ORIGINAL ARTICLE

Effect of Inorganic Additives on a Conventional Anionic–NonionicMixed Surfactants System in Aqueous Solution

Mehul Khimani • Sambhav Vora

Received: 18 January 2011 / Accepted: 28 April 2011 / Published online: 4 June 2011

� AOCS 2011

Abstract The interaction between an anionic surfactant

(sodium dodecyl sulfate) and a nonionic surfactant [poly-

oxyethylene (9.5) octyl phenyl ether] in aqueous salt

solution was investigated using the surface tension method.

The critical micelle concentration values were determined

for the individual surfactants and their corresponding

mixtures. The interaction parameter between the surfac-

tants in the mixed micelles, the activity and activity coef-

ficients in the mixed micelles, and the thermodynamic

parameters were calculated using various approaches, viz.,

Clint, Rubingh, and Maeda models. It was observed that

the critical micelle concentration of the mixed surfactants

system reveals little deviation from ideality.

Keywords CMC � Synergism � Interaction parameter �Activity � Activity coefficient � Mixed micelles �Thermodynamic parameters

Introduction

Surfactants are widely used in fields such as detergency [1],

cosmetics [2], pharmaceuticals [3], enhanced oil recovery

[4], etc. In many applications, binary mixture of surfactants

systems exhibit superior properties and are less expensive

than single unmixed surfactant systems. The abundant use of

mixed surfactant mixtures is of great importance for indus-

trial purposes as well as is a matter of curiosity for the

researchers to understand both the theoretical and practical

significance. Much investigation, articles, and research

papers have been published on the solution properties of

surfactant and mixed surfactants systems in the last three

decades [5–12]. A mixed surfactants system exhibits greater

surface activity, i.e., lower critical micelle concentration

(CMC) values, than that obtained with any of the individual

components of the mixture at the same concentration. Such

effect of the mixture is said to be synergistic. Synergism or

antagonism properties are often exhibited due to mixtures of

different types of surfactants [13–17]. The observed syner-

gism can be referred to as nonideal mixing, whereas the

antagonism property exhibits the repulsion between two

surfactants and the CMC is higher than the expected.

In the past, many studies [18, 19] reported that ionic single

alkyl chain compounds form spherical micelles. In 1936,

Hartley [20] described micelles to be spherical aggregates

whose alkyl groups form a hydrocarbon liquid-like core, and

polar groups which remain in contact with aqueous phase.

Later, with the development of novel-type surfactants,

micelles of different shapes and dimensions were encoun-

tered. The different geometries were found to depend gen-

erally on the structure of the surfactant, and also on

environmental conditions (e.g., concentration, temperature,

pH, electrolyte content). The associating self-assembly

structure plays a vital role in understanding the molecular

geometry and it is, thus, essential to study the actual packing

behavior of surfactant.

The addition of inorganic salts is known to modify the

properties of surfactant solutions, such as solubility, aggre-

gation numbers, shape of micelle, solute–solute and solute–

solvent interaction parameters, etc. In general, since inor-

ganic salts increase the ionic strength, the solubility of ionic

surfactant will be lower by ionic screening effects, resulting

in a greater tendency to form micelles at lower concentration,

i.e., decreasing of the CMC value. The addition of salt in

nonionic surfactants solution does not have drastic effects as

M. Khimani (&) � S. Vora

Department of Chemistry, Sir P.T. Sarvajanik College

of Science, Athwalines, Surat 395001, Gujarat, India

e-mail: khimani_mehul@yahoo.com

123

J Surfact Deterg (2011) 14:545–554

DOI 10.1007/s11743-011-1275-2

compared to the ionic surfactants [21, 22]. The CMCs of

nonionic surfactants are lowered by the addition of salts, but

not as much as that of ionic surfactants. In past research, the

decrease was explained in terms of the dehydration of

hydrophilic groups, namely, the salting out of the ethylene

oxide chains [23, 24]. However, it has been claimed that the

salting out of the hydrocarbon chains also contributes sig-

nificantly to the decrease in CMC [25, 26].

