Miscibility of sodium chloride and sodium dodecyl sulfate in the adsorbed film and aggregate

Abstract

The adsorption, micelle formation, and salting out of sodium dodecyl sulfate in the presence of sodium chloride were studied from the viewpoint of their mixed adsorption and aggregate formation. The surface tension of aqueous solutions of a sodium chloride–sodium dodecyl sulfate mixture was measured as a function of the total molality and composition of the mixture. Phase diagrams of adsorption and aggregate formation were obtained by applying thermodynamic equations to the surface tension. Judging from the phase diagrams, sodium chloride and sodium dodecyl sulfate are miscible in the adsorbed film at very large composition of sodium chloride and in the salted-out crystalline particle, while they are immiscible in the micelle. The miscibilities in the adsorbed film, micelle, and crystalline particle increase in the following order: particle > adsorbed film > micelle. The difference in miscibility among the oriented states was ascribed to the difference in geometry between the adsorbed film and micelle and to the interaction between bilayer surfaces in the particle.

Introduction

The adsorption and micelle formation of surfactants in the presence of inorganic salts have been studied from the viewpoint of additive effect of salts [1–5]. Enhanced adsorption and critical micelle concentration (CMC) lowering with added salts were observed for ionic surfactants. Tajima measured the adsorbed amounts of sodium dodecyl sulfate (SDS) in the presence of sodium chloride (NaCl) by a direct radiotracer method and also evaluated the surface excesses of ions by an application of the Gibbs adsorption equation to the surface tension of aqueous NaCl solutions of SDS [6]. He found almost zero or slightly negative adsorption of counterions at the molarities of NaCl below 10 mM. Ozeki et al. evaluated the Gibbs surface excesses of surfactant ions, counterions, and coions from the surface tension of aqueous NaCl solutions of dodecyldimethylammonium chloride. They obtained small negative adsorption of counterions at low NaCl concentrations and a positive one at NaCl concentrations higher than 0.5 M [4, 7]. In the above two studies, surface excesses of ions were evaluated from the dependence of surface tension on the respective concentrations of salt and surfactant.

However, thermodynamic treatment of surfactant mixture has been applied to mixtures of inorganic salt and surfactant in our previous studies [8–10]. We have measured the surface tension of aqueous solutions of a salt–surfactant mixture as a function of the total concentration and composition of the mixture instead of measuring it as a function of the respective concentrations of salt and surfactant. We then evaluated the composition of adsorbed film from the surface tension and obtained phase diagram of adsorption. The phase diagram was proved to be useful in clarifying the miscibility of inorganic salt and surfactant and the interaction between inorganic ions and the head group of surfactant in adsorbed films [8–13]. Furthermore, the adsorption and micelle formation have been studied separately in previous studies, even if the CMC was determined from the surface tension vs. concentration curve [4, 7, 14, 15]. On the other hand, for salt–surfactant mixtures, we have determined the composition of the adsorbed film and micelle coexisting at the CMC from the dependence of mixture CMC and surface tension at the CMC on the bulk composition. We then compared the miscibilities of salt and surfactant in the adsorbed film and micelle by using the phase diagram for adsorbed film–micelle equilibrium [8, 10–13].

It was found from the phase diagrams that (1) the polar head group of nonionic-surfactant molecule attract sodium ion a little in the adsorbed film and micelle, and (2) for a sodium chloride–dodecylammonium chloride mixture, dodecylammonium ions squeeze sodium ions out of the adsorbed film and micelle due to the electrostatic repulsion between the two cations [8–11]. As well as the miscibilities of sodium chloride with nonionic and cationic surfactants, it is of interest to investigate the miscibility of NaCl with an anionic surfactant in an adsorbed film and micelle.

