mixed micelle formation among anionic gemini surfactant (212) and its monomer (sdma) with...

Mixed Micelle Formation among Anionic Gemini Surfactant (212) and Its Monomer(SDMA) with Conventional Surfactants (C12E5 and C12E8) in Brine Solution at pH 11

Soumen Ghosh* and Tanushree ChakrabortyCentre for Surface Science, Department of Chemistry, JadaVpur UniVersity, Calcutta 700 032, India

ReceiVed: NoVember 22, 2006; In Final Form: April 30, 2007

The micellization of anionic gemini surfactant,N,N′-ethylene(bis(sodiumN-dodecanoyl-â-alaninate)) (212),and its monomer,N-dodecanoyl-N-methyl alaninate (SDMA), and polyethoxylated nonionic surfactants, C12E5

and C12E8, has been studied tensiometrically in pure and mixed states in an aqueous solution of 0.1 M NaClat pH 11 to determine physicochemical properties such as critical micellar concentration (cmc), surface tensionat the cmc (γcmc), maximum surface excess (Γmax) and minimum area per surfactant molecule at the air/waterinterface (Amin). The theories of Rosen, Rubingh, Motomura, Maeda, and Nagarajan have been applied toinvestigate the interaction between those surfactants at the interface and in the micellar solution, the compositionof the aggregates formed, the theoretical cmc in pure and mixed states, and the structural parameters asproposed by Tanford and Israelachvili. Various thermodynamic parameters (free energy of micellization andinterfacial adsorption) have been calculated with the help of regular solution theory and the pseudophasemodel for micellization.

Introduction

Conventional surfactant contains one hydrophilic and onehydrophobic group. Geminis are a special class of surfactants1-3

where two monomeric surfactants (two hydrophilic and twohydrophobic groups) are coupled together via a spacer. Geminishave attracted considerable interest4-9 for their various surface-active properties superior to those of corresponding conventionalsurfactants. These compounds have much lower critical micellarconcentration (cmc) values and much greater efficiency inreducing the surface tension of water.3 Due to the presence oftwo hydrophobic tails per gemini molecule, surface activity isenhanced and increased with increasing chain length. Becauseof the presence of hydrophilic spacers in a gemini molecule,solubility in water increases highly. Due to its enhanced surfaceactivity, emulsifying property, enzyme inhibiting activity, andmildness to skin,9 gemini finds manifold applications in thedetergent and cosmetic industries.

In practical fields, the properties of mixtures of surfactantsare important. The presence of two charge-sites in an anionicgemini surfactant proposes stronger interaction with neutral andcationic surfactants than that of conventional surfactants.10

Studies of anionic gemini surfactant with polyethoxylatednonionic surfactant show the search for synergism in micelli-zation. Recently, a study of anionic gemini surfactant andpolyethoxylated nonionic surfactant showed that a mixture ofan anionic gemini surfactant with a hydrophobic spacer and anonionic surfactant exhibits synergism, although a mixture ofan anionic gemini surfactant with a hydrophilic spacer and anonionic surfactant does not show synergism in micelliza-tion.11,12 Recently, an anionic gemini surfactantN,N′-ethyl-ene(bis(sodiumN-dodecanoyl-â-alaninate)), that is, (CH2)2-[N(COC11H23)CH2CH2CO2Na]2, named 212, havingN,N-dialkylamide and carboxylate groups in the molecule, a dimercorresponding to sodiumN-dodecanoyl-N-methyl alaninate

(SDMA), and its homologues have been studied.12-16 Thecommon behavior of this gemini is that it accepts a proton,releasing Na+ into the bulk phase during the micellizationprocess.13

Here, we report a detailed tensiometric study of the mixedmicellization and interfacial behavior of 212 and its mono-mer SDMA with nonionic surfactants, penta- and octaethyleneglycol monon-dodecyl ether (C12E5 and C12E8), respectively,in various compositions in 0.1 M NaCl solution at pH 11 andtemperature 303 K. The chemical structures of 212, thecorresponding monomer SDMA, C12E5, and C12E8 are presentedin Scheme 1.

The properties studied include the cmc, the surface tensionat the cmc (γcmc), the negative log of the surfactant molarconcentration required to reduce the surface tension of thesolvent by 20 mN/m (pC20), the maximum surface excess atthe air/water interface (Γmax), the minimum area per surfactantmolecule at the air/water interface (Amin), thermodynamicparameters, viz., the standard free energy of micellization (∆Gm

0 ) and the standard free energy of interfacial adsorption (∆Gad

0 ), and so forth. Rosen and Rubingh’s theories have beenused to calculate the interaction parameters at the air/waterinterface as well as within the micelles.∆Gm

0 obtained fromMaeda’s model has been compared with∆Gm

0 calculated fromthe pseudophase model. Israelachvili’s model has been used topredict the shape and packing parameter of the self-aggregatedsystems.

Experimental Section

Materials. The anionic gemini surfactant 212 and itsmonomer SDMA were gifted by K. Tsubone, Wakamiya 13-104, Kanagawa, 254-0911, Japan. The procedures for its (212)synthesis and purification have been reported.14 The nonionicamphiphiles C12E5 and C12E8 were the products of NikkolChemical Co. (Tokyo, Japan). All solutions were prepared indouble distilled water at pH 11 in the presence of 0.1 M NaCl,

* Corresponding author. E-mail: [email protected]. Phone:(0091) 332414 6411. Fax: (0091) 3324146266.

8080 J. Phys. Chem. B2007,111,8080-8088

10.1021/jp067761u CCC: $37.00 © 2007 American Chemical SocietyPublished on Web 06/21/2007

and experiments were done under thermostated conditions at303 K with an accuracy of(0.01 K.

