Cationic and anionic surfactants interaction in water and methanol

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water and methanol–water mixed solvent media and also the thermo- dynamic ... fied solvent had a density of 0.7911 g·cm−3 and a coefficient of viscosity.

Journal of Molecular Liquids 229 (2017) 153–160

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Cationic and anionic surfactants interaction in water and methanol– water mixed solvent media Ajaya Bhattarai ⁎, Kavita Pathak, Bikash Dev Department of Chemistry, M. M. A. M. C., Tribhuvan University, Biratnagar, Nepal

a r t i c l e

i n f o

Article history: Received 25 May 2016 Received in revised form 6 December 2016 Accepted 7 December 2016 Available online 18 December 2016 Keywords: Cationic surfactant Methanol Micelle Surface tension Conductivity Solvent parameters Solvophobic effect

a b s t r a c t The micellar properties between dodecyltrimethylammonium bromide (DTAB) and sodium dodecylsulfate (SDS) in water and 0.10, 0.20, and 0.30 volume fractions of methanol in methanol–water mixed solvent media have been studied by conductivity and surface tension measurements at 293.15 K. The concentration of dodecyltrimethylammonium bromide varied from 0.0001 to 0.03 mol·L−1 in the presence of ~0.01 mol·L−1 sodium dodecylsulfate and the concentration of sodium dodecylsulfate varied from 0.001 to 0.015 mol·L−1 in the presence of ~0.005 mol·L−1 dodecyltrimethylammonium bromide. Hence, the concentrations of cationic rich (DTAB–SDS) and anionic rich (SDS–DTAB) solutions have been taken in the ratio of 3:1. The critical micelle concentrations (cmc) of DTAB–SDS and SDS–DTAB solutions have been determined by conductivity and surface tension measurements at 293.15 K. The physicochemical properties such as Gibb's free energy of micellization (ΔGom), free energy of surfactant tail transfer (ΔGotrans), maximum surface excess concentration (Гmax), area occupied by surfactant molecule (Amin), surface pressure at the cmc (πcmc), packing parameters (P) and standard free energy interfacial adsorption (ΔGoads) are calculated in water, 0.10, 0.20 and 0.30 volume fractions of methanol–water at 293.15 K. Addition of methanol significantly affects the physicochemical properties between DTAB and SDS. With increasing concentration of methanol, the cohesive force and the dielectric constant decrease that affects the micellization and other physicochemical properties. The micellization between DTAB and SDS have been assessed in terms of different solvent parameters. The ratio of the solvent surface tension to the limiting surface tension at the cmc has been used as the solvophobic effect. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Research on surfactant mixtures is of considerable interest for numerous technical applications because surfactant mixtures enhance the performance of applications when compared to the use of single surfactants. When mixing surfactants, especially oppositely charged ones, new properties may appear. Aqueous mixtures of anionic and cationic surfactants exhibit many unique properties that arise from the strongly electrostatic interactions between the oppositely charged head groups [1]. It has been well-known for a long time that among the various types of binary surfactant systems, anionic/cationic binary systems exhibits the strongest synergisms in both such as reduction in surface tension and in mixed micelle formation [2]. Interaction between cationic and anionic surfactants in aqueous solution leads to various systems of great importance for both basic science and technological applications [3]. Cationic and anionic surfactant

⁎ Corresponding author. E-mail address: [email protected] (B. Dev).

http://dx.doi.org/10.1016/j.molliq.2016.12.021 0167-7322/© 2016 Elsevier B.V. All rights reserved.

mixtures are important for a wide range of applications in industries such as enhanced oil recovery, detergency, waste water treatment and pharmaceutical applications [4]. On mixing of the two anionic and cationic surfactants together can produce interesting microstructures not formed by the pure components (e.g. vesicles and/or rodlike micelles) and can dramatically decrease the concentration at which liquid crystalline phases form [5]. The formations of aggregations and their dependence on environmental factors (temperatures and additives etc), their thermodynamics of formation, counterion binding, aggregation numbers and so forth, are important physicochemical aspects that need detailed and intensive attention for understanding both the fundamental and application prospects [6,7]. Changing the solvent quality provides the opportunity to study the role of the co-solvent or solvophobic effect and the increasing use of surfactants in applications which require water free or water poor media makes this type of research more interesting. In recent years, however, many authors have turned their attention to micelle formation and aggregation process of micelles in solvent systems constituted by mixtures of water with some organic solvents having properties similar to water such as ethanol, formamide and glycerol., which have been

