Surface tension of binary liquid mixtures

Surface Tension of Binary Liquid Mixtures D. P A P A I O A N N O U AND C. P A N A Y I O T O U ~ Chemical Process Engineering Research Institute and Department of Chemical Engineering, University of Thessaloniki, 540 06 Thessaloniki, Greece

Received May 2, 1988; accepted July 15, 1988 Experimental measurements of the liquid-air interfacialtension are reported for the systemsbenzene + n-hexane at 20°C and acetone + isooctane at 25°C. The excess surface tension for both systems is negativewhilethe surfacetension itselffor the second system,when plotted againstcomposition, exhibits a fiat minimum. An attempt is made to interpret this behaviorin terms of basic thermodynamicquantities of the mixtures such as the excessfree enthalpy, the heat of mixing, the excessvolume, and the isothermal compressibility.

© 1989 Academic Press, Inc.

INTRODUCTION The surface tension of liquids and the variation of surface tension of liquid mixtures with composition are often required for a rational chemical process equipment design involving interphase heat and mass transfer. Because of the experimental difficulties encountered, careful measurements of surface tensions of liquid mixtures are rather rare ( 1 ). In fact it is impractical to measure this property for all mixtures of interest, and methods for predicting surface tension of liquid mixtures from pure c o m p o n e n t properties or other easily available mixture properties are of considerable practical importance. Although theoretical developments in the field of inhomogeneous fluids have been substantially advanced over the past decade (2, 3 ), a fully satisfactory theory of the gas-liquid interfacial tension of mixtures is not as yet available. In this respect semitheoretical predictive methods ( 4 - 9 ) are more often used. In this work we report measurements of surface tension for the systems benzene + nhexane at 20°C and acetone + isooctane at 25 °C obtained by the differential capillary rise technique ( 1, 10). The excess surface tension, ~rE, of both systems is negative. F r o m careful 1To whom correspondence should be addressed.

measurements of densities, relatively large and positive excess volumes are calculated especially for the system acetone + isooctane. Vapor-liquid equilibrium measurements ( 1 1, 12) indicate that the excess free enthalpy of both systems is, also, relatively large and positive. The heat of mixing for the system benzene + n-hexane is also large and positive (13). An attempt is made for the interrelation of these excess properties. This is accomplished through the use of the Lattice-Fluid theory of mixtures (14-16) and the Sanchez equation (17) relating surface tension to the liquid's isothermal compressibility and density. MATERIALS AND METHODS All pure liquids used in this work were proanalysis grades from Merck except for n-hexane, which was a spectrograde from Fluka. The reported purities which were verified by G L chromatography are the following: benzene > 99.7%, n-hexane > 99.5%, acetone > 99.5%, isooctane > 99.5%, n-heptane > 99.0%. No further purification was attempted. Pure component properties are reported in Table I. The mixtures were prepared by weight from the pure components with precision +0.0001 g. Precautions were taken to minimize evaporation losses during the preparation and the

432

0021-9797/89 $3.00 Copyright © 1989 by Academic Press, Inc. All fights of reproduction in any form reserved.

Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989

SURFACE

TENSION

OF LIQUID

TABLE I Pure Component Properties Density, kg m-3, Liquid Benzene

Surface tension, mN m- ~

T, °C

Measured

Literature

Measured

Literature

20

878.8

878.9 (24)

28.87

28.83 (25) 28.87 (19) 28.88 (26) 18.41 (18) 18.53 (29) 18.95 (19) 20.22 (18) 22.90 (25) 23.04 (29) 18.32 (29)

n-Hexane

20

659.5

659.5 (28)

18.42

n-Heptane Acetone

20 25

686.7 784.3

686.8 (18) 784.4 (28)

20.21 23.03

Isooctane

25

687.6

687.6 (30)