Method. The tensiometric experiments were performed usinga platinum ring by the ring detachment method in a calibrateddu Nouy tensiometer (Kru¨ss, Germany). The detailed procedurehas been reported earlier.17-23 Each experiment was repeatedseveral times to achieve good reproducibility. Theγ values wereaccurate within(0.1 mN m-1.

Theoretical Section

Both ideal and nonideal mixed micelles are possible. For idealmixed micelles, Clint’s equation24 is followed by the relation

whereas the formation of nonideal mixed micelles can beexpressed as

Here, Xi and fi denote the stoichiometric mole fraction ofcomponent “i”, and its activity coefficient in solution, respec-tively. The termsCi andCm are the cmc’s of theith componentand the mixture, respectively. Clint’s equation makes thedifference between ideal and nonideal mixtures.

Thermodynamically, Motomura25 considered mixed micellesas a macroscopic bulk phase, and the related energetic param-eters can be found from the excess thermodynamic quantities.The fundamental equation for the micellar mole fraction of ionicsurfactant in the binary surfactant mixture (XmI) is

whereXI and Cm may be defined as follows:

and

The subscripts I and N represent ionic and nonionic surfactants,respectively,X represents the stoichiometric mole fraction, andν represents the number of ions dissociated by the surfactant.

The interfacial molecular interaction parameter (âσ) at theair/water interface for the mixed monolayer formation can be

obtained from Rosen’s model26,27 following the “successivemethod”. For this purpose, a computer program has been madeon the basis of the following equations (4 and 5), and thatprogram was run to determine the values ofXσ and âσ. Thenecessary equations are

and

whereXI andXIσ are the stoichiometric mole fractions of ionic

surfactant in the mixture and in the adsorbed interfacialmonolayer, respectively.CI

0, CN0 , and Cm

0 are the molar con-centrations in the solution phase of ionic and nonionic surfac-tants and their mixture, respectively, at a constantγ value.

Again, in the mixed micellar system, the micellar molecularinteraction parameter (â) is calculated from Rubingh’s equation28

following a similar iterative or successive method, using

and

whereXmI andXI denote the same meaning as before, andCI,CN, andCm are the cmc’s of ionic and nonionic surfactants andtheir mixture, respectively.

The activity coefficients of ionic and nonionic componentsin the mixed micelle,fI and fN, can be evaluated from theequations

and

Maeda’s model29 is applicable for solutions with moderatelyhigh ionic strength where the short range of the electrostaticinteraction is no longer negligible. From the model, the decreasein ionic head group repulsion in an ionic/nonionic mixed micelleis due to the presence of nonionic surfactant molecules in themicellar phase. The proposed equation for the standard freeenergy change due to the micellization process as a polynomialfunction of the ionic mole fraction in the micellar phase,XI, is

where

XCN is the cmc of nonionic surfactant in the mole fraction unit.If the nonionic surfactants self-assemble among themselves, themicellar free energy change is expressed as a dimensionless

SCHEME 1

(XIσ)2 ln(XICm

0 /XIσCI

0)

(1 - XIσ)2 ln[(1 - XI)Cm

0 /(1 - XIσ)CN

0 ]) 1 (4)

âσ )ln(XICm

0 /XIσCI

0)

(1 - XIσ)2

(5)

(XmI)2 ln(XICm/XmI

CI)

(1 - XmI)2 ln[(1 - XI)Cm/(1 - XmI

)CN]) 1 (6)

â )ln(XICm/XmI

CI)

(1 - XmI)2

(7)

fI ) exp[â(1 - XmI)2] (8)

fN ) exp[âXmI

2] (9)

∆Gm0 ) RT(B0 + B1XI + B2XI

2) (10)

B0 ) ln XCN(11)

1

Cm

) ∑i)1

n (Xi

Ci) (1)

1

Cm

) ∑i)1

n ( Xi

fiCi) (2)

XmI) XI - (XNXI/Cm)(∂Cm/∂XI)T,P (3)

XI )νIXI

νNXN + νIXI

Cm ) (νNXN + νIXI)Cm

Micellization of 212 and SDMA with C12E5 and C12E8 J. Phys. Chem. B, Vol. 111, No. 28, 20078081

quantity,B0 () ln XCN ) ∆Gm0 /RT). The parameterB1 is related

to the standard free energy change associated with the introduc-tion of one ionic species into a nonionic micelle coupled withthe release of one nonionic species from the micelle; that is,B1

plays an essential role in a change in the cmc values of nonionicmicelles when an ionic species enters the micelle.29 B2 is theinteraction parameter in the micellar phase.R andT denote theuniversal gas constant and absolute temperature, respectively.Again,

(XCI is the cmc of ionic surfactant in the mole fraction unit),and

(â being the interaction parameter in the micellar phase obtainedfrom eq 7).

Very recently, Maeda30 proposed another theoretical modelbased on the Gibbs-Duhem equation considered by Hall31 topredict the excess free energy (gex) of the ionic-nonionic mixedmicelle, which is even applicable to the low ionic strengthregime. The model relatesgex andXmI as

whereXmI can be calculated from the lnCm versusXI plot usingthe equation

The degree of counterion binding (ν) is negligible in our casedue to the presence of an excess amount of salt in the medium,and the equation becomes

The activities of the ionic and nonionic components are givenby

and

â can be calculated from

According to Tanford,32 the equation for the equilibrium ofa monomeric surfactant in the bulk solution and in the micellaraggregate is

whereg is the aggregation number of the aggregate, and∆µg0

is the difference in the standard state chemical potential betweena surfactant monomer present in an aggregate and that in a singlydispersed state in solution.