A. Bhattarai et al. / Journal of Molecular Liquids 229 (2017) 153–160

2. Experimental 2.1. Materials Methanol (E. Merck, India, 99% pure) was first distilled with phosphorous pentoxide and then redistilled over calcium hydride. The purified solvent had a density of 0.7911 g·cm−3 and a coefficient of viscosity of 0.5944 mPa·s at 293.15 K; these values are in good agreement with those found in the literature [23]. DTAB and SDS were purchased from Merck Specialities Private Limited (Mumbai, India). DTAB was recrystallized several times until no minimum in the surface tension-concentration plot was observed and its cmc 15.38 mM agreed with the literature value [24] at 293.15 K. SDS was recrystallized several times for purification. The minimum in the surface tension-concentration plot was observed. The aqueous solutions of purified and unpurified samples of sodium dodecylsulfate exhibited minimum in the surface tension versus log C plot (C, concentration of sodium dodecylsulfate ). The minimum in the plot of γ versus log C for sodium dodecylsulfate is considered due to the presence of highly surface-active dodecyl alcohol molecules [25]. Dodecyl alcohol may be present as impurity in the supplied sample of sodium dodecylsulfate or it may be produced in the sodium dodecylsulfate solution by its hydrolysis. The cmc of sodium dodecylsulfate is taken to be the concentration of sodium dodecylsulfate corresponding to the minimum in the plot of γ versus log C and it is equal to 8.10 mmol kg−1 in

the absence of any added electrolyte at 25 °C. This value is in good agreement with the cmc values of sodium dodecylsulfate obtained from conductance (8.10 mmol kg−1) [26]. DTAB and SDS were kept in desiccators and used after drying for 1 h. All solutions were prepared in double-distilled water with a specific conductance of b 0.5 μS/cm at 293.15 K. To make the ratio of 3:1 of DTAB and SDS, first of all, 0.01 mol·L−1 SDS was dissolved in 250 ml volumetric flask with water and the volume make up of the SDS solution was done after 24 h at constant temperature 293.15 K in thermostat [27]. 0.03 mol·L−1 DTAB was dissolved in 100 ml volumetric flask by 0.01 mol·L− 1 SDS solution which was acted as the solvent here and the volume make up was done in the next day at constant temperature 293.15 K in the thermostat by the same 0.01 mol·L−1 SDS solution. Similarly, to make the ratio of 3:1 of SDS and DTAB, 0.005 mol·L−1 DTAB was dissolved in 250 ml volumetric flask with water and the volume make up of the DTAB solution was done after 24 h at constant temperature 293.15 K in the thermostat. 0.015 mol·L−1 SDS was dissolved in 100 ml volumetric flask by 0.005 mol·L−1 DTAB solution which was acted as the solvent here and the volume make up was done in the next day at constant temperature 293.15 K in the thermostat by the same 0.005 mol·L−1 DTAB solution. The methanol–water mixtures were prepared up to 0.3 volume fractions of methanol at 293.15 K by maintaining at constant temperature in the thermostat. The mixed solvents were used after 24 h to make the solutions of DTAB and SDS surfactants. Further, DTAB–SDS and SDS–DTAB solutions were prepared at constant temperature of 293.15 K. The reasons for limiting from water up to 0.3 volume fractions of methanol were due to the formation of precipitate on mixing DTAB rich with SDS (DTAB–SDS) and SDS rich with DTAB (SDS–DTAB) in 0.4 volume fraction of methanol and then higher volume fraction of methanol. Also, it was not possible to get the critical micelle concentration for DTAB–SDS and SDS–DTAB in methanol because of the linear variation of the plot between specific conductance versus concentration.

2.2. Apparatus and procedure 2.2.1. Conductance measurement The specific conductance measurements of freshly prepared solutions were carried out on a Pye-Unicam PW 9509 conductivity meter with a dip-type cell having a cell constant of 1.15 cm−1 with an uncertainty of 0.01%. The cell was calibrated using aqueous potassium chloride solution (0.1 Demal and 0.01 Demal) [28] at 293.15 K. 0.8

