Journal of Colloid and Interface Science 313 (2007) 288–295www.elsevier.com/locate/jcis
Thermodynamics of micelle formation of alkyltrimethylammoniumchlorides from high performance electric conductivity measurements
Tine-Martin Perger, Marija Bešter-Rogac ∗
Faculty of Chemistry and Chemical Technology, Aškerceva 5, University of Ljubljana, SI-1000 Ljubljana, Slovenia
Received 24 January 2007; accepted 18 April 2007
Available online 24 April 2007
Abstract
Understanding micelle formation requires its complete thermodynamic characterization. In this work micellization of the model ionic sur-factants decyltrimethylammonium chloride (DETAC), dodecyltrimethylammonium chloride (DTAC) and tetradecyltrimethylammonium chloride(TTAC) was investigated by high performance conductivity measurements, using instrumentation developed in our laboratory. The temperaturedependence of the critical micelle concentration exhibits a minimum characterized by �micH
0 = 0 (endothermic to exothermic process) andthe degree of micelle ionization increases slightly with increasing temperature. The temperature change of �micS
0 indicates that the process ofmicellization is entropically driven. �micG
0 is always negative and slightly temperature dependent. The temperature dependence of the thermo-dynamic parameters is discussed in terms of the alkyl chain length and nature of the counterion. The micellization process is more favourable forsurfactants with longer alkyl chain length and larger (less hydrated) counterions.© 2007 Elsevier Inc. All rights reserved.
Keywords: Electric conductivity; Thermodynamics of micelle formation; Trimethylammonium chloride; Micellization
1. Introduction
The self-association process of amphiphilic molecules intomicelles, vesicles, or membranes plays an important role inmany fields ranging from biological systems to technical ap-plications. This aggregation, as well as protein and nucleic acidfolding and their association, is governed by the intricate bal-ance between hydrophobic interactions and other types of non-covalent solute–solute and solute–solvent interactions [1].
Micelle formation from surfactant monomers has proved anexcellent model process for studying the hydrophobic effect [1–3]. There is no doubt that understanding micellization requiresits complete thermodynamic characterization. The parameterthat illustrates the temperature dependence of hydrophobic ef-fect is the heat capacity of micellization (�micc
0p) which is
highly negative and mainly reflects the amount of non-polarsolvent accessible area buried on micellization [3]. Since thethermodynamic parameters of micellization are often obtained
* Corresponding author. Fax: +386 1 2419 425.E-mail address: [email protected] (M. Bešter-Rogac).
0021-9797/$ – see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.jcis.2007.04.043
from measurements of the critical micelle concentration (cmc)it is important to note that �micc
0p < 0 causes a typical U-
shaped temperature dependence of cmc. Its minimum occursat a characteristic temperature (T ∗) that is often close to roomtemperature [4–6]. A comprehensive investigation of the tem-perature dependence of �micc
0p has recently been carried out
on non-ionic surfactants [7].Besides the essential contribution of the hydrophobic ef-
fect, the micellization of ionic surfactants in aqueous solution islargely influenced by the electrostatic interactions between theionized head-groups and their interactions with the surround-ing counterions and water molecules. Therefore, the effectivecharge of the micelle (degree of micelle ionization, β) and thenature of the counterion have a significant effect on the valuesof the thermodynamic parameters of micellization.
Whereas the effect of headgroup and chain length on thethermodynamic parameters of micellization has received muchattention during last decades, the effect of counterions on thethermodynamics has only rarely been analyzed [8–10].
Although a remarkable number of papers on micellar prop-erties and thermodynamics of micellization of alkyltrimethyl-ammonium salts have appeared in the literature, there is no
T.-M. Perger, M. Bešter-Rogac / Journal of Colloid and Interface Science 313 (2007) 288–295 289
systematic study on the influence of the counterion and lengthof the hydrophobic tails on the thermodynamic properties of themicelle formation process. Most reports on the micellar prop-erties of alkyltrimethylammonium salts refer to bromides [4–6,11–34].
The recently reported micellar properties of tetradecyltri-methylammonium nitrate (TTANO3) [35], decyltrimethylam-monium perfluoroacetate (DETAPA) [36], decyltrimethylam-monium perfluoropropionate (DETAPP) [36] and some alkyl-trimethylammonium chlorides [37–40] in aqueous solutionhave shown that the counterion specificity is very complex.