In the phenomenological model of Nagarajan,33 there are fourdifferent contributions for (∆µ0

g/kT), viz., (1) (∆µ0g/kT)T, which

is a negative free energy contribution arising out of the transferof the surfactant tail from solution to the more favorablehydrocarbon-like environment of the aggregate core;-1.4644and-3.6423 (at 303 K) contributions per-CH2- and-CH3

group were considered; (2) (∆µg0/kT)I, which is a positive

contribution that accounts for the allowance of the penetrationof water molecules to the aggregate core; (3) (∆µg

0/kT)H, whichis another positive contribution arising out of the repulsive (stericor electrostatic) interaction between the head groups crowdingat the aggregate surface; and (4) (∆µ0

g/kT)P, which is thecontribution of packing of a monomer within the core of theaggregate. Thus,

and, following Tanford’s rationale, the interfacial [(∆µg0/kT)I]

and head [(∆µg0/kT)H] contributions were calculated from

and

whereR is the headgroup repulsion parameter (R ) γae2), and

ae is the area per surfactant monomer at the interface of theaggregate core and was evaluated using

wheree is the electronic charge,d is the capacitor thickness inthe double-layer model,ε is the permittivity or dielectric constantof the bulk solution (80 for water),γ is the surface tension valuecalculated from Nagarajan’s model,κ-1 is the Debye lengthdepending on the ionic strength of the medium, andl0 is theextended tail length per surfactant monomer and was obtainedfrom Tanford’s equation

wherenc is the number of carbon atoms in the surfactant tail(12 in our case).

According to Israelachvili’s model,34 the packing parameter(P), dictating the shape of the aggregates is given as

where V0 is the volume of exclusion per monomer in theaggregate and is given by Tanford’s equation as

The micelles will be spherical (P < 1/3), nonspherical (1/3< P < 1/2), vesicles or bilayers (1/2< P < 1), or inverted

B1 + B2 ) ln(XCI

XCN) (12)

B2 ) -â (13)

gex ) XmIln fI + (1 - XmI

) ln fN (14)

XmI)

XI[1 - (1 - XI)(d ln Cm/dXI)]

[1 + ν(1 - XI){XI(d ln Cm/dXI) + 1}](15)

XmI(ν)0) ) XI[1 - (1 - XI)(d ln Cm/dXI)] (16)

aI ) XmIfI ) XI

Cm

CI

aN ) (1 - XmI)fN ) (1 - XI)

Cm

CN

â ) gex

XmI(1 - XmI

)(17)

ln XCI)

∆µg0

kT(18)

∆µg0

kT) (∆µg

0

kT )T

+ (∆µg0

kT )I+ (∆µg

0

kT )H

+ (∆µg0

kT )P

(19)

(∆µg0

kT )I) ( γ

kT)ae

(∆µg0

kT )H

) ( RkT) 1

ae

ae ) [2πe2dεγ ( 1

1 + κl0)]1/2

l0 e lmax ≈ (0.154+ 0.1265nc) nm

P )V0

l0ae

V0 ≈ (0.0274+ 0.0269nc) nm3

8082 J. Phys. Chem. B, Vol. 111, No. 28, 2007 Ghosh and Chakraborty

(P > 1), depending on the value of the packing parameter. Theradius of the aggregate,R was calculated from

Assuming that the tail deforms nonuniformly,35 the packing freeenergy can be calculated from

with

anda′e is given by

whereL is the length per unit segment, 4.6 Å.For the gemini, since the number of-CH2- units in the

spacer (2 in 212) is less thanae1/2/lCH2, the contribution of the

spacer to the (∆µg0/kT)T was not considered.36 It was also

neglected toward the packing free energy as [(S + 1)lCH2] >aeff, with aeff ) V0/ηπR, whereη is a shape-dependent constant() 1 for bilayer).

For double-tailed surfactants, a unit contribution for one tail,0.6 contribution for the other tail, and a total 1.6 contributionper monomer were accounted in (∆µg

0/kT)T, (∆µg0/kT)I, and

(∆µg0/kT)P, where contribution of the tail is important. Due to

the presence of two head groups per gemini molecule, acorrection for the nonuniformity effect in (∆µg

0/kT)H was donefollowing Camesano et al.36 For mixtures of nonionics withgemini, the weighted part in (∆µg

0/kT)I and (∆µ0g/kT)H was

corrected accordingly. From Nagarajan’s model, the value of∆Gm

0 was also evaluated, which is the sum of the chemicalpotential contributions over the different processes.

Results and Discussion

The high surface tension of water is due to strong hydrogenbonding among the water molecules, leading to enhancedcohesive force, which resists the separation of a water columninto two. When a surfactant is added in water, the surfactantmolecules first populate at the air/water interface in order toavoid the highly energetically unfavorable interaction of waterwith the hydrophobic tail of the surfactant, and the surfactanthead groups are buried in the aqueous environment while thetails remain in the air phase. This, in turn, hinders theintermolecular hydrogen bonding present on the surface of apure aqueous phase, and surface tension starts decreasing. Thedecrease in theγ value continues until the air/water interface issaturated with surfactant monomers. Beyond this saturation, theadded surfactants assemble among themselves to form ag-gregates to ensure a hydrophilic periphery, hiding the hydro-phobic tail within a cage to avoid water. Theγ value, therefore,does not change (beyondγcmc) after reaching a certain concen-tration of surfactant. This concentration of surfactant is calledthe cmc and is obtained from the break point in theγ versuslog[surfactant] profile (Figure 1). The constant value of surfacetension at the cmc is calledγcmc and is a measure of the efficacyof the surfactant to populate the air/water interface in the form

of a monolayer prior to micellization. The same can also bepredicted from the Gibbs surface excess (Γmax) obtained fromthe slope close to the micellization regime18,19of the aforemen-tioned plot using the equation