0.6

-1

most widely studied [8,9]. In the past two decades, many investigations have been carried out on various systems [10–12]. Zana et al. [13] investigated the Kraft temperature, cmc, micelle ionization degree of cetyltrimethylammonium in presence of an anionic dimeric (Gemini) surfactant through electrical conductivity; however, the thermodynamic properties were not calculated. Bhattarai et al. [14,15] have explained the influence of concentration, temperature and solvent composition of the binary mixtures of CTAB–SDS surfactant systems in water and methanol–water mixed solvent media and also the thermodynamic properties were calculated [15]. Aslanzadeh and Yousefi [16] have studied the effect of cosolvent (ethanol) on nanostructures of mixed cationic and anionic surfactants. Similarly, catanionic micelles were studied in the mixtures of cetyltrimethylammonium bromide (CTAB) and sodium-dodecyl sulfate (SDS) by Yousefi et al. [17]. Study of the variations in the self-diffusion coefficient and viscosity with the changing concentration of CTAB to SDS in the cationic-rich and anionic-rich regions revealed a phase transitions nanostructures from microstructures (vesicles) to nanostructures (mixed micelle) [18]. As far as we know, there is very little work in the literature that deals with the studies of anionic and cationic surfactant mixtures in nonaqueous solvents [19–21] and few works have been done on the effect of medium [14,15,22]. In this work, we have reported the results for conductance and surface tension measurements on SDS–DTAB and DTAB–SDS in water and methanol–water mixed solvent media at 293.15 K. The cmc has been calculated by using the data extracted from conductometry and tensiometry plots. The thermodynamic parameters and surface properties have also been studied. The obtained results based on the literature data for individual SDS and DTAB aqueous solution as well as the aqueous solutions of methanol have been compared with the mixed surfactants systems. This study would provide valuable information towards the extent of interactions of the surfactant systems studied. This article intends to discuss minutely about the effect of methanol–water system on micellization between DTAB and SDS at 293.15 K. The results have been analyzed in terms of the solvent parameters, viz., permittivity (D), Reichardt's parameter (ET(30)), Gordon parameter (G), viscosity (η0) and Hildebrand parameter (δ). The solvophobic effect can be described from the ratio of solvent surface tension to the limiting surface tension at the cmc.

κ ( mS.cm )

154

0.4

0.2

0 0

0.003

0.006

0.009

0.012

0.015

-1

C(mol.L )

Fig. 1. Concentration dependence of the conductance for SDS–DTAB in pure water (open circle) and (triangles, 0.10 volume fraction of methanol; closed inverted triangles, 0.20 volume fraction of methanol; squares, 0.30 volume fraction of methanol) at 293.15 K.

A. Bhattarai et al. / Journal of Molecular Liquids 229 (2017) 153–160

155

70

3

65 60 55

2

γ / mNm

-1

-1

κ ( mS.cm )

50 45 40

1

35 30 25

0 0

0.01

0.02

0.04

0.03

20 -3.3

-3.1

-2.9

-2.7

-2.5

-2.3

-2.1

-1.9

Log [C]

-1

C(mol.L )

Fig. 2. Concentration dependence of the conductance for DTAB–SDS in pure water (open circle) and (open triangles, 0.10 volume fraction of methanol; closed inverted triangles, 0.20 volume fraction of methanol; squares, 0.30 volume fraction of methanol) at 293.15 K.

2.2.2. Surface tension measurement The surface tension of freshly prepared solutions was determined with a calibrated Kruss K20S force tensiometer purchased from Germany which was funded by TWAS, Italy, using a platinum ring by the ring detachment technique [29]. The uncertainty of the measurements was within ±1 × 10−3 N·m−1. The tensiometer was connected to a water-flow cryostat to maintain the temperature equilibrium. Prior to each measurement, the ring was heated briefly by holding it above a Bunsen burner until glowing. The temperature control had an accuracy of ±0.1 °C.

3. Results and discussion 3.1. Conductance measurement and thermodynamics properties The conductance of SDS–DTAB and DTAB–SDS in water and in 0.10, 0.20 and 0.30 volume fractions of methanol for the calculation of the cmc at 293.15 K are depicted in Figs. 1–2. It is observed that the conductance of SDS–DTAB and DTAB–SDS decreases with the increase in methanol content in methanol–water mixed solvent system. The decrease in conductance with increase in methanol content is contributed by two parameters of the medium properties. Firstly, alcohol is known to have structure breaking effect and the second is the increase in viscosity of the medium with increasing the methanol content. For each plot, conductivity increases with increase in concentration with certain slope and at certain concentration, the slope changes. The

Fig. 3. Plot of surface tension versus Log[C] for SDS–DTAB at 293.15 K, in pure water (closed squares) and (closed triangles, 0.10 volume fraction of methanol; open circles, 0.20 volume fraction of methanol; crosses, 0.30 volume fraction of methanol).