In this paper, we report an investigation of the physio-

chemical properties of anionic–nonionic surfactants, i.e.,

sodium dodecyl sulfate (SDS) and polyoxyethylene (9.5)

octyl phenyl ether (POEOPE), in a mixed surfactants sys-

tem, especially in the presence of inorganic salts. The

purpose of our study is to discover the interaction between

surfactant components in mixed systems as well as the

composition of micelles in the presence of salt. The final

aim is to design a suitable composition of the mixture for a

desirable surface activity and optimal behavior for a spe-

cific application [27]. To obtain information regarding the

interaction between surfactants as well as the composition

in mixed micelles, we are applying different approaches,

and the results of mixed surfactants system aggregation is

thoroughly discussed, along with appropriate explanation.

Materials and Methods

Materials

Surfactants, viz., SDS and POEOPE (commercially well

known as Triton X-100) were supplied from Fluka (Buchs,

Switzerland). Inorganic additives like sodium chloride,

sodium bromide, sodium fluoride, and magnesium chloride

hexahydrate were purchased from Merck, and all of them were

of analytical grade. These salts were recrystallized two to

three times using deionized triply distilled water before use.

The conductivity of water was measured with an Eutech

digital conductivity meter (CON 510), with an accuracy of

±1%. It was calibrated by 0.1 N KCl solution. The conduc-

tivity of the deionized triply distilled water was close to 10 lS.

Methods

Surface Tension

The surface tension of aqueous solutions of a surfactant

was measured by the drop weight method using a modified

stalagmometer [28].

Viscosity

The viscosity measurements were carried out using a

Ubbelohde capillary viscometer suspended vertically in a

thermostatic water bath at 30 �C. The flow time of water

was always found at 200 S at the same temperature. All

binary mixtures of surfactant solution showed Newtonian

flow and no kinematic correction was introduced [29].

Theoretical Background

Clint Model

The Clint model is useful for understanding the ideal

behavior of binary surfactant systems [29, 30]. The ideal

CMC values for the mixed surfactants system (C12) can be

calculated more precisely using Clint’s theoretical concept

and the following equation:

1

C12

¼ a1

C1

þ ð1� a1ÞC2

ð1Þ

where C12, C1, and C2 are the CMC values of the mixture,

surfactant 1, and surfactant 2, respectively. a1 is the mole

fraction of surfactant 1 and a2 (i.e., 1 - a1) is the mole

fraction of surfactant 2, individually, in solution.

Regular Solution Theory

The regular solution theory (RST) is the simplest and most

used approach for the mixed surfactants systems. Formally,

the model was used only for nonionic surfactants, but the

approach was also applicable for understanding the

behavior of a binary mixture with ionic surfactants.

The value of the interaction parameter (bRST) is only true if

the excess entropy of mixing equals zero. Thus, the mixing

energy, i.e., the excess heat of mixing, is characteristic and

nonzero. In some cases, calorimetry study of the binary

surfactant system shows different mixing energies com-

pared to RST. If the approach is acceptable for nonideal

mixing behavior, the interaction parameter should be

invariable for every composition. However, for mixed

surfactants systems the value of bRST varies with the

solution composition. These variations in the bRST value

may exist either due to experimental error during mea-

surement of the CMC or limitations of the model. Further,

larger bRST values indicate that the RST model has some

limitations in describing nonideal mixing behavior [31–

33]. Therefore, an alternative model has been proposed by

Rubingh. The model is known as Rubingh’s regular solu-

tion theory.

Rubingh Model

Rubingh [34, 35] developed a model based on RST that is

applicable to focus on the interaction between any two

mixed surfactants system. In most cases, the experimental

546 J Surfact Deterg (2011) 14:545–554

123

CMC of the mixed surfactants system is intermediate in

value between those of the two individual components. In

some cases, the binary surfactant system CMC exhibits a

lower value than either of the two individual components,

i.e., results in synergism. In other cases, the mixed CMC

values of the system of two surfactants may be higher than

the two individual surfactants, in a so-called antagonism.

The interaction parameter (b12) and mole fractions of

component in mixed micelles (X1) are important in this

model. Calculating the values of these two parameters

helps us to predict the interaction or repulsion between the

two surfactants and the mole fraction of surfactant 1 in the

mixed micelles. Negative values of b12 indicate that there

is some synergism between the two surfactants. The

experimental CMC value in this case will be lower than

Clint’s ideal CMC values. A positive value of b12 denotes

the antagonism between the two surfactants. Here, the

experimental CMC will be higher than Clint’s ideal CMC

values. b12 values near to zero reveals that there is little

interaction between the two surfactants and the experi-

mental CMC is close to the ideal value. The theoretically

developed model is as follows.

