-To) for (I) glycol, (II) phenol,(III) o-toluidine, (IV) aniline,~(V) quinoline and (VI) m-toluidine.

showing non-Arrhenius behaviour. The values ofk' and To are given in Table 1.

The Doolittle equation has, however, been modi-fied in view of Eq. (2) by replacing Voby Vo, definedas the molar volume at To. The fluidities have con-sequently been least-squares fitted to the resultingequation and the parameters A', Bo and Vocomputed(Table 1) for the liquids showing non-Arrheniusbehaviour. The linear plots (Fig. 4) of logarithms offluidity against 1/(V-Vo) further support such ananalysis.

In order to examine the relative applicability of themodels proposed for this purpose the fluidity datahave been plotted against the molar volume and thelinear plots (Fig. 5) are obtained over the experimen-tal range for the majority of the organic liquidsstudied, except for glycol, phenol, aniline, amylalcohol and isopropyl alcohol. From the linear plotsthe corresponding values of the Hildebrand volume,VI<are obtained by extrapolation to zero fluidityand the value; of B are obtained from the slopes.The values of VB and B, listed in Table 2, show thatthese values for carbon tetrachloride and n-octanealmost reproduce the reported values",

While VB is the characteristic of a liquid whichstates that the liquid will cease to flow when it ac-quires the molar volume equal to VB, the B values

0{)65 0·0100·25 r.u 0·30

>--'5'0

III

4·0

V

3'0

2{)

1·00-055 IV-VI

()'05 '" 0-055 0·0606.~'~·1~0 ~O'~15~ ~0'~20~__ ~ ~~~~----~

0-045

OL- L- ~ ~ ~

O'()40 0-05010-6/(V-Vo) m-3mol

Fig. 4 _ Plots of In.,. versus 1/(V-Vo) for (I) phenol, (II) glycol, (III) aniline, (IV) o-toluidine, (V) m- toluidine and (VI) quinoline.

965

~oo

300

100

INDIAN J. CHEM., VOL. 20A, OCTOBER 1981

,,,,,,,,,,,,,,,,,,,

,IIII,

III,

IIII,

Fig. 5 - Plots of fluidity versus molar volume for (I) acetone, (II) pyridine, (Ill) dioxane, (IV) acetic anhydride, (V) carbontetrachloride (VI) toluene (VII) bromobenzene, (VIII) m-toluidine, (IX) o-toluidine, (X) n-valeric acid. (XI) quinoline,

, , (XII) n-octane and (XlII) nitrobenzene.

TABLE2- VALUESOF VB, B, TB, Tc AND MELTINGPOINTFORSEVERALORGANICLIQUIDS

Liquid 10' VB 10-1 B TB To m.p,( m' (N-l mt (K) (K) (K)

mol=") see-I)

Acetone 61.85 1793.9 156.8 408.0 254.0n-Octane 148.78 1931.4 209.5 569.0 152.0

(146.4) (1700.0)Toluene 98.36 2036.3 215.4 593.6 178.0Acetic anhydride 87.75 1426.2 226.2 569.0 200.0Pyridine 74.59 1375.0 214.6 617.0 231.5Carbon tetrachloride 91.13 1373.1 239.1 656.1 250.04

(89.9) (1340.0)Bromobenzene 98.34 1321.9 221.5 170.0 242.4Nitrobenzene 98.11 1141.8 246.2 710.0 218.1n-Valeric acid 105.25 1251.1 239.8 652.0 238.5m-Toluidine 106.75 1425.2 216.1 241.1o-Toluidine 105.65 1351.8 274.1 256.6Quinoline 115.80 1187.2 264.5 7793.0 299.5Dioxane 80.13 1331.2 231.3

Reported values are given in parentheses.

depend upon- the nature of the molecules, i. e. mcle-cules with less mass and free rotation will havehigher values of B. However, larger B-value ofn-octane as compared to acetone seems anomalousand indicates failure of Hildebrand equation. TheB-values for toluene, nitrobenzene and bromo-benzene seem to be in agreement as B-values varyin the order of molecular weight. Furthermore,considerably higher TB values (Table 3) reinforcethe view regarding the failure of Eq. (1).

966

The failure of Hildebrand equation in the cases ofglycol, phenol, aniline, amyl alcohol and isopropylalcohol may likely be due to the molecular associa-tion since Eq. (I) is only applicable to non-associatedliquids.

It seems that while it is very difficult to challengeHildebrand's reasoning that the fluidity is a functionof volume alone, his plea that fluidity is uniquelydetermined by the values, (V-VB) irrespective ofwhether changes in volume result from changes oftemperature or of pressure, seems to be certainlydoubtful, if not over the whole range of temperature,at least near the melting points. Despite the factthat many liquids in our study do not follow Hilde-brand equation, a large number of liquids followHildebrand model (Fig. 5), H not over the wholerange of temperature at least over the experimentaltemperature range. Nevertheless, the applicabilityof Hilde brand model has now been critically examinedeven over the limited temperature range after consi-dering the feasibility of its being a sound model.

In order to visualize the soundness of the Hilde-brand equation we may compare its fluidityequation with that of Arrhenius, i.e.