Moreover, in the study of foam films, added salts cause the formation of black films stabilized with surfactants due to the reduction of electrostatic repulsion between the two surfaces in a film [16–18]. To clarify the formation of black films, it is essential for us to have knowledge of the miscibility and interaction of surfactant with salt in the surface of a film-forming solution and the changes in miscibility and interaction associated with the interaction between surfaces in a black film [17, 19–22].

Ionic surfactants are salted out at high salt concentrations, and hydrated crystalline particles (coagels) are formed in solutions [5, 23]. Nakayama and Shinoda [24] and Shinoda et al. [25] investigated the effect of added salts on the solubilities and Krafft points of ionic surfactants. At the points on the solubility curve above the Krafft point, singly dispersed surfactant is in equilibrium with hydrated solid surfactant and micellar surfactant. Hence, it is expected that useful information on adsorbed films, micelles, and/or salted-out particles can be obtained from the measurements of surface tension at high salt concentrations. However, the surface tension of aqueous solutions of ionic surfactants has hardly been measured at high salt concentrations except the studies by Ikeda et al. [7, 14, 26–28]. Ikeda et al. ascribed the breaks on the surface tension vs. surfactant concentration curves even at high salt concentrations above 1 M to micelle formation. On the other hand, Villeneuve et al. [29] succeeded in clarifying the vesicle formation and vesicle–micelle equilibrium of anionic and cationic surfactant mixture by surface tension. It is therefore of interest to examine how the salting out and equilibrium between micelles and crystalline particles can be elucidated by surface tension.

The aim of the present study is to clarify the miscibility and interaction of SDS with NaCl in the adsorbed film, micelle, and crystalline particle by applying thermodynamic treatment of surfactant mixture to a NaCl–SDS mixture. The surface tension of aqueous solutions of the mixture was measured as a function of the total molality of the mixture and the mole fraction of SDS in the mixture over their wide ranges at 298.15 K under atmospheric pressure.

Experimental

Materials

SDS (Nacalai Tesque’s guaranteed reagent) was purified by recrystallizing it triply from water and twice from ethanol. Its purity was checked by no minimum on the surface tension vs. concentration curve around the CMC. The purified SDS was kept under a dried atmosphere and reduced pressure in a desiccator to prevent its hydrolysis. Sodium chloride is the same sample as that used in the previous study [10]. It was stored under a dried atmosphere in a desiccator. Water, deionized and distilled, was further purified by distilling it twice from dilute alkaline solution of potassium permanganate.

Measurements of surface tension

Equilibrium surface tension was measured by the drop volume technique previously described [30], as a function of the total molality of NaCl and SDS and the mole fraction of SDS in the mixture. Taking into account the dissociation of NaCl and SDS into ions in solutions, and are defined by

1

and

2

where m₁ is the molality of NaCl and m₂ the one of SDS. The density of aqueous NaCl solutions was used for the calculation of surface tension because the concentration of SDS is very low [31, 32]. A glass tip at which a solution drop is formed was weakly coated with dimethyl polysiloxane (Siliconize L-25, Fuji Systems, Japan) to give reproducible values of surface tension for anionic surfactants [33]. Temperature was kept at 298.15 K within 0.01 K by immersing the measuring cell in a water thermostat. The errors inherent in the measurement were less than 0.05 mN m⁻¹.

Determination of solubility

The aqueous solutions of a NaCl–SDS mixture became turbid at large and small . Figure 1 shows the surface tension γ vs. total molality curves for two typical at which turbidity takes place. The γ of transparent solutions decreases with increasing ; in sharp contrast, that of turbid solutions (solid circles) increases. Therefore, the lowest at which turbidity occurs was determined by a break on the γ vs. curve. Another break is observed on the curve of the higher at below the lowest , indicating the onset of micelle formation. Turbidity hence occurs in micellar solutions at higher and in monomeric solutions at lower . The solutions at concentrations far above the lowest became turbid within 20 min during its standing at 298.15 K in the water thermostat after preparation. However, the solutions at concentrations around the lowest were allowed to stand in the thermostat for 12 h before measurement so that equilibrium is reached because the lowest did not change after the aging of 12 h.