The chemical potential of the ith surfactant monomer in

the bulk of a mixed micellar solution can be written as

[35]:

li ¼ l0i þ RT ln CM

i ð2Þ

where l0i is the standard chemical potential and CM

i is the

concentration of monomeric surfactant i in the bulk. In the

mixed micelles, the chemical potential of the component

i can be written as:

lMi ¼ l0

i þ RT ln Ci þ RT ln fiXi ð3Þ

where Ci, fi, and Xi are the CMC of pure surfactant i, the

activity coefficient, and the mole fraction of surfactant i in

the mixed micelles, respectively. In the case of ideal

behavior, the value of the activity coefficient is 1. Since at

equilibrium li ¼ lMi ; the monomer concentration can be

written as:

CMi ¼ XifiCi ¼ aiC12 ð4Þ

where C12 is the mixed CMC and ai is the mole fraction of

surfactant i in the bulk. Now, for a binary surfactant

system, the mixed CMC can be represented as:

1

C12

¼X2

i¼1

ai

fiCið5Þ

In the case of binary nonideal mixtures, the activity

coefficients of the components can be expressed as [35]:

f1 ¼ exp b12ð1� X1Þ2 ð6aÞ

f2 ¼ exp b12X21 ð6bÞ

where b12 is an interaction parameter which indicates the

interaction between the two surfactant molecules in the

mixed micelles and is a measure of deviation from the ideal

behavior. The micellar mole fraction X1 can be calculated

by solving iteratively the following equation:

X21 lnða1C12=X1C1Þ

ð1� X1Þ2 lnðð1� a1ÞC12=ð1� X1ÞC2

¼ 1 ð7Þ

b12 can be now calculated by substituting the value of X1 in

the equation below:

lnða1C12=X1C1Þð1� X1Þ2

¼ b12 ð8Þ

The b12 parameter quantitatively captures the extent of

nonideality for a mixed surfactants system.

Maeda Model

Maeda’s model [36] is applicable to ionic–nonionic mixed

systems with moderately high ionic strength, where short-

range electric interaction is no longer negligible. There lies

a difference of this model from the RST, where only the

long-range electric interaction plays an important role in

the mixed system, whereas the Rubingh approach was

based on only head–head interaction between two surfac-

tants [37]. However, according to Ruiz and Aguiar [38] and

Maeda [36], chain–chain interactions are also present for

mixed surfactants systems. Maeda’s model [36] considered

both types of interaction, i.e., head–head as well as chain–

chain. The model assumes the decrease in repulsion among

the ionic head groups in anionic–nonionic mixed micelles

due to the presence of nonionic surfactant molecules in the

micellar phase. The proposed equation for free-energy

change due to the micellization process as a polynomial

function of X1 is as follows:

DG0Ma ¼ RTðB0 þ B1X1 þ B2X2

1Þ ð9Þ

B0 ¼ ln XCMCðNÞ ð10Þ

B1 þ B2 ¼ lnXCMCðIÞXCMCðNÞ

� �ð11Þ

B2 ¼ �b12 ð12Þ

where B0 is an independent term related to the CMC of the

nonionic surfactant, B1 and B2, expressed in the mole

fraction scale as XCMC(N) and XCMC(I), are related to the

CMC of the nonionic and ionic surfactant, respectively. B1

is chain–chain interaction parameter, related to the

standard free-energy change due to the replacement of a

nonionic monomer in the nonionic pure micelle by an ionic

J Surfact Deterg (2011) 14:545–554 547

123

monomer. B2 is the interaction parameter in the micellar

phase obtained from Eq. 8. In addition, the activity

coefficients (aM1 and aM

2 ) in the mixed micelles are

calculated using the following expressions [39, 40]:

aM1 ¼ f1X1 ð13Þ

aM2 ¼ f2 1� X1ð Þ ð14Þ

Thermodynamic Parameters of Micellization

As per our earlier discussion, the RST approach assumes

that the excess entropy of mixing is zero (SE) and the value

of the excess entropy of mixing is the same as the ideal

(DSE = DSideal). According to the RST model, the excess

entropy of mixing and ideal enthalpy (DHideal) are equal to

zero; therefore, the relation between excess free energy

(GE), excess enthalpy (HE), and enthalpy of micellization

(DHM) is written as follows [41]:

GE ¼ HE ¼ DHM ¼ RTX2

i¼1

Xi ln fi ð15Þ

Excess free energy of micellization represents a deviation

from ideality GE ¼ DGM � DGidealM

� �: However, the free

energy of ideal mixed micellization can be expressed as

[42]:

DGidealM ¼ RT

X2

i¼1

Xi ln Xi ð16Þ

Therefore, the free energy of micellization (DGM) is [41]:

DGM ¼ RTX2

i¼1

Xi ln Xifi ð17Þ

From Eqs. 15 and 17, the entropy of micellization can be

calculated as [43]:

DSM ¼HM � GM

Tð18Þ

Results and Discussion

The CMC values of pure SDS, POEOPE, and their mix-

tures in 0.5 M aqueous salt solutions were determined by

the drop weight method and are graphically presented in

Figs. 1 and 2. Clear break points (at CMC) were observed

in the drop weight method plots, indicating the initiation of

the micellization phenomenon.

CMC values for the mixed system (CMC12), mole

fraction of micelle (X1), interaction parameter (b12),

activity coefficients in the monolayers (f1 and f2), and the

activity coefficients in the mixed micelle (aM1 and aM

2 ) are

reported in Table 1. Generally, ionic surfactants have a

Fig. 1 Surface tension (c) versus Log C(M) for pure sodium dodecyl

sulfate (SDS), polyoxyethylene (9.5) octyl phenyl ether (POEOPE),

and their mixtures in 0.5 M NaCl at 30 �C. The insert shows surface

tension (c) versus Log C(M) for pure SDS, POEOPE, and their

mixtures in 0.5 M NaF at 30 �C. Plus signs POEOPE; open squares0.2 SDS; crosses 0.4 SDS; stars 0.6 SDS; asterisks 0.8 SDS; opencircles SDS

Fig. 2 Surface tension (c) versus Log C(M) for pure SDS, POEOPE,

and their mixtures in 0.5 M NaBr at 30 �C. The insert shows surface

tension (c) versus Log C(M) for pure SDS, POEOPE, and their

mixtures in 0.5 M MgCl2�6H2O at 30 �C. Plus signs POEOPE; opensquares 0.2 SDS; crosses 0.4 SDS; stars 0.6 SDS; asterisks 0.8 SDS,

open circles SDS

548 J Surfact Deterg (2011) 14:545–554

123

higher CMC than nonionic surfactants [44] because of their

charge density, which results in electrostatic repulsion

between their head groups. It is generally accepted that the

ethoxylated chains of the nonionic surfactant (POEOPE) is

wrapped around the charged head groups of the anionic

surfactant (SDS), thus, screening the electrostatic repulsions

and, thereby, favoring the micelle formation and decreasing

the CMC [45]. It has been reported that the added inorganic

salts are also responsible for the reduction in the CMC [46].

On the addition of high concentrations of inorganic salts,

electrostatic repulsion between the polar head group of ionic

surfactant will decrease with increasing ionic strength of the

aqueous medium due to increased sufficient shielding of the

electrostatic repulsion by the ionic atmosphere around each

charged site [47, 48]. Therefore, the charge on the micellar

head group becomes neutralized either due to the added salt

or due to the ethylene oxide chain present in nonionic sur-

factant [49]. Hence, at lower mole fractions of anionic sur-

factant, the interaction between these two surfactants are

higher, as well as the addition of salt also responsible for

lowering the CMC than pure nonionic surfactant, which

correlates well with our findings (Table 1).