The minimum area per surfactant head group at the air/waterinterface (Amin) is related toΓmax as

whereR is the universal gas constant (8.314 J mol-1 K-1), NA

is Avogadro’s number, andn is the number of ionic specieswhose concentration at the interface varies with the change inthe [surfactant] in the solution.13 In the presence of an excessamount of Na+ in 0.1 M NaCl, n ) 1.7,13 Γmax and Amin areexpressed in moles per square meter and square nanometersper molecule, respectively. Another physical quantity, pC20, isdefined as pC20 ) -log C20, whereC20 is the surfactant molarconcentration required to decrease the surface tension of purewater by 20 mN m-1 and is also an indication of the preferenceof a surfactant toward the air/water interface compared to thebulk prior to micellization.21-25 The pC20 value can measurethe efficiency of adsorption of the surfactant at the interface.21

A high value of pC20 denotes that the surfactant adsorbs moreefficiently at the interface, reducing the surface tension of thesolution.

The cmc value of the pure surfactant determined by thesurface tension method at pH 11 and 0.1 M NaCl increases inthe order of 212< C12E5 < C12E8 < SDMA. The nonionicshave naturally less cmc compared to the anionic SDMA, whichhas a similar tail length containing 12 carbon atoms. This isexpected by the charged head group present in SDMA, whichhas a greater tendency to populate the bulk water as a result ofsolvation by the polar solvent. Consequently, SDMA has thelowest efficacy to populate the air/water interface compared tothe nonionics, as evidenced from its lowest pC20 value. This isalso reflected in its lowestΓmax, as obtained from Table 1 usingeq 1. TheAmin is also largest for SDMA, as expected from thestronger electrostatic head-head repulsion at the air/waterinterface.

The higher cmc of SDMA compared to its dimer, 212, isfirst a consequence of the greater hydrophobicity of its dimer,owing to its double-tailed structure. 212 also has a greatertendency to be adsorbed at the air/water interface throughoutthe monolayer formation, as indicated by its larger pC20 andΓmax values given in Table 1. Although 212 is the dimer ofSDMA, theAmin of SDMA is greater than that of 212. Similarobservation has also been reported by Menger et al.9 So, inaddition to electrostatic repulsion, this greaterAmin of SDMAcan be explained on the basis of the formation of an intramo-lecular hydrogen-bonded ring structure betweenN-methylamideand protonated carboxylate groups in the SDMA molecule15 atthe monolayer, requiring a greater area of exclusion at theinterface. This type of ring formation is restricted in the dimericgemini 212 due to steric hindrance, which reduces the area ofexclusion and enhances surface population. Moreover, asreported earlier,13 there occurs an exchange of Na+ ions fromthe 212 monomer with H+ ions from water, decreasing thecharge of the head group of 212. This, in turn, reduces the head-head repulsion, and hence theAmin of 212 is smaller comparedto that of its monomer, reflecting compact packing of the

R )3V0

ae

(∆µg0

kT )P

) Qa′e

Qsph) (278 )V0L, Qcyl ) (20

8 )V0L, andQbilayer ) (108 )V0L

a′e ) (Rγ

+2Q/ae

γ/kT )

Γmax) - 12.303nRT

limCfcmc

∂γ∂ log C

(20)

Amin ) 1018

NAΓmax(21)


interface by 212 monomers compared to that by SDMA. Theoutcome of the above facts is the increasing values ofΓmax andpC20 of 212.

The nonionic amphiphiles in this study have the same tailgroups (12 carbon atoms) and a varied number of ether units inthe head groups. C12E8 has a greater cmc compared to C12E5,whereasγcmc and Γmax for C12E5 are larger; that is,Amin issmaller. All these variations are the manifestation of the presenceof a different number of ether groups in the head group of twoamphiphiles. Due to the higher degree of solvation of C12E8

compared to that of C12E5, the C12E8 molecule feels compara-tively comfortable within the bulk water and, consequently, hasa lesser tendency to populate the interface. The surfactantbulk

1

S surfactantinterface1 (superscript 1 corresponds to a monomer)

equilibrium, therefore, remains somewhat left-shifted for C12E8

than for its lower homologue. Correspondingly, surface satura-tion indicates a micellization threshold in tensiometric experi-ments and occurs at a somewhat greater concentration for C12E8

in contrast to that for C12E5. This is also reflected in the trendin Γmax, which reflects the tendency of the surfactant to beadsorbed at the air/water interface. TheAmin is also larger forC12E8, as expected due to the presence of greater number ofether moieties in the head group. For C12E8 with a longerethoxylate (EO) chain, the lowerγcmc value and higher pC20

reflect higher surface activity of a micellar solution due to agreater degree of solvation of the C12E8 head group.

The cmc for the mixed micelles of either of the nonionics(POE) with the gemini increases with increasing mole fractionof 212 (X212), presented in Table 2. For the comparison betweenthe same mole fractions of 212 with either of the POEs, the212/C12E8 always has the higher cmc. This fact is, again, theoutcome of an increased degree of solvation of the 212/C12E8

mixture compared to that of 212/C12E5 owing to the increasingether unit in C12E8. The value ofγcmc increases slightly withincreasingX212 for either mixture. These values are compara-tively higher for 212/C12E8 relative to those for 212/C12E5. The

Figure 1. Tensiometric plots showing the variation of surface tension (γ) with log[surfactant] at 0.1 M NaCl, pH 11 at 303 K: (a) 212/C12E8, (b)212/C12E5, (c) SDMA/C12E8, and (d) SDMA/C12E5.