intersection of these two lines having different slopes is estimated as the cmc. Ratio of post-micellar and pre-micellar slopes give degree of ionization (α). In this method, properties of SDS–DTAB and DTAB–SDS solutions are mainly exhibited by the plots of conductance with concentration of solution where there are different variations of preand post-micellar slopes. With the addition of methanol, these two slopes are varied which leads to difference in physicochemical properties of solution. The mixed surfactants show the largest pre-cmc slopes and smallest post-cmc slopes, leading to the smallest degrees of dissociation (Table 1). Both slopes (pre-cmc and post-cmc) decrease with increase of methanol in methanol–water mixed solvent media. The decrease in the value of the pre-cmc slopes of the mixed surfactants is sharp in comparison with the value of the post-cmc slopes upon addition of larger volumes of methanol at 293.15 K (Table 1). The cmc obtained for SDS–DTAB and DTAB–SDS system from conductometry measurements in water and 0.10, 0.20, and 0.30 volume fractions of methanol at 293.15 K is shown in Table 1. It is observed that both the cmc and α increase with the increase in methanol in the methanol–water mixed solvent medium (Table 1). Methanol contains the shortest carbon chain is more polar and more soluble than the other alcohols. The size of the chain of methanol is closer to that of the polar group than for the other alcohols, methanol can solvate the surfactant monomers more easily, increasing their dissolution in water. This hinders interaction of the monomers during formation of micelles and, consequently, the concentration of surfactant must be larger if total stability of the micellar aggregates is to be achieved. This could be the one reason why cmc increases with increasing methanol concentration [30]. Similar trends have been observed

Table 1 Values of pre-micellar slope (S1), post-micellar slope (S2), degree of ionization (α), critical micelle concentration(cmc), Gibb's free energy of micellization (ΔGom), free energy of surfactant tail transfer(ΔGotrans) of SDS–DTAB and DTAB–SDS in water and 0.10, 0.20 and 0.30 volume fraction of methanol at 293.15 K. Volume fractions of methanol SDS–DTAB system 0.00 0.10 0.20 0.30 DTAB–SDS system 0.00 0.10 0.20 0.30

S1 (mS cm−1 M−1)

S2 (mS cm−1 M−1)

α

cmc (mol·L−1)

ΔGom (kJmol−1)

ΔGotrans (kJmol−1)

64.5 54.8 46.7 39.6

36.3 34.2 29.8 27.7

0.56 0.62 0.64 0.70

0.00592 0.00633 0.00683 0.00738

−31.87 −30.34 −29.25 −27.60

1.53 2.62 4.27

105.0 82.8 69.6 62.0

35.8 35.0 33.2 32.0

0.34 0.42 0.48 0.52

0.01349 0 0.01470 0.01642 0.01761

−33.95 −31.81 −29.96 −28.68

2.14 3.99 5.27

156

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DTAB [24,38] at 293.15 K. For DTAB–SDS system, the cmc increases of value 14.70 mM in 0.1 volume fraction of methanol (Table 1). This same trend has been observed for DTAB in methanol–water mixture [31,37]. Hence, the methanol often increases the cmc of SDS–DTAB and DTAB–SDS with methanol concentration increase. The cmc of DTAB in 0.1 volume fraction of methanol at 293.15 K has not been reported elsewhere and thus the comparative study between the cmc of DTAB and DTAB–SDS in methanol–water mixture at 293.15 K is not possible. The free energies of micelle formation are calculated on the basis of a pseudo-phase separation model [39,40] and given in Table 1:

60

γ / mNm

-1

50

40

ΔGom ¼ ð2−αÞRT lnX cmc

30

20 -3.5

-3.0

-2.5

-2.0

-1.5

-1.0

Log [C]

Fig. 4. Plot of surface tension versus Log[C] for DTAB–SDS at 293.15 K, in pure water (closed squares) and (closed triangles, 0.10 volume fraction of methanol; open circles, 0.20 volume fraction of methanol; crosses, 0.30 volume fraction of methanol).

[31] who concluded that there is a significant increase in the cmc of surfactant with the increase in the volume fraction of methanol. It is known that an increase in the organic solvent content decreases the aggregation number of the micelles, which then causes an increment in the electrostatic repulsion between the cationic head group of DTAB and the anionic surfactant, i.e. SDS, and leads to a diminution in the electrical charge density at the micellar surface. This may be the reason for the increase in α [32,33]. The mixtures of SDS–DTAB are electrostatic neutrality and sufficiently high concentration of both was found to be precipitate. The ratios of SDS to DTAB as well as DTAB to SDS were kept 3:1. The cmc of SDS–DTAB decreased to a value of 5.92 mM in comparison with the cmc of 8.03 mM of SDS [34] at 293.15 K. The decrease in cmc is due to the larger synergistic effects when two oppositely charged surfactants are mixed together. A similar behavior was noticed by Herrington and Kaler [5] in 1993 when they studied the phase behavior of aqueous mixtures of DTAB and SDS and found a decrease in cmc. It is very interesting to compare the obtained results of cmc for SDS– DTAB in methanol–water solutions with the experimental data for cmc in SDS–methanol–water solutions [29,35–37]. It was observed that methanol often increases the cmc with increasing concentration of methanol. It is found in our study that the cmc of SDS–DTAB in 0.1 volume fraction of methanol decreased to a value of 6.33 mM in comparison with the cmc ~ 9.5 mM of SDS in 0.1 volume fraction of methanol [35] at 293.15 K. Similarly, the cmc of DTAB–SDS decreased to a value of 13.49 mM in comparison with the cmc of 15.38 mM of DTAB and 15.1 mmol·kg−1 of

