Experimental Study of Surface and Solution Properties of Gemini -conventional Surfactant Mixtures on Solubilization of Polycyclic Aromatic Hydrocarbon

doi:10.4236/mnsms.2013.34B004

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Modeling and Numerical Simulation of Material Science, 2013, 3, 17-25

doi:10.4236/mnsms.2013.34B004 Published Online October 2013 (http://www.scirp.org/journal/mnsms)

Experimental Study of Surface and Solution Properties of

Gemini -conventional Surfactant Mixtures on

Solubilization of Polycyclic Aromatic Hydrocarbon

M. Kamil*, Huma Siddiqui

Department of Petroleum Studies, Aligarh Muslim University, Aligarh-202002, India

Email: *[email protected]

Received May, 2013

ABSTRACT

Experimental data are presented on the enhanced solubilities of fluorene (FLR) resulting from solubilization in aqueous

solutions of t wo co nventio nal sur factan ts: catio nic cet yltri me thyla mmonium bromide (CTAB) , anionic sodium dodecyl

sulfate (SDS), nonioinic polyethylene glycol dodecyl ether (Brij35) and a cationic gemini bis (hexadecyldimet hylam-

monium) pentane dibromide (G5). The critical micellar concentration of surfactants was determined by surface tension

meas urement s and aque ous sol ubilitie s of fluor ene co mpound in surfactant solutions were measured spectrophotometr-

ically. Solubilization of PAH compound commenced at the surfactant critical micelle concentration and was propor-

tional to the concentration of surfactant in micelle. The results of the mixed systems were analyzed with the help of

regula r so luti on t heor y, in whi ch the d ev iatio n of CMC exp values for mixed sur facta nt s yst ems fr om C MCideal was mea s-

ured by evaluating the interaction parameter, βm. Negative values of βm were observed in all equimolar binary systems

which show synergism in the mixed micelle. Attraction force between two oppositely charged head groups lead the

strongest synergism effect between cationic gemini and anionic conventional surfacta nt. I n ad dition to mola r sol ubiliz a-

tion ratio (M SR) so lub iliz ation efficiency is also q uantified in terms of micelle-water partition co e fficient (Km).

Keywords: Gemi ni Surfactants; PAH s; Solubil iz ation; Mixed micelle; Solution Prop e r ties

1. Introduction

Hydrophobic organic contaminants (HOCs) are found in

the priority list of hazardous substances as listed by the

EPA and the agency for toxic substances and disease

registry of USA [1]. The hrdrophobicity of these conta-

minants is one of the factors that determine the fate of the

contaminant in the environment. Contamination of soil

and underground water by persistent organic pollutant is

a major environmental concern. Polycyclic aromatic hy-

drocarbons (PAHs) are one class of such pollutant s. T he y

are made of two or more fused benzene rings formed

mainly from the combustion of fossil fuels and are al-

ways found as a mixture o f individual compounds. T hey

are of special interest because (i) they are known or sus-

pected carcinogens or mutagens and (ii) they strongly

adsorb to soil sediments making them persist in the soil

for extended periods of time [2-7]. As a consequence,

remediation of PAHs in soil–water system is often de-

pendent on desorption of the contaminant from the soil

surface and its subsequent incorporation into the bulk

aqueous phase. In addition, owing to their low aqueous

solubility a nd low vap or pr essure, the ir removal from the

environment water and soil still presents a considerable

challenge to researchers involved in separation technol-

ogy. One promising technique, surfactant enhanced sub-

surface remediation (SESR) has emerged in which the

solubility of organic solutes is greatly enhanced by the

presence of surfactant micelles [8-13]. Micelles are

self-association of surfactant molecules with the surfac-

tant hydrophobic portion oriented towards the center of

the aggregates a nd the h ydrophilic p ortions lo cated at the

aggregate surface and facing the solvent molecules. The

central core of the micelle thus constitutes a hydrophobic

pseudo phase that may accommodate a certain amount of

a lipophilic solubilizate, resulting in an enhancement of

its solubilization. To get a better system, mixed micellar

systems have already been used for the significant en-

hancement of water solubility of poorly soluble organic

contaminants. Mixed surfactants improve the perfor-

mance of surfactant –enhanced remediation of soils and

sediments by decreasing the applied surfactant level and

thus its cost.

