How do temperature and chemical structure affect surface properties of aqueous solutions of carboxylic acids?

Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88

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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa

How do temperature and chemical structure affect surface properties of aqueous solutions of carboxylic acids? Ahmad Bagheri ∗ , Kolsum Alizadeh Department of Chemistry, Semnan University, P.O. Box, 35131-19111, Semnan, Iran

h i g h l i g h t s

g r a p h i c a l

a b s t r a c t

• The surface properties of binary • • • •

systems of aqueous–organic acid calculated. The activity coefficients of components have been calculated by UNIFAC methods. The interaction energy values were calculated by using LWW model. The U12 –U11 value shows same behavior for studied systems with rising temperature. The relative Gibbs adsorption increases with increasing the length of carboxylic acid chain.

a r t i c l e

i n f o

Article history: Received 21 August 2014 Received in revised form 13 November 2014 Accepted 17 November 2014 Available online 26 November 2014 Keywords: Surface tension Correlation UNIFAC Adsorption Interaction energy

a b s t r a c t Surface properties of binary mixtures of organic acids (formic, acetic, propanoic and butanoic acids) with water have been calculated by surface tension data at various temperatures (293.15–323.15) K. The surface tension data over the whole mole fraction range are correlated by the Li et al. (LWW) model, then the interaction energy between organic acids and water have been calculated with the results of this model. Also, adsorption isotherms of binary aqueous solutions of organic acids are determined using Gibbs adsorption equation with experimental data found in the literature and using the UNIFAC group contribution method. The values of adsorption for mixtures of organic acids/water increases with increasing the alkyl chain length of organic acid at different temperatures. Finally, the results have been discussed in terms of surface concentration and lyophobicity using the extended Langmuir (EL) isotherm. The results provide information on the molecular interactions between unlike molecules that exist at the surface and the bulk. © 2014 Published by Elsevier B.V.

1. Introduction The surface tension of a liquid mixture is not a simple 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. The deviations of the surface tension of a liquid mixture from

∗ Corresponding author. Tel.: +98 02333654057; fax: +98 02333654110. E-mail addresses: [email protected], [email protected] (A. Bagheri). http://dx.doi.org/10.1016/j.colsurfa.2014.11.037 0927-7757/© 2014 Published by Elsevier B.V.

linearity reflect changes of structure and cohesive forces during the mixing process. At the interface, there is a migration of the species having the lowest surface tension or free energy per unit area, at the temperature of the system [1–3]. Surface tension data are scarce for liquid mixtures over a wide range of composition and temperature and hence the calculation methods for estimating surface tension and surface properties of multicomponent systems are very necessary. Several different approaches have been used to predict the surface tension of nonideal liquid mixtures as a function of composition which include

A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88

the use of an equation of state together with the specific theory [4–6]. Covering the water surface with the solutes having weaker molecular interactions reduces surface energy observed as surface tension. Generally, the hydrophobic hydration and the surface adsorption are known to occur in binary aqueous–organic systems such as: alcohol–water, organic acid–water and, etc. [7]. The purposes of the present work are to clarify the surface phenomena which occur in aqueous solutions of formic acid, acetic acid, propanoic acid and butanoic acid at various temperatures: (i) The composition dependence of the surface tension of binary aqueous–organic acid mixtures is described using LWW and FLW models, and then in a new approach, the effect of temperature on the interaction energy values is explained in the binary mixtures [8–12]. (ii) A Langmuir type isotherm model (or the extended Langmuir (EL)) is employed to determine the surface mole fractions from the knowledge of the bulk mole fractions. The results provide information on the molecular interactions between the unlike molecules that exist at the surface and the bulk at various temperatures [13,14]. (iii) The surface adsorption is another parameter that produces some useful information about the surface behavior of mixtures. Adsorption of a component at the phase boundary of a system causes a different concentration in the interfacial layer and the adjoining bulk phases. The relative Gibbs adsorption,  2,1 , provides an exact relationship between bulk concentrations, total surface coverage and the surface tension changes produced at liquid interface. To evaluate  2,1 , a reliable data set of two parameters, the surface tension, , and the activity coefficient of solute (acid), ␥2 , is necessary for calculation. In the present study, the UNIFAC group-contribution model was adopted to calculate the activity coefficients because it can be applied to any kind of substances whenever the molecular structure is known [15–18]. Surface tension data are scarce for aqueous–organic acid mixtures over a wide range of composition and temperature. In this work, two different sets of experimental data have been selected from the literature (see the supplementary information) [19,20]. 2. Theory and methods 2.1. Temperature dependence of the interaction energy in organic acid–water solutions A few empirical and thermodynamic-based equations are available to correlate the surface tension some of which have recently been proposed and are well founded on a thermodynamic basis. To explain the surface tension, , the proposed model by Fu et al. (FLW), based on the modified Hildebrand–Scott equation, was used [10,21]: =

n  i=1

xi i∗

n

xf j=1 j ij

−

n n  

n

xi xj |i∗ − j∗ |

x f q=1 q iq

i=1 j=1

n

x f r=1 r jr

x1 1∗ x1 + x2 f12

+

x2 2∗ x2 + x1 f21

−

x1 x2 |1∗ − 2∗ | (x1 + x2 f12 )(x2 + x1 f21 )

The surface tension deviations, , were determined in order to get information about the type and the strength of the molecular interactions in the binary systems. The calculations of  were carried out from the well known general equation:  =  −

n 

xi i∗

(3)

i=1

where  is the surface tension of the mixture, and i∗ is the surface tension of the pure component i at the same temperature and pressure of the mixture, xi is the mole fraction of the component i and n is the number of components. The surface tension deviations of the above mentioned binary systems were correlated by two models. Li et al. (LWW) proposed a two-parameter equation to correlate the surface tension data with the composition in the binary systems which are based on the Wilson equation for the excess Gibbs energy [8,23]:  = −RT