TABLE 1: Surface Properties of Pure Components in 0.1 M NaCl at pH 11 and 303 K

pure comp.cmc× 105/mol dm-3

γcmc/mN m-1 pC20

Γmax × 106/mol m-2

Amin/nm2 molecule-1

-∆Gm0 /

kJ mol-1∆Sm

0 /J K-1 mol-1

-∆Gad0 /

kJ mol-1

212 1.44 31.6 6.05 2.82 0.59 37.38 123.36 51.38SDMA 265.0 40.1 3.36 2.54 0.65 24.52 84.49 36.73C12E8 4.34 31.0 5.51 3.48 0.48 34.66 114.38 46.18C12E5 3.64 32.4 5.40 3.97 0.42 35.09 115.81 44.84


values of pC20 increase a little bit with increase inX212 in thecase of 212/C12E8, whereas these values are irregular for othermixtures containing 212. Overall higherγcmc and lower pC20

values of the 212/C12E8 mixture indicate less surface activitycompared to the 212/C12E5 system due to greater steric repulsionbetween the molecules of 212 and C12E8 relative to that of 212and C12E5. The decreasedΓmax upon increasingX212 in eithermixture signified a decreased affinity of the mixtures for theinterfacial adsorption, as expected from increased solvation ofthe ionic head group of the gemini. Consequently, theAmin

values increase with increasingX212. The idealAmini is calcu-

lated with the help ofAmin values of pure components using

whereAminI andAmin

N are the minimum area per molecule at theair/water interface of ionic and nonionic surfactants, respectively.XI

σ is the mole fraction of ionic surfactant at the air/waterinterface. The smallerAmin compared toAmin

i , except whenX212

) 0.75 for the 212/C12E5 system, shows some contraction insurface packing. The divergence is maximum for the mixturecontaining less 212, showing greater compactness.

For both of the SDMA/POE mixtures, the cmc increases withincreasingXSDMA, as expected from the higher cmc of SDMA.These cmc values are between the individual cmc’s of pureamphiphiles. For the sameXSDMA, the cmc of the SDMA/C12E8

mixture is always greater than that of the SDMA/C12E5 mixture,as expected for the lower cmc of pure C12E5 compared to thatof its higher homologue. The value ofγcmc also increases withincreasingXSDMA. The decreasedγcmc of the mixtures comparedto pure SDMA reflects the enhanced surface activity of themixed micellar solution upon increasing the molar ratio ofSDMA. The values ofγcmc for the SDMA/C12E5 mixtures arelower than those of the corresponding SDMA/C12E8 mixtures,indicating the higher surface activity of the former pair. ThepC20 value decreases upon increasingXSDMA, showing thedecreasing tendency of mixed monolayer formation at the initialstage of surfactant addition. Due to the lower tendency of SDMAtoward interfacial adsorption,Γmax values of both SDMA/POEmixtures decrease with increasingXSDMA, pointing to thepropensity of surface adsorption of the mixed surfactant duringthe saturation of the monolayer. The higher value of pC20 andΓmax of the SDMA/C12E5 pair also indicates the increasedtendency of the mixture to be adsorbed at the air/water interfacethroughout the process of monolayer formation and the more

compact structure of the monolayer compared to that of theSDMA/C12E8 pair, as also evidenced by the decreased value ofthe area of exclusion,Amin, of the SDMA/C12E5 mixture. Thearea of each component of SDMA/C12E8 is greater than that ofSDMA/C12E5, denoting greater steric repulsion between theprotonated SDMA and C12E8 with a longer EO chain. The idealarea of exclusion,Amin

i , for all the mixtures, is less than thatobserved experimentally (Amin). This indicates that the mono-layer is expanded compared to that expected ideally. It happensprobably because of the presence of the ionic species in themonolayer, which effectively introduces the repulsive forceamong the surfactants at the interface.

Interfacial and Micellar Interaction Parameters. FromTable 2, it is observed that the experimental cmc values of allsystems are lower than the values calculated by Clint’s method,indicating nonideal behavior. The mole fraction of a surfactantin the mixed micelle (XmI) determined by Motomura’s equationand all the values for the binary mixtures in 0.1 M NaCl at pH11 evaluated by the models of Rosen and Rubingh are presentedin Table 3. It shows thatXmI determined by all these modelsincreases with increasingX212 and XSDMA. These values arehigher for 212/POE mixtures compared to those for SDMA/POE systems. The values ofXmI (Motomura’s model) can onlybe determined forXSDMA ) 0.75 of SDMA/POE systems. Forboth of the 212/POE mixtures withX212 ) 0.25,XI

σ (Rosen’smodel) and XmI (Rubingh’s model) are almost the same,indicating that both of the components of the mixtures haveequal surface activity as well as efficacy toward micellization,but, for other compositions, the ionic surfactant prevails overthe nonionic one in those activities. The reverse trend is observedin the case of SDMA/POE mixtures. For each case, bothâσ

and â values are negative (Table 3), indicating synergisticinteraction between two components of the solution and, hence,lowering of the cmc compared to that expected from Clint’sequation (Table 2).

For ionic-nonionic combinations, all the experiments weredone at constant ionic strength and counterion of the solutionby 0.1 M NaCl to maintain the accuracy in calculatingâ values.It is reported37 that a POE molecule (where each ether oxygenis interspaced by two methylene groups) in combination withanionic surfactant forms a “crown ether” by accepting an alkalimetal ion from the solution phase into the cavity center of theligand. In this arrangement, all the O atoms lie in the plane ofthe ring, pointing inward, toward the Na+ ion. Due to this

TABLE 2: Surface Properties of Different Binary Mixtures in 0.1 M NaCl at pH 11 and 303 K

X212 orXSDMA

cmc× 105/mol dm-3

γcmc/mN m-1 pC20

Γmax × 106/mol m-2

Amin/nm2 molecule-1

Aimin/

nm2 molecule-1Clint cmc× 105/

mol dm-3

212/C12E8

0.25 2.23 31.6 5.73 3.65 0.45 0.53 2.890.50 2.10 31.9 5.84 3.05 0.54 0.56 2.160.75 1.72 32.9 5.92 2.97 0.56 0.58 1.73