Conventional surfactant molecules are composed of a

long hydrophobic hydrocarbon tail with an ionic or polar

*Corresponding author.

M. KAMIL, H. SIDDIQUI

hydrophilic head. Gemini surfactants are made up of two

hydrocarbon tails and two ionic head groups connected

by a ‘spacer’ in the sequence: hydrocarbon tail / ionic

group / spacer / ionic group / hydrocarbon tail [14]. The

spacer can be attached directly to the identical ionic

groups, each of which is in turn bonded to an identical

hydrocarbon tail; alternatively, the two identical amphi-

philes are joined midway. Their various surface active

properties are superior to those of corresponding conven-

tional surfactants with one hydrophilic and one hydro-

phobic group. Thus, they have much lower CMC values

and are more efficient in lowering the surface tension of

water. As a result, the Gemini surfactants form larger

micelles than the conventional surfactants and thus

should have a better solubilizing capacity [15-16].

Thus in the open literature, only few studies are re-

ported on solubilization of PAHs in Gemini-conventional

mixed surfact ant s ystems are available. The objectives of

the present study are: (i) to compare the efficiency of few

Gemi ni-conventional mixed surfactants in enhancing the

water solubility of Fluorene and (ii) to have the idea

about the synergistic solubilizatio n of Fluorene by mixed

suefactant systems. This experimental study is aimed to

ascertain if a mixed surfactant solution may be used in

the SER of organic pollutants. In this study, we have

studied interfacial properties and molecular interactions

of individual as well as equimolar binary mixtures of

cati onic gemini and c onventional surfactants.

2. Experimental

2.1. Materials Used

The surfactants cetyltrimethyl ammonium bromide

(CTAB), sodium dodecyl sulphate or sodium lauryl sul-

phate (SDS), and polyethylene glycol dodecyl ether ( Brij

35) were purch ased fr om S igma Al drich an d us ed as re-

ceived. Gemini surfactant pentanediyl-1,5-bis (dimethyl-

cetylammonium bromide), abbreviated as G5 was syn-

thesized in the research laboratory of the Department of

Chemistry, AMU, Aligarh. Synthesis of gemini’s entail

reﬂuxing of 1,6-dibromohexane with N, N- di methylce-

tylamine (molar ratio 1:2.1) in dry ethanol. For maxi-

mum bisquaternization continuous stirring at 80°C is

done for 48 h to ensure as much as possible a complete

bisquaternization. The progress of the reaction was mo-

nitored by using TLC technique. The solvent was re-

moved under vacuum after the completion of the reac-

tion.

Fluorene was used as polycyclic aromatic hydrocarbon

in the present work and was also procured by sigma Al-

drich chemical company. Surfactant solutions were pre-

pared in double distilled water. Structures of above

chemicals are shown in Figure 1.

2.2. Methods

2.2.1. Critical Micelle Concentration Determination

by Surfa c e Te nsion Measureme nts

For CMC determination tensiometric experiments were

performed for single as well as for mixed surfactant sys-

tems. The apparatus used for the purpose was Hardson

tensiometer (Hardson make Kolkata, India), which works

on ring detachment method. The vertically hung ring was

initially dipped in the surfactant solution to measure its

surface tension. It was then forced to pull out from the

solution. The required force which was applied to pull

out the ring from the solution is its surface tension. Ex-

periments were repeated twice for each surfactant to en-

sure the reproducibility of the results. The surface tension

versus log [surfactant] plots for individual and mixed

surfa ctant syste ms are s hown in Figures 2 and, 3 respec-

tively. The concentration at which inflexion in curve is

obtained is the CMC of that substance.

