2013, Bagheri, Prediction of the Surface Tension, Surface Concentration

Prediction of the Surface Tension, Surface Concentrationand the Relative Gibbs Adsorption Isotherm of Non-idealBinary Liquid Mixtures

A. Bagheri A. A. Rafati A. Adeli Tajani A. R. Afraz Borujeni

A. Hajian

Received: 25 February 2013 / Accepted: 18 June 2013 / Published online: 25 October 2013 Springer Science+Business Media New York 2013

Abstract Surface properties of binary mixtures of 1,2-ethanediol, 1,2-propanediol and1,4-butanediol with acetonitrile have been measured by the surface tension method at

T = 298.15 K and atmospheric pressure. The surface tension has been predicted based on

the Suarez method. This method combines a model for the description of surface tension of

liquid mixtures by using the UNIFAC group contribution method for calculation of activity

coefficients. Also, the results have been discussed in terms of surface concentration and

lyophobicity using the extended Langmuir isotherm. The results provide information on

the molecular interactions between the unlike molecules that exist at the surface and the

bulk phase. Finally, experimental values of the surface tension have been correlated by the

RedlichKister and WangChen polynomial equations over the whole mole fraction range.

Keywords Surface tension Prediction Correlation Surface adsorption UNIFAC

1 Introduction

Surface tension is an important physico-chemical property due to its influence on several

natural phenomena, as well as industrial applications [1]. The surface tension of a liquid

mixture is not a simple a function of the surface tension of the pure components, because in

a mixture the composition of the interface is not the same as that of the bulk phase. The

deviation of the surface tension of a liquid mixture from linearity reflects changes of

structure and cohesive forces during the mixing process [2]. At the interface there is

migration of the species having the lowest surface tension, or Gibbs energy per unit area, at

A. Bagheri (&) A. A. TajaniDepartment of Chemistry, Semnan University, P.O. Box 35131-19111, Semnan, Irane-mail: [email protected]; [email protected]

A. A. Rafati A. R. A. Borujeni A. HajianDepartment of Physical Chemistry, Faculty of Chemistry, Bu-Ali Sina University, 65174 Hamedan,Iran

123

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the temperature of the system. This migration to the interface results in a liquid phase rich

in the component with the highest surface tension and a vapor phase rich in the component

with the lowest surface tension [24].

Models for calculation of surface tensions are normally based on the assumption that the

surface layer forms a separate phase with constant and uniform composition that is dif-

ferent from the composition of the adjacent vapor and bulk liquid phases. The models all

require values of the pure component surface tension for each component in the mixture.

The models differ in the way in which the molar surface areas of the components are

calculated and in the assumptions concerning the activity coefficients of the components,

both in the surface region and in the bulk liquid phases [5].

Several different approaches have been used to predict the surface tension and its

variation with composition: the classical thermodynamic method [69], corresponding

states models [10, 11], gradient theory [12], perturbation theory [13], the parachor method

[14], and also activity coefficient models such as Wilson, NRTL, and UNIFAC [5, 1517].

In this paper, we report experimental values of surface tension for binary mixtures of

diols {1,2-ethanediol (1,2-ED), 1,2-propanediol(1,2-PD), and 1,4-butanediol (1,4-BD)}

with acetonitrile, obtained using the ring method, and compare them with predicted surface

tensions from the Suarez method [5, 18, 19]. The model used here to estimate and predict

surface tension values for binary systems as a function of concentration and temperature

relates the surface concentration of each component to the individual activity coefficients

(in the liquid bulk phase and surface layer) and to the molar surface area of each com-

ponent [20]. The activity coefficients and the relative Gibbs adsorption were evaluated

using the UNIFAC group contribution model [2123].

The UNIFAC group contribution method is a gE (Gibbs energy) model that allows the

prediction of liquid phase activity coefficients ci in nonelectrolyte systems, as a function oftemperature and composition. The activity coefficient is calculated as the sum of the

combinatorial part and the residual part per pair of functional groups. The combinatorial

part represents the contribution of the excess entropy, which results from the different sizes

and shapes of the molecules considered. The residual part represents the contribution of the

excess enthalpy, which is caused by energetic interaction between the molecules [24, 25].

In addition to determining more information about the surface structure of binary

mixtures, surface mole fractions were calculated using the Suarez method (based on

UNIFAC model) and the extended Langmuir model (EL) [26]. The results obtained show a

good consistency between two applied methods, i.e., the Suarez method and EL model.

