8080
J. Phys. Chem. B 2007, 111, 8080-8088
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 Chakraborty Centre 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(sodium N-dodecanoyl-β-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 NaCl at pH 11 to determine physicochemical properties such as critical micellar concentration (cmc), surface tension at the cmc (γcmc), maximum surface excess (Γmax) and minimum area per surfactant molecule at the air/water interface (Amin). The theories of Rosen, Rubingh, Motomura, Maeda, and Nagarajan have been applied to investigate the interaction between those surfactants at the interface and in the micellar solution, the composition of the aggregates formed, the theoretical cmc in pure and mixed states, and the structural parameters as proposed by Tanford and Israelachvili. Various thermodynamic parameters (free energy of micellization and interfacial adsorption) have been calculated with the help of regular solution theory and the pseudophase model for micellization.
Introduction Conventional surfactant contains one hydrophilic and one hydrophobic group. Geminis are a special class of surfactants1-3 where two monomeric surfactants (two hydrophilic and two hydrophobic groups) are coupled together via a spacer. Geminis have attracted considerable interest4-9 for their various surfaceactive properties superior to those of corresponding conventional surfactants. These compounds have much lower critical micellar concentration (cmc) values and much greater efficiency in reducing the surface tension of water.3 Due to the presence of two hydrophobic tails per gemini molecule, surface activity is enhanced and increased with increasing chain length. Because of the presence of hydrophilic spacers in a gemini molecule, solubility in water increases highly. Due to its enhanced surface activity, emulsifying property, enzyme inhibiting activity, and mildness to skin,9 gemini finds manifold applications in the detergent and cosmetic industries. In practical fields, the properties of mixtures of surfactants are important. The presence of two charge-sites in an anionic gemini surfactant proposes stronger interaction with neutral and cationic surfactants than that of conventional surfactants.10 Studies of anionic gemini surfactant with polyethoxylated nonionic surfactant show the search for synergism in micellization. Recently, a study of anionic gemini surfactant and polyethoxylated nonionic surfactant showed that a mixture of an anionic gemini surfactant with a hydrophobic spacer and a nonionic surfactant exhibits synergism, although a mixture of an anionic gemini surfactant with a hydrophilic spacer and a nonionic surfactant does not show synergism in micellization.11,12 Recently, an anionic gemini surfactant N,N′-ethylene(bis(sodium N-dodecanoyl-β-alaninate)), that is, (CH2)2[N(COC11H23)CH2CH2CO2Na]2, named 212, having N,Ndialkylamide and carboxylate groups in the molecule, a dimer corresponding to sodium N-dodecanoyl-N-methyl alaninate * Corresponding author. E-mail:
[email protected]. Phone: (0091) 332414 6411. Fax: (0091) 3324146266.
(SDMA), and its homologues have been studied.12-16 The common behavior of this gemini is that it accepts a proton, releasing Na+ into the bulk phase during the micellization process.13 Here, we report a detailed tensiometric study of the mixed micellization and interfacial behavior of 212 and its monomer SDMA with nonionic surfactants, penta- and octaethylene glycol mono n-dodecyl ether (C12E5 and C12E8), respectively, in various compositions in 0.1 M NaCl solution at pH 11 and temperature 303 K. The chemical structures of 212, the corresponding monomer SDMA, C12E5, and C12E8 are presented in Scheme 1. The properties studied include the cmc, the surface tension at the cmc (γcmc), the negative log of the surfactant molar concentration required to reduce the surface tension of the solvent by 20 mN/m (pC20), the maximum surface excess at the air/water interface (Γmax), the minimum area per surfactant molecule at the air/water interface (Amin), thermodynamic parameters, viz., the standard free energy of micellization (∆ G0m) and the standard free energy of interfacial adsorption (∆ G0ad), and so forth. Rosen and Rubingh’s theories have been used to calculate the interaction parameters at the air/water interface as well as within the micelles. ∆G0m obtained from Maeda’s model has been compared with ∆G0m calculated from the pseudophase model. Israelachvili’s model has been used to predict the shape and packing parameter of the self-aggregated systems. Experimental Section Materials. The anionic gemini surfactant 212 and its monomer SDMA were gifted by K. Tsubone, Wakamiya 13104, Kanagawa, 254-0911, Japan. The procedures for its (212) synthesis and purification have been reported.14 The nonionic amphiphiles C12E5 and C12E8 were the products of Nikkol Chemical Co. (Tokyo, Japan). All solutions were prepared in double distilled water at pH 11 in the presence of 0.1 M NaCl,
10.1021/jp067761u CCC: $37.00 © 2007 American Chemical Society Published on Web 06/21/2007
Micellization of 212 and SDMA with C12E5 and C12E8