18.36

subsequent determination of densities and surface tensions. The densities, o, have been measured in a vibrating tube densitometer Model D M A 6 0 / 602 of Anton Paar. Bidistilled water and air were used as calibrating substances. The temperature in the measuring cell was regulated to 20.00 + 0.01°C or to 25.00 + 0.001°C through a Haake ultrathermostat and measured by a precision digital t h e r m o m e t e r Model S 1220 of Systemteknik. The estimated error in the density is +5 × 1 0 - 6 g cm -3. The surface tensions, f, have been measured by the differential capillary rise method (1, 10, 27). Two precision glass capillaries were used with radii rl = 0.383 m m and r2 = 0.073 m m , respectively. These radii were obtained from calibration at 20°C with n-hexane and n-heptane of known standard values of surface tension (18). The two capillaries were accurately vertical and immersed into the liquid under study contained in a glass tube of 3.5 cm internal diameter. This tube and the two capillaries were connected to a manifold of high-vacuum stopcocks which were used for pressure communication between tube and capillaries and for elevation and depression of the menisci in the precision capillaries with slightly overpressurized dry air. The complete system of glass tube containing the liquid, capillaries, and pressure connections was isolated from the dry air container and kept in a

433

MIXTURES

precision thermostat Model T a m s o n TMV40. After reaching equilibrium, the differential rise in the capillaries was measured by a cathetometer with an accuracy of +0.01 m m . The surface tension values were calculated according to o" -

rl r2gAo f(rl

[3Ah

-- (rl

-- r2)],

[1]

- r2)

where Ap is the density difference between the liquid and the gaseous phase; Ah is the measured difference in meniscus height between the two capillaries and g is the local acceleration due to gravity. The estimated error in surface tension is ___0.25% (+0.05 m N m - 1 in absolute values). RESULTS

The experimental values of the surface tensions of the binary mixtures over the whole concentration range are reported in Table II. The reported values are the average of at least two independent measurements. F r o m these values we calculated the excess surface tensions, rE, defined by f E ~_~ f f - - X l f l

-- X20"2,

[2]

where xi and fi are the mole fraction and the pure liquid surface tension of c o m p o n e n t i while f is the surface tension of the mixture of composition Xl. Each set of results was fitted with a Redlich-Kister-Scatchard type equation n fiE = X l X 2

~ j=o

bj(l - 2 x l ) j.

[3]

Coefficients bj along with standard deviation of fit are reported in Table III. The excess volumes, V E, have been determined from the experimental data on densities, 0, according to

where Mi is the molar mass of c o m p o n e n t i. The experimental data are well represented by Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989

434

PAPAIOANNOU AND PANAYIOTOU TABLE II

Coefficients vj along with standard deviation o f fit are reported in Table IV. Excess volumes are positive for both systems a n d especially for the system acetone + isooctane. In Fig. I are shown our experimental data on surface tension for the system benzene ( 1 ) + n - h e x a n e ( 2 ) along with the experimental data o f Ridgeway a n d Butler (19). The discrepancy between the two sets o f surface tension data at high n-hexane concentration might be due to chemical impurities, miscalibration, or some other experimental artifact. The surface tension o f n-hexane, reported by Ridgeway and Butler (19), differs f r o m literature values by ca. +0.5 m N m -1 as is shown in Table I. In Fig. 2 are shown our experimental data on surface tensions for the system acetone ( 1 ) + i s o o c t a n e ( 2 ) at 25°C. We were unable to find data on surface tension in the literature for this system for comparison. As shown in Fig. 2, the surface tension o f this system exhibits a fiat m i n i m u m when plotted against composition. This system as well as the system benzene + n-hexane exhibits negative excess surface tensions. In what follows we will att e m p t a rationalization o f this behavior.