Finally, surface tension deviations were calculated from experimental data and have

been correlated with the RedlichKister (RK) and WangChen (WCH) polynomial

equations [9, 27].

2 Experimental

2.1 Materials

Acetonitrile (mass fraction [ 0.999), 1,2-ED (mass fraction [ 0.999), 1,2-PD (massfraction [ 0.99) and 1,4-BD (mass fraction [ 0.995), were purchased from Merck andused without further purifications. The water was distilled twice. Table 1 reports a com-

parison between the pure component density, q, and surface tension, r, at 298.15 K withthe corresponding literature values [2834].

The measured results are in good agreement with the literature values.

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2.2 Apparatus and Procedure

The surface tensions of the pure liquids and their mixtures were measured using the platinum

iridium ring method with a KSV (Sigma 70, Finland) tensiometer. A technical suggestion by

KSV is that the ring be flamed prior to the measurements. The use of boiling distilled water

can be a good (alternative) procedure (for checking the performance of the KSV Sigma 70

system). However, the measurement of surface tension of water is very sensitive to dust or

grease which can occur on the ring. It often happens that the first measurements of surface

tension fall well below the literature values (e.g. values of 64.68 mNm-1 are obtained, whichis below the correct value of 71.97 mNm-1 at 298.15 K). Following our experience, onlyafter cleaning the ring several times after soaking in chromosulfuric acid for several hours is it

possible to achieve stable measurements with water. When surface tensions are measured

with the ring detachment method, they are corrected to the actual values by means of the Huh

and Mason compensation for interface distortion [35].

Each measurement was repeated up to ten times to check for reproducibility. The

uncertainty of the surface tension measurement is 0.2 mNm-1 of the final value ofsurface tension, and the corresponding reproducibility is 0.01 mNm-1. The temperaturewas kept constant by a water bath circulator (Pharmacia Biotech) and with an uncertainty

of 0.1 K. The binary mixtures were prepared by mass using a Sartorius analytical bal-

ance (model BP 121S, accurate to 0.1 mg). The uncertainty of the mole fractions was

estimated to be within 1 9 10-4. Densities of pure components were measured with an

AntonPaar digital precision densitometer (Model DMA 4500) operated in static its mode

and calibrated with bidistilled water.

3 Results and Discussion

3.1 Prediction of Surface Tension for Binary Systems

Experimental values of the surface tensions for all binary mixtures at 298.15 K are listed in

Table 2. In all of the mixture systems, the surface tension, r, decreases with increasing

Table 1 Comparison of experimental surface tension, r, and density, q, of pure components with literaturevalues at 298.15 K and atmospheric pressure

Component r (mNm-1) q (gcm-3)Exp. Lit. Exp. Lit.

Acetonitrile 28.10 28.25a, 28.16b 0.77679 0.77664c

1,2-ED 48.22 48.11a 1.10978 1.0991d, 1.1086e

1,2-PD 35.44 35.60f 1.03211 1.0322e

1,4-BD 45.33 45.47f 1.01271 1.0126 g

a Ref. [28]b Ref. [29]c Ref. [30]d Ref. [31]e Ref. [32]f Ref. [33]g Ref. [34]

J Solution Chem (2013) 42:20712086 2073

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acetonitrile mole fraction. This trend is nonlinear and the surface tension decreases rapidly

with increasing acetonitrile concentration (see Fig. 1). This behavior is typically explained

as resulting from a difference in distribution of molecules between the surface and the bulk

of the liquid [17]. In a characteristic case, the compound having the lower surface tension

is expelled from the bulk to the liquidvapor interface due to the attractive forces between

solvent molecules (diols).