J. Phys. Chem. B, Vol. 111, No. 28, 2007 8081 obtained from Rosen’s model26,27 following the “successive method”. For this purpose, a computer program has been made on the basis of the following equations (4 and 5), and that program was run to determine the values of Xσ and βσ. The necessary equations are
SCHEME 1
(XσI )2 ln(XIC0m/XσI C0I ) (1 - XσI )2 ln[(1 - XI)C0m/(1 - XσI )C0N]
)1
(4)
and
β ) σ
and experiments were done under thermostated conditions at 303 K with an accuracy of (0.01 K. Method. The tensiometric experiments were performed using a platinum ring by the ring detachment method in a calibrated du Nou¨y tensiometer (Kru¨ss, Germany). The detailed procedure has been reported earlier.17-23 Each experiment was repeated several times to achieve good reproducibility. The γ values were accurate within (0.1 mN m-1. Theoretical Section
n
)
Cm
∑ i)1
() Xi
Ci
(1)
(XmI)2 ln(XICm/XmICI) (1 - XmI)2 ln[(1 - XI)Cm/(1 - XmI)CN]
Cm
n
)
∑ i)1
() Xi
fiCi
(2)
Here, Xi and fi denote the stoichiometric mole fraction of component “i”, and its activity coefficient in solution, respectively. The terms Ci and Cm are the cmc’s of the ith component and the mixture, respectively. Clint’s equation makes the difference between ideal and nonideal mixtures. Thermodynamically, Motomura25 considered mixed micelles as a macroscopic bulk phase, and the related energetic parameters can be found from the excess thermodynamic quantities. The fundamental equation for the micellar mole fraction of ionic surfactant in the binary surfactant mixture (XmI) is
XmI ) Xˆ I - (Xˆ NXˆ I/C ˆ m)(∂C ˆ m/∂Xˆ I)T,P
(3)
where Xˆ I and C ˆ m may be defined as follows:
Xˆ I )
νIXI νNXN + νIXI
β)
The subscripts I and N represent ionic and nonionic surfactants, respectively, X represents the stoichiometric mole fraction, and ν represents the number of ions dissociated by the surfactant. The interfacial molecular interaction parameter (βσ) at the air/water interface for the mixed monolayer formation can be
(6)
ln(XICm/XmICI) (1 - XmI)2
(7)
where XmI and XI denote the same meaning as before, and CI, CN, and Cm are the cmc’s of ionic and nonionic surfactants and their mixture, respectively. The activity coefficients of ionic and nonionic components in the mixed micelle, fI and fN, can be evaluated from the equations
fI ) exp[β(1 - XmI)2]
(8)
fN ) exp[βXmI2]
(9)
and
Maeda’s model29 is applicable for solutions with moderately high ionic strength where the short range of the electrostatic interaction is no longer negligible. From the model, the decrease in ionic head group repulsion in an ionic/nonionic mixed micelle is due to the presence of nonionic surfactant molecules in the micellar phase. The proposed equation for the standard free energy change due to the micellization process as a polynomial function of the ionic mole fraction in the micellar phase, XI, is
and
C ˆ m ) (νNXN + νIXI)Cm
)1
and
whereas the formation of nonideal mixed micelles can be expressed as
1
(5)
(1 - XσI )2
where XI and XσI are the stoichiometric mole fractions of ionic surfactant in the mixture and in the adsorbed interfacial monolayer, respectively. C0I , C0N, and C0m are the molar concentrations in the solution phase of ionic and nonionic surfactants and their mixture, respectively, at a constant γ value. Again, in the mixed micellar system, the micellar molecular interaction parameter (β) is calculated from Rubingh’s equation28 following a similar iterative or successive method, using
Both ideal and nonideal mixed micelles are possible. For ideal mixed micelles, Clint’s equation24 is followed by the relation
1
ln(XIC0m/XσI C0I )
∆G0m ) RT(B0 + B1XI + B2XI2)
(10)
B0 ) ln XCN
(11)
where
XCN is the cmc of nonionic surfactant in the mole fraction unit. If the nonionic surfactants self-assemble among themselves, the micellar free energy change is expressed as a dimensionless
8082 J. Phys. Chem. B, Vol. 111, No. 28, 2007
Ghosh and Chakraborty
quantity, B0 () ln XCN ) ∆G0m/RT). The parameter B1 is related to the standard free energy change associated with the introduction of one ionic species into a nonionic micelle coupled with the release of one nonionic species from the micelle; that is, B1 plays an essential role in a change in the cmc values of nonionic micelles when an ionic species enters the micelle.29 B2 is the interaction parameter in the micellar phase. R and T denote the universal gas constant and absolute temperature, respectively. Again,
B1 + B2 ) ln
( ) XC I
(12)
XCN
(XCI is the cmc of ionic surfactant in the mole fraction unit), and
B2 ) -β
(13)
(β being the interaction parameter in the micellar phase obtained from eq 7). Very recently, Maeda30 proposed another theoretical model based on the Gibbs-Duhem equation considered by Hall31 to predict the excess free energy (gex) of the ionic-nonionic mixed micelle, which is even applicable to the low ionic strength regime. The model relates gex and XmI as
gex ) XmI ln fI + (1 - XmI) ln fN
Xm I )
[1 + ν(1 - XI){XI(d ln Cm/dXI) + 1}]
(15)
The degree of counterion binding (ν) is negligible in our case due to the presence of an excess amount of salt in the medium, and the equation becomes
XmI(ν)0) ) XI[1 - (1 - XI)(d ln Cm/dXI)]
(16)
The activities of the ionic and nonionic components are given by
aI ) XmIfI ) XI
( ) ( ) ( ) ( )
∆µ0g ∆µ0g ) kT kT
Cm CI
and
+
T
∆µ0g ∆µ0g + kT I kT