1 w ( k') ( V- VB )~= ~= A exp - T = B -v;;- ... (3)

A comparison of these two expressions, of course,cannot be done for the fluidity data of all sorts ofliquids. But this should hold good at least for everysimple liquids which are neither associated nor polarand in the temperature range well above the melting

ISLAM & IBRAHIM : FLOW BEHAVIOUR OF ORGANIC LIQUIDS

, points. We shall, therefore, take the examples ofcarbon tetrachloride, n-octane (both liquids havebeen studied by Hildebrand himself and follow hismodel satisfactorily) and toluer e (present study)for such a comparison. Taking log of Eq. (3) andthen differentiating with respect to temperature,we get

din tP k' VB 1 dVdT = p= V-VB· VB dT

or

k'(V-VB)=TlI.~~ ... (4)

Equation (4) requires that the plot T2 ~ against

molar volume should be linear and the slope shouldgive the value of k' (=EtP/R) and the intercept thevalue of -k'VB• Thus Eq. (4) should be so usefulfor those liquids which follow the Arrhenius equation

TABLE3 - VALUESOF 2T + p :~~!(:~)FOR VARIOUSORGANIC LIQUIDS

d2Vj(dV)2T + T2 dT' dT at temperature (K)

Liquid

n-OctaneTolueneAcetic anhydridePyridineCarbon tetrachlorideBromobenzeneNitrobenzeneQuinolineo-Toluidinem-ToluidineDioxaneAnilinePhenolGlycolIsopropyl alcoholAmyl alcoholAcetonen-Valeric acid

288.CO 293.00 298.00 303.00 308.00 313.00 318.00 323.00 318.00 333.00 338.00 343.09 348.00 353.00

814.30 832.46803.16 820.83817.01 835.29792.42 809.61816.13 834.37778.65 795.24772.14 788.44738.89 753.81761.68 777.55762.85 778.77794.97 812.27760.15 775.95754.40 769.96729.14 743.66

797.73 815.75 833.97769.57 786.33 803.25826.06 845.40 864.98754.05 770.13 786.35

869.41 888.20 945.92856.72 874.97 930.93872.49 891.42 949.57844.52 862.25 916.53871.49 890.38 948.38828.89 845.95 898.15821.51 838.27 889.49783.98 799.23 845.66809.69 825.97 875.65811.01 827.35 877.20847.41 865.25 919.94807.95 824.16 873.63801.47 817.41 866.04773.00 787.83 832.91

852.40 871.05 889.92 909.01 928.33 947.87 967.65820.34 837.59 855.3 872.63 890.42 908.38 926.53884.83 904.95 925.33802.72 819.24 835.90 904.12 869.70 886.83 956.96 921.57 939.18

762.30 779.91736.55 752.98788.13 806.97

738.11

1005.72988.79

1009.85972.56

1008.51951.89942.17893.14926.66928.39976.40924.39915.90878.93

987.67944.87 963.39

160 165 170 175 III

o

10x1cr':-:- .L-_~.L---....."....-----_'_:__,.------.J100 105 6 110 115 I,ll

10 v,m3mofl

>11-."."N'.1-

25xlcr

oo

15xlcr

II

Fig. 6 - Plots of P dV/dT versus molar volume for (1)toluene, (ll) carl::on tetrachloride and (Ill) n-octane.

967

INDIAN J. CHEM., VOL. 20A, OcrOBER 1981

as well as Hildebrand that even without measuringthe fluidity data we should be able to find out notonly the value of activation energy of flow, butalso the value of VB, the Hildebrand volum.e, onlywith the help of density measurements at differenttemperatures. Unfortunately Eq. (4) never ~oldsgood, even for a single liquid, no .m~tter ~ow SImplethat liquid may be while the deviations ill the casesof toluene and n-octane are small but in the ca~e of

.carbon tetrachloride the deviations are appreciable(Fig. 6).

The above equation may be differ~ntiated furtherwith respect to temperature to obtain,

, dV ? d2V dVk . dT = T". dT2 + 2T. dT

or

k' = P d2V/dV + 2Tst» dT

... (5)

For the liquids which follow the Alybenius eq';1a-tion as well as Hildebrand model the right hand sideof Eq. (5) for any temperature, T should remainconstant and should be equal to k'( ~~ Ef>/ R) suggest-ing that only density measurements should be enoughto determine the activation energy of flow. The

d2Vj dV .values of2T + P-- -d are found to increasedP T

successively with the increase in temperature and

968

? d2V / dV . .no two values of T" dP dT + 2T for any liquid

coincide for two different values of T, no matterhow close or away the two values of temperaturesare (Table 3). We, therefore, conclude that theHildebrand model is inadequate not only in the casesof non-associated and non-polar liquids at lowertemperatures but also in any temperature range ofstudy .

AcknowledgementFinancial assistance to one of the authors (M. I.)

by the UGC, New Delhi is gratefully acknowledged.

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1164.3. BARLOW, A. J., LAMB, J. & MATHESON, A. J., Proc. roy.

Soc .• London. (1965), 292, 322.4. BATSCHINSKI, A. J., Z. physik, Chim .• 84 (1913), 643.5. HILDEBRAND, J. H., Science. 174 (1971), 490.6. HILDEBRAND, J. H. & LAMOREAUX, R. H., Proc. natl. Acad.

Sci .. USA, 69 (1972), 3428.7. EICHER, L. D. & ZWOLINSKI, B. J., Science. 1"17(1972),

369.8. HILDEBRAND, J. H. & LAMOREAUX, R. H., J. phys, Chem.,

77 (1473), 1971.9. (a) McLAUGHLIN, E. & UBBELOHDE, A. R., Trans. Faraday

Soc., 53 (1957), 628; 54 (1958), 1804; 56 (1960),988.(b) MAGILL, J. H. & UBBELOHDE, A. R., Trans. Faraday

Soc., 54 (1958), 1811.10. TANFORD, c., Physical chemistry of macromolecules (John

Wiley, New York), 1961, 329.