J. Chem. Thermodynamics 44 (2012) 107–115

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J. Chem. Thermodynamics

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Aggregation behavior and intermicellar interactions of cationic Geminisurfactants: Effects of alkyl chain, spacer lengths and temperature

Marjan Hajy Alimohammadi a, Soheila Javadian a,⇑, Hussein Gharibi a, Ali reza Tehrani-Bagha b,Mohammad Rashidi Alavijeh a, Karim Kakaei c

a Department of Physical Chemistry, Tarbiat Modares University, P.O. Box 14115-117, Tehran, Iranb Institute for Colour Science and Technology, Tehran, Iranc Department of Chemistry, Maragheh University, Maragheh, Iran

a r t i c l e i n f o

Article history:Received 29 May 2011Received in revised form 2 August 2011Accepted 6 August 2011Available online 16 August 2011

Keywords:Surface tensionEnthalpy–entropy compensationThermodynamicMicellizationGemini surfactantsAggregationIntermicellar interaction

0021-9614/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.jct.2011.08.007

⇑ Corresponding author. Fax: +98 21 82883755.E-mail addresses: javadian_s@modares.ac.ir, javadi

a b s t r a c t

The aggregation behavior of the cationic Gemini surfactants CmH2m+1N(CH3)2(CH2)S (CH3)2 N CmH2m+1,2Br�

with m = 12, 14 and s = 2, 4 were studied by performing surface tension, electrical conductivity, pulsed fieldgradient nuclear magnetic resonance (PFG-NMR), and cyclic voltammetry (CV) measurements over thetemperature range 298 K to 323 K. The critical micelle concentration (CMC), surface excess (Umax), meanmolecular surface area (Amin), degree of counter ion dissociation (a), and the thermodynamic parametersof micellization were determined from the surface tension and conductance data. An enthalpy–entropycompensation effect was observed and all the plots of enthalpy–entropy compensation exhibit excellentlinearity. The micellar self-diffusion coefficients (Dm) and intermicellar interaction parameters (kd) wereobtained from the PFG-NMR and CV measurements. These results are discussed in terms of the intermicel-lar interactions, the effects of the chain and spacer lengths on the micellar surface charge density, and thephase transition between spherical and rod geometries. The intermicellar interaction parameters werefound to decrease slightly with increasing temperature for 14–4–14, which suggests that the micellar sur-face charge density decreases with increasing temperature. The mean values of the hydrodynamic radius,Rh, and the aggregation number, Nagg, of the Gemini surfactants’ m–4–m micelles were calculated from themicellar self-diffusion coefficient. Moreover, the Nagg values were calculated theoretically. The experimen-tal values of Nagg increase with increases in the chain length and are in good agreement with both previousresults and our theoretical results.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Gemini surfactants are composed of two hydrophobic chainsand two hydrophilic head groups connected by a spacer that canbe hydrophilic or hydrophobic and rigid or flexible [1,2]. These sur-factants have attracted considerable interest within both academicand industrial circles over the last decade because Gemini surfac-tants are superior to the corresponding conventional monomericsurfactants in a number of aspects. Gemini surfactants have a high-er surface activity, a lower CMC [3], better solubilizing power [4],much lower Krafft points [3–5], and better wetting [6], viscoelas-ticity, gelification, and shear thickening [4] than the correspondingconventional monomeric surfactants. Owing to their remarkableproperties, considerable effort has been invested in the designand synthesis of new Gemini surfactants [7–12] to study the rela-tionship between their molecular structures and their aggregationmorphologies in aqueous solution [13–17] and to examine the

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ans@yahoo.com (S. Javadian).

factors underlying the variation of their thermodynamic propertieswith the lengths of their chains and spacers [18–28].

There is no doubt that understanding the micellization requiresits complete thermodynamic characterization. The thermodynamicchanges associated with adsorption and micelle formation havebeen investigated from the theoretical and experimental view-points by many research groups.

In the present study, we carried out an investigation of the aggre-gation behaviors of several Gemini surfactants, including their ther-modynamics of micellization, adsorption in the air–liquid interface,the structures of their aggregates, and the variation of their intermi-cellar interactions with temperature. We used techniques includingsurface tension, conductometry, PFG-NMR, and CV. First, the ther-modynamic properties of micellization were determined by usingCMC and a values. Second, the PFG-NMR and CV measurements en-abled the investigation of the structures of the surfactants’ aggre-gates and their intermicellar interactions. Finally, by comparingthe results for these surfactants, we determined not only the effectsof varying the number of carbon atoms of the alkyl chain on thesolution properties of the Gemini surfactants but also the effects

108 M. Hajy Alimohammadi et al. / J. Chem. Thermodynamics 44 (2012) 107–115

of varying the hydrophobicity of the spacer chain on micelle forma-tion. In addition to the determination of the abovementioned micel-lar parameters, this research demonstrates, for the first time, theusefulness of CV in the study of the effects of increasing the lengthsof the hydrophobic tail and spacer of Gemini surfactants and thoseof varying the temperature on their micellar parameters, intermi-cellar interactions, and sphere to rod geometry changes.

2. Experimental

2.1. Materials

Gemini surfactants with quaternary ammonium bromide headgroups and linear alkyl tails with the general formula [CmH2m+1–N+–(CH3)2–(CH2)n–(CH3)2–N+–CmH2m+1]2 Br�, where m = 12 and14 and n = 2 and 4, referred to here as m–n–m, 2 Br� surfactants,were synthesized and purified by the known methods reportedpreviously [29].

2.1.1. Surface tension measurementsThe surface tension measurements were performed with a

Krüss K12 tensiometer by using the ring method [30,31]. The plat-inum ring was thoroughly cleaned and flame dried before eachmeasurement. The uncertainty of the measurements was±0.1 mN �m�1. In all cases, more than three successive measure-ments were carried out, and the standard deviation did not exceedmore than 0.08 mN �m�1. The temperature was maintained at aconstant value by circulating the thermostatted water throughthe jacketed vessel containing the solution. The temperature con-trol accuracy was within ±0.1 K.