Relations for the surface tension of nonelectrolyte solutions can be derived based on the

assumption that the surface layer can be treated thermodynamically as a separate phase

from the bulk phase. The chemical potential of a component i in the bulk phase (b), li,b, ofa nonelectrolyte solution is given by the relation:

li;b l0i;b RTlnai;b 1where l0i;b is the standard chemical potential of component i in the bulk phase and ai,b is theactivity of component i in the bulk phase. R and T are the gas constant and absolute

temperature, respectively. In the surface phase (s), the chemical potential of a component

can be similarly written as

Table 2 Experimental and calculated values of the surface tension, r, of binary acetonitrile (2)/diol (1)mixtures

x2 rexp (mNm-1) rcal (mNm-1) x2 rexp (mNm-1) rcal (mNm-1) APD (%)

Acetonitrile (2)/1,2-ED (1)

0.0109 47.82 47.63 0.2999 36.35 37.36 1.12

0.0199 47.46 47.16 0.3500 34.90 35.94

0.0361 46.85 46.36 0.4345 33.00 34.33

0.0720 45.45 44.75 0.4888 32.25 33.81

0.0845 44.97 44.23 0.5699 31.53 32.86

0.1012 44.23 43.58 0.6321 31.02 32.15

0.1402 42.70 42.17 0.7099 30.49 31.19

0.1862 40.78 40.71 0.7765 30.17 30.44

0.1992 40.13 40.33 0.8499 29.71 29.66

0.2569 37.76 38.79 0.9525 29.01 29.19

Acetonitrile (2)/1,2-PD (1)

0.0543 35.25 35.32 0.5217 32.25 31.37 1.78

0.0843 35.22 35.05 0.6503 31.43 30.43

0.0899 35.13 35.00 0.7504 30.83 29.75

0.2043 34.65 34.00 0.8106 30.50 29.67

0.2785 34.19 33.36 0.8895 29.66 29.57

0.4600 32.74 31.85 0.9493 28.69 28.51

Acetonitrile (2)/1,4-BD (1)

0.0086 45.30 45.21 0.4583 33.88 35.08 0.19

0.0341 45.13 44.47 0.4958 33.12 34.45

0.0544 44.88 43.90 0.6903 31.03 31.63

0.0997 44.10 42.68 0.7476 30.65 30.91

0.1963 41.70 40.29 0.8272 30.16 29.98

0.2813 38.81 38.42 0.8797 29.82 29.41

0.3504 36.59 37.03 0.9497 28.95 28.69

2074 J Solution Chem (2013) 42:20712086

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li;s l0i;s RTlnai;s rAi 2where r is the surface tension of the solution, ai,s the activity of component i in the surfacephase, and Ai the partial molar surface area of component i in the solution. For a purecomponent with surface tension ri and molar surface area Ai, it can be written as

l0i;s l0i;b rAi: 3At equilibrium, the chemical potentials of component i in the bulk and surface phases

are equal, i.e.,

li;s li;b 4Combining Eqs. 14 leads to

rAi rAi RT ln ai;sai;b

: 5

The activities ai in Eq. 5 can be written in terms of activity coefficients, ci, as

rAi rAi RT lnxi;sci;sxi;bci;b

!6

where xi,b and xi,s are the mole fractions in the bulk and surface liquid phases, respectively,

and ci,b and ci,s are the corresponding activity coefficients.Furthermore, the sum of the mole fractions over all components in the solution for both

bulk and surface liquid phases is unity:Xi

xi;b 1;X

i

xi;s 1 7

In the present work, we used two assumptions: (i) the bulk and surface phases are in

equilibrium; (ii) the partial molar surface area of component i is the same as the molar

surface area of i. Using these assumptions leads to the following equation [19, 25, 36, 37]:

28

31

34

37

40

43

46

49

0 0.2 0.4 0.6 0.8 1x 2

/(m

N.m

-1 )

Fig. 1 The experimental surface tension values, r, for the binary systems of acetonitrile (2)/diol (1) versusx2: 1,2-ED (closed circle), 1,2-PD (closed square), 1,4-BD (closed triangle)

J Solution Chem (2013) 42:20712086 2075

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r ri RTAi

lnxi;sci;sxi;bci;b

!8

Application of Eqs. 7 and 8 requires knowledge of: (i) the surface tensions of the pure

components ri; (ii) the molar surface areas Ai (the estimation of Ai will be discussed in thefollowing section), and (iii) a model for calculating the activity coefficients ci,s and ci,b (inthis work the modified UNIFAC group-contribution method is used with the parameters

presented by Gmehling et al. [24]).