Figure 1. Structures of reagents used in the stu dy polyethylen e glycol dodecyl ether (B rij 35), cetyltri methyla mmoni um bro-

mide (CTAB), sodium lauryl sulphate (SDS), gemini sur factant ( G 5), and fl uorene.

M. KAMIL, H. SIDDIQUI

-6.2 -6.0 -5.8 -5.6-3.6 -3.4 -3.2 -3.0 -2.8

Log [surfactant] (mM)

Surface Tension (mNm-1)

Brij35

CTAB

-5.5 -5.0 -4.5-0.50.00.51.0

Surface Tension (mN m -1)

Log [surfactant] (mM )

SDS

Figure 2. Surface tension versus. log [surfactant] plots for single surfactant systems.

-5.8 -5.6 -5.4 -5.2 -5.0 -4.8 -4.6 -4.4 -4.2

Surface Tension (mN m -1)

Log [surfactant] (mM)

G5-BR IJ35

G5-CTAB

G5-SDS

Figure 3. Surface tension versus log [surfactant] plots for

G5/conventional mixed surfactant systems.

2.2.2. Solubilization Ex pe riment s

Solubility of Fluorene in surfactant system was deter-

mined by solubilization experiments. Solutions of con-

centration higher than their corresponding CMC were

prepared. These solutions were then filled in borosilicate

screw-capped glass vials of capacity of 5 ml with an

excess amount of Fluorene. Extra amount of Fluorine

was added to ensure maximum solubility in surfactant

solution. These samples are then agitated on magnetic

stirrer for a period of 24 h at 30°C. To ensure good agita-

tion magnetic teflon pieces were also dropped in each

vial. After this, a portion of the samples are collected in

eppendorf tubes and centrifuged at 12000 rpm, using a

high speed micro centrifuge (REMI, RM-12C) to settle

do wn the und issol ved F luore ne. T he co ncentr ation o f the

solubilized Fluorine of centrifuged sample was deter-

mined spectrophotometrically using Shimadzu spectro-

photometer (model UV mini-1240), following by appro-

priate dilution of a sample of the supernatant with the

corresponding surfactant solution. Before taking spectra

baseline correction was done with the surfactant solution

of same concentration.

3. Results and Discussion

3.1. Critical Micelle Concentration

The surfactant concentration at which monomers begin t o

assemble in ordered, colloidal aggregates or micelle is

termed as critical micelle concentration (CMC or cmc).

The CMC values of pure as well as of binary surfactant

mixtures (cmcexp) were evaluated on the basis of tensi-

ometric measurements. Surface tension decreases as the

concentration of the surfactant increases. Surfactant mo-

lecules at low concentrations adsorb at the liquid/air in-

terface until the surface of the solution is completely oc-

cupied. Then the excess molecules tend to self-associ- ate

in the solution to form micelles, and surface tension be-

comes constant. Two opposite effects control micelliza-

tion: the effect of the hydrophobic group is an important

driving force in micellization and the effect of the hy-

drophilic group opposing it. The cmc values were deter-

mined by noting inflections in the surface tension (γ)

versus logarithm of surfactant concentration isotherms

and are given in Table 1. The gemini surfactant has re-

markably low cmc value as compared to the co nventional

surfactants because of its two polar head groups and two

hydrophobic chains which transfer at the same time from

the aqueous phase to micellar phase.

M. KAMIL, H. SIDDIQUI

3.2. Inter facial P roper ti es

The surface properties such as max

Γ (the maximum

surface excess), Amin (the minimum surface area per mo-

lecule), and thermodynamic par ameters, m

G∆ (Gibbs free

energy of micellization),

ΔGad

(the standard Gibbs

energy of adsorption, Gmin (the free energy of air/water

interface) of individual as well as equimolar binary sur-

factant systems were determined.

The adsorption efficacy of selected surfactants and

their mixtures at the air/solution interface were evaluated

with the help of the Gibbs adsorption equation [17-19].

max

2.303* **loglogP

nRTdX



Γ=





(1)

whe re ,

is surface tension of the solution, R is the

universal gas constant (8.314 JK−1 mol−1), T is tempera-

ture in the absolute scale, X is concentration of the sur-

factant in solution, and ‘n’ is a constant, which depends

on the number of species con stituting the surfactant.