+
H
∆µ0g kT
P
(19)
and, following Tanford’s rationale, the interfacial [(∆µ0g/kT)I] and head [(∆µ0g/kT)H] contributions were calculated from
( ) ()
∆µ0g γ ) a kT I kT e
(14)
where XmI can be calculated from the ln Cm versus XI plot using the equation
XI[1 - (1 - XI)(d ln Cm/dXI)]
where g is the aggregation number of the aggregate, and ∆µ0g is the difference in the standard state chemical potential between a surfactant monomer present in an aggregate and that in a singly dispersed state in solution. In the phenomenological model of Nagarajan,33 there are four different contributions for (∆µ0g/kT), viz., (1) (∆µ0g/kT)T, which is a negative free energy contribution arising out of the transfer of the surfactant tail from solution to the more favorable hydrocarbon-like environment of the aggregate core; -1.4644 and -3.6423 (at 303 K) contributions per -CH2- and -CH3 group were considered; (2) (∆µ0g/kT)I, which is a positive contribution that accounts for the allowance of the penetration of water molecules to the aggregate core; (3) (∆µ0g/kT)H, which is another positive contribution arising out of the repulsive (steric or electrostatic) interaction between the head groups crowding at the aggregate surface; and (4) (∆µ0g/kT)P, which is the contribution of packing of a monomer within the core of the aggregate. Thus,
and
( ) () ∆µ0g kT
)
H
R 1 kT ae
where R is the headgroup repulsion parameter (R ) γae2), and ae is the area per surfactant monomer at the interface of the aggregate core and was evaluated using
ae )
[ ( )] 2πe2d 1 γ 1 + κl0
1/2
where e is the electronic charge, d is the capacitor thickness in the double-layer model, is the permittivity or dielectric constant of the bulk solution (80 for water), γ is the surface tension value calculated from Nagarajan’s model, κ-1 is the Debye length depending on the ionic strength of the medium, and l0 is the extended tail length per surfactant monomer and was obtained from Tanford’s equation
l0 e lmax ≈ (0.154 + 0.1265nc) nm aN ) (1 - XmI)fN ) (1 - XI)
Cm CN
where nc 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
β can be calculated from
β)
gex XmI(1 - XmI)
(17)
According to Tanford,32 the equation for the equilibrium of a monomeric surfactant in the bulk solution and in the micellar aggregate is
ln XCI )
∆µ0g kT
(18)
P)
V0 l0ae
where V0 is the volume of exclusion per monomer in the aggregate and is given by Tanford’s equation as
V0 ≈ (0.0274 + 0.0269nc) nm3 The micelles will be spherical (P < 1/3), nonspherical (1/3 < P < 1/2), vesicles or bilayers (1/2 < P < 1), or inverted
Micellization of 212 and SDMA with C12E5 and C12E8 (P > 1), depending on the value of the packing parameter. The radius of the aggregate, R was calculated from
R)
3V0 ae
nonuniformly,35
Assuming that the tail deforms energy can be calculated from
( ) ∆µ0g kT
P
)
the packing free
Q a′e
( )
a′e )
(
1 ∂γ Γmax ) lim 2.303nRT Cfcmc ∂ log C
Amin )
27 20 10 Qsph ) V L, Qcyl ) V L, and Qbilayer ) VL 8 0 8 0 8 0 and a′e is given by
of a monolayer prior to micellization. The same can also be predicted from the Gibbs surface excess (Γmax) obtained from the slope close to the micellization regime18,19 of the aforementioned plot using the equation
(20)
The minimum area per surfactant head group at the air/water interface (Amin) is related to Γmax as
with
( )
J. Phys. Chem. B, Vol. 111, No. 28, 2007 8083
( )
)
R 2Q/ae + γ γ/kT
where L 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 than ae1/2/lCH2, the contribution of the spacer to the (∆µ0g/kT)T was not considered.36 It was also neglected toward the packing free energy as [(S + 1)lCH2] > aeff, with aeff ) V0/ηπR, where η 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 contribution per monomer were accounted in (∆µ0g/kT)T, (∆µ0g/kT)I, and (∆µ0g/kT)P, where contribution of the tail is important. Due to the presence of two head groups per gemini molecule, a correction for the nonuniformity effect in (∆µ0g/kT)H was done following Camesano et al.36 For mixtures of nonionics with 0 gemini, the weighted part in (∆µ0g/kT)I and (∆µ g/kT)H was corrected accordingly. From Nagarajan’s model, the value of ∆G0m was also evaluated, which is the sum of the chemical potential contributions over the different processes. Results and Discussion The high surface tension of water is due to strong hydrogen bonding among the water molecules, leading to enhanced cohesive force, which resists the separation of a water column into two. When a surfactant is added in water, the surfactant molecules first populate at the air/water interface in order to avoid the highly energetically unfavorable interaction of water with the hydrophobic tail of the surfactant, and the surfactant head groups are buried in the aqueous environment while the tails remain in the air phase. This, in turn, hinders the intermolecular hydrogen bonding present on the surface of a pure aqueous phase, and surface tension starts decreasing. The decrease in the γ value continues until the air/water interface is saturated with surfactant monomers. Beyond this saturation, the added surfactants assemble among themselves to form aggregates to ensure a hydrophilic periphery, hiding the hydrophobic tail within a cage to avoid water. The γ value, therefore, does not change (beyond γcmc) after reaching a certain concentration of surfactant. This concentration of surfactant is called the cmc and is obtained from the break point in the γ versus log[surfactant] profile (Figure 1). The constant value of surface tension at the cmc is called γcmc and is a measure of the efficacy of the surfactant to populate the air/water interface in the form