In order to obtain a more complete understanding of theeffect of counterions on the micellar properties of alkyltrimeth-ylammonium salts, we have determined the temperature de-pendence of cmc and β of decyltrimethylammonium chloride(DETAC), dodecyltrimethylammonium chloride (DTAC) andtetradecyltrimethylammonium chloride (TTAC) in aqueous so-lution by means of electric conductivity measurements.
The thermodynamic parameters of micellization (�micG0,
�micH0, �micS
0, �micc0p) for all systems have been estimated
by means of the pseudo-phase separation model [41–44]. Theresults, taking into account the those reported in the literature,are compared and discussed in terms of the chain length and thenature of the counterion.
2. Experimental
2.1. Materials
Decyltrimethylammonium chloride (DETAC, >98%), dode-cyltrimethylammonium chloride (DTAC, >98%) and tetrade-cyltrimethylammonium chloride (TTAC, >99%) were obtainedfrom Anatrace, Inc. (Maumee, OH, USA) and stored in a re-frigerator. They were used as received. Demineralized waterwas bi-distilled in a quartz apparatus (DESTAMAT Bi18E, Her-aeus). The final product, with a specific conductivity of lessthan 5 × 10−7 S cm−1, was distilled into a flask that allowedstorage under an atmosphere of nitrogen.
Stock solutions were prepared by adding a weighed amountof water to a weighed amount of the surfactant. The concentra-tions of all stock solutions were finally checked by potentiomet-ric titration with AgNO3 standard solution (Merck) using Cl−ion selective electrode.
2.2. Methods
2.2.1. Conductivity measurementsConductivity was recorded with a PC-interfaced LCR Meter
Agilent 4284 A connected to a three-electrode measuring celldescribed elsewhere [45]. The cell was calibrated with dilutepotassium chloride solutions [46] and immersed in the high pre-cision thermostat described previously [47]. The monoethyleneglycol/water bath was set to each temperature of a tempera-ture programme with a reproducibility within 0.005 K. Thetemperature was additionally checked with a calibrated Pt100resistance thermometer (MPMI 1004/300 Merz) connected toan HP 3458 A multimeter.
After measuring the solvent conductivity at all temperaturesof the programme a weighed amounts of a stock solution ofthe surfactant were added. Molal concentrations m were deter-mined from the weights.
A home-developed software package was used for temper-ature control and acquisition of conductance data. The mea-suring procedure, including corrections and extrapolation ofthe sample conductivity to infinite frequency, has been de-scribed [47]. Taking into account the sources of error (calibra-tion, titration, measurements, impurities) the specific conduc-tivities are accurate to within 0.2%.
The time of temperature stabilization before resistance mea-surement was found to be crucial. In the proximity of the cmcvalue it took at least 2 h for resistance values to become stableand reproducible. This fact alone made computer managementessential.
2.2.2. Critical micelle concentration, degree of micelleionization and thermodynamics of micellization
The critical micelle concentration, cmc, of the surfactantswas determined by the intersection of two straight lines of theconductivity–concentration plots above and below the changein the slope [48,49]. The ratio of the slopes of the linear frag-ments above and below the break gives an estimate of the degreeof micelle ionization, β [50].
According to the pseudo-phase separation model [41–44] thestandard Gibbs free energy of micellization, �micG
0, was cal-culated from the relation
(1)�micG0 = (2 − β)RT lnXcmc,
where Xcmc is the mole fraction of the surfactant at the cmc.The pseudo-phase separation model used here is a simplifi-
cation of the equilibrium model of micellization in which theaggregation number n → ∞ and the ratio of the correspondingactivity coefficients are assumed to be constant within a mea-sured concentration range [41,51]. At high aggregation num-bers, the terms containing n in the expression for �micG
0 be-come negligible and result in the pseudo-phase model relation(Eq. (1)). For n = 50 ± 20, which is characteristic for the alkylchain length of the surfactant molecules used in this work [52],the terms containing n and β are usually taken to be indepen-dent of temperature. A more detailed explanation is given in thesupporting material.
Knowledge of the temperature dependence of the cmc and β
enables the standard enthalpies of micelle formation, �micH0,
to be calculated from the Gibbs–Helmholtz relation
(2)�micH0 = −RT 2(2 − β)
[∂ lnXcmc
∂T
]P
.