  ∂ij 

x

i

xj

xj ij

i

∂A

j

(4) T,P,X

j

where ij = exp

 −

Uij − Uii



 ,

RT

∂ij ∂A

 =− T,P,X

ij RT



∂(Uij − Uii ) ∂A

(5) T,P,X

In the preceding relations, Uij − Uii is the difference in the interaction energy between molecular pair ij, and the derivative [∂(Uij − Uii )/∂A]T,P,x reflects the energy change with the increase in surface area. Li et al. [8,22] made the assumption Uij = (Uii + Ujj )/2, decreasing the number of adjustable parameters from four to two for a binary system, i.e., U12 − U11 and [∂(U12 − U11 )/∂A]T,P,x ; hence, the resultant equation is given by: x1 x2 RT  = x2 + x21



∂21 ∂A



1−

1 21

(6)

where (∂21 /∂A) and 21 are adjustable parameters. Myers–Scott (MS) proposed an equation to correlate the surface tension deviation data with the composition in the binary systems [9,11,12]:

⎡  m Bp (xi − xj )p ⎢ ⎢ p=0  = xi xj ⎢ m ⎢  ⎣ 1+

Cl (xi − xj )

⎤ ⎥ ⎥ ⎥ ⎥ l⎦

(7)

l=1

where Bp and Cl are adjustable parameters. In this paper, the Levenberg–Marquardt method (as a nonlinear regression algorithm for fitting data) is used to estimate the adjustable parameters.

(1) 2.2. Application of the UNIFAC model for calculation of the relative Gibbs adsorption of binary systems

where the fij ’s are adjustable parameters for the binary systems. This equation was also used to predict the ternary surface tension. For a binary mixture, the above equation reduces to =

79

(2)

where f12 and f21 are adjustable parameters for the binary systems and xi is the mole fraction of the component i in the mixture [22].

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. The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension. For a binary system containing two components, from the Gibbs

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A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88

equation, relative adsorption,  2,1 , was calculated according to the expression:

∂ ∂2

=− T,P

1 RT



∂ ∂ ln a2

70



65

(8)

60

T,P

where 2 and a2 =  2 x2 are the chemical potential and activity of component 2 in the mixture, respectively. The values of  2 were obtained using the UNIFAC model [15–17,24].

-1

2,1 = −



σ/(mN.m )



75

55 50 45 40

2.3. Estimation of the surface concentration of components in binary systems

35 30

An applied model (Extended Langmuir, EL) was reported recently, which describes the surface tension of binary liquid mixtures as a function of the bulk composition [13,14,25]. If 2,s is the volume fraction of component 2 in the surface phase, and 2 is the volume fraction of component 2 in the bulk phase, then we define them in general as follow:

n2 v2 = 1 − 1 n1 v1 + n2 v2

2,s

(11)

where the parameter ˇ = ( 2,s / 2 )/( 1,s / 1 ) is a measure of the lyophobicity of 2 relative to 1. In this model, the surface tension of non-ideal binary mixtures is given by:  = 1,s 1 + 2,s 2 − 1,s 2,s 0

(12)

where  1 and  2 are the surface tensions of the pure components 1 and 2, respectively; 0 is the positive difference between them | 1 – 2 | (1 is the component of higher surface tension); and is a parameter that represents the effect of unlike-pair interactions on the surface tension of the mixture. From Eq. (11), the surface pressure,  =  1 − , can be written as:  = 0 2,s (˛ 1,s + 2,s )

(13)

where ˛ = + 1; and substituting for 2,s and ( 1,s = 1 − 2,s ) from Eq. (11) yields: =

0 ˇ[ˇ + ˛( 1 / 2 )] [ˇ + ( 1 / 2 )]

2

0.2

0.3

0.4

0.5

x2

0.6

0.7

0.8

0.9

1

75

(10)

where ni is the number of moles of the ith component, v1 and v2 are molar volume of the 1 and 2. Briefly, this model considers the surface of a binary liquid mixture as a thin but finite layer and the following expression was developed for the relationship between 2,s and 2 : ˇ 2 = 1 + (ˇ − 1) 2

0.1

(9)

(14)

An iterative method has been used to derive the ˛ and ˇ parameters by inserting experimental values in Eq. (14) [26]. 3. Results and discussion Figs. 1 and 2 show the behavior of surface tension of acid in water, typically. In all the systems, the surface tension, , decrease with the increase of acid concentration. This trend is nonlinear, with the change in surface tension caused by a given change in acid mole fraction being larger at low mole fractions than at high mole fractions. A regularly decreasing value of the solution surface tension indicates that two compounds, the water and acid, are present at gas–liquid interface. This behavior shows a difference in distribution of molecules between the surface and the bulk of the liquid. In a characteristic case, the compound having a lower surface tension

70 65 60 -1

2 =

n2,s v2 = 1 − 1,s n1,s v1 + n2,s v2

0

Fig. 1. Surface tension, , against mole fraction, x2 , for the binary systems of carboxylic acid (2)/water(1) at 298.15 K. The symbols refer to the experimental data, and the dashed curves represent the correlation with Eq. (2): (䊉) formic acid, () acetic acid, () propanoic acid and () butanoic acid.

σ/(mN.m )

2,s =

25

55 50 45 40 35 30 0.0

0.1

0.2

0.3

0.4

0.5

x2

0.6

0.7

0.8

0.9

1.0

Fig. 2. Surface tension, , against mole fraction, x2 , for the binary systems of formic acid(2)/water(1) at various temperatures. The symbols refer to the experimental data, and the dashed curves represent the correlation with Eq. (2): (䊉) 293.15 K, () 303.15 K, () 313.15 K and () 323.15 K.

(acid) is expelled from the bulk to the liquid–vapor interface due to the attractive forces between solvent molecules [9,27,28]. The surface tension of the binary systems was well-correlated using the FLW model. As can be seen from Figs. 1 and 2 and Tables 1 and 2, the MS model correlates the surface tensions of these systems well, even for the system butanoic acid/water, which is highly nonsymmetrical with strong decrease in surface tension at very low concentrations of carboxylic acid. In Tables 1 and 2, the adjusted coefficients of the FLW and MS equations used to correlate the binary data are listed as well as the respective standard deviations of the fittings.