1018 NAΓmax
(21)
where R is the universal gas constant (8.314 J mol-1 K-1), NA is Avogadro’s number, and n is the number of ionic species whose concentration at the interface varies with the change in the [surfactant] in the solution.13 In the presence of an excess amount of Na+ in 0.1 M NaCl, n ) 1.7,13 Γmax and Amin are expressed in moles per square meter and square nanometers per molecule, respectively. Another physical quantity, pC20, is defined as pC20 ) -log C20, where C20 is the surfactant molar concentration required to decrease the surface tension of pure water by 20 mN m-1 and is also an indication of the preference of a surfactant toward the air/water interface compared to the bulk prior to micellization.21-25 The pC20 value can measure the efficiency of adsorption of the surfactant at the interface.21 A high value of pC20 denotes that the surfactant adsorbs more efficiently at the interface, reducing the surface tension of the solution. The cmc value of the pure surfactant determined by the surface tension method at pH 11 and 0.1 M NaCl increases in the order of 212 < C12E5 < C12E8 < SDMA. The nonionics have naturally less cmc compared to the anionic SDMA, which has a similar tail length containing 12 carbon atoms. This is expected by the charged head group present in SDMA, which has a greater tendency to populate the bulk water as a result of solvation by the polar solvent. Consequently, SDMA has the lowest efficacy to populate the air/water interface compared to the nonionics, as evidenced from its lowest pC20 value. This is also reflected in its lowest Γmax, as obtained from Table 1 using eq 1. The Amin is also largest for SDMA, as expected from the stronger electrostatic head-head repulsion at the air/water interface. The higher cmc of SDMA compared to its dimer, 212, is first a consequence of the greater hydrophobicity of its dimer, owing to its double-tailed structure. 212 also has a greater tendency to be adsorbed at the air/water interface throughout the monolayer formation, as indicated by its larger pC20 and Γmax values given in Table 1. Although 212 is the dimer of SDMA, the Amin of SDMA is greater than that of 212. Similar observation has also been reported by Menger et al.9 So, in addition to electrostatic repulsion, this greater Amin of SDMA can be explained on the basis of the formation of an intramolecular hydrogen-bonded ring structure between N-methylamide and protonated carboxylate groups in the SDMA molecule15 at the monolayer, requiring a greater area of exclusion at the interface. This type of ring formation is restricted in the dimeric gemini 212 due to steric hindrance, which reduces the area of exclusion and enhances surface population. Moreover, as reported earlier,13 there occurs an exchange of Na+ ions from the 212 monomer with H+ ions from water, decreasing the charge of the head group of 212. This, in turn, reduces the headhead repulsion, and hence the Amin of 212 is smaller compared to that of its monomer, reflecting compact packing of the
8084 J. Phys. Chem. B, Vol. 111, No. 28, 2007
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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. 212 SDMA C12E8 C12E5
cmc × 105/ mol dm-3
γcmc/ mN m-1
pC20
Γmax × 106/ mol m-2
Amin/ nm2 molecule-1
-∆G0m/ kJ mol-1
∆S0m/ J K-1 mol-1
-∆G0ad/ kJ mol-1
1.44 265.0 4.34 3.64
31.6 40.1 31.0 32.4
6.05 3.36 5.51 5.40
2.82 2.54 3.48 3.97
0.59 0.65 0.48 0.42
37.38 24.52 34.66 35.09
123.36 84.49 114.38 115.81
51.38 36.73 46.18 44.84
interface by 212 monomers compared to that by SDMA. The outcome of the above facts is the increasing values of Γmax and pC20 of 212. The nonionic amphiphiles in this study have the same tail groups (12 carbon atoms) and a varied number of ether units in the head groups. C12E8 has a greater cmc compared to C12E5, whereas γcmc and Γmax for C12E5 are larger; that is, Amin is smaller. All these variations are the manifestation of the presence of a different number of ether groups in the head group of two amphiphiles. Due to the higher degree of solvation of C12E8 compared to that of C12E5, the C12E8 molecule feels comparatively comfortable within the bulk water and, consequently, has a lesser tendency to populate the interface. The surfactant1bulk S surfactant1interface (superscript 1 corresponds to a monomer) equilibrium, therefore, remains somewhat left-shifted for C12E8 than for its lower homologue. Correspondingly, surface saturation indicates a micellization threshold in tensiometric experiments and occurs at a somewhat greater concentration for C12E8