The surface tension predictions are found to be extremely sensitive to the values of the

molar surface areas used in the computation. There are two methods to calculate the molar

surface area: (i) Paquette molar surface areas, or (ii) Rasmussen molar surface areas [5, 38,

39]. In our previous work were evaluated the sensitivity of two methods (Rasmussen and

Paquette) in the prediction of surface tension [39]. In this paper, we used only the Paquette

method for calculation of molar surface areas. The equation for the Paquette molar surface

area is based on the assumption that the molecules are spherical and that the appropriate

geometrical area presented at the surface is the cross-sectional area of the molecule [38

40]:

Ai 1:021 108V6=15i;c V4=15i;b 9Here Vi,c is the critical molar volume and Vi,b the bulk phase liquid molar volume of the

ith component, where Vi,c and Vi,b are in cm3mol-1 and Ai is in cm2mol-1.

For an N-component nonelectrolyte solution (i = 1 to N) with known composition (i.e.,

known xi,b), Eq. 8 forms a set of N equations in N unknowns (N - 1 independent mole

fractions xi,s and r). This set of equations is solved iteratively by the NewtonRaphson [23]technique, and the values of ci,s and ci,b can be estimated by the UNIFAC group contri-bution model [22, 39].

The surface tension values of the three binary organic systems predicted by this method,

and some derived parameters as well as experimental values, are tabulated in Table 2.

Also, the absolute percentage deviations (APD) have been calculated using the following

equation and the results are given in Table 2.

APD 100N

Xi

ri;exp ri;cal

ri;exp10

where N is the number of experimental data points.

The results obtained (Table 2) indicate that this method gives reliable predictions of the

surface tension. By considering the APD values, it has been shown that the proposed

method can be applied to estimate the surface tension for the binary mixtures of compo-

nents with the same chemical nature and molecular sizes.

There is a difference between r values obtained from the UNIFAC model and for theexperimental results (see Table 2). These discrepancies are due to the following: (i) exact

solutions of the equations were not possible, so an approximation method was used.

Therefore, the error will increase. It goes without saying that as the number of parameters

in the equation increases, the error will decrease. (ii) Due to the lack of values for molar

surface areas (A) for mixtures, we assume the same value of A for both pure materials and

their mixtures. On the other hand, the value of A has been considered to be the same for

bulk phase and surface. On the whole, by taking into account the above approximations,

our values obtained for APD are smaller than those reported by other researchers for

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similar systems, which suggests that the prediction method is reliable for determining the

surface tension of mixed solutions [5, 16].

3.2 Relative Gibbs Adsorption and Study of Surface Properties

The adsorption process involves the transport of molecules from the bulk solution to the

interface, where they form specially oriented molecular layers according to the nature of

the two phases. Adsorption of a component at the phase boundary of a system causes a

different concentration in the interfacial layer compared to the adjoining bulk phases. For

the adsorption of a component onto the fluid interface, the relative Gibbs adsorption values,

C2,1, have been evaluated from the surface tension concentration data using the Gibbsadsorption equation. Values of C2,1 based on the arbitrary placement of the Gibbs dividingplane near the fluid interface is quantitatively related to the composition of the surface

phase. From the Gibbs equation, the relative adsorption was calculated according to the

expression:

C2;1 orol2

T ;p

1RT

orolna2

T ;p

11

where l2 and a2 c2x2 are the chemical potential and activity of component 2 in themixture, respectively. The values of c2 were obtained using the UNIFAC model.

Figure 2 shows the variation of C2,1 versus acetonitrile mole fraction (x2) in the bulksolution. The positive value of C2,1 in binary mixtures of the solvents indicates adsorptionof species No. 2 onto the surface (acetonitrile in our present study) and the addition of this

species to solutions causes the surface tension of the solution to decrease.

The C2,1 value increases with increasing concentration of acetonitrile and finally reachesmaximum value of the saturated surface adsorption (Cmax2;1 ). The values of C

max2;1 (or C2,1) for

0

0.75

1.5

2.25

3

3.75

4.5

0.0 0.2 0.4 0.6 0.8

x 2

2,1

/(

mo

l. m

-2 )

Fig. 2 The values of relative Gibbs adsorption, C2,1, against x2 for the binary systems; the symbols werecalculated using the data and the continuous dashed curve is just a guide for the eyes: acetonitrile (2)/1,2-ED(1) (closed circle), acetonitrile (2)/1,2-PD (1) (closed square), acetonitrile (2)/1,4-BD (1) (closed triangle)

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mixtures of diol (1,2-ED, 1,2-PD and 1,4-BD)/acetonitrile increase as follows: 1,2-

ED [ 1,4-BD [ 1,2-PD. On the other hand, the Cmax2;1 (or C2,1) decrease with increasingdifferences between the surface tension values of the pure compounds.