ð1Þ

where Xcmc is mole fraction of surfactant at cmc, R is universal gas constant and T is the temperature. The effect of alcohol on micellization process can be studied by means of free energy of surfactant tail transfer, ΔGotrans, which is defined by [31] ΔGotrans ¼ ΔGom

 alcoholþwater

− ΔGom



ð2Þ

water

Gibb's free energy of micellization (ΔGom) and free energy of surfactant tail transfer (ΔGotrans) values of SDS–DTAB and DTAB–SDS in water, 0.10, 0.20, and 0.30 volume fractions of methanol–water at 293.15 K are displayed in Table 1. The free energy of micelle formation of SDS–DTAB in water is found to be −31.87 kJ/mol [Table 1] where as the free energy of micelle formation of SDS in water is reported to be −34.6 kJ/mol [34]. This indicates that the formation of micelle is less favorable for SDS–DTAB in comparison with SDS system. The free energy of micelle formation of DTAB–SDS in water is found to be −33.95 kJ/mol [Table 1] whereas the free energy of micelle formation of DTAB in water is reported to be −34.76 kJ/mol [38]. This indicates that the formation of micelle is less favorable for DTAB–SDS in comparison with DTAB system. It is evident from Table 1 that the free energy of micelle formation is negative in all cases and becomes less negative as the methanol content increases, indicating that the formation of micelles become less favorable at higher methanol content. Similar trends were also observed in the literature [29,31]. Moreover, the free energy of micelle formation is less negative in SDS–DTAB solutions in comparison to DTAB–SDS solutions in water and methanol–water mixed solvent media. This also indicates the formation of micelles become less favorable for SDS–DTAB solutions in comparison with DTAB–SDS solutions. According to the theory of surfactant self-assembly [41], the major contribution to the standard free energy of micellization is associated with transfer of the surfactant tail from solvent into the micelle. The ΔGotrans values in Table 1 are all positive and increase with the increasing volume fraction of methanol in water for SDS–DTAB and

Table 2 Values of slope, critical micelle concentration (cmc), maximum surface excess concentration (Γmax), area occupied by per surfactant molecule (Amin), surface pressure (πcmc), packing parameter (P), standard free energy interfacial adsorption(ΔGoads)of SDS–DTAB and DTAB–SDS in water and 0.10, 0.20 and 0.30 volume fraction of methanol at 293.15 K. Slope (mNm−1 ln M−1)

cmc (mol·L−1)

Γmax106 (mol m−2)

Amin (Å2molecule−1)

πcmc (m Nm−1)

P

ΔGoads (kJmol−1)

SDS–DTAB system 0.00 0.10 0.20 0.30

−41.70 −39.30 −37.20 −34.80

0.006011 0.006501 0.006701 0.007203

3.71 3.50 3.31 3.09

44.70 47.43 50.11 53.57

41.95 31.47 23.97 19.79

0.47 0.44 0.42 0.39

−43.2 −39.3 −36.5 −33.9

DTAB–SDS system 0.00 0.10 0.20 0.30

−32.10 −31.20 −29.70 −29.00

0.01300 0.01399 0.01599 0.01702

2.86 2.78 2.65 2.58

58.07 59.75 62.77 64.28

45.74 34.62 27.14 22.89

0.36 0.35 0.34 0.33

−49.9 −44.3 −40.2 −37.5

Volume fractions of methanol

A. Bhattarai et al. / Journal of Molecular Liquids 229 (2017) 153–160

DTAB–SDS solutions indicating the transfer of the surfactants tail from the bulk into the micelle is less favorable. Such positive and increase in the values of ΔGotrans when increase of methanol are also found in single surfactant system [31].