Fig. 1.

Surface tension vs. total molality curves at constant composition: , (2) 0.000214; filled circle turbid solution

Results and discussion

Surface tension and aggregate formation

Figure 2a shows the surface tension vs. total molality curves at constant for higher , and Fig. 2b shows those for lower including the results in Fig. 1. The γ vs. curves of single NaCl and SDS are in good agreement with those in previous studies [34–36]. The γ vs. curve of mixture changes its shape regularly with the change in and has one or two breaks indicating the onset of micelle formation and/or turbidity. The onset of turbidity, which is the formation of crystalline particle, is denoted by an arrow for each in Fig. 2b. The CMC of the mixture and the lowest to bring about turbidity, which we call critical particle concentration , were determined from the breaks in Fig. 2. The and are plotted as a function of in Fig. 3. The magnification in Fig. 3 shows that the vs. and vs. curves meet at . Micelles and particles coexist in equilibrium at the intersection; we denote the and at the intersection by and , respectively. It is noticed that the increases with decreasing below the ; however, it is almost constant above the . We will later examine the coexistence of micelles and crystalline particles at the for higher than the . The logarithm of CMC of SDS vs. logarithm of the counterion concentration obtained from the vs. curve, known as the Corrin–Harkins plot [1], gave a straight line below approximately 0.18 mol kg⁻¹ of the NaCl concentration. However, the vs. curve is more useful than the Corrin–Harkins plot because the former gives the composition of mixed micelle as shown later. The surface tension γ^C at the and γ^Pat the , taken from Fig. 2, are plotted against in Fig. 4. It is worth noting that γ^C decreases as decreases, in contrast, γ^P increases in the range of below the and remains almost constant above the , as depicted in the magnification.

Fig. 2.

Surface tension vs. total molality curves at constant composition: a, (2) 0.7893, (3) 5,826, (4) 0.3970, (5) 2,517, (6) 0.1303, (7) 0.0790, (8) 0.0315, (9) 0.0135, (10) 0; b, (2) 0.001997, (3) 0.001462, (4) 0.001050, (5) 0.0006592, (6) 0.0004569, (7) 0.0003699, (8) 0.0002894, (9) 0.0002136, (10) 0.0001582, (11) 0.0001257, (12) 0.0000992, (13) 0; filled circle turbid solution. Arrows show the breaks at the critical particle concentration

Fig. 3.

Critical aggregate concentration vs. composition curves: empty circle, filled circle

Fig. 4.

Surface tension vs. composition curves at critical aggregate concentration: empty circle γ^C, filled circle γ^P

Miscibility in the adsorbed film

The mole fraction of SDS in the adsorbed film is expressed by

3

where the surface density of NaCl is defined as that of chloride ion Cl⁻, and of SDS as of dodecyl sulfate ion DS⁻ [37]. Numerical values of were evaluated by applying

4

(refer to Appendix) to the vs. curves in Fig. 5. Here, the vs. curves were obtained by taking the values at a given γ from the γ vs. curves in Fig. 2, and is the dependence of mean activity coefficient of NaCl on defined by

5

Fig. 5.

Total molality vs. composition curves at constant surface tension: γ = (1) 40, (2) 50, (3) 60 mN m⁻¹; empty circle vs. , solid line vs.

The literature value of was used for the evaluation of [38]. To draw the phase diagram of adsorption, the values are shown in the form of vs. curve together with the vs. curve, in Fig. 5 [37]. is larger than unity at higher , which shows the negative adsorption of Cl⁻ by the definition of (Eq. 3). Therefore, we conclude that the mixed adsorbed film of SDS with NaCl at higher is composed of SDS, and adsorbed DS⁻ ions expel Cl⁻ ions from the adsorbed film. Figure 5 further exhibits that the electrostatic repulsion between DS⁻ and Cl⁻ is enhanced at higher γ because DS⁻ is less densely packed in the adsorbed film at higher γ. Such repulsion of coions by surfactant ions is also observed for the adsorbed film of a mixture of NaCl and dodecylammonium chloride (DAC) [8].