Experimental Data on Surface Tensions (a) Benzene(l) + n-hexane(2) at 293.15 K xl

a × 103, N m -I

0.099 0.200 0.352 0.455 0.493 0.599 0.700 0.812 0.900 0.951

18.78 19.23 20.08 20.81 21 .O3 21.76 22.68 24.24 25.92 27.27

(b) Acetone(1) + isooctane(2) at 298.15 K xl

o-× 103, N m x

0.051 0.101 0.202 0.297 0.395 0.403 0.496 0.590 0.681 0.698 0.750 0.799 0.849 0.900 0.949

18.30 18.23 18.23 18.24 18.31 18.34 18.44 18.57 18.82 18.84 19.16 19.40 19.87 20.51 21.54

DISCUSSION

a Redlich-Kister-Scatchard type equation analogous to Eq. [ 3 ], namely n

V E .~ X l X

vj(1

2 ~

-- 2Xl)

j.

[5]

j=O

As already noticed, vapor-liquid equilibrium data from the literature ( 11, 12) indicate that both systems exhibit large positive deviations from R a o u l t ' s law at ambient temperatures and especially the system benzene + nhexane, which exhibits an azeotrope. Experimental heats o f mixing (13) for the system benzene + n-hexane are also positive. D a t a on the heats o f mixing for the second system

TABLE III Coefficients of Eq. [2] and Standard Deviation of Fit (SDF) System

N°

b0

bj

b2

b3

SDF

Benzene + n-hexane Acetone + isooctane

12 17

- 10.343 -9.063

7.329 6.473

-6.363 -6.068

1.468 5.449

0.025 0.022

Number of data points. Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989

435

SURFACE TENSION OF LIQUID MIXTURES 24

TABLE IV

I

I

I

I

I

I

I

I

Coetficients of Eq. [4] and Standard Deviation of Fit (SDF) System

v0

vl

v2

SDF

Benzene + n-hexane Acetone + isooctane

1.6636 4.3114

0.0297 0.2511

0.1724 0.9308

0.0029 0.0072

I

y //

~"

are n o t available b u t as m a y be inferred f r o m the excess G i b b s free energy d a t a ( 1 2 ) a n d the d a t a for the v o l u m e s o f mixing, the heats o f m i x i n g for this system m u s t also be positive. This behavior, o n a qualitative basis, is in a g r e e m e n t with the c o m m o n observation (20) t h a t large negative excess surface t e n s i o n s are as a rule a c c o m p a n i e d b y large positive deviations f r o m R a o u l t ' s law. T h e o b s e r v a t i o n o f the e n r i c h m e n t o f the interfacial region with the c o m p o n e n t o f low surface t e n s i o n is also c o m m o n . T h e occurrence, however, o f ext r e m a in surface t e n s i o n o f m i x t u r e s requires s o m e further c o n s i d e r a t i o n . I f F2,~ is the relative a d s o r p t i o n o f c o m p o -

30

I

I

I

I

I

I

~

I

21

///

'E z

/

f 18

0.0

I

I

I

/ /' f

18 0.0

I

I

I

I

I

I

¢0

I 0.5

I

I

I

0.5

I

I

I

I

1.0

X1 FIG. 2. Surface tensions for the system acetone( 1 )

+ isooctane (2) at 25°C. Circles are experimental data. Dashed line was calculated according to Acree's scheme (21 ). Solid line was calculated using the LF model.

--daT =

~0

I

n e n t 2 at the interface, the G i b b s a d s o r p t i o n i s o t h e r m m a y b e w r i t t e n as

I

/Z~

O

//

1.0

X1

FIG. |. Surface tensions for the system benzene( 1) + n-hexane ( 2 ) at 20 °C. (A) Experimental data of Ridgeway and Buffer (19). (O) Experimental data of the present work. Dashed line was calculated according to Acree's scheme (21). Solid line was calculated using the LF model.