in contrast to that for C12E5. This is also reflected in the trend in Γmax, which reflects the tendency of the surfactant to be adsorbed at the air/water interface. The Amin is also larger for C12E8, as expected due to the presence of greater number of ether moieties in the head group. For C12E8 with a longer ethoxylate (EO) chain, the lower γcmc value and higher pC20 reflect higher surface activity of a micellar solution due to a greater 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 fraction of 212 (X212), presented in Table 2. For the comparison between the same mole fractions of 212 with either of the POEs, the 212/C12E8 always has the higher cmc. This fact is, again, the outcome of an increased degree of solvation of the 212/C12E8 mixture compared to that of 212/C12E5 owing to the increasing ether unit in C12E8. The value of γcmc increases slightly with increasing X212 for either mixture. These values are comparatively higher for 212/C12E8 relative to those for 212/C12E5. The
Micellization of 212 and SDMA with C12E5 and C12E8
J. Phys. Chem. B, Vol. 111, No. 28, 2007 8085
TABLE 2: Surface Properties of Different Binary Mixtures in 0.1 M NaCl at pH 11 and 303 K X212 or XSDMA
cmc × 105/ mol dm-3
γcmc/ mN m-1
pC20
0.25 0.50 0.75
2.23 2.10 1.72
31.6 31.9 32.9
5.73 5.84 5.92
0.25 0.50 0.75
2.00 1.91 1.69
25.8 28.6 29.6
0.25 0.50 0.75
5.34 7.78 15.5
0.25 0.50 0.75
4.36 6.50 13.0
Γmax × 106/ mol m-2
Amin/ nm2 molecule-1
Aimin/ nm2 molecule-1
Clint cmc × 105/ mol dm-3
212/C12E8 3.65 3.05 2.97
0.45 0.54 0.56
0.53 0.56 0.58
2.89 2.16 1.73
5.88 5.81 6.22
212/C12E5 4.02 3.52 2.64
0.41 0.47 0.62
0.50 0.53 0.55
2.63 2.06 1.70
34.3 35.6 36.3
5.21 5.07 4.80
SDMA/C12E8 3.27 2.88 2.63
0.51 0.58 0.63
0.48 0.49 0.50
5.76 8.54 16.5
32.0 33.5 34.3
5.47 5.15 4.89
SDMA/C12E5 3.38 3.33 3.06
0.49 0.50 0.57
0.44 0.47 0.49
4.83 7.18 14.0
values of pC20 increase a little bit with increase in X212 in the case of 212/C12E8, whereas these values are irregular for other mixtures containing 212. Overall higher γcmc and lower pC20 values of the 212/C12E8 mixture indicate less surface activity compared to the 212/C12E5 system due to greater steric repulsion between the molecules of 212 and C12E8 relative to that of 212 and C12E5. The decreased Γmax upon increasing X212 in either mixture signified a decreased affinity of the mixtures for the interfacial adsorption, as expected from increased solvation of the ionic head group of the gemini. Consequently, the Amin values increase with increasing X212. The ideal Aimin is calculated with the help of Amin values of pure components using
Aimin ) XσI AImin + (1 - XσI )ANmin
(22)
where AImin and ANmin are the minimum area per molecule at the air/water interface of ionic and nonionic surfactants, respectively. XσI is the mole fraction of ionic surfactant at the air/water interface. The smaller Amin compared to Aimin, except when X212 ) 0.75 for the 212/C12E5 system, shows some contraction in surface packing. The divergence is maximum for the mixture containing less 212, showing greater compactness. For both of the SDMA/POE mixtures, the cmc increases with increasing XSDMA, as expected from the higher cmc of SDMA. These cmc values are between the individual cmc’s of pure amphiphiles. For the same XSDMA, 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 that of its higher homologue. The value of γcmc also increases with increasing XSDMA. The decreased γcmc of the mixtures compared to pure SDMA reflects the enhanced surface activity of the mixed micellar solution upon increasing the molar ratio of SDMA. The values of γcmc for the SDMA/C12E5 mixtures are lower than those of the corresponding SDMA/C12E8 mixtures, indicating the higher surface activity of the former pair. The pC20 value decreases upon increasing XSDMA, showing the decreasing tendency of mixed monolayer formation at the initial stage of surfactant addition. Due to the lower tendency of SDMA toward interfacial adsorption, Γmax values of both SDMA/POE mixtures decrease with increasing XSDMA, pointing to the propensity of surface adsorption of the mixed surfactant during the saturation of the monolayer. The higher value of pC20 and Γmax of the SDMA/C12E5 pair also indicates the increased tendency of the mixture to be adsorbed at the air/water interface throughout the process of monolayer formation and the more
compact structure of the monolayer compared to that of the SDMA/C12E8 pair, as also evidenced by the decreased value of the area of exclusion, Amin, of the SDMA/C12E5 mixture. The area of each component of SDMA/C12E8 is greater than that of SDMA/C12E5, denoting greater steric repulsion between the protonated SDMA and C12E8 with a longer EO chain. The ideal area of exclusion, Aimin, for all the mixtures, is less than that observed experimentally (Amin). This indicates that the monolayer is expanded compared to that expected ideally. It happens probably because of the presence of the ionic species in the monolayer, which effectively introduces the repulsive force among the surfactants at the interface. Interfacial and Micellar Interaction Parameters. From Table 2, it is observed that the experimental cmc values of all systems are lower than the values calculated by Clint’s method, indicating nonideal behavior. The mole fraction of a surfactant in the mixed micelle (XmI) determined by Motomura’s equation and all the values for the binary mixtures in 0.1 M NaCl at pH 11 evaluated by the models of Rosen and Rubingh are presented in Table 3. It shows that XmI determined