2.1.2. Electrical conductivity measurementsThe measurements of the conductivity of the surfactant solu-

tions were performed with a conductometer, Jenway 4510. Afterinvestigating the conductivity of the solvent, three successive mea-surements of the conductivity of the surfactant solutions were car-ried out at a controlled constant temperature. The uncertainty ofthe measurements was ±0.01 lS � cm�1. The employed conductiv-ity cell was shown in SM.

2.1.3. NMR measurementsNMR self-diffusion measurements were performed on a Bruker

DRX 500 Avance NMR spectrometer at room temperature. A longi-tudinal eddy-current delay with a bipolar pulse pair (LEDBPP)pulse sequence [32] was used to determine the self-diffusion coef-ficients (D). In this technique, micelle self-diffusion is monitored byanalyzing the signals from trace amounts of tetramethylsilane(Me4Si) added to the solution, which are assumed to be completelysolubilized in the micellar phase. All NMR measurements wereperformed at 25 �C. The basic sequence was used with pulse fieldduration, d, of 5 ms and a time interval, D, of 200 ms between gra-dient pulses.

2.1.4. CV measurementsCV was performed by using an electrochemical analyzer, SAMA

500. A three-electrode system consisting of a working Pt electrode(the interface at which the redox reaction of interest occurs), a sat-urated Ag/AgCl reference electrode with a salt bridge containing3 M aqueous KCl solution (the electrode with a stable potentialagainst which the potential at the working electrode is measured)and the counter electrode (a Pt wire through which all the currentrequired to maintain the redox reaction at the working electrodeflows). The working electrode was polished with slurry of aluminapowder and then washed carefully with distilled water before eachmeasurement. Ferrocene (0.001 mol � dm�3) was used as the

electroactive probe and KCl (0.1 mol � dm�3) was used as the sup-porting electrolyte. Note that this concentration of the electroac-tive probe does not significantly affect the micellization of thesurfactants and their mixtures [33].

2.1.5. Computational methodsDFT (density functional theory) calculations were carried out

with the Gaussian 98, Revision A.7 (Gaussian, Inc., Pittsburgh PA).First, geometry optimization was performed at the B3LYP/6-311+G(d,p) level in the gas phase. PCM (polarizable continuummodel) calculations were then performed at the B3LYP level withthe 6-311+G(d,p) basis set and the gas-phase optimized geome-tries. The micellar radius was determined as the distance betweenthe quaternary nitrogen and the farthest H of the terminal methylgroup. The value of Nagg was calculated from this radius and thevolume of the hydrated monomer, as obtained with the PCM byassuming that the micellar aggregates are spherical.

3. Results and discussion

3.1. The CMC and the thermodynamics of micellization

The CMC values for m–s–m, (m = 12, 14 and s = 2, 4) have beenobtained with conductivity and surface tension measurements;representative examples for both techniques are shown in figuresSM-1 and SM-2 respectively. The agreement between the CMCs de-rived from these two methods is satisfactory; note that the CMCgenerally depends on the determination method (table 1). As indi-cated in table 1, the CMC values for 14–2–14 and 14–4–14 are notstrongly dependent on temperature within the range 298 K to318 K, whereas the CMC values of 12–2–12 and 12–4–12 initiallydecrease and then increase as the system temperature increases.The initial decrease in the CMC is a direct consequence of the de-crease in the hydrophilicity of the surfactant molecules[18,19,34]. The increase in temperature also results in an increasein the breakdown of the structure of the water molecules sur-rounding the hydrophobic alkyl group, which is unfavorable tothe formation of micelles. As a result, the onset of micellizationtends to occur at higher concentrations as the temperature in-creases [34]. The value of the CMC decreases with increases inthe hydrophobic chain length of the Gemini surfactants (table 1).Increasing the spacer length of the Gemini surfactants also resultsin increases in the CMC (table 1). These results are in good agree-ment with those of previous studies [17,21].

According to the Frahm’s Method, the a was calculated from theratio of the slopes above and below the CMC in plots of conductiv-ity against surfactant concentration [35]. The a values are tabu-lated in table 1 [35]. Frahm’s method is an approximate methodsince the contribution of conductivity of micelles above the CMCis neglected. Then, the a values were calculated for 12–4–12 and14–4–14 in T = 298 K using Evans’ method (table 1) [36]. As shownin table 1, the difference of a values calculated by Evans to themethod of Frahm is more than 100%. Consequently, ignoring themicellar contribution leads to large differences in the a values cal-culated by two methods. However, use of the Evans method re-quires knowledge of Nagg, and these are not always available.

As can be seen in table 1, the a increases with increases in thechain length of the m–n–m Gemini surfactant homologues. This re-sult indicates that the binding of the bromide counter ions to thesurfactant ammonium heads weakens with increasing hydropho-bicity. The increases in a (table 1) within the series of surfactantsindicate that increasing the length of the hydrophobic spacermeans that the distance between the charges increases, and as aresult the necessity of partial neutralization by counter ions be-comes less. Table 1 shows that the a value of each species tends

TABLE 1CMC, a, interfacial and thermodynamic parameters of micellization of Gemini surfactants at different temperatures

Compound T/k CMCa � 104/(mol � dm�3)

CMCb � 104/(mol � dm�3)

ab Cmax � 106/(mol �m�2)

Amin/(nm2 �molecule�1)

cCMC/(mN �m�1)

�DHfe/(kJ �mol�1)

Tc/K

12–2–12 298 8.09 8.40, 8.05c 0.20, 0.13c 1.69 0.98 26.1 34.78 ± 0.01 293.3 ± 0.1303 7.75 9.09, 9.1c 0.21, 0.13c 1.71 0.97 26.9308 7.75 9.35, 9.1c 0.23, 0.13c 1.70 0.98 26.9313 8.42 10.1.10c 0.23, 0.11c 1.63 1.02 26.6318 9.09 10.9 0.24 1.50 1.11 26.2