It is noticed that is smaller than unity at very small . The smaller than unity indicates that (1) NaCl and SDS are miscible in the adsorbed film, and (2) is positive due to enhanced adsorption of Na⁺ and highly weakened repulsion between DS⁻ and Cl⁻ in the adsorbed film. To show the miscibility in terms of surface density, we calculated the surface densities of individual ions by substituting the values of in Fig. 5 and the total surface density into the following equations:

6

7

and

8

where the surface density of sodium ion Na⁺ is given by

9

from electroneutrality condition and was evaluated by applying Eq. 26 in Appendix to the γ vs. curves in Fig. 1.

Figure 6 represents those surface densities as a function of at 40 mN m⁻¹. The gradual increase in with decreasing in the range of from 1 to approximately 0.002 is due to the electrostatic screening of the repulsion between the head groups of adsorbed DS⁻ ions by the presence of adsorbed Na⁺. On the other hand, the negative , the desorption of Cl⁻, in the range of from 1 to 0.04 shows the repulsion between DS⁻ and Cl⁻ in the adsorbed film. Furthermore, , which shows adsorbed DS^- is neutralized by Na⁺. Taking into consideration that Na⁺ adsorbs at the surface of an adsorbed film of a nonionic surfactant caused by ion–dipole interaction between Na⁺ and the polar head group of surfactant molecule [9, 11, 12], larger than at below 0.04 shows that Na⁺, after the neutralization, further adsorbs at the surface of the adsorbed film probably due to attractive interaction between Na⁺ and the sulfinyl groups in the head group of adsorbed DS⁻ [39]. Moreover, Fig. 6 shows that the excess adsorption of Na⁺ over the adsorption of DS⁻ is accompanied by the positive adsorption of Cl⁻ so as to satisfy the electroneutrality condition. Such positive adsorption of inorganic coions is also observed for the NaCl–dodecyldimethylammonium chloride system at large NaCl concentrations [7]. It is worth noticing that below , decreases with decreasing whereas and increase. The decrease in is probably due to the penetration of Na⁺ among the head groups of adsorbed DS⁻ [40–42] and/or the repulsion between the head groups of neutralized DS⁻ caused by the Na⁺ accumulated around the head groups of DS⁻ in the adsorbed film.

Fig. 6.

Surface density vs. composition curves at 40 mN m^-1: (1) , (2) , (3)

Miscibility in the aggregates

Miscibility of NaCl and SDS in the micelle can be examined by using the mole fraction of SDS in the micelle defined by

10

where and are respectively the excess numbers of NaCl and SDS in one micelle defined with respect to the spherical dividing surface around the micelle so as to make the excess number of water molecules zero [43]. The was numerically evaluated by applying

11

(refer to Appendix) to the vs. curves in Fig. 3.

Since crystalline particles in solutions are coagels of the hydrated multilayers with a stacked bilayer structure in equilibrium with the surrounding solution [44, 45] and the particle concentration is extremely small at the , particle formation can be treated in a manner similar to micelle formation using the excess number of NaCl and of SDS in one particle defined with respect to the dividing surface, which makes the corresponding excess number of water molecules zero. The mole fraction of SDS in the particle defined by

12

was calculated by applying

13

to the vs. curve below in Fig. 3. We depict the resulting and in the form of vs. and vs. curves, together with the vs. and vs. curves, in Fig. 7. Figure 7 can be called phase diagram of aggregate formation because it shows the relations between the composition of aggregates and solution at the critical aggregate concentration or . The finding that is larger than unity shows the expulsion of Cl⁻ from the micelle by DS⁻. In contrast, is smaller than unity and decreases with decreasing . We therefore conclude that sodium ions highly adsorb at the bilayer surfaces in a particle, like at the surface of the adsorbed film at extremely small .