In Fig. 2 there are two principal factors which induce the diol molecules to principally

avoid the interface: the lower surface tension of acetonitrile and the fact that the polar

interaction between diol molecules can be accomplished more efficiently in the bulk liquid

phase instead of at the interface. Therefore, the acetonitrile molecules are expelled from

the bulk to the liquidvapor interface due to the attractive force among diol molecules (see

Fig. 3) [41, 42].

The surface layer concentration, x2,s, is the other quantity estimated simultaneously

using the calculation scheme proposed in this work (from Eq. 8 or the Suarez method).

Table 3 reports the x2,s values for the binary systems of diols (1,2-ED, 1,2-PD and 1,4-BD)

with acetonitrile at T = 298.15 K.

Also, the variation of x2,s versus x2 for acetonitrile/diol mixtures is shown in Fig. 4 using

the above model. This diagram shows that the surface is enriched with solute (acetonitrile)

relative to the bulk composition. It is well recognized that, for processes that involve mass

transfer between liquid and vapor phases, surface tension plays an important role, and

according to what we have observed from the surface layer concentration curves, this

property is a consequence of the preferential migration of molecules of the different com-

ponents of a given mixture to the surface layer and eventually to the vapor phase [17, 25].

A new model (extended Langmuir, EL) was reported recently which describes the

surface tension of binary liquid mixtures as a function of the bulk composition [26, 43].

Briefly, this model considers the surface of a binary liquid mixture as a thin but finite layer

and starts by developing the following expression for the relationship between the volume

fractions of component 2 in the surface and the bulk, us2 and /2, respectively.

us2 bu2

1 b 1u212

where the parameter b us2u2us1u1 is a measure of the lyophobicity of compo-

nent 2 relative to component 1. In this model, the surface tension of non-ideal binary

mixtures is given by:

25

30

35

40

45

50

0.0 0.2 0.4 0.6 0.8 1.0x 2

/(m

N.m

-1 )

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

2,1

/(

mol.

m-2 )

Fig. 3 The experimental surface tension values, r, and adsorption isotherms, C2,1, against x2 for acetonitrile(2)/1,2-ED (1) mixtures at 25 C

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r us1r1 us2r2 kus1us2p0 13where r1 and r2 are the surface tensions of the pure components 1 and 2, respectively, p

0 is

the positive difference between them r1r2j j, and k is a parameter that represents theeffect of unlike-pair interactions on the surface tension of the mixture. Also, we continue to

regard component 1 as the component with higher surface tension. From Eq. 12, the

surface pressure, p = r1 - r, can be written as:

p p0us2aus1 us2 14where a = k ? 1. By substituting for us2 and (u

s1 1 us2) from Eq. 12 into Eq. 14:

p p0b b a/1=/2 b /1=/2 2

15

Table 3 The surface mole fraction of acetonitrile as a function of its bulk mole fraction, calculated on thebasis of the two models for the binary systems studied in this work