r2,1d/.t2,

[6]

where #2 is the c h e m i c a l p o t e n t i a l o f c o m p o n e n t 2 in the m i x t u r e . T h i s e q u a t i o n indicates that for a given state to exhibit a n e x t r e m e value o f the surface t e n s i o n at c o n s t a n t t e m p e r a t u r e it is necessary a n d sufficient t h a t the relative a d s o r p t i o n F2d be zero ( 2 0 ) . In the case o f the system a c e t o n e + i s o o c t a n e this m i g h t be viewed as the o u t c o m e o f two c o m peting factors: o n the one hand, the t e n d e n c y o f the low surface t e n s i o n c o m p o n e n t (isooct a n e ) to be a d s o r b e d at the interfacial region and, on the o t h e r h a n d , the t e n d e n c y o f the m o r e volatile c o m p o n e n t ( a c e t o n e ) to e n r i c h the gaseous phase. In the case o f the system b e n z e n e + n - h e x a n e the escaping t e n d e n c y o f b o t h c o m p o n e n t s is significant, resulting in the azeotrope, a n d a p p a r e n t l y this t e n d e n c y o f b o t h c o m p o n e n t s in this system c a n n o t balance the t e n d e n c y o f the low surface t e n s i o n Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989

436

PAPAIOANNOU AND PANAYIOTOU

benzene to enrich the interfacial region, thus always leaving I'2,1 < 0. Although these arguments may be used for a qualitative and oversimplified explanation of the behavior of our systems, they cannot give any quantitative information. As already noticed the influence of nonspherical molecular force fields on the structure of the inhomogeneous (interfacial) region is still poorly understood (2, 3 ). In a recent work Sanchez (17), using statistical mechanical arguments, concluded that the surface tension of a liquid in its normal liquid range is related to its isothermal compressibility, 3, and mass density, o, by 0"(/3110) 112 =

[7]

A~ 12.

Ao appears to be an invariant characteristic of the liquid. For hydrocarbons as well as oxygenand nitrogen-containing organics, Ao varies only by about 20%. The simple mathematical nature of this relationship suggests applicability to multicomponent mixtures. This has been done, indeed, by Acree (21 ), who used as logical approximation for/3, 0, and A0 in the mixture the volume fraction averages /3(mixture) = ~ 1/31 + ~o2/32

[8]

0(mixture) = ~Pl01 + @2p2

[9]

A~/2(mixture) = ~Ol(A1/2)l + ~p2(A~/2)2, [10] ~pi being the volume fraction of component i in the mixture. /3i, Oi, and (A~/2)i are properties of the pure liquid i at the temperature and pressure of the mixture. Dashed lines in Figs. 1 and 2 have been calculated by applying Eqs. [7] to [ 10] to our systems. As observed, the agreement between calculated and experimental surface tensions is rather poor. No essential improvement is observed by using mole fraction instead of volume fractions in Eqs. [81 to [10l. Nevertheless, before drawing any conclusions about the applicability ofEq. [ 7 ] to mixtures we should realize that erroneous estimations of/3 and 0 by Eqs. [8] and [9] in Journal of Colloid and Interface Science, Vol. 130,No. 2, July 1989

opposite directions may lead to estimations of a that are in significant error. Experimental data, on the other hand, on mixture densities are rather easily available while correponding data on isothermal compressibilities are rather scarce. These properties may, however, be estimated with reasonable accuracy by successful equation-of-state theories ( 14, 15, 22, 23 ). In this work we reconsidered the applicability of Eq. [7] to mixtures by using the mixture properties /3 and p as estimated by the Lattice-Fluid (LF) theory of mixtures (1416). According to LF theory, each fluid i is characterized by three scaling constants T*, P*, and p* for the temperature, pressure, and density, respectively, or, equivalently, by the constants ri, v*, and E* = sici/2 = P ' v * = R T * for the number of segments per molecule, the hard core volume per segment, and the interaction energy. R is the gas constant and si the number of intermolecular contacts per segment. Entirely analogous scaling constants may be defined, in the one-fluid approach, for the mixture in terms of the volume fraction ~i and the surface fraction 0r of each component i. Thus v* in the mixture may be obtained from the classical quadratic mixing rule ~

2 • 2 ~01O 1 -It- ~021) 2 ~- 2~01~02U~2 .