157

-30

It is seen from Figs. 3–4 that the surface tension of SDS–DTAB and DTAB–SDS decrease with increase in methanol content in water. It is evident from Fig. 3 that the surface tension initially decreases with increasing concentration of SDS–DTAB and then reaches a minimum, indicating that micelle are formed and the concentration of the breakpoint corresponds to the cmc whereas for Fig. 4 of DTAB–SDS, the surface tension is reduced by adsorption of surfactant at the interface, and a sigmoidal curve between surface tension (γ) and log [surfactant] is produced by distinct break is produced after which surface tension remains almost unchanged. This break point gives the cmc [42]. Table 2 lists out the cmc of SDS–DTAB and DTAB–SDS by surface tension method which is very close to that obtained by conductivity method (Table 1). The hydrophobic effect of catanionic surfactant molecules is weaker, which is a disadvantage for micelle formation. Methanol addition, on the other hand, strengthens the attractive electrostatic interaction between their two oppositely charged polar groups and consequently is an advantage for micelle formation [10,43–45]. In surfactant mixtures, it overcomes the disadvantageous influence of methanol addition on the hydrophobic effect. It can be seen that the presence of methanol in the bulk phase affects the micellization process of surfactant mixtures and leads to a more spontaneous process. It can be understood as the basis of a reduction in the solvophobic interactions caused by the improved salvation, which leads to an increase in the solubility of the hydrocarbon tails and electrostatic repulsion between head group in the presence of methanol and consequently in an increase in the cmc as shown in Table 2. The cmc of SDS–DTAB decreased to a value of 6.01 mM in comparison with the cmc of 8.00 mM and 7.7 mM of SDS [46,47] and the cmc of DTAB–SDS decreased to a value of 13.0 mM in comparison with the cmc of 14.8 mM of DTAB [48] at 293.15 K by surface tension methods. ) of sigmoidal curve, where C is the concentration of surThe slope (d dγ logC

factant solution in mol L−1, gives various information about the surface Þ of SDS– properties of surfactant solution [42]. Variation of slope (d dγ logC DTAB and DTAB–SDS solutions with volume fraction of methanol– water mixed solvent is shown in Fig. 5. The slope strongly affects the surface properties of mixed surfactants as the slope is the key factor for the calculation of surface properties (Table 2). It is seen in Fig. 5 that both the curves having slight difference in nature. For SDS–DTAB, the curve is fitted with polynomial of 2nd degree fit where as for DTAB–SDS, the curve is fitted with polynomial of 3rd degree fit.

dγ /d Log C

3.2. Surface tension measurement and surface properties

-40

ð3Þ

Fig. 5. Variation of ðd dγ Þ with volume fractions of methanol–water for DTAB–SDS (○) and logC

The value of the surface pressure at the CMC (πcmc) is obtained as πcmc ¼ γo −γcmc

where N is Avogadro's number.

ð5Þ

where γo and γcmc are the values of surface tension of water and the surfactant solution at the cmc respectively. Israelachvili et al. [49] proposed that the micellar shape is mainly governed by the geometry of the surfactant and its packing. The surface area of amphiphiles in mixed micelles and micellar growth (spherical– nonspherical) can be used to find out the packing parameters, P,



Vo Amin lc

ð6Þ

where, Vo is the volume of exclusion per monomer in the micelle, given by Tanford's formula [50]. Vo = [27.4 + 26.9(nc − 1)]2Å3, lc = [1.54 + 1.26(nc − 1)]Å, is the maximum chain length and ncis the number of carbon atoms in the hydrocarbon chain.

-27

-1

-30

m

-33

where R is the gas constant (8.314 J mol−1 K−1). The constant n takes the values 2 for conventional surfactant where the surfactant ion and the center line are univalent [31]. The area occupied by surfactant molecule (Amin) at the air/methanol–water interface has been obtained by, Amin ¼ 1=NГmax

30

SDS–DTAB (●) at 293.15 K.

0

  1 dγ 2:303nRT d logC T;P

20

Volume fraction of methanol

ΔG / kJ mol

Гmax ¼ −

10

0

) of sigmoidal curve, the maximum surface excess From slope (d dγ logC concentration at the air/methanol–water interface can be calculated by applying Gibb's isotherm [42],

-35

ð4Þ

-36 60

61

62

63

ET (30)

Fig. 6. ΔGom vs ET(30) at 293.15 K: SDS–DTAB (●) and DTAB–SDS (○)

64

158

A. Bhattarai et al. / Journal of Molecular Liquids 229 (2017) 153–160 -25.0

-27.5

-27.5

-30.0

m

0

m

0

ΔG / kJ mol

ΔG / kJ mol

-1

-1

-30.0

-32.5

-32.5

-35.0

-35.0 1.0

1.2

1.4

1.6

1.5

1.8

2.0

3.0

2.5 -3

η0 / mPa.s

G /J m

Fig. 9. ΔGom vs G at 293.15 K: SDS–DTAB (●) and DTAB–SDS (○).