by all these models increases with increasing X212 and XSDMA. These values are higher for 212/POE mixtures compared to those for SDMA/ POE systems. The values of XmI (Motomura’s model) can only be determined for XSDMA ) 0.75 of SDMA/POE systems. For both of the 212/POE mixtures with X212 ) 0.25, XσI (Rosen’s model) and XmI (Rubingh’s model) are almost the same, indicating that both of the components of the mixtures have equal surface activity as well as efficacy toward micellization, but, for other compositions, the ionic surfactant prevails over the nonionic one in those activities. The reverse trend is observed in the case of SDMA/POE mixtures. For each case, both βσ and β values are negative (Table 3), indicating synergistic interaction between two components of the solution and, hence, lowering of the cmc compared to that expected from Clint’s equation (Table 2). For ionic-nonionic combinations, all the experiments were done at constant ionic strength and counterion of the solution by 0.1 M NaCl to maintain the accuracy in calculating β values. It is reported37 that a POE molecule (where each ether oxygen is interspaced by two methylene groups) in combination with anionic surfactant forms a “crown ether” by accepting an alkali metal ion from the solution phase into the cavity center of the ligand. In this arrangement, all the O atoms lie in the plane of the ring, pointing inward, toward the Na+ ion. Due to this
8086 J. Phys. Chem. B, Vol. 111, No. 28, 2007
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TABLE 3: Molecular Interaction Parameters of Binary Mixtures in 0.1 M NaCl at pH 11 and 303 K Rosen’s model σ
Rubingh’s model βσ
Motomura’s model
β
fI/fN
Xm I
212/C12E8 0.50 0.74 0.90
-1.03 -0.15 -0.06
0.77/0.77 0.99/0.92 1.00/0.95
0.245 0.659 0.886
-3.40 -1.75 -1.71
212/C12E5 0.47 0.69 0.88
-1.11 -0.37 -0.04
0.73/0.78 0.97/0.84 1.00/0.97
0.243 0.599 0.834
0.04 0.05 0.06
-3.18 -2.44 -1.50
SDMA/C12E8 0.06 0.09 0.10
-2.94 -2.16 -1.00
0.07/0.99 0.17/0.98 0.44/0.99
0.498
0.11 0.22 0.29
-5.30 -6.92 -7.41
SDMA/C12E5 0.08 0.09 0.10
-3.52 -2.40 -1.19
0.05/0.98 0.14/0.98 0.38/0.99
0.498
X212 or XSDMA
XI
0.25 0.50 0.75
0.49 0.72 0.89
-0.86 -0.21 -0.10
0.25 0.50 0.75
0.49 0.63 0.77
0.25 0.50 0.75 0.25 0.50 0.75
Xm I
rearrangement, POE behaves as a positively charged surfactant. Table 3 shows that the βσ and β values of SDMA/C12E5 are greater than those of 212/C12E5, and those of SDMA/C12E8 are greater than those of 212/C12E8. This is probably due to the synergistic electrostatic interaction between the hydrophilic groups of the anionic SDMA molecule and the positively charged POE molecule, rather than some steric repulsive interaction occurring between the two hydrophilic groups of protonated 212 molecules and the positively charged POE molecule. Again, according to Fajan’s rule, the smaller the size and greater the charge density of the cation, the more effective is its polarizing power. So, here, due to smaller size of C12E5 relative to that of C12E8 (although both of them have the same charge density), it also interacts more strongly with anionic 212 or SDMA, which is reflected in the βσ and β values of these mixtures. The synergistic interaction in the mixed micelle of all the mixtures, except when X212 ) 0.25 in 212/C12E8 systems, is weaker than that in the mixed adsorption film because it is more difficult to incorporate two hydrophobic groups of the surfactants into the mixed micelle than it is to accommodate them at the planar interface. In each case, except for 212/C12E8 (X212 ) 0.25), βσ - β values are negative, indicating a greater tendency toward population of the surface than toward micellization. Table 3 denotes that the activity coefficients (fI and fN) of the mixtures (212/POE) increase with increasing mole fraction, and fI (or f212) ) 1 shows ideal behavior at X212 ) 0.75. For SDMA/POE systems, fI (or fSDMA) shows low value whereas fN (or fPOE) represents the value close to unity, indicating ideality. Thermodynamics of Micellization and Interfacial Adsorption. Considering the negligible degree of counterion dissociation of 212,13 the standard free energy of micellization (∆G0m) is calculated from regular solution theory using
∆G0m ) RT ln XCm
(23)
where XCm is the cmc of the mixture in the mole fraction unit. The standard free energy of interfacial adsorption, ∆G0ad, at the air/saturated monolayer interface of the micelle has been determined from the relation17-23,38
∆G0ad ) ∆G0m -
( ) Πcmc Γmax
(24)
TABLE 4: Thermodynamic Parameters of Binary Mixtures in 0.1 M NaCl at pH 11 and 303 K Maeda’s modela X212 or XSDMA
-B0
B1
B2
-∆G0m/ -∆G0m/ ∆S0m/ -∆G0ad/ kJ mol-1 kJ mol-1 J mol-1 K-1 kJ mol-1
0.25 0.50 0.75
14.06 -2.14 1.03 -1.26 0.15 -1.16 0.06
212/C12E8 36.61 37.10 36.91 37.25 37.54 37.76
122.45 122.95 124.61
47.92 50.11 50.62
0.25 0.50 0.75
14.24 -2.03 1.11 -1.30 0.37 -0.96 0.04
212/C12E5 36.97 37.38 37.27 37.49 37.64 37.80
123.36 123.74 124.76
48.65 49.57 53.52
0.25 0.50 0.75
14.06
1.17 2.94 1.95 2.16 3.12 1.00
SDMA/C12E8 34.22 34.90 31.61 33.95 28.13 32.22
115.19 112.06 106.33
46.16 46.28 45.45
0.25 0.50 0.75
14.24
0.76 3.52 1.89 2.40 3.10 1.19
SDMA/C12E5 34.83 35.41 31.98 34.41 28.33 32.66
116.88 113.56 107.79
46.98 45.70 44.69
a
Reference 29.