212/C12E5

0.25 2.00 25.8 5.88 4.02 0.41 0.50 2.630.50 1.91 28.6 5.81 3.52 0.47 0.53 2.060.75 1.69 29.6 6.22 2.64 0.62 0.55 1.70

SDMA/C12E8

0.25 5.34 34.3 5.21 3.27 0.51 0.48 5.760.50 7.78 35.6 5.07 2.88 0.58 0.49 8.540.75 15.5 36.3 4.80 2.63 0.63 0.50 16.5

SDMA/C12E5

0.25 4.36 32.0 5.47 3.38 0.49 0.44 4.830.50 6.50 33.5 5.15 3.33 0.50 0.47 7.180.75 13.0 34.3 4.89 3.06 0.57 0.49 14.0

Amini ) XI

σAminI + (1 - XI

σ)AminN (22)


rearrangement, POE behaves as a positively charged surfactant.Table 3 shows that theâσ and â values of SDMA/C12E5 aregreater than those of 212/C12E5, and those of SDMA/C12E8 aregreater than those of 212/C12E8. This is probably due to thesynergistic electrostatic interaction between the hydrophilicgroups of the anionic SDMA molecule and the positivelycharged POE molecule, rather than some steric repulsiveinteraction occurring between the two hydrophilic groups ofprotonated 212 molecules and the positively charged POEmolecule. Again, according to Fajan’s rule, the smaller the sizeand greater the charge density of the cation, the more effectiveis its polarizing power. So, here, due to smaller size of C12E5

relative to that of C12E8 (although both of them have the samecharge density), it also interacts more strongly with anionic 212or SDMA, which is reflected in theâσ and â values of thesemixtures. The synergistic interaction in the mixed micelle ofall the mixtures, except whenX212 ) 0.25 in 212/C12E8 systems,is weaker than that in the mixed adsorption film because it ismore difficult to incorporate two hydrophobic groups of thesurfactants into the mixed micelle than it is to accommodatethem at the planar interface. In each case, except for 212/C12E8

(X212 ) 0.25),âσ - â values are negative, indicating a greatertendency toward population of the surface than toward micel-lization.

Table 3 denotes that the activity coefficients (fI and fN) ofthe mixtures (212/POE) increase with increasing mole fraction,and fI (or f212) ) 1 shows ideal behavior atX212 ) 0.75. ForSDMA/POE systems,fI (or fSDMA) shows low value whereasfN(or fPOE) represents the value close to unity, indicating ideality.

Thermodynamics of Micellization and Interfacial Adsorp-tion. Considering the negligible degree of counterion dissocia-tion of 212,13 the standard free energy of micellization (∆Gm

0 )is calculated from regular solution theory using

whereXCm is the cmc of the mixture in the mole fraction unit.

The standard free energy of interfacial adsorption,∆Gad0 , at

the air/saturated monolayer interface of the micelle has beendetermined from the relation17-23,38

Here, Πcmc denotes the surface pressure (γwater - γcmc) atthe cmc. The higher the negative value of∆Gad

0 , the higher isthe efficacy of the surfactant to be adsorbed at the air/waterinterface. Table 1 shows that gemini 212 has greater surfaceactivity than its monomer SDMA. The same trend can also bereflected in their mixtures with POE. In the case of binarymixtures, the surface adsorption increases with increasing molefraction of the ionics in 212/POE mixtures, but the reverse trendis observed in SDMA/POE mixtures. The same prediction canalso be drawn from the pC20 values of the mixtures as discussedearlier.

The ∆Gm0 values for the pure surfactants are tabulated in

Table 1 (the lower value of SDMA is compensated byconsidering the degree of counterion dissociation). This freeenergy is compared with that obtained using the model of Maeda(∆Gm

0 ).29 The values of∆Gm0 , B0, B1, andB2 are presented in

Table 4. For a binary system, theB0 value is constant. For 212/POE systems, bothB1 andB2 values decrease with increasingvalue of X212. But for SDMA/POE systems, the values ofB1

increase with increasingXSDMA, althoughB2 decreases. In thecase of SDMA/POE, the increase ofB1 is due to the formationof intramolecular hydrogen bonds in the SDMA molecule. Thenegative values ofB1 of 212/POE systems indicate the major

TABLE 3: Molecular Interaction Parameters of Binary Mixtures in 0.1 M NaCl at pH 11 and 303 K

Rosen’s model Rubingh’s model Motomura’s model

X212 or XSDMA XIσ âσ XmI â fI/fN XmI

212/C12E8

0.25 0.49 -0.86 0.50 -1.03 0.77/0.77 0.2450.50 0.72 -0.21 0.74 -0.15 0.99/0.92 0.6590.75 0.89 -0.10 0.90 -0.06 1.00/0.95 0.886

212/C12E5

0.25 0.49 -3.40 0.47 -1.11 0.73/0.78 0.2430.50 0.63 -1.75 0.69 -0.37 0.97/0.84 0.5990.75 0.77 -1.71 0.88 -0.04 1.00/0.97 0.834

SDMA/C12E8

0.25 0.04 -3.18 0.06 -2.94 0.07/0.990.50 0.05 -2.44 0.09 -2.16 0.17/0.980.75 0.06 -1.50 0.10 -1.00 0.44/0.99 0.498

SDMA/C12E5

0.25 0.11 -5.30 0.08 -3.52 0.05/0.980.50 0.22 -6.92 0.09 -2.40 0.14/0.980.75 0.29 -7.41 0.10 -1.19 0.38/0.99 0.498

∆Gm0 ) RT ln XCm

(23)