12–4–12 298 9.45 10.7 0.24(0.14) 1.58 1.05 36.2 32.09 ± 0.05 290.0 ± 0.3303 8.70 11.0, 15d 0.27, 0.32d 1.53 1.09 35.4308 8.93 11.6, 16d 0.29, 0.35d 1.45 1.14 34.9313 9.45 12.5, 19d 0.31, 0.38d 1.27 1.30 32.1318 10.7 12.6, 19d 0.34, 0.41d 1.18 1.40 31.6

14–2–14 308 1.47 1.49, 1.9c 0.24, 0.15c 2.23 0.74 27.8 �40.40 ± 0.03 304.3 ± 0.1313 1.47 1.49, 1.9c 0.25, 0.16c 2.19 0.76 27.2318 1.55 1.77 0.29 1.85 0.90 27.1323 1.55 1.78 0.31 1.42 1.17 27.2333 1.62 1.78 0.36 1.07 1.55 25.7

14–4–14 298 1.61 1.46 0.34(0.160) 1.68 0.99 34.1 �36.09 ± 0.01 295.9 ± 0.1303 1.59 1.51 0.35(0.165) 1.64 1.01 32.7308 1.59 1.72 0.37(0.168) 1.61 1.03 32.3313 1.59 1.76 0.38(0.171) 1.40 1.18 32.5318 1.61 1.75 0.40(0.180) 1.24 1.33 32.4

The a values in parentheses were calculated using Evans method.a The CMC values obtained from surface tension measurements.b The CMC and a values obtained from conductometry measurements.c Data taken from reference [18].d Data taken from reference [23].e The thermodynamic parameters were calculated by using the CMC values obtained from surface tension measurements and a values calculated according to the Frahm’sMethod.f These temperatures are below the Kraft temperature of 14–2–14.

M. Hajy Alimohammadi et al. / J. Chem. Thermodynamics 44 (2012) 107–115 109

to increase with temperature. Note that even though a shallowminimum is observed in the CMC–temperature curves, the overalltrend in the respective curves is of increases in the CMC with tem-perature. If the CMC is regarded as reflecting the solubility of themicelles, a increases with temperature in parallel with the in-creased solubility of the micelles. The a is determined by variousfactors such as the temperature, the electrical potential aroundthe micelle, the micellar radius, and the dielectric constant of themedium, etc. [37]. The gross features of counter ion dissociationor distribution between the kinetic micelle and the bulk solutioncan be described with simplified electrostatic models [37], inwhich the stabilization of micelles by counter ion binding resultsfrom a balance between the kinetic motion of the ions and the elec-tric potential on the micellar surface; this balance eventually re-sults in increases in a with increases in temperature. In otherwords, the binding of counter ions (their adsorption onto themicellar surface) is an exothermic process whereas the electrolyticdissociation of micelles (the desorption of counter ions) is an endo-thermic process.

The surface excess {Cmax/(mol � cm�2)} is an effective measureof adsorption at the air/water interface. The concentration of thesurfactant is always greater at the surface than in the bulk. The sur-face excess (Cmax) and the minimum area per molecule (Amin) werecalculated by using the Gibbs adsorption equation [38,39]. In table1, it can be seen that the surface excess concentrations, Cmax, of theGemini surfactants decrease with increasing temperature. Thisbehavior arises because thermal motions increase as the tempera-ture increases.

The surface excess concentration, Cmax, decreases with in-creases in the spacer length because the surface area per surfactantmolecule occupied by head groups is larger for larger spacers.

Due to hydrophobic interactions between the chains, the mag-nitude of Cmax is lower for longer hydrophobic chains, suggestingthat the air/water interface is close-packed and therefore that the

orientation of the surfactant molecule at the interface is almostperpendicular to the interface. As expected, the trend in Amin is in-verse with temperature (table 1).

The variations of CMC and a with temperature enable us toanalyze the thermodynamic energetics of micelle formation inwater. The collected data for the variations of CMC and a with tem-perature are given in table 1 and enable us to analyze the thermo-dynamic energetics of micelle formation in water. First, thestandard Gibbs free energy change upon micelle formation wasexamined. By applying mass action law, the Gibbs free energy ofmicellization has been derived for general type of ionic surfactantcontaining i polar groups of valency zs bonded to j alkyl chains,with counterions of valency zc as follow [21,40]:

DG�mic=ðkJ �mol�1Þ ¼ RT 1=jþ ð1� aÞ ijjzs=zcj

� �ln XCMC

þ RTði=jjzs=zcjð1� aÞ ln i=jjzs=zcj � ln j=jÞ; ð1Þ

where XCMC and a are the CMC value on the mole fraction scale andthe degree of counterion dissociation respectively. For the dimericsurfactants (i = j = 2 and jzsj ¼ jzcj ¼ 1), equation (1) becomes:

DG�mic=ðkJ �mol�1Þ ¼ RTð1:5� aÞ ln XCMC � ðRT=2Þ ln 2: ð2Þ

The second term in the right hand side of equation (2) is small withrespect to the first one and negligible. The values of DG�mic obtainedby using equation (2) are plotted in figure 1. The DG�mic values ofthese surfactants do not change significantly with increases in tem-perature. The Gibbs free energy of micellization becomes more neg-ative with increases in the hydrophobicity of a surfactant, whichmeans that for the studied surfactants micelle formation is mostfacile for 14–2–14.

By applying the Gibbs–Helmholtz equation to equation (2), theenthalpy of micellization can be obtained [18]. This method is aneasy one, as it only involves CMC and a determinations, but several

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295 300 305 310 315 320

295 300 305 310 315 320

The

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mol

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T/K

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295 300 305 310 315 320

The

rmod

ynam

ic p

aram

eter

s/kJ

mol

-1

T/K

a

b

c

d

FIGURE 1. Plot of thermodynamic parameters of micellization (- - - the Gibbs free energy of micellization ðDG�micÞ, — standard enthalpy ðDH�micÞ and � � � standard entropyðTDS�micÞ) of Gemini surfactants: (h) 12–2–12; (⁄) 12–4–12; (D) 14–2–14; (s) 14–4–14 versus temperatures. The thermodynamic parameters were calculated by using theCMC values obtained from surface tension measurements and a values calculated according to the method of Frahm.