It was found [44,53,54] that the �micH0 values obtained from
Eq. (2) agree with the direct calorimetric estimates and there-fore Eq. (2) has been widely used as an indirect method fordetermining �micH
0.The term (∂ lnXcmc/∂T )P was calculated by fitting a
second-order polynomial to plots of lnXcmc versus tempera-ture [44] and taking the corresponding temperature derivative.
290 T.-M. Perger, M. Bešter-Rogac / Journal of Colloid and Interface Science 313 (2007) 288–295
Fig. 1. Electric conductivities of aqueous solutions of DETAC from 278.15 to318.15 K (in steps of 5 K).
Table 1Critical micelle concentration, cmc, degree of ionization of the micelles, β , ob-tained from electric conductivity measurements for decyltrimethylammoniumchloride (DETAC), dodecyltrimethylammonium chloride (DTAC) and tetrade-cyltrimethylammonium chloride (TTAC) in aqueous solution at different tem-peraturesa
T DETAC DTAC TTAC
(K) cmc β cmc β cmc β
278.15 107.4 0.460 26.0 0.373 6.45 0.328283.15 105.0 0.461 25.0 0.399 6.07 0.337288.15 97.7 0.491 23.6 23.1b 0.398 0.328b 5.80 0.352293.15 95.8 0.505 22.6 22.1b 0.417 0.354b 5.68 0.362298.15 94.7 0.526 22.2 21.3b 0.424 0.389b 5.63 0.377303.15 90.4 0.545 21.7 20.4b 0.447 0.421b 5.63 0.392308.15 86.8 0.570 21.9 19.6b 0.451 0.450b 5.66 0.410313.15 86.4 0.587 22.2 0.464 5.86 0.424318.15 89.0 0.601 22.7 0.486 5.96 0.443
a Units: cmc (mmol kg−1). Uncertainties: cmc (DETAC, DTAC), ±0.1; cmc(TTAC), ±0.05; β , ±0.005.
b Ref. [38].
The coefficients of polynomials are given in Table A in support-ing material. The standard entropies of micellization, �micS
0,and the molar heat capacities of micelle formation, �micc
0p,
were obtained from well-known relations (Eqs. (M) and (O) insupporting material).
3. Results and discussion
The typical dependence of solution conductance on molalityof surfactant is shown in Fig. 1 (also Figs. A and B in support-ing material). At a given temperature, the cmc was observedto decrease substantially with increasing alkyl chain length ofthe surfactant (Table 1), cmc (298.15 K) being 94.7, 22.21 and5.63 mmol kg−1 for DETAC, DTAC and TTAC, respectively.
The change of specific conductivity with molality in the re-gion of the breaks was found to be lower at higher temperature.This behaviour indicates that micelles of smaller aggregationnumber, n, and/or higher degree of ionization, β , are formed athigher temperatures. Whereas β increases with temperature for
Table 2Micellization parameters from conductivity data of investigated alkyltrimethyl-ammonium salts and comparison with the literature dataa
cmc (298.15 K) β (298.15 K) cmc∗ T ∗
This workDETAC 94.7 ± 0.1 0.526 ± 0.005 87.2b 319.8b
DTAC 22.2 ± 0.1 0.424 ± 0.005 21.7b 305.8b
TTAC 5.63 ± 0.05 0.377 ± 0.005 5.61b 301.3b
Literature dataDETAC 96c 95.4c 310c
DTAC 21.3d, 22c 0.389d 22.6c 308c
TTAC 5.5e, 5.5c 0.33e 5.2c 305c
OTAC 0.32f 296.7f
DETAB 67.0g, 66.9h, 65.6i,66.3j, 69.2k, 66.9l
0.40g, 0.315h,0.30i, 0.28k
65.0j,62.7m,67g
301.15j,298.15m,300g
DETAPA 41.8g 0.37g 40g 313g
DETAPP 24.3g 0.28g 23g 312.5g
DTAB 15.7h, 15.34i,15.2n, 14.6j, 16.1k,15.6l, 16.0p
0.282h, 0.274i,0.251n, 0.23k,0.3p
14.1o,14.3j,14.6m
297.3o,293.15j,293.15m
TTAB 3.8e, 3.94h, 3.943i,3.72j, 3.7k, 3.8l,3.78n, 3.75r
0.24e, 0.273h,0.269i, 0.20k,0.227n, 0.23r
3.6j 288.15j
TTANO3 3.38s 0.236s 3.345s 291.4s
a Units: cmc, cmc∗ (mmol kg−1); T ∗ (K).b Values are obtained from the corresponding derivative of the polynomial
(Table A in supporting material).c Ref. [40], values are taken from Figs. 3 and 4.d Ref. [38].e Ref. [24].f Ref. [37].g Ref. [36] values of cmc∗ and T ∗ were calculated by fitting a second-order
polynomial to the data in Table 2.h Ref. [21].i Ref. [34].j Ref. [31].k Ref. [28].l Ref. [25].