∆Gad0 ) ∆Gm

0 - (Πcmc

Γmax) (24)

TABLE 4: Thermodynamic Parameters of Binary Mixturesin 0.1 M NaCl at pH 11 and 303 K

Maeda’s modela

X212 orXSDMA -B0 B1 B2

-∆Gm0 /

kJ mol-1-∆Gm

0 /kJ mol-1

∆Sm0 /

J mol-1 K-1-∆Gad

0 /kJ mol-1

212/C12E8

0.25 14.06 -2.14 1.03 36.61 37.10 122.45 47.920.50 -1.26 0.15 36.91 37.25 122.95 50.110.75 -1.16 0.06 37.54 37.76 124.61 50.62

212/C12E5

0.25 14.24 -2.03 1.11 36.97 37.38 123.36 48.650.50 -1.30 0.37 37.27 37.49 123.74 49.570.75 -0.96 0.04 37.64 37.80 124.76 53.52

SDMA/C12E8

0.25 14.06 1.17 2.94 34.22 34.90 115.19 46.160.50 1.95 2.16 31.61 33.95 112.06 46.280.75 3.12 1.00 28.13 32.22 106.33 45.45

SDMA/C12E5

0.25 14.24 0.76 3.52 34.83 35.41 116.88 46.980.50 1.89 2.40 31.98 34.41 113.56 45.700.75 3.10 1.19 28.33 32.66 107.79 44.69

a Reference 29.


role of the tail-tail interaction in the stability of the mixedmicelles. Here, gemini 212 has two chains of 12 carbons,whereas monomer SDMA and nonionics have only one 12-carbon tail. Hence,B1 values are positive for SDMA/POEsystems due to less tail-tail interactions. From Table 4, theclose resemblance of∆Gm

0 calculated from regular solutiontheory and that from Maeda’s model for the 212/POE systemsalso reflects negligible counterion dissociation of the geminias described earlier.13 These values are almost constant. ForSDMA/POE mixtures, there is some discrepancy between thevalues of the free energy of micellization obtained from eithermethod upon increasingXSDMA. It may be due to the very large(∼100-fold) difference in the cmc of the pure POEs and SDMA.It has also been observed that the cmc of the mixture is not asclose to the cmc of the nonionics as required by the Maeda’smodel.

Table 5 shows that micellar mole fractions of 212/POEsystems are higher than the corresponding stoichiometric molefractions. But discrepancy is observed in the case of SDMA/POE systems. The values of activity coefficients of the ionicspecies (fI) decrease with the increasing mole fraction of 212in the case of 212/POE systems, whereas the reverse is true for

the POE species. This discrepancy is probably due to the largedifference in the cmc values of POE and SDMA, which is notpermitted in Maeda’s model. For this system,gex andâ valuesdecrease with the increasing stoichiometric mole fraction of 212,and negative values ofâ indicate synergism.

Applying the Gibbs-Helmholtz equation, the standard en-tropy of micellization,∆Sm

0 can be evaluated, which is equiva-lent to-(∆Gm

0 /T). The cmc and∆Hm0 of pure SDMA at 0.1 M

NaCl and pH 11 at 303 K were measured in an ITC micro-calorimeter, Omega (USA) to be 2.40 mM and 1.08 kJ mol-1,respectively, and the∆Sm

0 of SDMA was calculated consider-ing the ∆Hm

0 value. Except for SDMA, the value of standardenthalpy of micellization,∆Hm

0 , is so low that it cannot bemeasured in a microcalorimeter and has been neglected incalculating ∆Sm

0 . Table 4 shows that∆Sm0 increases with

increasing X212 for 212/POE systems, whereas this valuedecreases with an increase inXSDMA for SDMA/POE mixtures.A high value of∆Sm

0 indicates that the process of micellizationis entropy controlled.17-23

The calculated free energy contributions from each part, thetotal free energy change, the cmc’s, and the packing parametersof the pure components and their mixtures are reported inTable 6, whereby good correlation with the experimentallyobserved cmc was obtained. This Table shows that purecomponents and their mixtures form nonspherical micelleswhere the micellar radius exceeds the critical chain length.

Conclusions

1. The anionic gemini surfactant 212 in its pure state andmixtures with POEs show a greater tendency to be adsorbed atthe air/water interface than its monomer, SDMA, and SDMA/POE mixtures, observed from their pC20 and∆Gad

0 values. Thesurface activity increases with increasing mole fraction of ionicsfor 212/POE mixtures, but the reverse trend is observed in thecase of SDMA/POE mixtures.

2. Although SDMA is the monomer of gemini 212, it has agreater area of exclusion at the surface due to the formation ofan intramolecular hydrogen bond. Similarly, in the binarymixtures, systems of 212/POE have lowerAmin values comparedto those of SDMA/POE.

TABLE 5: Free Energy and Interaction Parameters fromMaeda’s Modela

mole fraction(XI) d ln Cm/dXI XmI fI fN gex â

212/C12E8

0.25 -0.24 0.30 1.31 0.55 -0.35 -1.660.50 -0.52 0.63 1.16 0.65 -0.07 -0.280.75 -0.80 0.90 1.00 0.99 -0.01 -0.06

212/C12E5

0.25 -0.18 0.28 1.22 0.58 -0.34 -1.660.50 -0.34 0.58 1.14 0.63 -0.12 -0.480.75 -0.49 0.84 1.05 0.73 -0.01 -0.09

SDMA/C12E8

0.25 1.51 -0.030.50 2.13 -0.030.75 2.76 0.23 0.19 1.16 -0.27 -1.53

SDMA/C12E5

0.25 1.60 -0.050.50 2.18 -0.050.75 2.77 0.23 0.16 1.16 -0.31 -1.74

a Reference 30.