Fig. 7. ΔGom vs η0 at 293.15 K: SDS–DTAB (●) and DTAB–SDS (○).

The standard free energy interfacial adsorption at the air/saturated monolayer interface can be evaluated from the relation [49]. ΔGoads ¼ ΔGom −πcmc =Γmax

ð7Þ

The maximum surface excess concentration at the air/methanol– water interface (Гmax), area occupied per surfactant molecule (Amin) at the air/methanol–water interface, surface pressure at the cmc (πcmc), packing parameters (P) and standard free energy interfacial adsorption (ΔGoads) are calculated respectively by Eqs. 3 to 7 for SDS–DTAB and DTAB–SDS solutions in water and methanol–water at 293.15 K and are displayed in Table 2. With the help of the literature [46], the data were recalculated from [51]. The plot between the slope and log(C/M) of SDS [42] were extrapolated and obtained the surface properties of SDS in water at 293.15 K as Γmax(4.18), Amin(39.65), πcmc(35.45) calculating from γcmc(mN/m): 37.3 [48] and γo = 72.75 [52], P(0.53) and ΔGoads (−43.06) calculating from ΔGom: −34.6 [34]. These values were checked with temperature effect from the literature [29] in water at 303.15 K and found the accurate pattern like DTAB in water [31] and hence the comparison has been done with the surface properties of SDS–DTAB solutions in water [Table 2] at 293.15 K. Similarly, with the help of the literature [31], the data were extrapolated and obtained the surface properties of DTAB in water at 293.15 K as Γmax(2.92), Amin(56.44), πcmc (34.89), P(0. 39) and ΔGoads (−48.53)

and hence the comparison has been done with the surface properties of DTAB–SDS solutions in water [Table 2] at 293.15 K. It is observed that there is a decrease in Γmax, P and ΔGoads and increase in Amin , πcmc for SDS–DTAB and DTAB–SDS system in comparison with single surfactants SDS and DTAB in water at 293.15 K. The data from Table [2] show that Гmax as well as πcmcdecreases with increase in methanol content indicating less population and surface pressure due to surfactant molecules. Such trends are also found in ionic surfactants with increase of methanol content [29,31]. However, Amin values are increasing with increase in methanol content which indicates that surfactant molecules are occupying more surface area at air/ methanol–water interface. Similar trends are also observed in the ionic surfactants with increase of methanol content [29,31]. Negative values of ΔGoads indicate that the adsorption of surfactant molecules on the surface is spontaneous. The ΔGoads values become less negative with increasing volume fraction of methanol at constant temperature which indicates less spontaneity of adsorption of surfactant molecules on the surface. Similar types of behaviors are found in the literature [29,31]. The value of packing parameter (P) suggests the shape of micelle acquired. Israelachivili et al. [49] suggested that in general micelles are spherical for P b 1/3, cylindrical for P b 1/2. In our investigation, from Table 2, it is seen that in absence and presence of methanol, P values for both SDS– DTAB and DTAB–SDS are higher than 0.3 indicating cylindrical or rodshaped micelles.

-25.0 -27.5

-27.5

-30.0

m

0

m

0

ΔG / kJ mol

-1

ΔG / kJ mol

-1

-30.0

-32.5

-32.5

-35.0 0.0120

0.0125

0.0130

0.0135

0.0140

1/D

Fig. 8. ΔGom vs 1/D at 293.15 K: SDS–DTAB (●) and DTAB–SDS (○).

0.0145

-35.0 48

50

52

54

δ

Fig. 10. ΔGom vs δ at 293.15 K: SDS–DTAB (●) and DTAB–SDS (○).

A. Bhattarai et al. / Journal of Molecular Liquids 229 (2017) 153–160

159

Table 3 Various physicochemical parameters of the mixed solvents (methanol–water) at 293.15 K. Volume fraction of methanol

Dielectric constant

Solvent surface tension γo/(mN m−1) [52]

Solvent molar volume Vm/(dm3 mol−1)

Gordon parameter G(J m−3)

ΔGom(DTAB–SDS) (kJ/mol)

ΔGom(SDS–DTAB) (kJ/mol)

Coefficient of viscosity (mPa·s)

Reichardt's parameter (ET/kcal mol−1) [66]

Water 0.1 0.2 0.3 Methanol

80.2 [62] 76.86 73.15 69.31 33.45 [63]