m Ref. [5].n Ref. [26].o Ref. [4].p Ref. [39].r Ref. [19].s Ref. [35], values are taken from Fig. 2.
all the systems investigated, it decreases considerably with in-creasing chain length, β (298.15 K) = 0.526, 0.424 and 0.377for DETAC, DTAC and TTAC, respectively. All values arelisted in Table 1, together with the data reported in the litera-ture [38]. Values of cmc and β at 298. 15 K are compared for anumber of alkyltrimethylammonium analogues (Table 2).
The cmc values obtained in this work agree well with thoseof Hayami et al. [40], who quote cmc (298.15 K) = 96, 22 and5.5 mmol kg−1 for DETAC, DTAC and TTAC, respectively, ob-tained from surface tension measurements. The absence of aminimum of the cmc for DTAC in water solution in this temper-ature range, observed by conductivity measurements by Mehta
T.-M. Perger, M. Bešter-Rogac / Journal of Colloid and Interface Science 313 (2007) 288–295 291
et al. [38], is probably due to the temperature range investigatedbeing too narrow.
The cmc values reported for decyltrimethylammonium bro-mide (DETAB), dodecyltrimethylammonium bromide (DTAB)and tetradecyltrimethylammonium bromide (TTAB) are con-siderably lower than those for the corresponding chlorides in-vestigated here, cmc (298.15 K) = 67 ± 1, 15 ± 1 and 3.8 ±0.1 mmol kg−1 for DETAB, DTAB and TTAB, respectively,whereas cmc values for TTAB and TTANO3 are rather close,cmc (298.15 K,TTANO3) = 3.38 mmol kg−1.
The cmc values for decyltrimethylammonium surfactantsdecrease in the order Cl− > Br− > C2F3COO− > C3F5COO−,while for tetradecyltrimethylammonium Cl− > Br− > ≈NO−
3 .This decrease can be explained by considering the binding
of counterions to micelles. For monovalent alkali counterionsit was shown recently that the hydration shell of cations lim-its the distance of closest approach, resulting in the cmc ofalkyl sulphates decreasing in the order Li+ > Na+ > K+ >
Cs+ [9].The differences between the anions can be explained in
a similar manner. The ionic radii are 0.181 nm for Cl−,0.196 nm for Br− and 0.196 for NO−
3 [55]. For C2F3COO− andC2F5COO− even larger radii values can be assumed. Large,singly charged ions, with low charge density, exhibit weakerinteractions with water. If the size of anions follows the orderCl− < Br− ≈ NO−
3 < C2F3COO− < C2F5COO−, the strengthof their interaction with water molecules (hydration) is in thereverse order.
Weakly hydrated counterions, such as C2F5COO−, can beadsorbed more readily on the micellar surface, resulting indecreased charge repulsion between the ionic surfactant headgroups. In contrast, the charge on the heavily hydrated Cl− ispartially screened by the surrounding polar water molecules andthese counterions are thus less effective in reducing the chargerepulsion. Cl− cannot approach the highly charged surface ofthe micelle as closely as less hydrated ions. Therefore, it canneither screen the charge at the surface of micelles nor reducethe surface potential as effectively as other, less hydrated ions.This results not only in higher values of cmc but also in highervalues of the degree of micelle ionization, β .
The β values obtained for chlorides are considerably largerthan those reported for other anions (Table 2). The β valuescan be ranked in the order Cl− > Br− ≈ NO−
3 > C2F3COO− >
C2F5COO−.Consequently, the cmc decreases when the size of counterion
increases and the interaction with water lessen, while the degreeof counterion binding (≡ 1 − β) increases.
The temperature dependence of the cmc shows the typicalU-shaped form (Fig. 2), reaching a minimum (cmc∗) at thetemperature T ∗. Values of T ∗ and cmc∗ are listed in Table 2,together with some literature data for other analogues.