TABLE 6: The Parameters Obtained from Models of Nagarajan and Israelachvili

surf/X212/XSDMA ae/(Å)2 P R/Å κ-1/Å -(∆µg0/kT)T -(∆µg

0/kT)I -(∆µg0/kT)H -(∆µg

0/kT)P -∆Gm0 /kJ mol-1 cmc× 105/M

pure212 69.65 0.58 9.66 9.58 31.60 13.36 2.78 0.09 38.73 1.17SDMA 48.52 0.43 14.44 9.45 19.75 5.10 5.10 0.06 23.90 421.13C12E8 49.42 0.42 14.17 9.57 19.75 5.87 0.57 34.81 5.54C12E5 49.44 0.42 14.17 9.58 19.75 5.88 0.57 34.82 5.52

212/C12E8

0.25 59.54 0.52 8.59 9.57 25.68 9.24 1.62 0.07 37.12 2.210.50 64.39 0.55 9.15 9.57 28.52 11.12 2.22 0.08 38.02 1.550.75 67.63 0.57 9.47 9.57 30.42 12.47 2.58 0.09 38.52 1.27

212/C12E5

0.25 58.94 0.51 8.52 9.56 25.32 9.02 1.54 0.072 36.99 2.330.50 63.38 0.54 9.04 9.57 27.93 10.72 2.11 0.079 37.85 1.650.75 67.22 0.56 9.44 9.58 30.18 12.30 2.53 0.085 38.45 1.31

SDMA/C12E8

0.25 49.36 0.42 14.19 9.57 19.75 5.87 0.706 0.057 33.05 11.100.50 49.37 0.42 14.19 9.57 19.75 5.86 1.060 0.057 32.16 15.820.75 49.33 0.42 14.19 9.56 19.75 5.86 1.178 0.057 31.86 17.81

SDMA/C12E5

0.25 49.37 0.42 14.19 9.57 19.75 5.87 0.942 0.057 32.45 1.410.50 49.36 0.42 14.19 9.57 19.75 5.87 1.060 0.057 32.15 1.590.75 49.35 0.42 14.19 9.57 19.75 5.87 1.178 0.057 31.86 17.94


3. The free energy of micellization (∆Gm0 ) obtained from

Maeda’s model is comparable with that calculated from regularsolution theory for 212/POE mixtures, but deviates withincreasing mole fraction of SDMA (XSDMA) in SDMA/POEmixtures.

4. High values of∆Sm0 of all the binary mixtures denote that

the process of micellization is entropy controlled.5. All the pure surfactants and their binary mixtures accom-

modate the nonspherical shape, and thus the micellar radiusexceeds the critical chain length.

Finally, at 0.1 M NaCl at pH 11, both gemini and its monomershow significant interaction with preferentially low-chain POEnonionic surfactants.

Acknowledgment. T.C. thanks CSIR, Govt. of India, for aJunior Research Fellowship and is also thankful to K. Tsubone,Japan, for providing the samples.

References and Notes

(1) Menger, F. M.; Littau, C. A.J. Am. Chem. Soc. 1991, 113, 1451.(2) Menger, F. M.; Littau, C. A.J. Am. Chem. Soc.1993, 115, 10083.(3) Rosen, M. J.CHEMTECH1993, 23, 30.(4) Zana, R.Nature1993, 362, 228.(5) Alami, E.; Beinert, G.; Marie, P.; Zana, R.Langmuir1993, 9, 1465.(6) Frindi, M.; Zana, R.Langmuir1994, 10, 1140.(7) Song, L. D.; Rosen, M. J.Langmuir1996, 12, 1149.(8) Rosen, M. J.; Mathias, J. H.; Davenport, L.Langmuir 1999, 15,

7340.(9) Menger, F. M.; Keiper, J. S.Angew. Chem., Int. Ed.2000, 39, 1906.

(10) Rosen, M. J.Cosmet. Toiletries1998, 113, 49.(11) Alagova, G.; Kochijashky, I. I.; Sierra, M. L.; Kwetkat, K.; Zana,

R. J. Colloid Interface Sci.2001, 235, 119.(12) Tsubone, K.; Tajima, K.J. Oleo Sci.2002, 51, 123.(13) Tsubone, K.; Arakawa, K. Y.; Rosen, M. J.J. Colloid Interface

Sci.2003, 262, 516.(14) Kunieda, H.; Masuda, N.; Tsubone, K.Langmuir2000, 16, 6438.

(15) Tsubone, K.; Ghosh, S.;J. Surfactants Deterg. 2003, 6, 225.(16) Tsubone, K.; Ghosh, S.J. Surfactants Deterg.2004, 7, 47.(17) Moulik, S. P.; Ghosh, S.J. Mol. Liq. 1997, 72, 145.(18) Ghosh, S.; Moulik, S. P.J. Colloid Interface Sci.1998, 208, 357.(19) Ghosh, S.J. Colloid Interface Sci. 2001, 244, 128.(20) Khatua, P. K.; Ghosh, S.; Ghosh, S. K.; Bhattacharya, S. C.J.

Dispersion Sci. Technol.2004, 25, 741.(21) Chakraborty, T.; Ghosh, S.; Moulik, S. P.J. Phys. Chem. B2005,

109, 14813.(22) Ghosh, S.; Banerjee, A.Biomacromolecules2002, 3, 9.(23) Ghosh, S.Colloids Surf., A: Physicochem. Eng. Aspects2005, 6,

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1984, 262, 948. Motomura, K.; Aratono, M.; Ogino, K.; Abe, M. InMixedSurfactant Systems; Ogino, K., Abe, M., Eds.; Dekker: New York, 1993;p 99.

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mixed micelle formation among anionic gemini surfactant (212) and its monomer (sdma) with...

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