Scheme 1. H-bonding between carboxylic acid and water.

A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88

81

Table 1 Adjustable parameters and standard deviation, S, of the FLW model used to correlate surface tension with the composition for the binary systems at various temperatures. T/K

Formic acid/water

293.15 298.15 303.15 308.15 313.15 318.15 323.15

Acetic acid/water

Propanoic acid/water

f12 × 102

f21

S/(mN m−1 )

f12 × 102

f21

S/(mN m−1 )

f12 × 102

f21

S/(mN m−1 )

7.60 7.94 7.75 7.88 7.97 7.79 8.12

3.65 3.56 3.55 3.51 3.48 3.47 3.41

0.21 0.18 0.17 0.17 0.16 0.16 0.15

2.33 2.38 2.34 2.36 2.35 2.37 2.36

4.80 4.74 4.64 4.55 4.47 4.40 4.33

0.70 0.68 0.69 0.68 0.66 0.67 0.63

0.82 0.88 0.82 0.83 0.84 0.83 0.84

17.55 17.79 17.34 17.17 17.06 16.93 16.72

0.81 0.86 0.82 0.81 0.81 0.82 0.83

Table 2 Adjustable parameters and standard deviation, S, of the MS model used to correlate surface tension deviation with the composition for the binary systems at various temperatures. Systems

Parameters

T/K 293.15

298.15

303.15

308.15

313.15

318.15

323.15

Formic/water

B0 C1 C2 S/(mN m−1 )

−45.35 0.7012 −0.0602 0.109

−45.07 0.7096 −0.0469 0.077

−44.82 0.7008 −0.0580 0.070

−43.97 0.7046 −0.0524 0.073

−44.43 0.7048 −0.0530 0.077

−43.73 0.7054 −0.0539 0.068

−43.23 0.7087 −0.0479 0.069

Acetic/water

B0 C1 C2 S/(mN m−1 )

−68.37 0.9071 −0.0105 0.049

−68.11 0.9105 −0.0070 0.086

−67.48 0.9078 −0.0111 0.023

−66.98 0.9110 −0.0082 0.040

−66.26 0.9089 −0.0108 0.043

−65.97 0.9126 −0.0078 0.042

−65.37 0.9075 −0.0134 0.047

Propanoic/water

B0 C1 C2 S/(mN m−1 )

−82.48 0.9549 0.0162 0.545

−81.86 0.9891 0.0192 0.288

−81.45 0.9776 0.0070 0.118

−80.94 0.9792 0.0086 0.118

−80.16 0.9807 0.0103 0.123

−79.78 0.9830 0.0119 0.123

−78.89 0.9859 0.0146 0.143

Butanoic/water

B0 C1 C2 S/(mN m−1 )

−84.96 1.0963 0.1046 0.688

The standard deviations (S) are reported in these tables were computed by applying the following equation:

i=1

M−P

1/2 (15)

where Y stands for  or , M the number of data points and P the number of adjustable parameters used for fitting the experimental data in various equations. As expected, the highest values of the mean standard deviation are obtained for the butanoic acid/water system which have the maximum value of surface tension reduction in low concentrations of acid. Unfortunately, up to now the experimental surface tension data have been reported only at 298.15 K for butanoic acid/water system. The  values are negative over the entire concentration range and at all temperatures. As Figs. 3 and 4 show, the values of || for mixtures of organic acid (formic, acetic, propanoic and butanoic)/water decrease with increasing temperature and alkyl chain length of the carboxylic acid but slope of changes is sharper in later. The correlation results using LWW model and the relevant results (Uij − Uii the difference in interaction energy between molecule pair ij and ii) are listed for the binary systems are listed in Table 3. As can be seen from Figs. 3 and 4 and Table 3, the LWW model correlates the surface tensions of these systems well, even for the system butanoic acid/water, which is highly nonsymmetrical with large values of . In this section, we present an application of the adjustable parameters of LWW model to explain the influence of temperature on interaction energy values between components.

0 -5 -10 -15 -1

S=

M  (Yi,exp − Yi,cal )2

Δσ /(mN.m )



As can be seen from Eq. (6), the surface tension deviation ( ) arises from the cross interaction between species i and j. For an ideal solution, the interaction energy between any two species is almost identical, i.e., Uii − Ujj − Uij . In this case, the surface tension

-20 -25 -30 -35 -40 -45

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x2 Fig. 3. Surface tension deviation, , against mole fraction, x2 , for the binary systems of carboxylic acid(2)/water(1) at 298.15 K. The symbols refer to the experimental data, the solid curves represent the correlation with Eq. (6) and the dashed curves represent the correlation with Eq. (7): (䊉) formic acid, () acetic acid, () propanoic acid and (*) butanoic acid.

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A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88

Table 3 Adjustable parameters and the obtained interaction energy values of the LWW model for the binary systems at various temperatures. Systems

Parameters

293.15

298.15

303.15

308.15

313.15

318.15

323.15

Formic/water

Aa Bb /(m−2 ) Cc /(kJ mol−1 ) Dd /(mJ m−2 mol−1 )

141.570 −17.408 −4.764 −29.970

143.413 −17.319 −4.814 −29.935

143.060 −16.867 −4.901 −29.716

143.207 −16.481 −4.971 −29.484

143.679 −16.119 −5.059 −29.209

142.359 −15.589 −5.156 −28.965

143.511 −15.342 −5.216 −28.722

Acetic/water

Aa Bb /(m−2 ) Cc /(kJ mol−1 ) Dd /(mJ m−2 mol−1 )