The values of T ∗ = 319.8, 503.8 and 301.3 K for DETAC,DTAC and TTAC, respectively, are in accord with that reportedfor octadecyltrimethylammonium chloride, OTAC [37]. More-over, our results confirm the well-known fact that T ∗ for bothnon-ionic and ionic surfactants decreases with increasing lengthof the non-polar tail of the surfactant [6]. The values of T ∗ for
Fig. 2. The temperature dependence of cmc/cmc∗ for DETAC (!), DTAC (")and TTAC (E). Lines are the corresponding polynomial fits.
TABs show the same tendency, and cmc∗ values show a similardependence on the type of counterion to that already discussedfor cmc values.
The position of this minimum of cmc has thermodynamicsignificance. According to the pseudo-phase model, the Gibbsfree energy of micellization, �micG
0, is a function of tem-perature (Eq. (1)), therefore the minimum in cmc leads to aminimum in (�micG
0/T ). According to the Gibbs–Helmholtzrelation (Eq. (K) in supporting material) �micH
0 has to passthrough zero.
Values of �micG0, �micH
0 and �micS0 for all systems have
been estimated with the help of Eqs. (1), and (2), and (N) in sup-porting material, �micG
0 is seen to be moderately temperaturedependent, whereas �micS
0 and �micH0 are highly temper-
ature dependent for all the systems investigated (Table B insupporting material).
The thermodynamic parameters of micellization at 298.15 Kfor the systems investigated are compared with those forthe alkyltrimethylammonium analogues (Table 3). The val-ues of �micG
0 for all listed compounds range from −23 to−44 kJ mol−1. Longer alkyl chain lengths result in consider-ably more negative values of �micG
0 (−23.28, −30.56 and−37.01 kJ mol−1 for DETAC, DTAC and TTAC, respectively).The influence of the counterion is also significant: at a givenchain length, �micG
0 is more negative the larger the counte-rion. Thus, in the series of surfactants studied, DETAC is seento form relatively weak micelles.
All �micS0 values are positive, with a small dependence on
the alkyl chain length, �micS0 (298.15 K) is increasing with the
chain length. Values for all the analogues similar, showing thatthe entropy of micellization is not significantly affected by thecounterion nature.
The variation of �micH0 with temperature for all the sys-
tems investigated, together with that for DETAB, DTAB, TTABand TTANO3, is shown in Fig. 3.
Equation (2) predicts that the temperature at which �micH0 =
0 (T0) is T ∗. It appears that this is true for DETAC, DTACand TTAC, where the polynomial fits of �micH
0 versus T
292 T.-M. Perger, M. Bešter-Rogac / Journal of Colloid and Interface Science 313 (2007) 288–295
Table 3Thermodynamic functions of micellization for investigated systems and litera-ture data at 298.15 Ka
�micG0 �micH
0 �micS0 Tc �micH
∗ �micc0p
This workDETAC −23.28 5.90 97.9 240 ± 2 −17.8 −247.8DTAC −30.56 4.27 116.8 273.5 ± 0.2 −27.8 −541.4TTAC −37.01 1.95 130.7 268.8 ± 0.2 −33.3 −587.8
Literature dataDTACb −31.43 9.61 138OTACc −27.9 −3.88 70 274 ± 25 −32.6 −1400
DETAB −29.0d,−26.7k
0.0d, 0.2e,1.8h, 0.8k,1.6l
97.0d,98.6e,92.1k
308f
255 ± 10k−30f,−23k
−302g,−289d,−335.8i,−319k
DETAPAj −29.1 6.3 118.5 257 −24.2 −354.8
DETAPPj −33.0 8.4 138.8 247 −25.8 −502
DTAB −37.2d,−36.0e
−2.2d, −1.6k,−2.3e, 1.5h
117.3d,112.7e
308f −38f −406g,−439d
TTAB −44.0e,−42.1n
−4.9e, −4.9h,−5.0k,−4.3l,−4.08n
131.5e,127.5n
308f,314–325m,280n
−45f,−30.8n
−499g,−660n
TTANO3o −42.2 −4.0 128.8 274.4 −39.4 −631
a Units: �micG0, �micH
0, �micH∗ (kJ mol−1); �micS
0, �micc0p
(J mol−1 K−1); Tc (K).b Ref. [38], conductometry.c Ref. [37], Tc, �micH
∗ and �miccp were evaluated from the reported data
for �micH0 and �micS
0.d Ref. [5].e Ref. [33], calorimetry.f Ref. [6], values of �micH
∗ are taken from Fig. 9.g Ref. [32].h Ref. [30], enthalpy of dilution measurements.i Ref. [11].j Ref. [36], values were recalculated from the reported temperature depen-
dence of cmc in β .k Ref. [16], calorimetry.l Ref. [14], calorimetry.