x2 Suarez method EL x2 Suarez method ELx2,s x2,s x2,s x2,s


0.0109 0.0177 0.0165 0.2999 0.4224 0.3943

0.0199 0.0321 0.0299 0.3500 0.4810 0.4500

0.0361 0.0579 0.0538 0.4345 0.5730 0.5386

0.0720 0.1134 0.1055 0.4888 0.6277 0.5923

0.0845 0.1322 0.1230 0.5699 0.7034 0.6681

0.1012 0.1571 0.1461 0.6321 0.7568 0.7230

0.1402 0.2135 0.1986 0.7099 0.8182 0.7881

0.1862 0.2773 0.2580 0.7765 0.8662 0.8407

0.1992 0.2947 0.2743 0.8499 0.9147 0.8959

0.2569 0.3695 0.3444


0.0543 0.0647 0.0481 0.5217 0.5702 0.4898

0.0843 0.0999 0.0749 0.6503 0.6939 0.6207

0.0899 0.1065 0.0800 0.7504 0.7860 0.7257

0.2043 0.2368 0.1843 0.8106 0.8396 0.7902

0.2785 0.3184 0.2536 0.8895 0.9257 0.9136

0.4600 0.5085 0.4285 0.9493 0.9583 0.9428


0.0086 0.0131 0.0171 0.4583 0.5760 0.6285

0.0341 0.0513 0.0660 0.4958 0.6134 0.6629

0.0544 0.0811 0.1032 0.6903 0.7867 0.8168

0.0997 0.1458 0.1813 0.7476 0.8316 0.8556

0.1963 0.2756 0.3282 0.8272 0.8898 0.9054

0.2813 0.3810 0.4391 0.8797 0.9255 0.9360

0.3504 0.4609 0.5190 0.9497 0.9701 0.9742

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An iterative method has been used to derive the a and b parameters by insertingexperimental values in Eq. 15. Table 4 lists the values of the adjustable parameters a and bobtained by fitting Eq. 15 to the experimental results.

For some binary systems, values of a = 1 (k = 0) imply that the interactions do notsignificantly affect the surface tension of the solution and the deviation of surface tension

from ideal behavior is attributable exclusively to lyophobicity differences. The fitting of

experimental results for some mixtures yields b[ 1, which indicates that the surface phaseis richer in the component with lower surface tension.

We calculated the surface volume fractions of solutes, us2, by using Eq. 12 and thenconverted them to the surface mole fraction x2,s by the equation:

us2 x2;sv2

x1;sv1 x2;sv2 16

where x2,s is the number of moles of the 2nd component in the surface, and v1 and v2 are

molar volumes of components 1 and 2. The x2,s values obtained using the EL method are

comparable with those calculated via the Suarez method (see Table 3).

Also, the variation of x2,s - x2 with x2 is shown in Fig. 5. The x2,s - x2 values are

positive in the whole composition range. This plot shows that the that the x2,s - x2 values

increase with increasing difference of the surface tensions of the pure compounds (the

highest value of x2,s - x2 is for an acetonitrile/1,2-ED mixture).

3.3 Correlation of Surface Tensions for Binary Systems

Finally, the deviations from ideal behavior can be quantified by surface tension deviations,

Dr, defined as:

Dr r X2

i1 xiri 17

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0x 2

x2,s

Fig. 4 Calculated concentration of acetonitrile at the liquidvapor interface (x2,s) as a function of (x2) forthe binary systems of acetonitrile (2)/diol (1): 1,2-ED (closed circle), 1,2-PD (closed square), 1,4-BD (opentriangle)

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where xi and ri are the mole fraction and surface tension of component i, respectively. Forthe correlation of surface tensions of binary systems, an equation proposed by Redlich

Kister (RK) was used to describe the behavior of the observed systems [27]:

Dr xixjXpm

p0 Apxi xjp 18

where the Ap are the adjustable parameters determined by a nonlinear least-squares opti-

mization method.

Wang and Chen (WCH) proposed an equation to correlate the surface tension data with

the composition of the binary systems [9, 44]:

r xiBijri xjrjxiBij xj Dijxixj 19

where ri and rj are the surface tensions of pure component i and j, respectively, and Bij andDij are the adjustable binary parameters.

In Table 5 the adjusted coefficients of the equations used to correlate the binary data are

listed as well as the respective standard deviations of the fits.

The standard deviation of the fits, S, is defined as:

S XMi1

Drexp Drcal2M P

" #1=220

Table 4 Values of the parame-ters a and b, obtained by fitting ofEq. 15 with surface tension data

Systems a b

Acetonitrile (2)/1,2-ED (1) 1.78 1.52

Acetonitrile (2)/1,2-PD (1) 1.00 0.83

Acetonitrile (2)/1,4-BD (1) 1.31 2.01

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.0 0.2 0.4 0.6 0.8 1.0x 2

x2,

s - x

2

Fig. 5 Values of x2,s - x2 against x2 for the binary systems: acetonitrile (2)/1,2-ED (1) (closed circle),acetonitrile (2)/1,2-PD (1) (closed square), acetonitrile (2)/1,4-BD (1) (open triangle)

J Solution Chem (2013) 42:20712086 2081

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where Drexp and Drcal are the experimental and calculated surface tensions deviations,M the number of data points and P the number of adjustable parameters used for fitting the

experimental data with various equations.