Here, Πcmc denotes the surface pressure (γwater - γcmc) at the cmc. The higher the negative value of ∆G0ad, the higher is the efficacy of the surfactant to be adsorbed at the air/water interface. Table 1 shows that gemini 212 has greater surface activity than its monomer SDMA. The same trend can also be reflected in their mixtures with POE. In the case of binary mixtures, the surface adsorption increases with increasing mole fraction of the ionics in 212/POE mixtures, but the reverse trend is observed in SDMA/POE mixtures. The same prediction can also be drawn from the pC20 values of the mixtures as discussed earlier. The ∆G0m values for the pure surfactants are tabulated in Table 1 (the lower value of SDMA is compensated by considering the degree of counterion dissociation). This free energy is compared with that obtained using the model of Maeda (∆G0m).29 The values of ∆G0m, B0, B1, and B2 are presented in Table 4. For a binary system, the B0 value is constant. For 212/ POE systems, both B1 and B2 values decrease with increasing value of X212. But for SDMA/POE systems, the values of B1 increase with increasing XSDMA, although B2 decreases. In the case of SDMA/POE, the increase of B1 is due to the formation of intramolecular hydrogen bonds in the SDMA molecule. The negative values of B1 of 212/POE systems indicate the major
Micellization of 212 and SDMA with C12E5 and C12E8
J. Phys. Chem. B, Vol. 111, No. 28, 2007 8087
TABLE 5: Free Energy and Interaction Parameters from Maeda’s Modela mole fraction (XI)
a
d ln Cm/dXI
XmI
fI
fN
gex
β
0.55 0.65 0.99
-0.35 -0.07 -0.01
-1.66 -0.28 -0.06
0.25 0.50 0.75
-0.24 -0.52 -0.80
212/C12E8 0.30 1.31 0.63 1.16 0.90 1.00
0.25 0.50 0.75
-0.18 -0.34 -0.49
212/C12E5 0.28 1.22 0.58 1.14 0.84 1.05
0.58 0.63 0.73
-0.34 -0.12 -0.01
-1.66 -0.48 -0.09
0.25 0.50 0.75
1.51 2.13 2.76
SDMA/C12E8 -0.03 -0.03 0.23 0.19
1.16
-0.27
-1.53
0.25 0.50 0.75
1.60 2.18 2.77
SDMA/C12E5 -0.05 -0.05 0.23 0.16
1.16
-0.31
-1.74
Reference 30.
role of the tail-tail interaction in the stability of the mixed micelles. Here, gemini 212 has two chains of 12 carbons, whereas monomer SDMA and nonionics have only one 12carbon tail. Hence, B1 values are positive for SDMA/POE systems due to less tail-tail interactions. From Table 4, the close resemblance of ∆G0m calculated from regular solution theory and that from Maeda’s model for the 212/POE systems also reflects negligible counterion dissociation of the gemini as described earlier.13 These values are almost constant. For SDMA/POE mixtures, there is some discrepancy between the values of the free energy of micellization obtained from either method upon increasing XSDMA. 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 as close to the cmc of the nonionics as required by the Maeda’s model. Table 5 shows that micellar mole fractions of 212/POE systems are higher than the corresponding stoichiometric mole fractions. But discrepancy is observed in the case of SDMA/ POE systems. The values of activity coefficients of the ionic species (fI) decrease with the increasing mole fraction of 212 in the case of 212/POE systems, whereas the reverse is true for
the POE species. This discrepancy is probably due to the large difference in the cmc values of POE and SDMA, which is not permitted in Maeda’s model. For this system, gex and β values decrease with the increasing stoichiometric mole fraction of 212, and negative values of β indicate synergism. Applying the Gibbs-Helmholtz equation, the standard entropy of micellization, ∆S0m can be evaluated, which is equivalent to -(∆G0m/T). The cmc and ∆H0m of pure SDMA at 0.1 M NaCl and pH 11 at 303 K were measured in an ITC microcalorimeter, Omega (USA) to be 2.40 mM and 1.08 kJ mol-1, respectively, and the ∆S0m of SDMA was calculated considering the ∆H0m value. Except for SDMA, the value of standard enthalpy of micellization, ∆H0m, is so low that it cannot be measured in a microcalorimeter and has been neglected in calculating ∆S0m. Table 4 shows that ∆S0m increases with increasing X212 for 212/POE systems, whereas this value decreases with an increase in XSDMA for SDMA/POE mixtures. A high value of ∆S0m indicates that the process of micellization is entropy controlled.17-23 The calculated free energy contributions from each part, the total free energy change, the cmc’s, and the packing parameters of the pure components and their mixtures are reported in Table 6, whereby good correlation with the experimentally observed cmc was obtained. This Table shows that pure components and their mixtures form nonspherical micelles where the micellar radius exceeds the critical chain length. Conclusions 1. The anionic gemini surfactant 212 in its pure state and mixtures with POEs show a greater tendency to be adsorbed at the air/water interface than its monomer, SDMA, and SDMA/ POE mixtures, observed from their pC20 and ∆G0ad values. The surface activity increases with increasing mole fraction of ionics for 212/POE mixtures, but the reverse trend is observed in the case of SDMA/POE mixtures. 2. Although SDMA is the monomer of gemini 212, it has a greater area of exclusion at the surface due to the formation of an intramolecular hydrogen bond. Similarly, in the binary mixtures, systems of 212/POE have lower Amin values compared to those of SDMA/POE.