43.031 −6.556 −7.667 −37.136

43.166 −6.451 −7.790 −37.046

42.545 −6.179 −7.957 −36.610

42.291 −6.001 −8.108 −36.351

42.085 −5.806 −8.248 −35.917

41.604 −5.624 −8.410 −35.755

41.493 −5.461 −8.549 −35.360

Propanoic/water

Aa Bb /(m−2 ) Cc /(kJ mol−1 ) Dd /(mJ m−2 mol−1 )

14.795 −2.559 −10.269 −42.148

15.111 −2.596 −10.392 −42.586

14.887 −2.487 −10.616 −42.100

14.845 −2.426 −10.786 −41.866

14.751 −2.350 −10.977 −41.485

14.530 −2.269 −11.193 −41.311

14.444 −2.198 −11.385 −40.899

Butanoic/water

Aa Bb /(m−2 ) Cc /(kJ mol−1 ) Dd /(mJ m−2 mol−1 )

a b c d

∂21× 10  3. 21

∂A

T,P,X

∂A

4.171 −0.773 −13.583 −45.921

× 107 .

U11 ). (U∂12(U−−U ) 12

T/K

11

T,P,X

.

deviation term disappears (  = 0) and the surface tension of the ideal mixture is equal to the mole fraction average of the surface tension of the pure components at the system’s temperature and pressure [8,9,22,29]. The physical significance of the LWW parameters can be understood as follows: U12 − U11 is directly related to the dimensionless parameter ij via Eq. (6), which is used to account the local composition effect and the term [∂(U12 − U11 )/∂A]T,P,x reflects the energy change with increase in surface area, and hence, it contributes to the surface tension deviation. Table 3 summarizes U12 − U11 and [∂(U12 − U11 )/∂A]T,P,x values that obtained from LWW model. Since the U12 − U11 , depends on mainly on variation in intermolecular interactions between two components into contact, if interaction energy between unlike molecules (Uwater–acid or U12 ) are weaker than those existing between like molecules (Uwater–water or U11 ), negative values of U12 − U11 will be observed at various temperatures. Considering molecular structure of organic acids shows that strength of hydrogen bond (the interaction energy) between 0

-1

Δσ/(mN.m )

-5

-10

A

-15

Table 4 Hansen parameter values of components [31].

-20 B

-25

0.0

0.1

0.2

COOH group of acid and water molecules decreases with increasing the alkyl chain length of organic acid (from formic to butanoic) at given temperature. It is clear that the value of U11 (Uwater–water ) is equal in three system, so it seems that the major season for abovementioned difference is absolute measure of U12 (Uwater–acid ). Therefore, at constant value of Uwater–water and at any temperature, the values of Uwater–acid change in such order as follow: Uwater–propanoic < Uwater–acetic < Uwater–formic [29,30]. The present dipoles in carboxylic acid structures allow these compounds to participate in energetically favorable hydrogen bonding (H-bonding) interactions with water, functioning as both a H-bond donor and acceptor as shown below (Scheme 1): Table 4 shows the Hanson parameter for “non-polar”, “polar aporotic” and “polar porotic” solvents. The “polar aporotic” molecules have higher levels of ␦P (for example acetonitrile or DMSO) and the “polar porotic” solvents have higher levels of ␦H (for example organic acid or alcohol) [31,32]. Polar protic solvents (carboxylic acids) strongly interact with other protic solvent (for example water) via hydrogen bonding. ␦P (polar bond) and ␦H (hydrogen bond) values decreases with increasing the number of carbon atoms in hydrocarbon chain of carboxylic acid. Consequently, hydrogen bond strength between components (acid–water) decreases. The data in Fig. 5 shows the interaction energy between the carboxylic acid and water (U12 ) decreased with increase of the alkyl chain length of acid (from formic acid to butanoic acid at 298.15 K) due to the less interaction between acid and water. Fig. 5 (from surface tension data) confirms the reported results in Table 4. The best reported value for binding energy of the water dimmer

0.3

0.4

0.5 x2

0.6

0.7

0.8

0.9

1.0

Fig. 4. Surface tension deviation, , against mole fraction, x2 , for the binary systems: (A) formic acid(2)/water(1) and (B) acetic acid(2)/water(1). The symbols refer to the experimental data, the dashed curves represent the correlation with Eq. (6) at various temperatures: (䊉) 298.15 K and () 323.15 K.

Solvent

␦Da

␦Pb

␦Hc

Propanoic acid Acetic acid Formic acid Water

14.7 14.5 14.6 15.5

5.3 8.0 10.0 16.0

12.4 13.5 14.0 42.3

a b c

Dispersion bonds. Polar bonds. Hydrogen bonds.

A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88

83

18

-1

U12/(kJ.mol )

15

12

9

6

0

0.5

1

1.5

2

2.5

3

n Fig. 5. The interaction energy, U12 , against number of carbon atoms in hydrocarbon chain of carboxylic acid at 298.15 K.

(U11 = 5.0 Kcal mol−1 ) was used for calculation of U12 from U12 − U11 in binary systems [33–36]. This result shows a liner dependence between hydrogen bond strength, U12 , and alkyl chain length of acid with structural formula, Cn H2n+1 COOH(n = 0–3), at 298.15 K: U12 = −2.8911n + 16.092(kJ mol−1 )

(16)

The U12 − U11 values in three systems decrease with increasing temperature. This trend is linear with negative slope. Increasing temperature increases the average kinetic energy of molecules, disrupts hydrogen bonding and shifts the equilibrium in favor way for monomeric form. Figs. 6 and 7 show U12 − U11 value as a function of temperature in three systems: The negative slope of these curves is proportional to the hydrogen bond strength between acid and water. Fig. 6 shows that the negative slopes of U12 − U11 versus temperature for these three systems are different and increase (more negative) with the increase of the length of carboxylic acid chain. This is evidence confirming that carboxylic acid–water interaction depends on the length of carboxylic acid chain. This interaction is

Fig. 7. Three-dimensional representation of U12 –U11 /(J mol−1 ) for carboxylic acid/water systems at various temperatures, calculated using parameters of Eq. (6) (the effect of the alkyl chain length of the carboxylic acid on the interaction energy).