Fig. 7.

Critical aggregate concentration vs. composition curves: (1) vs. , (2) vs. ; empty circle vs. , solid circle vs.

Comparison between the miscibilities in the adsorbed film and aggregate

The miscibilities in the adsorbed film and aggregate can be compared with each other by use of the phase diagram for adsorbed film–aggregate equilibrium. We have

14

for the adsorbed film–micelle equilibrium and

15

for the adsorbed film–particle equilibrium (refer to Appendix), where and are the and at the , respectively, and and are the corresponding ones at the .

The was calculated by applying Eq. 14 to the γ^C vs. curve in Fig. 4 and substituting the values in Fig. 7 and the values into Eq. 14. In a manner similar to the evaluation of , we obtained the numerical values of from the vs. curve. Figure 8 shows the and together with the and in the form of the surface tension vs. composition curves at the and . It is noticed that and . The former inequality stems from the fact that the ionic head groups of DS⁻ ions are less densely packed in the micelle than in the adsorbed film due to the difference in geometry between the adsorbed film and micelle. The latter one shows that the miscibility of NaCl and SDS in the adsorbed films of bilayers in a crystalline particle is larger than the corresponding one in the adsorbed film at water/air interface. Taking into consideration that the curvature effect on miscibility is negligible for the adsorbed films of the bilayers because the crystalline particles are much larger than the micelles, we can attribute the smaller than to larger adsorption of Na⁺ at the bilayer surfaces compared with the corresponding one at the bulk surface. The above view is substantiated by the fact evidenced on the foam films stabilized with SDS and with decyl methyl sulfoxide that the adsorption of Na⁺ at the surfaces of a Newton black film, a model of bilayer, is larger than the corresponding one of a thick film [17, 19–22].

Fig. 8.

Surface tension vs. composition curves at critical aggregate concentration: (1) γ^C vs. , (2) γ^C vs. , (3) γ^P vs. , (4) γ^P vs. ; empty circle γ^C of single SDS

The decrease in γ of micellar solutions with increasing in Figs. 1 and 2 can be explained by comparing the γ^C vs. curve in Fig. 8 with the γ^C vs. curve in Fig. 4. The corresponding increase in γ of turbid solutions with increasing at a given can be explained by comparing the γ^P vs. curve with the γ^P vs. curve because the two curves form a phase diagram of particle formation: A transparent solution at a given becomes turbid, and particles appear at the and further increase in the total molality at the causes an increase in the amount of particles and a decrease in the mole fraction of SDS in the solution surrounding the particles because the is larger than the and the increases with decreasing .

Equilibrium between the micelle and crystalline particle

Let us consider the micelle-particle equilibrium in solutions in the range of and shown in the magnification in Fig. 3. Mass balance relations are given by

16

for the total solutes and

17

for SDS, where and are the ascribed to the micelle and particle, respectively, and and are the and at the (see Fig. 7). As increases at a given above the (see the magnification in Fig. 3), a micellar solution becomes turbid at the where micelles are in equilibrium with an infinitesimal amount of crystalline particles, that is, . Eliminating the in Eqs. 16 and 17 and solving the resulting equation for at , we have the relation between and for the micellar solutions at :

18

Here is defined as at which micelles coexist with an infinitesimal amount of particles at equilibrium. Equation 18 expresses the vs. curve, one of the two micelle particle coexisting curves.

Further increase in at the causes the disappearance of micelles in the turbid solution at , the at which particles are in equilibrium with an infinitesimal amount of micelles, then we have . Eliminating the in Eqs. 16 and 17 and solving the resulting equation for at give

19

for the other coexisting curve vs. .