TABLE 6: The Parameters Obtained from Models of Nagarajan and Israelachvili ae/(Å)2
P
R/Å
κ-1/Å
-(∆µ0g/kT)T
-(∆µ0g/kT)I
212 SDMA C12E8 C12E5
69.65 48.52 49.42 49.44
0.58 0.43 0.42 0.42
9.66 14.44 14.17 14.17
9.58 9.45 9.57 9.58
31.60 19.75 19.75 19.75
pure 13.36 5.10 5.87 5.88
0.25 0.50 0.75
59.54 64.39 67.63
0.52 0.55 0.57
8.59 9.15 9.47
9.57 9.57 9.57
25.68 28.52 30.42
0.25 0.50 0.75
58.94 63.38 67.22
0.51 0.54 0.56
8.52 9.04 9.44
9.56 9.57 9.58
0.25 0.50 0.75
49.36 49.37 49.33
0.42 0.42 0.42
14.19 14.19 14.19
0.25 0.50 0.75
49.37 49.36 49.35
0.42 0.42 0.42
14.19 14.19 14.19
surf/X212/XSDMA
-(∆µ0g/kT)H
-(∆µ0g/kT)P
-∆G0m/kJ mol-1
cmc × 105/M
2.78 5.10
0.09 0.06 0.57 0.57
38.73 23.90 34.81 34.82
1.17 421.13 5.54 5.52
212/C12E8 9.24 11.12 12.47
1.62 2.22 2.58
0.07 0.08 0.09
37.12 38.02 38.52
2.21 1.55 1.27
25.32 27.93 30.18
212/C12E5 9.02 10.72 12.30
1.54 2.11 2.53
0.072 0.079 0.085
36.99 37.85 38.45
2.33 1.65 1.31
9.57 9.57 9.56
19.75 19.75 19.75
SDMA/C12E8 5.87 5.86 5.86
0.706 1.060 1.178
0.057 0.057 0.057
33.05 32.16 31.86
11.10 15.82 17.81
9.57 9.57 9.57
19.75 19.75 19.75
SDMA/C12E5 5.87 5.87 5.87
0.942 1.060 1.178
0.057 0.057 0.057
32.45 32.15 31.86
1.41 1.59 17.94
8088 J. Phys. Chem. B, Vol. 111, No. 28, 2007 3. The free energy of micellization (∆G0m) obtained from Maeda’s model is comparable with that calculated from regular solution theory for 212/POE mixtures, but deviates with increasing mole fraction of SDMA (XSDMA) in SDMA/POE mixtures. 4. High values of ∆S0m of all the binary mixtures denote that the process of micellization is entropy controlled. 5. All the pure surfactants and their binary mixtures accommodate the nonspherical shape, and thus the micellar radius exceeds the critical chain length. Finally, at 0.1 M NaCl at pH 11, both gemini and its monomer show significant interaction with preferentially low-chain POE nonionic surfactants. Acknowledgment. T.C. thanks CSIR, Govt. of India, for a Junior 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. CHEMTECH 1993, 23, 30. (4) Zana, R. Nature 1993, 362, 228. (5) Alami, E.; Beinert, G.; Marie, P.; Zana, R. Langmuir 1993, 9, 1465. (6) Frindi, M.; Zana, R. Langmuir 1994, 10, 1140. (7) Song, L. D.; Rosen, M. J. Langmuir 1996, 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. Toiletries 1998, 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. Langmuir 2000, 16, 6438.
Ghosh and Chakraborty (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. B 2005, 109, 14813. (22) Ghosh, S.; Banerjee, A. Biomacromolecules 2002, 3, 9. (23) Ghosh, S. Colloids Surf., A: Physicochem. Eng. Aspects 2005, 6, 264. (24) Clint, J. H. J. Chem. Soc., Faraday Trans. 1975, 71, 1327. (25) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948. Motomura, K.; Aratono, M.; Ogino, K.; Abe, M. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Dekker: New York, 1993; p 99. (26) Rosen, M. J. In Surfactants and Interfacial Phenomena, 2nd ed.; Wiley: New York, 1989. (27) Rosen, M. J.; Dahanayake, M. In Industrial Utilization of Surfactants: Principles and Practice; AOCS Press: Champaign, IL, 2000; pp 28-29. (28) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1, p 337. (29) Maeda, H. J. Colloid Interface Sci. 1995, 172, 98. (30) Maeda, H. J. Phys. Chem. B 2005, 109, 15933. (31) Hall, D. G. J. Chem. Soc., Faraday Trans. 1991, 87, 3529. (32) Tanford, C. In The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley and Sons: New York, 1980. (33) Nagarajan, R.; Ruckenstein, E. Langmuir 1991, 7, 2934. Nagarajan, R. Langmuir 2002, 18, 31. (34) Israelachvili, J. N. In Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991; Chapter 17, p 370. (35) Semenov, A. N. SoV. Phys. JETP 1985, 61, 733. (36) Camesano, T. A.; Nagarajan, R. Colloids Surf., A: Physicochem. Eng. Aspects 2000, 167, 165. (37) Huheey, J. E.; Keiter, E. A.; Keiter, R. L. In Principles of Structure and ReactiVity, 4th ed.; Harper Collins College Publication: New York, 1993; p 525. (38) Rosen, M. J.; Dahanayake, M., A.; Cohen, W. Colloids Surf. 1982, 5, 159. Rosen, M. J.; Aronson, S. Colloids Surf. 1981, 3, 201.