110 M. Hajy Alimohammadi et al. / J. Chem. Thermodynamics 44 (2012) 107–115

factors that affect DH�mic, are not explicitly considered in data treat-ment by Van’t Hoff analysis [21,41]. In the van’t Hoff approach,DG�mic=T versus 1/T is plotted for several temperatures. The qualityof these plots depends on the number of data points and their

accuracy. For example, the use of a small number of data pointsusually leads to a linear dependence of DG�mic=T on 1/T, hence toa single value of DH�mic for the temperature range studied. In thiswork, this problem can be circumvented by fitting the curve with

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0

20

40

60

-0.03 0.02 0.07 0.12 0.17 0.22 0.27

ΔΗ˚ m

ic/k

Jmol

-1

ΔS˚mic/kJmol-1K-1

FIGURE 2. Plot of standard enthalpy ðDH�micÞ versus standard entropy ðDS�micÞ, for Gemini surfactants: (h) 12–2–12; (⁄) 12–4–12; (D) 14–2–14; (s) 14–4–14.

TABLE 2Parameters obtained in the presence of supporting electrolyte for Gemini Surfactants at their respective CMC values

Compound T/K Dma � 10�11/(m2 � S�1) Dm

b � 10�11/(m2 � S�1) D�m � 10�11=ðm2S�1Þ R�h=Å Nagg kd/(dm3 �mmol�1) (Nagg)th Nagg

12–2–12 298 2.25 1.54 8.86 – – 0.042 – 48c

12–4–12 298 7.61 5.85 11.38 2.153 35 0.025 27 36d,55e

14–2–14 313 – – 9.08 – – 0.028

14–4–14 298 5.38 4.83 9.4 2.606 51 0.026 38303 6.31 10.7 2.599 50 0.021308 7.06 11.7 2.678 54 0.019313 9.32 13.4 2.620 51 0.015318 11.30 14.2 2.747 59 0.011

a The diffusion coefficient values obtained from the PFG-NMR technique in the absence of supporting electrolyte (Ctot = 0.019 mol � dm�3).b The diffusion coefficient values obtained from CV technique in the presence of supporting electrolyte (Ctot = 0.019 mol � dm�3).c To calculate P, we calculated a0 values using surface tension plots and volume and length values were determined by Tanford equations (the values in parentheses) andtheoretical calculations. The volume and length values obtained by two methods are given in SM.d Data taken from reference [24].e Data taken from reference [13].

M. Hajy Alimohammadi et al. / J. Chem. Thermodynamics 44 (2012) 107–115 111

polynomial of higher order to get temperature-dependent DHmic.More importantly, however, is that there is no provision in thevan’t Hoff equation for factors that are important for micelle for-mation of ionic surfactants, in particular, the dependence of micel-lar geometry, aggregation number, surface-charge density, andhydration of the head group on T [41]. On the other hand, the ef-fects of T on the above-mentioned micellar parameters are in-cluded in the direct (i.e., calorimetric) determination of DH�mic.

The enthalpy of micellization, DH�mic, is dependent on tempera-ture (figure 1). The temperature dependence of DH�mic might be dueto changes in aggregation number (size) and shape [42,43]. Posi-tive values of DH�mic, such as those observed at low temperatures,are usually attributed to the release of structural water from thehydration layers around the hydrophobic parts of the surfactantmolecule [44]. It has been suggested [45] that negative DH�mic val-ues are evidence that London-dispersion interactions are a majorforce in micellization.

The entropy contribution to the micellization process can beestimated from the calculated enthalpy and Gibbs free energy val-ues [21]. From Gibbs free energy relationship, any uncertaintyintroduced in the calculation of DH�mic will be carried over toDS�mic [41].

It can be seen in figure 1that the absolute value of TDS�mic for allthese surfactants decreases with increasing temperature, whichindicates that raising the temperature leads to a reduction in theentropy or randomness of the system. The comparison of theenthalpy and entropy terms (see figure 1) suggests the presenceof a mutual relationship in the form of the enthalpy–entropycompensation phenomenon [43]. The enthalpy–entropy compen-

sation phenomenon has been found for a variety of processes ofsmall solutes [46], including those of surfactants [47–51].

In general, such compensation phenomena can be describedwith a linear relationship of the form [34,52]:

DH�mic=ðkJ �mol�1Þ ¼ DH�mic þ TCDS�mic: ð3Þ

An acceptable linear relationship was obtained in all compensationplots, as shown in figure 2; these lines have approximately the sameslope but different intercepts at DS�mic ¼ 0. Note that the interceptDH�mic gives the enthalpy effect under the condition DS�mic ¼ 0. An in-crease in the value of the intercept DH�mic thus corresponds to a de-crease in the stability of the structure of the micelles. It was foundthat the intercept, DH�mic, that characterizes the solute–solute inter-action is dependent on not only the hydrophobic chain length butalso on the length of the spacer group. Our results indicate that14–2–14 has a larger negative value (DH�mic) than the other surfac-tants studied here. The micellar stabilities decrease in the order 14–2–14 > 14–4–14 > 12–2–12 > 12–4–12. The compensation tempera-tures range approximately 295 K to 304 K for all these surfactants.

3.2. Intermicellar interactions

From a structural point of view, the most important parametersof a micellar system are the mean micellar aggregation numberand the hydrodynamic radius, which were determined by usingself-diffusion coefficient measurements with PFG-NMR spectros-copy and CV techniques.

0

2

4

6

8

10

12

14

16

295 300 305 310 315 320T/K

10-1

1 Dm

/m2 .

s -1

FIGURE 3. Self-diffusion coefficient, Dm as a function of temperature in the presence of various concentrations of 14–4–14, 2Br�: (⁄) 0.010; (h) 0.015; (D) 0.020 mol � dm�3.

0

0.005

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0.015

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0.025

0.03

295 300 305 310 315 320

T/K

kd/

dm3 m

mol

-1

FIGURE 4. Plot of intermicellar interaction parameter (kd) against temperature in micellar solutions (14–4–14).

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0.0 1 0.01 2 0.01 4 0.01 6 0.01 8 0.0 2 0.02 2 0.024

kd/ dm3 mmol-1

U(r

FIGURE 5. Plot of the micellar interaction energy (U(r)) against intermicellar interaction parameter (kd) in micellar solutions.