The factor

loglog

was obtained from the slopes

of the plots of surface tension vs. log [surfactant]. max

values were used to calculate the minimum area per sur-

factant molecule (Amin) at the air/water interface using

the equati on:

min max

=Γ

(2)

where, N = Avogadro’s Number

The minimum area per surfactant molecule was found

to be minimum for Brij 35, and maximum for SDS as

given in Table 2. For the case of gemini surfactants, an

increase in Amin was observed with increase in carbon

number of spacer group. The values of the surface pres-

sure at the CMC (

CMC

) were obtained from the fol-

lowing equation:

CMC

= γ

o - γCMC (3)

Table 1. Experimental and literature CMC values of surfac tants.

Table 2. Maximum surface excess (

max

), the minimum surface area per molecule (Amin ), degree of micellar ionization , the

standard Gibbs energy of adsorption (ΔGad), Gibbs free en ergy of micellization (

G∆

), the free energ y of air/w ater interface

(Gmin) values.

M. KAMIL, H. SIDDIQUI

where γo is the surface tension of pure solvent and γCMC

is the surface tension at CMC. The standard Gibbs free

energy of micelliza tion per mole was estimated using the

equation:

G∆

= R * T * ln CMC * 0.001 (4)

The standard free energy of adsorption at air/water in-

terface can be derived fro m this standard free energy, as:

max

CMC

ad m



∆ =∆−





(5)

Table 2 clearly shows that both m

∆ and ad

∆ are

negative and their magnitudes showed a somewhat im-

pulsive nature of ad

G∆, which causes surfactant mole-

cules movements toward air/water interface. With this

finding, it was revealed that adsorption is primary and

micelle formation process is secondary process, during

surfactant addition in water. The maximum ad

G∆is ob-

served for the G5/Brij 35 combination. Further, Amin of

conventi onal surfact ants follow the order S DS > CT AB >

Brij35 (anionic > cationic > non-ionic). For the mixed

systems the ord er is: G5-Brij35 > G5-CTAB > G5-SDS.

3.3. Surfactant – surfactant Interaction

To determine, whether the binary systems follows ideal

or nonideal behavior, the experimental CMC values of

equimolar binary surfactant systems were compared with

ideal CMC values. The CMC ideal values were calculated

using Clint equation [20]:

ideal1 2

αα

CMCCMC CMC

= +

(1)

where CMC1, CMC2, α1 and α2 are the critical micelle

concentrations and the mole fractions of component 1

and 2 in mixed surfactant solutions. In Table 1, it is ob-

served that all CMCexp values were less than CMCideal, as

predicted by above equation which shows that the forma-

tion of mixed micelles exhibits a negat ive deviation with

respect to ideal mixture.

From Table 1, it is clear that CMCs of ionic surfac-

tants are muc h higher t han nonionic surfactant. This fact

can be justified as nonionic surfactant molecules show

hydrophobic interaction among hydrocarbon chains,

which are easily separated from the aqueous environment,

whereas ionic surfactants requires higher concentrations

to overcome the electrostatic repulsion between ionic

head groups while aggregating [21]. Moreover it was

also observed that the CMCexp values of binary systems

are lower than their corresponding ideal values, which

indicate synergistic interaction in all mixed systems .

In the light of the re gular sol utio n theor y, the deviatio n

of CMCexp values for mixed surfactant systems from

CMCideal can be measured by evaluating the interaction

parameter, β. This parameter can be calculated with the

help of Rubingh’s equation [22]:

( )( )

12 1122

112 2

CMCαCMCα

lnln lnln

CMC XCMCX

β1X 1X

 

 

 

= =

−−

(2)

where

are the micellar mole fraction of sur-

factant 1 and 2 in the mixed micelles, and CMC1, CMC2

and CMC12 are critical micelle concentrations of surfac-

tants 1 and 2, and C MC o f mi xed surfa cta nt s yste m, co n-

sisting of surfactant 1 and 2, both respectively, α1, and α2

are their corresponding bulk mole fractions. The micellar

mole fraction m

X was calculated with the help of fol-

lowing equation for nonideal binary mixture of surfac-

tants by solvin g iter a tively [22,23].