For the NaCl–SDS mixture, we obtain and from Fig. 3 and and from Fig. 7. Substitution of those values into Eqs. 18 and 19 leads to for a little larger than the because the is much smaller than the and . The experimental evidence shown in Fig. 3 that is almost in the range of above the is consistent with the requirement from Eqs. 18 and 19. Since micelle formation can be regarded as an appearance of macroscopic phases [46, 47], the number of degrees of freedom for the solutions of the present mixture in which micelles and particles coexist at equilibrium can be approximated to be two from the Gibbs phase rule. The experimental evidence at 298.15 K and atmospheric pressure in Fig. 4 that γ^P is almost constant at above the satisfies the requirement of phase rule.

In a future study, we will apply the present thermodynamic approach to a mixture of calcium chloride (CaCl₂) and SDS in which strong electrostatic attraction is expected between calcium ion and dodecyl sulfate ion in the adsorbed film and micelle, and the salting out will occur at around the bulk molar ratio CaCl₂/SDS = 1/2.

Conclusions

The thermodynamic treatment of surfactant mixture has been applied to the NaCl–SDS mixture. The miscibility of NaCl and SDS in the adsorbed film was clarified by the use of the phase diagram of adsorption. Sodium chloride and SDS are immiscible in the adsorbed film at higher due to the electrostatic repulsion between adsorbed dodecyl sulfate ion and chloride ion. On the other hand, they are miscible in the adsorbed film at lower probably due to ion–dipole interaction between sodium ion and the head group of neutralized dodecyl sulfate ion.

The miscibility has been compared between the adsorbed film and micelle by the use of the phase diagrams of adsorption and micelle formation. Sodium chloride and SDS are immiscible in the micelle. The difference in miscibility between the adsorbed film and micelle can be ascribed to their difference in geometry.

The salting out of SDS by NaCl has been clarified by measuring surface tension and treating the formation of crystalline particles in a manner similar to micelle formation. Judging from the phase diagram of aggregate formation, NaCl and SDS are miscible in the crystalline particle. The difference in miscibility between the adsorbed film and crystalline particle is attributable to the interaction between bilayer surfaces in the particle. The miscibilities in the adsorbed film, micelle, and particle coexisting at equilibrium were in the following order: particle > adsorbed film > micelle.

The equilibrium between micelles and particles in solutions has been thermodynamically considered by using the composition of micelle and particle at the . The coexisting curves in the range of a little larger than the were in good agreement with the experimental results. The experimental evidence that the surface tension at the coexistence remained almost constant irrespective of was in conformity with the requirement of the Gibbs phase rule.

From the above, the application of thermodynamic treatment of surfactant mixture to the NaCl–SDS mixture is confirmed to be useful.

Appendix

We apply the thermodynamic treatment of surfactant mixture [37, 43] to the NaCl–SDS mixture of which the aqueous solutions are nonideal [12]. The total differential of surface tension can be expressed for the mixture by

20

at constant temperature T and pressure p, where the surface densities of ions are defined with respect to the two dividing planes chosen so as to make the excess numbers of moles of water and air zero [48], is the electrochemical potential of j ion, and the mean chemical potential of component i. Here, the total surface density is defined by

21

Since the molality of the common ion Na⁺ is given by

22

we have

23

where and are the mean standard chemical potential and mean activity coefficient of i, respectively. Substituting the total differential of into Eq. 20 leads to

24

where denotes

25

The ideal version of Eq. 24 was derived in the previous studies [37, 48]. We assume that and , considering that our measurements range in concentration from 0 to 2.5 mol kg⁻¹ for m₁ and from 0 to approximately 10 mmol kg⁻¹ for m₂ [7]. We then obtain from Eq. 24

26

and

27

The equations for micelle formation corresponding to Eqs. 20 and 27 can be expressed by

28

and

29

respectively. Equation 20 can be written as

30

at the . Combination of Eqs. 28 and 30 and substitution of the total differentials of mean chemical potentials into the resulting equation give

31

The equations for crystalline particle formation can be derived in a manner similar to micelle formation.