It was found from Table 1 that the �b12 value obtained

for all systems is small, which indicates little deviation

from ideality [9]. The value of interaction parameter b12

decreases with an increase in ionic surfactant due to the

repulsion between head groups, as discussed earlier. The

values of activity coefficients (f1 and f2) at 0.6 and 0.8 mol

fraction is close to 1, which reveals ideal behavior of the

surfactants in the mixed system [50, 51]. From Fig. 3, we

observe that the experimental CMC values for mixed sys-

tems are lower than the ideal behavior (calculated by

Clint’s method). Also, the negative deviation from ideality

confirms a constitutional interaction between the two sur-

factants in the binary mixture. Figure 4 shows that, at

a = 0.2 and 0.4, the mixed micelles (X1) are sufficiently

rich in SDS content, whereas at 0.6 and above, they

become almost equal.

Rathman and Scamehorn [52] developed localized and a

mobile adsorption model on the basis of electrostatic

Table 1 Displayed micellization parameter values of sodium dodecyl sulfate (SDS), polyoxyethylene (9.5) octyl phenyl ether (POEOPE), and

their mixtures in the presence of the different electrolytes

aSDS CMC12 (mM) Ideal CMC (mM) X1(SDS) Xideal b12�b12

f1 f2 aM1 aM

2

SDS ? POEOPE in 0.5 M NaF

0 0.25 -0.47

0.2 0.23 0.27 0.24 0.12 -1.07 0.54 0.93 0.13 0.70

0.4 0.28 0.30 0.30 0.27 -0.38 0.83 0.96 0.25 0.67

0.6 0.31 0.34 0.46 0.45 -0.29 0.91 0.93 0.42 0.50

0.8 0.37 0.38 0.68 0.69 -0.13 0.98 0.94 0.67 0.29

1 0.44

SDS ? POEOPE in 0.5 M NaCl

0 0.35 -0.67

0.2 0.29 0.37 0.25 0.15 -1.41 0.45 0.90 0.11 0.67

0.4 0.33 0.40 0.36 0.32 -0.80 0.72 0.89 0.26 0.56

0.6 0.39 0.43 0.51 0.51 -0.30 0.92 0.92 0.47 0.44

0.8 0.44 0.46 0.72 0.73 -0.18 0.98 0.90 0.71 0.25

1 0.50

SDS ? POEOPE in 0.5 M NaBr

0 0.56 -0.72

0.2 0.44 0.58 0.28 0.16 -1.55 0.45 0.88 0.12 0.63

0.4 0.50 0.61 0.39 0.34 -0.86 0.72 0.87 0.28 0.53

0.6 0.59 0.64 0.53 0.54 -0.29 0.93 0.91 0.50 0.43

0.8 0.65 0.67 0.74 0.76 -0.17 0.98 0.90 0.73 0.23

1 0.70

SDS ? POEOPE in 0.5 M MgCl2�6H2O

0 0.33 -0.87

0.2 0.26 0.35 0.26 0.15 -1.72 0.40 0.87 0.11 0.63

0.4 0.31 0.37 0.36 0.36 -0.80 0.71 0.89 0.25 0.57

0.6 0.39 0.40 0.51 0.51 -0.08 0.98 0.97 0.50 0.47

1 0.47

J Surfact Deterg (2011) 14:545–554 549

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approach to describe the binding of counterions. For ionic

and nonionic mixed surfactants, micelles are mainly com-

posed of nonionic surfactants at lower ionic counterparts. A

localized adsorption model is preferred, when the counte-

rions adsorb or bind onto the charged hydrophilic head

groups on the micelle. However, it is difficult to know the

exact distinction between the bound and free counterions; it

depends on the technique and adsorption model utilized.

We interpret the effect of anions on the binding of cationic

counterion.

The position of an anion in a Hofmeister series is related

with the hydrated radius. Anions with a small ion have

higher hydrated radius (F- = 0.352 nm, Cl- = 0.332 nm,

Br- = 0.330 nm), as well as higher lyotropic number

(F- [ Cl- [ Br-). Thus, it can be postulated that a higher

lyotropic number has probably hindered the counterion

(Na?) binding. However, in higher ionic strength aqueous

solutions, a greater number of counterions bind to the

micelle surfaces (which promote a decrease in CMC); thus,

the swamping of higher lyotropic numbers of electrolytes is

not as effective as compared to those with lower lyotropic

numbers. Hence, NaF exhibits more ideal behavior than

NaCl. This behavior is also observed in the interaction

parameter from Table 1. It can be further observed that the

trend of CMC values by adding electrolytes is NaF \ -

NaCl \ NaBr. The addition of the same salt concentration

of NaCl and MgCl2�6H2O has no apparent effect on the

value of b12 [53].