[11]

The following general combining rule may be used for v~2, i)~2 ~___~12 (I/~ I/3 "~ 1)~ 1/3) 3

2

,

[12]

(12 being a binary parameter (equal to one for hard spheres). The interaction energy e* of the mixture is given by (15) ~:* = ~1~.~ -[- ~ 2 ( . ~ -- R T ~ O l O - 2 X 1 2 ,

[131

where

X,2 =

-$2

--

VS2 RT

el E2

[141

~-12 is a second binary parameter. The ratio sl /

& may be obtained from molecular size and

SURFACE TENSION OF LIQUID MIXTURES shape characteristics o f fluids 1 and 2 (15). Volumetric properties o f the mixture are obtained from the equation o f state, which m a y be written as ( 14, 15) /~ + ~2 + 7~[ln(1 _ ~)

+(1-

1/r)~] = 0 ,

[15]

where the reduced temperature, pressure, and density are defined, respectively, by T-

T T*'

P /~-P*'

p ~=o-~"

[16]

The equation for the isothermal compressibility obtained from Eq. [ 15 ] m a y be written

as +1)__2~2}

1.

437

The full fines in Fig. 1 and 2 were calculated by Eqs. [ 7 ] and [ 10 ], where Eqs. [ 15 ] and [ 171 have been used for the estimation o f o and /3. As observed, although there is no quantitative agreement between calculated and experimental values, there is a significant i m p r o v e m e n t over Acree's scheme (21 ). The L F model does predict a m i n i m u m in the surface tension for the system acetone + isooctane. It is important to point out that a m o r e strict test o f Eqs. [7] a n d [ 10] would require a consistent set o f experimental data on a, O, and/3 for the mixture. It is h o p e d that the present work will stimulate experimental work toward that end.

[17] ACKNOWLEDGMENTS

Scaling constants for our pure liquids are given in Table V along with the binary p a r a m eters for the two binary mixtures. These latter parameters were obtained as follows: The ratio Sl/S2 was obtained from B o n d i ' s scheme (31, 32) for the estimation o f van der Waals volu m e and surface area o f the molecules. ~'12for the system benzene + n-hexane was obtained, as usually, from heat o f mixing data (13). For lack o f this kind o f data for the system acetone + isooctane its ~'12 parameter was estimated f r o m excess free energy data ( 1 2 ) . (12 for both systems was obtained, as usually, from data on excess volumes. TABLE V LF scaling constants and binary parameters Liquid

T*, K

P*, MN m -2

p*, kg rn -3

Acetone Benzene n-Hexane Isooctane

484 523 476 487

534 444 298 266

917 994 755 804

Binary parameters System

Benzene(l) + n-hexane(2) Acetone(l) +isooctane(2)

~12

~12

s~/s2

0.960 0.943

1.006 1.030

0.88 1.10

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25. "Beilsteins Handbuch d. Organischen Chemie," 3.u.4. E. W. Springer-Veflag, Berlin. 26. Jasper, J. J., J. Phys. Chem. Ref. Data 1, 841 (1972). 27. Strey, R., and Schmeling, T., Ber. Bunsenges. Phys. Chem. 87, 324 (1983). 28. Bauer, H., and Meeflender, G., Rheol. Acta 23, 514 (1984). 29. Daubert, T. E., and Danner, R. P., "Data Compilation Tables of Properties of Pure Compounds," AIChE Symp. Ser., Vol. 75, No. 203, 1985. 30. Riddick, J. A., and Bunger, W. B., "Organic Solvents. Techniques of Organic Chemistry," Vol. II. WileyInterscience, New York, 1970. 31. Bondi, A., "Physical Properties of Molecular Crystals, Liquids and Glasses." Wiley, New York, 1968. 32. Sorensen, J. M., and Arlt, W., "Liquid-Liquid Equilibrium Data Collection," Dechema, Chem. Data Series, Vol. V. Frankfurt, 1979.