72.75 59.63 50.15 43.93 22.95

18.07 19.47 20.86 22.26 32.04

2.77 2.22 1.82 1.56 0.72

−33.95 −31.81 −29.96 −28.68

−31.87 −30.34 −29.25 −27.60

1.002 [64] 1.2105 1.4812 1.6648 0.5944 [65]

63.10 62.33 61.56 60.79 55.80

However, when volume fractions of methanol are varied the values of P decrease for both SDS–DTAB and DTAB–SDS. Similar behavior was observed for effect of methanol on SDS [29] and DTAB [31]. It is evident from the literature [16] that a water-structure breaker additive alters the surface and thermodynamic properties of mixed surfactants. Hence, in our case methanol alters the surface and thermodynamic properties of SDS–DTAB and DTAB–SDS systems. Similar trends were found by Sohrabi et al. [2].

Mukhim and Ismail [60] proposed that the ratio of the solvent surface tension to the limiting surface tension at the cmc, γ/ γlim, can be used as a probable new scale to describe the solvophobic effect [61]. Fig. 11 shows the variation of the ratio of the solvent surface tension to the limiting surface tension at the cmc with volume fraction of alcohol.

3.3. Correlation of ΔGom with solvent parameters

The experimental results for the conductance and surface tension of salt-free solution of SDS–DTAB and DTAB–SDS mixtures in water and methanol–water mixed solvent media have been presented as a function of surfactant concentration. The conductance was found to be increased with increasing the concentration of surfactant mixtures whereas the values were also found to be decreased with increasing methanol content in the mixed-solvent system. The estimation of the pre-cmc slope and post-cmc slope for both SDS–DTAB and DTAB–SDS systems provide pertinent view regarding the solution behavior of mixed surfactant. The cmc and degree of micellar dissociation were found be increased and the free energies of micelle formation were found to be less negative with the increasing volume fraction of methanol. The free energy of surfactant tail transfer is found to be positive and increased with increasing volume of methanol. The surface tension was found to be decreased initially with increasing the concentration of surfactant mixtures in the mixed-solvent system. The cmc was found to be increased whereas the value of maximum surface excess, surface pressure and packing parameter are found to be decreased and minimum area per molecule followed the opposite trend i.e. increased with the increasing methanol. The standard free energy interfacial adsorption is found to be negative and negative decrease with increasing volume of methanol. It can be seen that Gibb's free energy of micellization values in both SDS–DTAB and DTAB–SDS system in methanol–water media do not show a straight forward linear correlation with the different studied solvent parameters i.e. D, ET(30), G, η0 and δ. Variation of the ratio of the solvent surface tension to the limiting surface tension at the cmc with the volume fraction of methanol give the new scale to describe the solvophobic effect.

We can correlate ΔGom with different solvent parameters namely dielectric constant, viscosity, Reichardt's parameter [53], the Hildebrand parameter [54–56], and the Gordon parameter [57]. Because micellization consists of molecular association, the fluidity, polarity and solvent structure are expected to influence the process [29]. Here, we use methanol–water mixed solvent media to see the effect of SDS–DTAB and DTAB–SDS on the ΔGom values. ΔGom is the best thermodynamic parameter. Especially for ionic surfactants, the counterion binding influences ΔGom. In Figs. 6–10, the dependence of ΔGom (SDS–DTAB and DTAB–SDS) on the solvent parameters, ET(30), η0, D, G and δ of methanol–water mixed solvent media are presented. The ET(30), η0 and D were taken from the literature [58], G values were determined by us (Table 3) and δ values were calculated with the empirical relationship given elsewhere [55– 56] between δ and dielectric constant which works best for hydrogen bonded liquids: δ ¼ 0:45D þ 18:5

ð8Þ

All parameters produced curvilinear correlations with ΔGom. Such types of trends were also observed in single surfactants [29,59].

2.8

2.6

2.4

4. Conclusion

γο / γcmc

Acknowledgments One of the authors (Ajaya Bhattarai) is thankful to the world academy of sciences(TWAS), Italy for providing Research Grant(12-164 RG/ CHE/AS_I-UNESCOFR:3240271347) on this work and also grateful to University Grants Commission, Nepal and Nepal Academy of Science and Technology(NAST) for providing funds for purchasing DTAB and SDS to conduct this research work.

2.2

2.0

1.8 0

0.1

0.2

0.3

Volume fraction of methanol

Fig. 11. γ0/γcmc vs Volume fraction of alcohol at 293.15 K: SDS–DTAB (●) and DTAB–SDS (○).

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