112 M. Hajy Alimohammadi et al. / J. Chem. Thermodynamics 44 (2012) 107–115

The self-diffusion coefficient values obtained with PFG-NMR arelisted in table 2. The increases in the self-diffusion coefficient aremainly due to decreases in the size of the micelles. The low self-dif-fusion coefficient values of 12–2–12 and 14–2–14 indicate that thepresence of these Gemini surfactants with short spacers results inthe formation of aggregates that are less curved. It was found [13]in an electron microscopy experiment that a Gemini surfactant withs = 2 forms rod-like micelles. Electron micrographs of 12–2–12 solu-tions have found long cylindrical micelles [15,21]. An investigationwith cryogenic transmission electron microscopy found that 12–s–12 surfactants with 4 6 s 6 12 form spheroidal micelles [13].

The CV measurements were used to determine the diffusioncoefficients of the micelles and the intermicellar interactionparameters [53]. In the present study, ferrocene was chosen asthe electroactive probe; ferrocene can be used provided that it does

not perturb the micelle and that its rates of entrance/exit into theaggregates with fast and reversible electron transfer are at leastcomparable to those of the surfactant monomers. The electrochem-istry of ferrocene in non-aqueous, aqueous, and micellar environ-ments is described elsewhere [54–58].

The cyclic voltammograms for the one- electron oxidation offerrocene (equation (4)) in 12–4–12 at various scan rates for thepotential range 0.0–0.5 V are given in figure SM 3.

Fc() Fcþ þ e�: ð4Þ

In CV, the peak current ipa for a redox-active reversible system isgiven by the Randles–Sevcik equation [59]:

ipa ¼ 0:4463FACnnFmD

RT

� �12

; ð5Þ

M. Hajy Alimohammadi et al. / J. Chem. Thermodynamics 44 (2012) 107–115 113

where n is the number of electrons involved in oxidation or reduc-tion, A is the area of the electrode (A was determined as the methoddescribed in SM), F is Faraday’s constant, R is the gas constant, T isthe absolute temperature, D is the diffusion coefficient of the elec-troactive (EC) probe, C is the concentration of the EC probe in thesolution, and v is the scan rate. For micellar systems involving anEC probe completely solubilized in the micelles, the D in equation(5) corresponds to the micelle diffusion coefficient Dm since theprobe diffuses with the micelles. Hence, from the slope of the ipa

versus v1/2 plot, the Dm values were obtained for various micelleconcentrations; the concentration of ferrocene was fixed at1 � 10�3 mol � dm�3. The Dm was found to decrease with decreasingspacer length for surfactants 12–s–12 and 14–s–14 (table 2), whichis in good agreement with the PFG-NMR data. In CV measurements,the addition of supporting electrolyte causes a decrease in Dm ormicellar growth due to reduction electrostatic repulsion betweenhead groups (table 2). These results are in agreement with previousfindings [55].

At concentrations above, but not far from, the CMC micellesmutually interact; consequently, the calculated values of diffusioncoefficients are lower than that at the CMC. As attenuation of themass-transport parameters is a linear function of surfactant con-centration therefore linear interaction theory (see SM) was usedfor calculation of intermicellar interaction parameters [60,61].Consequently, extrapolation to infinite dilution (to the CMC) yieldsmass-transport parameters that are independent of interparticleinteractions

Dm ¼ D0m½1� kdðCs � CMCÞ�; ð6Þ

where kd is the intermicellar interaction parameter, D0m is the self-

diffusion coefficient in the absence of micellar interaction, CMC isthe critical micelle concentration, and Cs is the surfactant concen-tration. The representative profiles of Dm versus (Cs-CMC) for 12–2–12, 12–4–12, 14–4–14, and 14–2–14 (in the presence of support-ing electrolyte) are shown in figure SM 4. The values of D0

m or DCMC

were calculated from the dependence of Dm on surfactant concen-tration. The results are shown in table 2. These data were used tocalculate the micellar hydrodynamic radius by using the Stokes–Einstein equation [62–65].

For s = 2, spherical micelles cannot form and the Stokes–Ein-stein equation is not valid. For a Gemini surfactant with a longerspacer, the surface area per surfactant molecule occupied by headgroups is larger than for a Gemini surfactant with a shorter spacer,i.e., there is a smaller packing parameter, which facilitates the for-mation of spherical rather than worm-like micelles. According tothe experimental data [21], 12–4–12 and 14–4–14 are likely toform spherical micelles.

The hydrodynamic radius values are shown in table 2. The Rh

values can be used to compute the aggregation number of the mi-celles. By assuming spherical micelles and neglecting their intrinsicinstability, the aggregation number can be computed. The Nagg val-ues are collected in table 2, along with the theoretically calculatedaggregation numbers, Nagg,theor, and those obtained with othertechniques. The CV-based Nagg values are in excellent agreementwith the values obtained using other techniques [13,29]. The Nagg

values are dependent on the chain length of the surfactant hydro-phobic tail in the presence of electrolyte. The increases in Nagg withincreases in the length of the R group are due to increases in thepacking factor, because such increases affect the volume of thehydrophobic group more than its length (for the same head group).In addition, the actual diffusion coefficient, D0

m, hydrodynamic ra-dius, Rh, and aggregation numbers, Nagg of the 14–4–14 micellesare shown for various temperatures in table 2. The results indicatean increase in D0

m with increasing temperature. At least part of thischange in D0

m is due to the decrease in solvent viscosity (see the

supporting material). Note no significant variation in Rh withincreasing temperature, which might be due to an increase in theaggregation number and a decrease in micellar solvation. Previ-ously, Borse and co-workers found that the hydration of micelles(hE) decreases in cationic Gemini surfactants with increasing tem-perature [66]. By assuming that there is no substantial change inmicellar solvation, the aggregation numbers can be calculated atvarious temperatures. The values in table 2 demonstrate that theNagg values of 14–4–14 remain predominantly constant with theincrease in temperature. A small variation in Nagg values of 14–4–14 are in line with the similar variation in the CMC values of thissurfactant. Consistent with the present work, the previous studieshave noted a small variation of Nagg with the increase in the tem-perature for cationic Gemini surfactants [18,21].