( )

m2 1 12

1 12

αCMC

X lnlnX1

1αCMC

1 Xlnln1 XCMC





 =



−



−





(3)

A negative value of β shows negative deviation of

CMCexp from CMCid eal, which indicates a reduction in

free energy of micellization over that predicted by the

ideal solution theory [23]. This implies good interaction

between sur facta nts in mi xed sys tem. A po sitive va lue o f

signifies antagonism between components of surfac-

tant combination. Another parameter, activity coefficient

f and 2

f within t he mixed micelles derived from Ru-

bingh equations was equated as :

( )

{ }

expexpβ1

fX= −

(4)

( )

{ }

2expexpβm

fX=

(5)

The values of β obtained experimentally for the se-

lected surfactants are given below in Table 3.

All negative β value s in Ta ble 3 indicate good interac-

tion between the components of mixed system and dem-

onstrate synergistic effect for all binary equimolar mixed

surfactant systems. The larger negative value of β de-

notes the greater negative deviation of CMCexp from

CMCideal. The order of deviation exhibited through β is

G5-SDS > G5-CTAB > G5-Brij35. The strongest syn-

ergis m effec t is fo und be twee n catio nic gemini and a nio-

nic co n ve nti o nal surfa ctant. T he r ea so n behind t hi s mi g ht

be the attractive forces between oppositely charged head

groups. The least value was for cationic gemini and nonio-

nic conventional surfactant, as Brij35 has polyoxyethylene

(POE) groups with large number of oxygen atoms and a

lone pair o f electro n, thus it ma y have a te ndency to react

coulombically with cationic gemini surfactant, but the

M. KAMIL, H. SIDDIQUI

existence of long polyoxyethylene head group imposes

some steric constraints due to thermal vibrations, which

causes control on effective head group interactions and

give reason to reduce the value of β [24,25].

Rubingh’s model observes the attractive interaction in

the mixed micelle formation. To analyze interaction be-

tween the amphiphiles in a mixed surfactant system at

air/water interface, Rosen model was used. According to

Rosen model the mole fraction of surfactant 1 at the

mixed adsorbed film can be calculated iteratively as [26]:

( )

σ1 12

αC

Xlnln CX 1

1αC

1 Xln1X C





 =



−

−

−





(6)

where C12, C1 a nd C2 are t he concentration of mixture at a

fixed surface tension value and the concentrations of

indivi d ua l s ur fac t ant s at a f ixe d sur fac e t e nsion value a nd

α1 was the mole fraction of surfactant 1. From this ex-

pre ssio n t he val ue o f

was obtained, which was then

used to evaluate the interaction parameter,

at air/

water interface, with the help of following equation:

( )( )

12 1122

σσ

112 2

σσ

CαCα

lnln lnln

CX CX

β1X 1X

 

 

 

= =

−−

(7)

The values o f

and

are presented in Ta ble 4.

The negative values of

indicate attractive intera c tion.

The activity coefficients (

and

) were calculated

through Rosen approach within the mixed micelle with

the help of interaction parameters as given below:

( )

{ }

expexpβ1fX

σσ

= −

(8)

( )

{ }

expexpβfX

σσ

(9)

From Tab le 4, it was ob served that all the systems e x-

hibits positive value of interaction parameter, which

shows antagonistic effect between components of mixed

surfactant s ystem.