more influenced by temperature when we deal with longer carboxylic acid so that we can observe a more intense reduction in U12 − U11 value with increasing of temperature. Also, the values of [∂(U12 − U11 )/∂A]T,P,x in Table 3 reflect contribution of the surface tension deviation from ideal behavior. These values show the deviations from ideal behavior for acid/water systems at all temperatures as follows:  (propanoic acid) <  (acetic acid) < (formic acid) The resultant values are in good agreement with experimental results and Figs. 3 and 4 in the present work. On the other hand, the variation trends of  with the increase of temperature (obtained from the experimental data) have suitable adaptation with the obtained values from correlation of LWW model ([∂(U12 − U11 )/∂A]T,P,x ):  min (293.15 K) <  min (298.15 K) <  min (303.15 K) <  min (308.15 K) <  min (313.15 K) <  min (318.15 K) <  min (323.15 K) These results confirm those of LWW model: [∂(U12 − U11 )/∂A]T,P,x (293.15 K) < [∂(U12 − U11 )/∂A]T,P,x (298.15 K) < [∂(U12 − U11 )/∂A]T,P,x (303.15 K) < [∂(U12 − U11 )/∂A]T,P,x (308.15 K) < [∂(U12 − U11 )/∂A]T,P,x (313.15 K) < [∂(U12 − U11 )/∂A]T,P,x (318.15 K) < [∂(U12 − U11 )/∂A]T,P,x (323.15 K)

Fig. 6. Three-dimensional representation of U12 –U11 /(kJ mol−1 ) for carboxylic acid/water systems at various temperatures, calculated using parameters of Eq. (6)) (the effect of temperature on the interaction energy).

As can be seen in Table 3 and Fig. 8, the agreement between the experimental results () and the obtained values of the model is reasonable. A useful section of information in the study of surface behavior is the surface adsorption. Adsorption of a component at the phase boundary of a system results in a different concentration in the interfacial layer than that in the adjoining bulk phases. For the adsorption of a component on the fluid interface, the relative Gibbs adsorption values,  2,1 , have been evaluated from the surface

84

A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88 Table 5 Activity coefficients and the relative Gibbs adsorption isotherm calculated for the binary systems of formic acid(2)/water(1) at 298.15 K. ␥2

␥1

(mN m−1 )

(mN m−1 )

 21 (␮mol.m−2 )

Exp. 0.020 0.042 0.065 0.089 0.115 0.144 0.207 0.281 0.370 0.477 0.610 0.779

1.1613 1.1450 1.1296 1.1151 1.1009 1.0870 1.0621 1.0406 1.0230 1.0102 1.0025 0.9998

1.0001 1.0006 1.0014 1.0024 1.0039 1.0058 1.0107 1.0174 1.0257 1.0351 1.0443 1.0502

68.11 64.82 61.91 59.33 57.07 55.21 51.68 48.88 46.18 43.73 41.31 39.14

−3.20 −5.72 −7.83 −9.57 −10.92 −11.76 −13.09 −13.30 −12.89 −11.59 −9.36 −5.62

1.707 2.428 2.847 3.146 3.387 3.597 3.934 4.217 4.473 4.712 4.948 5.188

Cal.b 0.010 0.014 0.019 0.023 0.028 0.032 0.037 0.041 0.046 0.050

1.1692 1.1657 1.1622 1.1588 1.1554 1.1521 1.1488 1.1457 1.1425 1.1395

1.0000 1.0001 1.0001 1.0002 1.0003 1.0004 1.0005 1.0006 1.0007 1.0008

69.88 69.03 68.23 67.47 66.76 66.08 65.43 64.82 64.23 63.66

−1.78 −2.49 −3.12 −3.74 −4.27 −4.81 −5.29 −5.76 −6.17 −6.60

1.027 1.385 1.651 1.856 2.028 2.171 2.298 2.407 2.507 2.596

x2 a

Fig. 8. Three-dimensional representation of the energy change with the increase in surface area, [∂(U12 − U11 )/∂A]T,P,x , for carboxylic acid/water systems at various temperatures, calculated using parameters of Eq. (6).

tension-concentration data using the Gibbs adsorption equation. Values of  2,1 based on the arbitrary placement of the Gibbs dividing plane near the fluid interface is quantitatively related to the composition of the surface phase(Eq. (8)). It has to be mentioned here that, the use of Eq. (8) corresponds to the exact way of calculating the Gibbs adsorption isotherm because the non-ideality of the system under study is incorporated through the derivative of the surface tension with respect to the activity of component 2. Activity coefficient values for the two components in the bulk liquid phase are calculated using the UNIFAC model together with binary group interaction parameters from Gmehling et al. [17]. The main purpose of this section is to report precise surface adsorption data for a set of three binary aqueous-organic acid mixtures which are highly non-ideal, and show a broad range of differences between the surface tension of the pure components. The maximum changes of relative Gibbs adsorption occurs in low concentration of solute in which unfortunately in this concentration range the surface tension data for liquid mixtures at various temperatures do not exist (or are scarce) and estimation methods are therefore required. To solve this problem, by using a proper FLW equation with calculated adjustable coefficients that obtained from experimental data fitted for any binary system (Eq. (2)), we are able to calculate the surface tension value for any required mole fraction in low concentration level. The calculated data in low concentration can be seen in Tables 5–8. Tables 5–8 show the activity coefficients for both components in the bulk liquid phase, which are evaluated using the UNIFAC activity coefficient model [17], the experimental surface tension data from the literature [19], the calculated surface tension data from FLW equation in low concentrations of carboxylic acid and the calculated values of the relative Gibbs adsorption isotherm using Eq. (8) at 298.15 K, typically. The obtained results show that the activity coefficients, , and the relative Gibbs adsorption values,  2,1 , of these mixtures depend systematically on the alkyl chain length of the carboxylic acid, composition and temperature. For example, values of activity coefficients of carboxylic acid in aqueous solution at 298.15 K are summarized in the above tables.

a b

From Ref. [19]. This data is calculated using Eq. (2) for low concentration of formic acid.