In Maeda’s approach, which is based on the phase

separation model, the thermodynamic stability is described

by Gmic, which is given as a function of the mole fraction

of the ionic component in the mixed micelle. Its calculation

was carried out by using Eqs. 9–12 and is listed in Table 2.

According to Maeda [36], the CMC of mixed surfactants

systems are lower than the CMC of nonionic surfactants

due to the entry of ionic species into nonionic micelles,

thus, the B1 value is negative and vice versa. It was

Fig. 3 Plot of critical micelle concentration (CMC) value versus

aSDS for all systems at 30 �C. Squares NaF; asterisks NaCl; trianglesNaBr; circles MgCl2�6H2O. The dark lines are the ideal CMC values

calculated by the Clint equation and the dotted lines are the

experimental CMC values

Fig. 4 The micelle mole

fraction of SDS (XRST) in mixed

micelles for all systems at 30 �C

a NaF, b NaCl, c NaBr, and

d MgCl2�6H2O. The dark linesrepresent regular solution theory

(RST) and the dotted linesindicate the ideal state (Xideal)

by applying Clint’s equation

550 J Surfact Deterg (2011) 14:545–554

123

observed from Table 2 that the B1 values which are ini-

tially negative at low mole become positive as the SDS

concentration increases. This indicates that the chain–chain

interaction is initially stronger and became weaker with

higher SDS concentration, which makes mixed micelles

less stable (this is also reflected by DGm values).

The values of different thermodynamic functions at 30 �C

are calculated from the experimental data and are presented

in Table 2. The difference in DG values can be attributed to

the fact that Maeda’s approach uses the mole fraction,

whereas thermodynamic calculation (Eq. 17) requires the

activity coefficient. According to thermodynamics, the

conditions for spontaneous process are DG \ 0, DH \ 0,

and DS [ 0. It can be observed from Table 2 that the free

energy of micellization appears to be negative, which favors

the mixed micelles formation. Figure 5 also provides some

information about the micelle formation and its stability. It is

observed from Fig. 5 that there is a large deviation at 0.2 mol

Table 2 Values of the thermodynamic parameters and Maeda model for SDS, POEOPE, and their mixtures in the presence of the different

electrolytes

aSDS Maeda model Thermodynamic parameter

B0 B1 B1 (avg.) B2 = -b12 DGMa (KJ/mol) DGM (KJ/mol) DHM (KJ/mol) DSM (J/mol)

SDS ? POEOPE in 0.5 M NaF

0 -1.38 0.1

0.2 -0.5 1.07 -3.62 -1.91 -0.50 4.65

0.4 0.20 0.37 -3.24 - -0.19 -

0.6 0.28 0.29 -2.99 -1.92 -0.18 5.73

0.8 0.45 0.12 -2.56 -1.64 -0.07 5.19

1

SDS ? POEOPE in 0.5 M NaCl

0 -1.03 -0.33

0.2 -1.07 1.41 -3.07 -2.13 -0.68 4.75

0.4 -0.46 0.8 -2.75 -2.12 -0.47 5.46

0.6 0.03 0.3 -2.35 -1.93 -0.19 5.75

0.8 0.16 0.18 -2.07 -1.57 -0.09 4.90

1

SDS ? POEOPE in 0.5 M NaBr

0 -0.57 -0.49

0.2 -1.32 1.55 -2.07 -2.28 -0.79 4.93

0.4 -0.63 0.86 -1.74 -2.20 -0.51 5.55

0.6 -0.07 0.29 -1.32 -1.92 -0.18 5.73

0.8 0.05 0.17 -1.10 -1.51 -0.08 4.72

1

SDS ? POEOPE in 0.5 M MgCl2�6H2O

0 -1.09 -0.40

0.2 -1.38 1.72 -3.36 -2.35 -0.86 4.90

0.4 -0.47 0.80 -2.91 -2.11 -0.47 5.43

0.6 0.26 0.08 -2.45 -1.79 -0.05 5.75

1

Fig. 5 Excess Gibbs free energy of micellization versus mole

fraction of SDS for all systems at 30 �C. Squares NaF; asterisksNaCl; triangles NaBr; circles MgCl2�6H2O

J Surfact Deterg (2011) 14:545–554 551

123

fraction, thus, indicating that micellization is more favorable

at this mole fraction and that mixed micelles are more stable.