3.4. Solubilization by Single Surfactants

To determine the extent of solubilization of PAH in sur-

factant, absorbance of PAH in surfactant solution (of

known concentration) is checked with the help of spec-

trophoto meter. Before examining the so lubilization power

of binary mixtures, single systems were first studied, to

get an idea about the efficiency of gemini in comparison

with co nve ntiona l surfa ctant s. Gr aphs o f the sol ubili ty o f

FLR as a function of the concentration of surfactant are

plotted in Fig ures 4 and 5. Both plots show that on in-

creasing surfactant concentration, concentration of dis-

solved FLR is also increasing, or its solubility increases

linearly with the increasing surfactant concentrations

above CMC [27 ]. This behavio r indicates that sol ubiliza-

tion is related to micellization. Though, the reduced

CMC value does not absolutely represent the increased

solubilizatio n abili t y. Thus, wa ter so lub i lit y enha nc e me nt

of FLR by selected single and equimolar binary surfac-

tant systems was further to evaluate and compare.

Table 3. Micellar mole fraction (

), interaction parameter (β), activity coefficients (f1and f2) values for gemi-

ni/conventional mixed surfactant systems at 30oC

Table 4. Surface composition at air/water interface (

), interaction parameter (

), activity coefficients (f1

and f2

)

val ue s for gemini-conventional mixed surfactant systems at 30 oC

M. KAMIL, H. SIDDIQUI

-1 0123 20 30 40 50 60 70

0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

[Fluorene] (mM )

[Surfactant] (mM)

BRIJ35

CTAB

SDS

Figure 4. Variation of solubility of FLR with surfactant

concent ration.

-0.20.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.82.02.22.42.6

0.00000

0.00002

0.00004

0.00006

0.00008

0.00010

0.00012

0.00014

0.00016

0.00018

[Fluorene] (mM )

[G 5 ] (mM)

G5-BR IJ35

G5-CTAB

G5-SDS

Figure 5. Variation of solubility of Fluorene with G5 con-

centration in 1: 1 binary surfactant.

A measure of the effectiveness of a surfactant in solu-

bilizing a given solubilizate is the Molar Solubilization

Ratio, ( MSR) which is given by [25, 28-33].

MSR = {[St] – [Scmc]} / {Ct – CMC} (10)

where Scmc and St are the solub ilities at CMC a nd at total

surfactant concentration Ct respectively. Since (Ct - CMC)

was the concentration of the surfactant in the micellar

form, MSR was equal to the ratio of solubilizate concen-

tration in the micelles to the concentration of surfactant

in the form of micelles. Value of MSR is obtained from

the slope of solubilizate concentration versus surfactant

concentration plot.

In the presence of excess FLR, MSR values of both

single and mixed surfactants can be obtained from the

slope of the linearl y ﬁtted line in which the concentration

was plotted against surfactant concentration above the

CMC (both the concentrations were in mM) given in

Figures 4-5. One can obtain the fact that as on increasing

surfactant concentration, FLR concentration is also risen

up, which provides positive value of MSR. The effec-

tiveness of solubilization can also be expressed with the

help of the partition coefficient Km [17,32] which is

deﬁned as distribution of the mole fraction of FLR be-

tween surfactant micelles and the aqueous phase. It may

be calculated as [32]:

Km= Xm / Xa (11)

where Xm and Xa are the mole fraction of F LR in micelle

phase and mole fraction of FLR in aqueous phase. The

quantity Xm can be expressed in terms of MSR, as

mMSR

X1MS)

(12)

Mole fraction of the solute in the aqueous phase was

approximated for dilute solution by:

Xa = SCMC VW (13)

where SCMC is the total appa rent solubilit y of the sol ute at

CMC and VW is the molar volume of water (1.807 * 10-2

L / mol at 30oC). So, the Km expression can be rear-

ranged as:

( )

mW CMC

MSR

K1MSR V S

(14)

As observed from Table 4 the MSR and Km values

were highest for cationic surfactant and lowest for anio-

nic and foll ow the o rder as Brij35 > G5 > CTAB > SDS.

The order of solubilizing power for organic solutes by

inner nonpolar core of micelles has been reported to be

nonionic > cationic > anionic surfactant having same

nonpolar chain length [24, 31-32]. For the case of FLR

our observed data support these findings. The difference

in solubilization capabilities of surfactant is because of

their different structures. Higher solubilization power of

Brij35 than G5 and SDS may b e due to its larger micellar

size helping in more micellar core solubilization [22].