In an ideal solution, these values would all be unity. The activity coefficients of carboxylic acid in mixtures depend strongly on composition and the activity coefficient of component 1(water) is considered equal to unity. Fig. 9 shows the variation of the activity of acid, aacid , and surface tension, , versus carboxylic acid mole fraction (x2 ) for studied systems. As observed in this figure, the variation of aacid with composition follows distinctively different patterns at three mixtures. The straight line (in Fig. 9) is aacid versus x2 for the ideal solutions that obeys Henry’s law. For formic acid, aacid is almost ideal over Table 6 Activity coefficients and the relative Gibbs adsorption isotherm calculated for the binary systems of acetic acid(2)/water(1) at 298.15 K. x2

␥2

␥1

(mN m−1 )

(mN m−1 )

 21 (␮mol m−2 )

Exp.a 0.016 0.032 0.050 0.070 0.091 0.114 0.167 0.231 0.310 0.412 0.545 0.730

3.2176 2.9701 2.7320 2.5080 2.3100 2.1281 1.8112 1.5550 1.3521 1.1950 1.0852 1.0199

1.0007 1.0027 1.0062 1.0117 1.0190 1.0286 1.0559 1.0964 1.1543 1.2369 1.3494 1.4995

61.72 55.58 51.24 48.01 45.44 43.46 40.34 37.62 35.79 33.82 32.03 29.76

−9.57 −14.99 −18.53 −20.86 −22.49 −23.43 −24.17 −24.02 −22.30 −19.70 −15.51 −9.48

3.615 4.242 4.613 4.869 5.054 5.200 5.426 5.601 5.759 5.924 6.111 6.346

Cal.b 0.008 0.012 0.015 0.019 0.022 0.026 0.029 0.033 0.036 0.040

3.3562 3.2925 3.2327 3.1732 3.1173 3.0617 3.0093 2.9573 2.9083 2.8595

1.0002 1.0004 1.0006 1.0009 1.0013 1.0017 1.0022 1.0028 1.0034 1.0041

65.28 63.15 61.35 59.81 58.46 57.26 56.19 55.22 54.34 53.53

−6.37 −8.32 −9.99 −11.35 −12.56 −13.58 −14.52 −15.31 −16.05 −16.68

2.950 3.310 3.561 3.761 3.918 4.053 4.165 4.266 4.352 4.431

a b

From Ref, [19]. This data is calculated using Eq. (2) for low concentration of acetic acid.

A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88 Table 7 Activity coefficients and the relative Gibbs adsorption isotherm calculated for the binary systems of propanoic acid(2)/water(1) at 298.15 K. ␥2

␥1

(mN m−1 )

(mN m−1 )

 21 (␮mol m−2 )

7.834 6.809 5.868 5.077 4.380 3.806 2.863 2.198 1.724 1.388 1.167 1.041

1.001 1.004 1.009 1.016 1.027 1.040 1.080 1.139 1.225 1.351 1.534 1.799

52.44 44.62 40.44 37.76 35.92 33.63 32.76 31.47 30.43 29.52 28.58 27.51

−18.97 −26.20 −29.69 −31.64 −32.65 −34.07 −32.83 −31.56 −29.34 −25.90 −20.83 −13.05

4.690 5.357 5.727 5.949 6.102 6.205 6.342 6.429 6.509 6.615 6.779 7.038

60

a

a b

8.588 8.314 8.049 7.568 7.340 7.123 6.923 6.725 6.535

1.000 1.000 1.001 1.001 1.002 1.003 1.003 1.004 1.005

60.33 56.58 53.76 49.70 48.17 46.86 45.71 44.71 43.81

−11.45 −15.06 −17.75 −21.58 −22.97 −24.14 −25.20 −26.06 −26.82

3.648 4.142 4.476 4.906 5.063 5.193 5.300 5.396 5.480

From Ref. [19]. This data is calculated using Eq. (2) for low concentration of propanoic acid.

the entire concentration. On the other hand, the deviations from ideality are quite substantial for acetic or propanoic acid/water systems. Fig. 10 shows the variation of  2,1 versus carboxylic acid mole fraction (x2 ) in bulk solution. The positive value of  2,1 in binary mixtures of solvents indicates the adsorption of species no. 2 onto the surface and the addition of this species to solutions causes a decreasing effect in the surface tension of the solution. It seems that the results are in good agreement with Figs. 3 and 4 and previous discussions. The  2,1 value increases with the increase of concentration of solute and finally reaches a maximum value of the saturated max ). In Fig. 10, comparison of  max values surface adsorption (2,1 2,1 Table 8 Activity coefficients and the relative Gibbs adsorption isotherm calculated for the binary systems of butanoic acid(2)/water(1) at 298.15 K. x2

-1

0.6

40 30

0.4

20 0.2 10 0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0

x2

b

Cal. 0.005 0.008 0.011 0.016 0.019 0.022 0.024 0.027 0.030

0.8

50

σ/mN.m

Exp. 0.013 0.026 0.041 0.057 0.075 0.094 0.140 0.196 0.267 0.362 0.493 0.686

1

70

a2

x2

85

␥2

␥1

(mN m−1 )

(mN m−1 )

 21 (␮mol m−2 )

24.713 24.682 24.422 23.913 23.322 22.020 21.193 18.815 16.676 14.058 10.582 8.990 6.462 5.407 2.591 1.744 1.421 1.184 1.111 1.041 1.015 1.002

1.000 1.000 1.000 1.000 1.000 1.000 1.001 1.002 1.004 1.008 1.020 1.029 1.056 1.076 1.224 1.396 1.549 1.786 1.924 2.158 2.326 2.511