Then, it decreases due to increasing repulsion between the

anionic hydrophilic head groups.

Ruiz and Aguiar [43, 54] reported that hydration plays a

vital role on the stability of mixed micelles. Therefore, the

hydration of mixed micelles increases with more ionic

component in the micelle, as more hydrated formed structure

increases the stability of mixed micelles. Nevertheless, an

opposite behavior was observed when the nonionic surfac-

tant POEOPE was used [38]. The difference was attributed to

the open structure of POEOPE. The mixed micelles have

more open arrangements, so that the penetration of water is

more favorable. From Table 1, it can be observed (see X1)

that the contribution of POEOPE in the case of 0.2 mol

fraction is more than that of the ionic surfactant. Hence, at

that mole fraction, the micelles are more hydrated and more

stable. This can also be ascribed from the lowest entropy

value (and most negative DGm). At ionic surfactant mole

fractions 0.4 and 0.6, the hydration stability of micelle

decreases because the POEOPE participant reduces the

entropy increase. At the 0.8-mol fraction, the repulsion

between head groups is essentially due to high electrical

charge density. Thus, the penetration of water molecules is

more than that of the 0.6-mol fraction and the micellar

structure becomes more hydrated then stability increasing.

Therefore, the entropy of micellization decreases.

In lower concentrations, surfactant molecules aggregate

to form micelles with an aggregation of 50–100 monomers.

Mostly, these micelles have spherical shape with low vis-

cosity. On the addition of additives (i.e., inorganic salts and

organic salts), increasing concentration of surfactant

solution, increasing temperature, increasing alkyl chain

length, and increasing the counterion all grow the micelles

and change its shape from spherical to cylindrical, rod, or

bilayer. In general, with a surfactant having a high solu-

bility in aqueous medium, there is no change observed in

the viscosity; thus, the micelles formed are small and

spherical. SDS with Li? and Na? counterion do not show

sufficient growth, whereas K? and Cs? results in a sudden

change in the micellar shape. Pure nonionic surfactant with

shorter EO (4–6) unit dramatically changes the micellar

growth, while 8 or more EO units have an insignificant

effect [27]. In our experiments, the viscosities of surfactant

solutions in mixed systems were examined at 30 �C. All of

the measurements were made above the CMC. Figure 6

shows that there was no apparent change in the relative

viscosity by adding 0.5 M NaCl and NaF, indicating that

the micelles do not lose their symmetry [55].

Conclusions

The effect on critical micelle concentration (CMC) as well

as other micellar parameters by the addition of inorganic

salts in mixed surfactants systems are described below:

1 The mixed surfactants systems of sodium dodecyl

sulfate (SDS) and polyoxyethylene (9.5) octyl phenyl

ether (POEOPE) in different mole fractions reveal the

nonideal behavior in 0.5 M aqueous salt solutions. The

synergism is larger at 0.2 SDS mole fraction.

2 Due to the large amount of inorganic salt concentration,

the value of the interaction parameter b12 slightly

decreases because the salt ions surround the anionic

surfactant head and further weaken it.

3 The order of CMC increase is as follows:

NaF \ NaCl \ NaBr.

4 The activity coefficient of the binary mixture is greater

at 0.2 and 0.4 mol fractions, demonstrating that the

micelles are rich in SDS, and that above 0.6, it comes

closer to the standard state in the mixed micelle.

5 Viscosity data give evidence that micelles do not lose

their symmetry at 0.5 M concentration.

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Author Biographies

Mehul Khimani completed his M.Sc. in physical chemistry in 2008

and is pursuing his doctoral research work.

Sambhav Vora was awarded his doctorate at Veer Narmad South

Gujarat University (VNSGU). He is currently an assistant professor at

the Department of Chemistry, Sir P.T. Sarvajanik College of Science,

Surat. He has published several research papers. His research area of

interest is in surfactant science and adsorption.

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