The cationic surfactant exhibited lower MSR than nonio-

nic due to limited solubilization at micelle/water inter-

face and core of micelle.

3.5. Solubilization by Equ imo lar B inar y Mix ed

Surfactant Systems

When MSR values were compared for all the mixed sys-

tems, the order was found as: G5-SDS > G5- Brij35 >

G5-CTAB. MSR and log Km values of cationic-nonionic

surfactants were found higher than for cationic-cationic

mixed surfactant solutions as previously reported by Wei

et al. [30].

This is because nonionic micelle processing higher

micellar core solubilization characteristic interpolates to

the micelle–water interface producing greater solubiliza-

tion power towards PAHs. In addition, the solubilization

M. KAMIL, H. SIDDIQUI

Table 5. Molar solubilization ratio (MSR), log Km, the free energy of solubilization (ΔG0s), R, and, B values for FLR sol ubi-

lized in individual and mixed surfactant sys tems at 30℃.

of PHE and FLR by mixed gemini/nonionic surfactant

soluti ons i s also higher than those in si ngle no nionic sur-

factant. In the intere st of ascertaining the mixing effect of

mixed surfactants on solubilization for PAHs and seeing

the nature of deviation, the deviation ratio (R) between

the MSRexp and the MSRideal can be determined by the

following equation:

exp

ideal

MSR

(15)

MSRideal is the MSR for organic compounds in mixed

surfactant system at the ideal mixed state and can be es-

timated using the MSR of single surfactant solutions

based on the ideal mixing rule:

MSRideal = MSR1 X1 + MSR2 X2 (16)

where X1, X2, MSR1 and M SR2 are the mole fraction and

the molar solubilization ratio for solute of components 1

and 2 in mixed surfactant solutions, respectively. The

data of parameter R from Table 5 obviousl y indi cate tha t

the MSRexp values have positive deviation from ideal

mixture for the gemini/nonionic and gemini/anionic sur-

factant systems meaning that they have positive mixing

effect on solubilizatio n of FLR. Another parameter Km12,

the partition coefficient of a neutral organic solute be-

tween micelles and aqueous phase in a mixed surfactant

has been used by Treiner et al. [32]. This parameter pro-

vides better understanding of the mixing effect of mixed

surfactant systems on solubilization of solutes.

This partition coefficient’s expression is based on the

regular solution approximation as follows:

ln Km12 = m

X ln Km1 + (1 − m

X) ln Km2

+ B m

X (1 − m

X) (17)

where Km1, Km2 are the micelle–water partition

coefﬁcients of individual surfactant solutes constituting

the mixed micelles and

represents the micellar

mole fraction of a surfactant having the value of Km1. B

is an empirical parameter involving both the surfactant–

surfactant and surfactant–solute interactions. If value of

B becomes 0 it means there would be no mi xing effe ct on

partitioning of a solute between aqueous and micellar

phase. Whereas for B > 0 (<0) implies that Km12 in the

mixed surfactant system is larger (smaller) than predicted

by idea l mi xing r ule. As p rese nted in Table 5 , the B val-

ues are found to be negative for all the equimolar binary

mixe d systems.

4. Conclusions

The experimental results obtained in the present study

may be useful for the selection of appropriate mixed sur-

factant systems. This study would also facilitate the de-

sign and optimization o f new surfactant s ystems for their

better performance. The mixed micelles of gemini sur-

factant G5 with all the conventional surfactants i.e.

Brij35, CTAB and SDS are studied. Highest attracting

interaction in mixed micelle formation is observed in

G5-SDS and lowest attracting interaction G5-Brij35,

which indicates good synergism in mixed micelles.

G∆

and ad

∆ values are negative in all systems and

show the spontaneity. The values of

G∆

are negative

for all mixed systems, demonstrating the stability of the

micelles.

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