The values of the intermicellar interaction coefficient (kd) werecalculated from the slopes of plots of Dm versus the surfactant con-centration (see figure SM4), as described by linear interaction the-ory [60]. In table 2, it can be seen that the kd values are influencedby increases in the lengths of the tail and the spacer. The intermi-cellar interaction parameter decreases with increases in the chainlengths of the Gemini surfactants. This behavior is mainly due tothe growth of micelles and decreases in the micellar surface chargedensity [18,66]. On the other hand, an unexpected increase in kd

was found for decreasing spacer length. This increase is due tothe change from sphere to rod micellar morphology. Small angleneutron scattering and cryo-TEM studies of the m–s–m Gemini sur-factants revealed the formation of less curved aggregates when thespacer is short enough [21]. Cryo-TEM showed that the 12–2–12micelles are threadlike, whereas those of 12–4–12 are spheroidal[13,21].

In order to examine the effects of varying the temperature onintermicellar interactions, voltammetric experiments were carriedout for 14–4–14 over the temperature range 298 K to 318 K. Figure3 shows the variation of Dm with temperature at three concentra-tions. As expected, the Dm values increase with increasing temper-ature. The kd values were obtained with linear interaction theoryand are plotted as a function of temperature in figure 4. It is obvi-ous that kd decreases linearly with increasing temperature. Twofactors control the value of kd in colloidal systems: inter-particleattractive or repulsive interactions. According to our results,decreasing kd with temperature suggests a decrease in repulsiveinteractions due to a reduction in surface charge density and an in-crease attractive interactions. This temperature effect is consistentwith the results of a previous study by Borse et al. [66]. They re-ported that the equilibrium distances (d) between the head groupsof surfactant 12–4–12 are 0.742 and 0.771 nm at T = 303 K and323 K, respectively. An increase in the attractive interaction or de-crease in repulsive interaction leads to micellar growth. The smallmagnitude of the increase in the micellar size or Nagg (table 2) sug-gests that the increase in attractive interaction or decrease inrepulsive interaction has only a small effect on micelle size, butin our work the structure of Gemini surfactant is the dominant fac-tor for determination of the micelle size. While, the results ofCharlton et al. showed a decrease in interaction parameter withtemperature due to increase in attractive interaction, then the in-crease in the attractive interaction leads to micellar growth for Tri-tonX-100 [56]. Further, the intermicellar interaction parametersfor the monomeric form of these surfactants such as cetyltrimeth-ylammonium bromide (CTAB) [67], cetyltrimethylammoniumchloride (CTACl) [68] and sodium dodecyl benzene sulfonate(SDBS) [69] increase with increasing temperature.

To examine further the observed behavior, the intermicellarinteraction energy (Coulombic potential) for two identical spheri-cal macro-ions of diameter r was calculated [70]. A plot of U(r) ver-sus kd is shown in figure 5. It is evident that the intermicellarinteraction parameter is a function of the Coulombic interaction

114 M. Hajy Alimohammadi et al. / J. Chem. Thermodynamics 44 (2012) 107–115

potential. The interaction parameter decreases gradually withincreases in temperature as the Coulombic interaction (U(r)/kT)varies between 1.74 and 1.13.

4. Conclusion

In our surface tension and conductometry study ofCmH2m+1N(CH3)2(CH2)S (CH3)2 N CmH2m+1,2Br� with m = 12, 14and s = 2, 4 over the temperature range 298 K to 323 K, the varia-tions of CMC and a with temperature have been obtained. TheCMC values pass through a minimum as the temperature is in-creased from 298 K to 323 K. The a values increase slightly withtemperature. This study also enabled us to obtain the thermody-namic parameters of micellization. The Gibbs free energy of micel-lization has a weak dependence on temperature for these Geminisurfactants. A clear linear relation (enthalpy–entropy compensa-tion relation) was found between DH0

m and DS0m for these Gemini

surfactants.By performing CV measurements, several important micellar

parameters were estimated and the intermicellar interactions wereanalyzed. The effects of varying the temperature can be interpretedin terms of decreasing electrostatic repulsions of head groups andincreasing attractive interactions of spacers. This study has shownthat CV is a simple and sensitive technique for probing the struc-tural changes of micelles and in particular their dependence onthe spacer and chain lengths of the hydrophobic tails of Geminisurfactants, and for obtaining information about intermicellarinteractions in aqueous solutions.

5. Calculations

As can be seen from figure SM2, plots of solution conductivityversus surfactant concentration are composed of two straight linesintersecting at the CMC. We employed the method of Frahm andthat of Evans to calculate the a value.

The method of Frahm is given by [35]

a ¼ s2=s1; ð7Þ

where s1 and s2 are the slopes k plots below and above the CMC,respectively.

The method of Evans for calculating a is given by [36]:

1000s2 ¼ ða2=N�2=3agg Þð1000s1 �KBr� Þ þ aKBr� ; ð8Þ

where s1, s2 are those defined above; the KBr� is the equivalent con-ductivity of Br� at infinite dilution.

The surface excess (Cmax) and the minimum area per molecule(Amin) were calculated by using the Gibbs adsorption equation[38,39],

Cmax=mol �m�2 ¼ ð�1=2:303RTÞ½dc=d log C�T;P ð9Þ

and

Amin=nm2 �molecule�1 ¼ 1018

NACmax; ð10Þ

where dc/d log C is the maximum slope in each case. The R, T, C,and N are the gas constant, absolute temperature, concentration,and Avogadro’s constant, respectively. The slope of the tangent ata given concentration of the c versus log C plot was used to calcu-late C by using curve fitting to a polynomial equation of the formy = ax2 + bx + c.By applying the Gibbs–Helmholtz equation toequation (2), the enthalpy of micellization can be obtained from[18]:

DH�mic=ðkJ �mol�1Þ ¼ �RT2ð1:5� aÞð@ ln XCMC=@TÞpþRT2LnXCMCð@a=@TÞ: ð11Þ

To evaluate the enthalpy of micelle formation, the CMC and a valueswere first correlated by using a polynomial equation [18]:

‘nXCMCðTÞ ¼ aþ bT þ CT2 þ dT3; ð12Þ

a ¼ a0 þ b0T þ c0T2; ð13Þ

where constants a, b, c, d, a’, b’, and c’ were determined by usingleast-squares regression analysis.