71.12 70.47 66.32 60.32 55.12 46.34 42.12 35.88 31.94 29.24 28.48 28.35 28.23 28.15 27.92 27.73 27.66 27.56 27.42 27.13 26.90 26.51

−0.89 −1.54 −5.66 −11.62 −16.76 −25.41 −29.55 −35.51 −39.15 −41.40 −41.33 −40.93 −39.82 −39.12 −34.77 −30.55 −26.89 −21.37 −18.18 −12.64 −8.37 −3.40

0.234 0.435 2.321 3.337 3.904 4.577 4.846 5.350 5.636 5.875 6.076 6.132 6.177 6.177 6.114 6.106 6.143 6.246 6.321 6.463 6.575 6.706

Fig. 9. The surface tension, , and activity of carboxylic acid, a2 , versus x2 for the binary systems of carboxylic acid(2)/water(1) at 298.15 K: (䊉) formic acid, () acetic acid and () propanoic acid.

shows that surface activity of components is as follows: propanoic max (or  acid > acetic acid > formic acid. On the other hand, the 2,1 2,1 ) is decreased with the increase in the difference of surface tension values of pure compounds. There are two significant factors in patterns of Fig. 10: (i) the lower surface tension of the carboxylic acid (as noted above), (ii) the hydrogen bonding interaction between carboxylic acid and water decreased with increasing the alkyl chain length of carboxylic acid (from formic to propanoic acid) which can influence more efficiently on the transfer of carboxylic acid molecules from bulk phase to surface phase. The values of  2,1 are presented graphically versus x2 for the carboxylic acid(2)/water(1) mixtures at four temperatures in Figs. 11–13. It is obvious that the values of  2,1 decrease by increasing of temperature. In the other section of this work, the surface mole fractions (x1,s and x2,s ) were determined by using EL (Extended Langmuir) model at 298.15 K for four mixtures [13,14]. Briefly, this model considers the surface of a binary liquid mixture as a thin but finite layer and the following expression was developed for the relationship between the volume fractions of component 2 in the surface and the bulk.

a

Exp. 0.00004 0.0001 0.0006 0.0016 0.0028 0.0056 0.0075 0.0136 0.0201 0.0299 0.0480 0.0596 0.0865 0.1034 0.2033 0.2997 0.3810 0.5038 0.5763 0.7036 0.8019 0.9189 a

From Ref. [20].

Fig. 10. The values of relative Gibbs adsorption,  2,1 , against x2 for the binary systems of carboxylic acid(2)/water(1) at 298.15 K. The symbols were calculated using the data and the continuous dashed curve is a guide for the eyes: (䊉) formic acid, () acetic acid and () propanoic acid.

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A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88

6

8

5

7

-2

Γ2,1 /µmol.m

Γ2,1 /µmol.m

-2

4 3 2 1 0 0.0

6

5

4

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3 0.0

x2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x2

Fig. 11. The values of relative Gibbs adsorption,  2,1 , against x2 for the binary systems of formic acid(2)/water(1) at various temperatures: (䊉)298.15 K, ()303.15 K, ()313.15 K and ()323.15 K. The symbols were calculated using the data and the continuous dashed curve is a guide for the eyes.

Table 9 Values of the parameters ˛ and ˇ, obtained by fitting Eq. (14) to surface tension data at 298.15 K. Acid

˛

ˇ

0

Formic acid Acetic acid Propanoic acid

1.0006 0.9960 1.0074

2.5445 4.4199 12.0106

34.13 43.88 44.83

An iterative method has been used to derive ˛ and ˇ parameters by inserting experimental values in Eq. (14) (as explained in Section 2.3). Table 9 lists the values of the adjustable parameters ˛ and ˇ obtained by fitting Eq. (14) to the experimental results. Fig. 14 shows the experimental surface pressure () values together with the fitting curves obtained using the EL model for the acid/water systems. The agreement between the experimental surface pressure values and those calculated from the EL model relation was found

Fig. 13. The values of relative Gibbs adsorption,  2,1 , against x2 for the binary systems of acetic acid(2)/water(1) at various temperatures: (䊉)298.15 K, ()303.15 K, ()313.15 K and ()323.15 K. The symbols were calculated using the data and the continuous dashed curve is a guide for the eyes.

to be satisfactory. The  value increases with the increase of concentration of carboxylic acid and finally reaches a maximum value of the surface pressure (max ). In Fig. 14, comparison of max values shows that surface activity of components is as follows: formic acid > acetic acid > propanoic acid. Upon analysis of the obtained results for the acid/water mixtures, it was found that parameter ˇ is greater than unity and parameter is zero (˛ ≈ 1). This result indicates that the negative values of  are due to the fact that the surface phase is richer in the component with lower values of surface tension (carboxylic acid in this study). Table 9 also indicates that the ˇ (lyophobicity) value in the acid/water systems is amplified with increasing the alkyl chain length of the carboxylic acid (see Fig. 15). The surface volume fractions of solutes, 2,s and 1,s , were calculated using Eq. (11) (after the calculation of ˇ from Eq. (14)) and then it was converted to the surface mole fraction, x2,s , by Eq. (9). The variation of x2,s versus x2 for acid/water mixtures is given in

7

Γ 2,1

/µmol.m

-2

6

5

4

3

2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x2 Fig. 12. The values of relative Gibbs adsorption,  2,1 , against x2 for the binary systems of acetic acid(2)/water(1) at various temperatures: (䊉)298.15 K, ()303.15 K, ()313.15 K and ()323.15 K. The symbols were calculated using the data and the continuous dashed curve is a guide for the eyes.

A. Bagheri, K. Alizadeh / Colloids and Surfaces A: Physicochem. Eng. Aspects 467 (2015) 78–88 0.7

50 45

0.6

40 35

0.5

30 25

x 2,s-x 2

-1

π /(mN.m )

87

20

0.4 0.3

15 0.2

10 5 0

0.1

0

0.1

0.2

0.3

0.4

0.5 x2

0.6

0.7

0.8

0.9

1

Fig. 14. Surface pressure, , against x2 for the binary systems of carboxylic acid(2)/water(1) at 298.15 K. The symbols refer to the experimental surface pressure and the dashed curves were calculated using the EL model: (䊉) formic acid, () acetic acid, () propanoic acid and () butanoic acid.