In Figs. 6 and 7 we have plotted the experimental and fitted surface tensions of the

binary systems of acetonitrile/diol as a function of the composition with the RK and WCH

models. All of the binary mixtures show asymmetrical Dr behavior. As can be seen, theagreement between the experimental data and correlated values are reasonable. All values

Table 5 Fitted coefficients and standard deviation, S, of the models used to correlate surface tension withthe composition for the binary systems at 298.15 K

Model A B C D E S (mNm-1)


RKa -24.46 15.91 13.04 -15.01 0.07

WCHb 2.23 -6.97 0.58


RKa 2.51 0.61 10.87 0.75 -9.63 0.06

WCHb 10.03 0.68 0.15


RKa -14.76 -1.57 30.02 -6.02 -7.29 0.06

WCHb 10.18 -12.09 0.81

a The coefficients A, B, C, D and E correspond to A1, A2, A3, A4 and A5, respectivelyb The coefficients A and B correspond to B and D, respectively

Fig. 6 Surface tension deviation, Dr, as a function of the mole fractions of acetonitrile, for the binarysystems of acetonitrile (2)/diol (1). The symbols refer to the experimental data, and the dashed curvesrepresent the correlation with Eq. 18: 1,2-ED (closed circle), 1,2-PD (closed triangle), 1,4-BD (closedsquare)

2082 J Solution Chem (2013) 42:20712086

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of Dr, except those for the 1,2-PD/acetonitrile system, are negative over the wholecomposition range.

Although the mixture of 1,4-BD with acetonitrile has slightly positive Dr values in theregion that is very rich in the 1,4-BD, it is suggested that the surface tension deviations

25

30

35

40

45

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x 2

/(m

N.m

-1 )

Fig. 7 Values of the surface tension, r, against the mole fraction of acetonitrile, for the binary systems ofacetonitrile (2)/diol (1). The symbols refer to the experimental data, and the dashed curves represent thecorrelation with Eq. 19: 1,2-ED (closed circle), 1,2-PD (closed square)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-7

-6

-5

-4

-3

-2

-1

0

1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

x 2- x

2,s

/(m

N.m-1)

x2

Fig. 8 The surface tension deviations, Dr and x2,s - x2, versus x2 for the binary systems of acetonitrile (2)/diol (1): 1,2-ED (closed circle), 1,4-BD (closed triangle)

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indicate different distributions of unlike components between the surface and the bulk

region. The most negative values are reached in the mixture containing the pure com-

pounds showing the greatest difference in surface tension, that is 1,2-ED with acetonitrile.

The asymmetry in the curves of the 1,2-ED/acetonitrile and 1,2-PD/acetonitrile systems

indicates that the components with the strongest molecular interactions in each binary

mixture settle down in the bulk liquid phase instead of moving into the surface phase

between the liquid and vapor phases, shifting the curves to the rich region of these

compounds. Figure 8 is a typical plot showing the surface tension deviations (Dr) andx2,s - x2 as a function of composition for the acetonitrile/1,2-ED and acetonitrile/1,4-BD

systems. As observed in this figure, the variation of Dr and x2,s - x2 with compositiondistinctively follows the pattern. In these systems the Dr values are negative (rarelypositive) with a pronounced minimum and a specific maximum for x2,s - x2 at the same

mole fraction of the component 2.

4 Conclusion

Surface tension values for binary mixtures of diols (1,2-ethanediol, 1,2-propanediol, and

1,4-butanediol) with acetonitrile are reported in this paper. The experimental results have

been compared with predictions by the Suarez method. The UNIFAC methods are used for

activity coefficients of the surface and bulk phases. Comparisons of the calculated surface

tensions with experimental data yield APD values, in the best case of less than 0.2 % for

the systems studied. Therefore, it is important to stress that this model can also give good

predictions for systems with a large polarity and asymmetrically range. We calculated

values of the surface mole fractions of solute using the EL model and compared them with

values obtained from the UNIFAC model. Finally, values of the experimental surface

tension were correlated by means of the RedlichKister and WCH equations that provide a

series of adjustable parameters for predicting surface tensions of such mixture systems.

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Prediction of the Surface Tension, Surface Concentration and the Relative Gibbs Adsorption Isotherm of Non-ideal Binary Liquid MixturesAbstractIntroductionExperimentalMaterialsApparatus and Procedure

Results and DiscussionPrediction of Surface Tension for Binary SystemsRelative Gibbs Adsorption and Study of Surface PropertiesCorrelation of Surface Tensions for Binary Systems

ConclusionReferences

2013, Bagheri, Prediction of the Surface Tension, Surface Concentration

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