The enthalpy of micelle formation was then calculated numer-ically by substituting equations (13) and (14) into equation(12).The entropy contribution to the micellization process can beestimated from the calculated enthalpy and Gibbs free energy val-ues as

TDS�mic ¼ DH�mic � DG�mic: ð14Þ

The micellar hydrodynamic radius was calculated by using theStokes–Einstein equation [62–65]:

Rh ¼kT

6pgD0m

; ð15Þ

where k is the Boltzmann constant, T is the absolute temperature,and g is the viscosity of the solution, which can be approximatedas that of water.

The aggregation number can be computed with the followingequation:

Nagg ¼ð4=3ÞpR3

h

½VA þ nh;AV�H2O þ bðV con þ nh;conV�H2OÞ�; ð16Þ

where VA, Vcon, and V�H2O are the molecular volumes of the Geminisurfactants, the counter ion, and H2O, and nh,A and nh,con are thehydration numbers of the head groups of the surfactants and coun-ter ions [71]. Finally, b is defined as the degree of attachment.Theintermicellar interaction energy (Coulombic potential) for two iden-tical spherical macro-ions of diameter r was calculated [70]

UðrÞ ¼ pee0r2w20 exp½�jðr � rÞ�=r; ð17Þ

where r is the micellar center-to-center distance, e is the dielectricconstant of the medium (H2O), e0 is the permittivity of free space, kis the Debye–Huckle inverse screening length as determined fromthe ionic strength of the solution, and r ¼ 2R0

h , where R0h is the

micellar hydrodynamic radius. R0h can be obtained from D0

m, whichcan be determined with the Stokes–Einstein relation (equation(16)). The value for r can be calculated from the micellar volumefraction (u) (obtained from R0

h) as follows:

r ¼ 2R0h þ l; ð18Þ

l3 ¼ ½8p=21=3�uðR0hÞ: ð19Þ

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.jct.2011.08.007.

References

[1] F.M. Menger, C.A. Littau, J. Am. Chem. Soc. 115 (1993) 10083–10090.[2] F.M. Menger, C.A. Littau, J. Am. Chem. Soc. 113 (1991) 1451–1452.[3] M.J. Rosen, Chemtech 23 (1993) 30–33.[4] F. Devinsky, I. Lacko, T. Imam, J. Colloid Interf. Sci. 143 (1991) 336–342.[5] G. Bai, J. Wang, H. Yan, Z. Li, R.K. Thomas, J. Phys. Chem. B105 (2001) 3105–

3108.

M. Hajy Alimohammadi et al. / J. Chem. Thermodynamics 44 (2012) 107–115 115

[6] R. Zana, Dimeric (Gemini) Surfactants, in: K. Esumi, M. Ueno (Eds.), Structure–Performance Relationships in Surfactants, Dekker, New York, 1997, p. 255.

[7] M.J. Rosen, J.H. Mathias, L. Davenport, Langmuir 15 (1999) 7340–7346.[8] M. Dreja, W. Pyckhout-Hintzen, H. Mays, B. Tieke, Langmuir 15 (1999) 391–

399.[9] T.J. Gao, M.J. Rosen, J. Am. Oil Chem. Soc. 71 (1994) 771–776.

[10] F.L. Duivenvoorde, M.C. Feiters, S.J. Van der Gaast, J.B.F.N. Engberts, Langmuir13 (1997) 3737–3743.

[11] M. Blanzat, E. Perez, I. Rico-Lattes, D. Prome, J.C. Prome, A. Lattes, Langmuir 15(1999) 6163–6169.

[12] Y.-P. Zhu, A. Masuyama, Y. Kirito, M. Okahara, M.J. Rosen, J. Am. Oil chem. Soc.69 (1992) 626–632.

[13] D. Danino, Y. Talmon, R. Zana, Langmuir 11 (1995) 1448–1456.[14] R. Oda, I. Huc, D. Danino, Y. Talmon, Langmuir 16 (2000) 9759–9769.[15] A. Bernheim-Groswasser, R. Zana, Y. Talmon, J. Phys. Chem. B 104 (2000)

4005–4009.[16] X. Huang, Y.C. Han, Y.X. Wang, Y. Wang, J. Phys. Chem. B 111 (2007) 12439–

12446.[17] R. Zana, J. Colloid Interf. Sci. 248 (2002) 203–220.[18] M.S. Bakshi, A. Kaura, R.K. Mahajan, Colloids and Surfaces A: Physicochemical

and Engineering Aspects 262 (2005) 168–174.[19] A. Bendjeriou, G. Derrien, P. Hartmann, C. Charnay, S. Partyka, Thermochim.

Acta 434 (2005) 165–170.[20] G. Bai, H. Yan, R.K. Thomas, Langmuir 17 (2001) 4501–4504.[21] R. Zana, J. Xia, Gemini Surfactants: Synthesis, Interfacial and Solution Phase

Behaviour, and Application, Marcel Dekker, New York, 1998.[22] L. Grosmaire, M. Chorro, C. Chorro, S. Partyka, S. Lagerge, Thermochim. Acta

379 (2001) 255–260.[23] M.S. Borse, S. Devi, Adv. Colloid Interf. Sci. 123 (2006) 387–399.[24] L. Grosmaire, M. Chorro, C. Chorro, S. Partyka, R. Zana, J. Colloid Interf. Sci. 246

(2002) 175–181.[25] R. Oda, S.J. Candau, I. Huc, Chem. Commun. (1997) 2105–2106.[26] S. Lagerge, A. Kamyshny, S. Magdassi, S. Partyka, J. Therm. Anal. Calorim. 71

(2003) 291–310.[27] L. Chen, Y. Li, H. Xie, J. Dispers. Sci. Tech. 29 (2008) 1098–1102.[28] Y. Jiang, H. Chen, X.-H. Cui, S.-Z. Mao, M.-L. Liu, P.-Y. Luo, Y.-R. Du, Langmuir 24

(2008) 3118–3121.[29] A.R. Tehrani Bagha, H. Bahrami, B. Movassagh, M. Arami, F.M. Menger, Dyes

Pigments 72 (2007) 331–338.[30] M.A. Rodriguez, M. Munos, M.M. Graciani, M.S.F. Pachon, M.L. Moya, Colloids

and Surfaces A: Physicochemical and Engineering Aspects 298 (2007) 177–185.