0

0

0.1

0.2

0.3

0.4

0.5

x2

0.6

0.7

0.8

0.9

1

Fig. 17. The values of x2,s –x2 against x2 for the binary systems of carboxylic acid(2)/water(1) at 298.15 K: (䊉) formic acid, () acetic acid, () propanoic acid and () butanoic acid. The symbols were calculated using the experimental data and the continuous dashed curve is a guide for the eyes.

25 20

β

15 10 5 0

0

1

2

n

3

Fig. 15. Plot of the lyophobicity (ˇ) against number of carbon atoms in hydrocarbon chain of carboxylic acid for the binary systems of carboxylic acid/water at 298.15 K.

Fig. 16, typically. This figure shows that the mole fraction of acid at the surface is greater than its mole fraction in the bulk at all concentration ranges. This property is a consequence of the preferential migration of acid molecules of a given mixture to the surface layer and eventually to the vapor phase. The “non-ideality” of the surface tension of a given system is also reflected using the surface layer concentration. A plot of the

surface mole fraction, x2,s , versus the bulk mole fraction, x2 , gives us the possibility of establishing the non-ideality of a given system by observing the form of the corresponding curve (see Fig. 16). For ideal systems, this curve tends to be a line very close to the one a hypothetical ideal system would show, which corresponds to a 45◦ slope straight line [37]. In fact, the x2,s results are in full accordance with ˇ values. From another point of view, when something is dissolved, solvent molecules arrange around molecules of the solute. This arrangement is meditated by the respective chemical properties of the solvent and solute, such as hydrogen bonding, dipole moment and polarizability. The role of dipole moment and polarizability in the observed patterns (in Fig. 16) is very important. As a consequence, in the water-rich region, both of the above factors will favor the preferential adsorption of acid at the interface [14]. Fig. 17 shows the variation of x2,s –x2 with x2 for the carboxylic acid/water solutions. Generally, a basic trend is shown by Fig. 17, x2,s –x2 value increased with increasing acid concentration and this process to reach a maximum, then with more increasing acid

1

0.8

x 2,s

0.6

0.4

0.2

0

0

0.1

0.2

0.3

0.4

0.5

x2

0.6

0.7

0.8

0.9

1

Fig. 16. Surface mole fraction, x2,s , against x2 for the binary systems of carboxylic acid(2)/water(1) at 298.15 K: (䊉) formic acid, () acetic acid, () propanoic acid and () butanoic acid. The continuous dashed curve is a guide for the eyes and straight solid line represent the ideal behavior.

Fig. 18. The surface tension deviations, , and x2,s –x2 , versus x2 for the binary systems of carboxylic acid(2)/water(1) at 298.15 K: (䊉) formic acid and ()acetic acid. The symbols were calculated using the experimental data and the curves is a guide for the eyes.

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concentration x2,s –x2 decreased. The x2,s –x2 values are positive in the whole composition range and increase with increase of the length of the hydrocarbon chain of carboxylic acids. This figure confirms that the x2,s –x2 values increase with increasing in the difference of the polarity of pure compounds (the highest value of x2,s –x2 belongs to butanoic acid/water mixture). Fig. 18 is a typical plot showing the surface tension deviations () and x2,s –x2 as a function of composition for formic acid/water and acetic acid/water systems. As observed in this figure, the variation of  and x2,s –x2 with composition follows distinctively same patterns. In these systems,  is negative with a pronounced minimum and a specific maximum for x2,s –x2 at the same mole fraction of the component 2. 4. Conclusion The LWW model is a powerful tool to study the thermodynamic properties of mixtures containing hydrogen-bonded components. In a new approach, we have presented a thermodynamic investigation to estimate values of the interaction energy of carboxylic acid–water systems using surface tension data and the LWW model. The obtained results show the interaction energy between acid and water (Uacic–water ) decreases with the rise of temperature, and rapidly decreases with the increase of the alkyl chain length of the carboxylic acid (due to the lesser interaction between acid and water). The values of surface mole fractions of solute were calculated using the EL model. The extracted ˇ values indicate the greater affinity of carboxylic acid for the surface, and this trend is amplified with the increase of the alkyl chain length of the carboxylic acid. The x2,s results confirm that the surface concentration of carboxylic acid is higher than its bulk concentration. The UNIFAC model was used for calculation of the activity coefficients of species in the bulk phase at various temperatures. The relative Gibbs adsorption ( 2,1 ) of four binary systems has been calculated by combining concentration-surface tension data and UNIFAC model. Our calculations indicate that  2,1 is generally of the order of micron affected by varying of composition, temperature and structure of carboxylic acid. Acknowledgments The authors are grateful to Dr. Bita Dadpou who kindly read the manuscript and made some helpful suggestions. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.colsurfa.2014.11.037. References [1] S. Nath, Surface tension of nonideal binary liquid mixtures as a function of composition, J. Colloid Interface Sci. 209 (1999) 116–122. [2] A. Villares, B. Giner, H. Artigas, C. Lafuente, F.M. Royo, Study of the surface tensions of cyclohexane or methylcyclohexane with some cyclic ethers, J. Solut. Chem. 34 (2005) 185–198. [3] U. Domanska, M. Królikowska, K. Walczak, Effect of temperature and composition on the density, viscosity, surface tension and excess quantities of binary mixtures of1-ethyl-3-methylimidazolium tricyanomethanide with thiophene, Colloids Surf. A 436 (2013) 504–511. [4] H.W. Yarranton, J.H. Masliyah, Gibbs–Langmuir model for interfacial tension of nonideal organic mixtures over water, J. Phys. Chem. 100 (1996) 1786–1792.

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