[31] C.C. Ruiz, J.A. Molina-Bolivar, J. Aguiar, G. MacIsaac, S. Moroze, R. Palepu,Langmuir 17 (2001) 6831–6840.

[32] D.H. Wu, A.D. Chen, C.S. Johnson, J. Magn. Reson. Ser. A 115 (1995) 260–264.[33] Z. Yang, Y. Lu, J. Zhao, Q. Gong, X. Yin, J. Phys. Chem. B 108 (2004) 7523–7527.[34] L.-J. Chen, S.-Y. Lin, C.-C. Huang, J. Phys. Chem. B 102 (1998) 4350–4356.[35] J. Frahm, S. Diekmann, A. Haase, Ber. Bunsenge. Phys. Chem. 84 (1980) 566–

571.[36] H. Evans, J. Chem. Soc 78 (1956) 579–586.[37] Y. Moroi, in: Micelles: Theoretical and Applied Aspects, Plenum, New York,

1992, pp. 41–90.

[38] M.J. Rosen, Surfactants and Interfacial Phenomena, third ed., John Wiley andSons, New Jersey, 2004.

[39] M.J. Rosen, Langmuir 7 (1991) 885–888.[40] R. Zana, Langmuir 12 (1996) 1208–1211.[41] P. Galgano, O. El Seoud, J. Colloid Interf. Sci. 345 (2010) 1–11.[42] M. Hisatomi, M. Abe, N. Yoshino, S. Lee, S. Nagadome, G. Sugihara, Langmuir 6

(1999) 1515–1521.[43] G.C. Kresheck, W.A. Hargraves, J. Colloid Interf. Sci. 48 (1974) 481.[44] G.C. Kresheck, in: F. Franks (Ed.), Water: A Comprehensive Treatise, Plenum,

New York, 1975.[45] D. Rubingh, in: K.L. Mittal (Ed.), Solution Chemistry of Surfactants, Plenum,

New York, 1979.[46] C.V. Krishnan, H.L. Friedman, J. Solution Chem. 2 (1973) 37–51.[47] T. Okano, T. Tamura, T.-Y. Nakano, S.-I. Ueda, S. Lee, G. Sugihara, Langmuir 16

(2000) 3777–3783.[48] J.A. Molina-Bolivar, J. Aguiar, J.M. Peula-Garcia, C.C. Ruiz, J. Phys. Chem. B 108

(2004) 12813–12820.[49] J.L. López-Fontán, A. González-Pérez, J. Costa, J. Ruso, G. Prieto, P. Schulz, F.

Sarmiento, J. Colloid Interf. Sci. 297 (2006) 10–21.[50] D. Das, K. Ismail, J. Colloid Interf. Sci. 327 (2008) 198–203.[51] J. Das, K. Ismail, J. Colloid Interf. Sci. 337 (2009) 227–233.[52] R. Lumry, S. Rajender, Biopolymers 9 (1970) 1125.[53] B. Geetha, A. Mandal, Langmuir 13 (1997) 2410–2413.[54] I.D. Charlton, A.P. Doherty, J. Phys. Chem. B 104 (2000) 8327–8332.[55] T.L. Ferreira, B.M. Sato, O.A. El Seoud, M. Bertotti, J. Phys. Chem. B 114 (2009)

857–862.[56] I.D. Charlton, A.P. Doherty, Colloids and Surfaces A: Physicochemical and

Engineering Aspects 182 (2001) 305–310.[57] I.D. Charlton, A.P. Doherty, Langmuir 15 (1999) 5251–5256.[58] Z.X. Chen, S.P. Deng, X.K. Li, J. Colloid Interf. Sci. 318 (2008) 389–396.[59] K. Chokshi, S. Qutubuddin, A. Hussam, J. Colloid Interf. Sci. 129 (1989) 315–

326.[60] E. Dickinson, Chapter 2. Annual Reports on the Progress of Chemistry Section

C: Physical Chemistry 80 (1983) 3–37.[61] A.B. Mandal, Langmuir 9 (1993) 1932–1933.[62] Z. Yang, J. Zhao, Y. Xie, Y. Bai, Z. Du, Z. Phys. Chem. 217 (2003) 1109–1118.[63] H. Gharibi, B. Sohrabi, S. Javadian, M. Hashemianzadeh, Colloids Surf. A:

Physicochem. Eng. Aspects 244 (2004) 187–196.[64] A. Einstein, R. Fürth, Investigations on the Theory of the Brownian Movement,

Dover Publications, New York, 1956.[65] J.N. Israelachvili, D.J. Mitchell, B.W. Ninham, J. Chem. Soc., Faraday Trans. 2

(72) (1976) 1525–1568.[66] M. Borse, V. Sharma, V.K. Aswal, P.S. Goyal, S. Devi, J. Colloid Interf. Sci. 284

(2005) 282–288.[67] R.B. Dorshow, J. Briggs, C.A. Bunton, D.F. Nicoli, J. Phys. Chem. 86 (1982) 2388–

2395.[68] R.B. Dorshow, C.A. Bunton, D.F. Nicoli, J. Phys. Chem. 87 (1983) 1409–1416.[69] D.C.H. Cheng, E. Gulari, J. Colloid Interf. Sci. 90 (2004) 410.[70] J.B. Hayter, J. Penfold, Mol. Phys. 42 (1981) 109–118.[71] J. Zhao, S. Deng, J. Liu, C. Lin, O. Zheng, J. Colloid Interf. Sci. 311 (2007) 237–242.

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