m Ref. [12], value depends on the used model.n Ref. [19].o Ref. [35], values were recalculated from the reported temperature depen-
dence of cmc in β .
curves resulted in values for T0 = 319.7 ± 0.1, 305.7 ± 0.1and 301.3 ± 0.1 K for DETAC, DTAC and TTAC, respectively.This has also been observed for many other systems [56–60].
The formation of micelles is an endothermic process atlow temperatures and exothermic at higher temperatures. FromFig. 3 it is evident that at the given temperatures, �micH
0 de-creases in the order Cl− > Br− ≈ NO−
3 . Literature data onthermodynamic parameters of DETAPA and DETAPP do notallow comparison.
Since the process of micelle formation consists mainly of(i) the destruction of water structure surrounding the hydropho-bic part of surfactant when is escapes from water and aggregatesas liquid core inside the micelle and (ii) the dehydration of thepolar part and its electrostatic interaction due to aggregation,the decrease in �micH
0 from Cl− to Br− (NO−) results mainly
3Fig. 3. The enthalpy of micellization �micH0 of DETAC (!), DTAC (") and
TTAC (E) in aqueous solutions as a function of T . The corresponding heat ca-pacity, �micc
0p, is obtained from the slopes. For comparison the literature data
of �micH0 for DETAB (1) [30], DTAB (2) [30], TTAB (3) [30] and TTANO3
(4) [35] are shown as lines representing the best fits of reported data.
from the heat required to overpass the electrostatic repulsion be-tween headgroup. Electrostatic repulsion between ionic head-groups prevents the aggregation but is screened by counterions.
As mentioned above, weakly hydrated counterions (largerionic radius, e.g., Br−) decrease charge repulsion between theionic surfactant head groups more than do heavily hydratedions (smaller ionic radii, e.g., Cl−), whose counterion chargeis partially screened by the surrounding (tightly bound) polarwater molecules and these counterions are thus less effectivein reducing the charge repulsion. As the counterion binding(≡ 1 − β) decreases in the order Br− ≈ NO−
3 > Cl−, reflectedin increased electrostatic repulsion between headgroups, theenergy required to overcome this repulsion is larger, and theprocess is more endothermic. The curves in Fig. 3 are shiftedregularly on going from Cl− to Br− (and NO−
3 ).An increase in chain length is accompanied in an increase in
the temperature dependence of the enthalpy of micellization. Atlow temperatures (T < 293 K), the chain length has less effecton the micellization enthalpy whereas, at higher temperatures,increasing chain length decreases more strongly the enthalpyvalues.
The heat capacity �micc0p (Eq. (O) in supporting material) is
a linear function of T , since �micH0 is described as a second-
order polynomial function of temperature. It was determinedfor DETAC, DTAC and TTAC (Table B in supporting material)from the variation of �micH
0 with T (Fig. 3).All values are negative, as usually observed for the self-
association of amphiphiles [7,53], and can be ascribed to theremoval of large areas of non-polar surface from contact withwater on micelle formation [1]. It follows that, on increasingthe chain length of a surfactant molecule, the heat capacity ofmicellization should become more negative, which is the casefor DETAC, DTAC, and TTAC and for other surfactants, listedin Table 3.
T.-M. Perger, M. Bešter-Rogac / Journal of Colloid and Interface Science 313 (2007) 288–295 293
It has been proposed [5] that �micc0p is a linear function of
the hydrophobic surface that is exposed to water during demi-cellization and increases with the length of the alkyl chain by anaverage of about 50 J mol−1 K−1 per added methylene group.
If the heat capacity were influenced solely by the hydropho-bic chain, the value should be the same for all counterions ata given chain length and should decrease only with decreasingchain length. However, the data collected in Table 3 indicatethat the counterion plays a definite role.
Although the literature data �micc0p for TABs are not
consistent, an average value of about 50 J mol−1 K−1 peradded methylene group may be assumed. For TACs, �micc
0p
(298.15 K) decreases from −541.4 J mol−1 K−1 for DTAC to−587.8 J mol−1 K−1 at TTAC, but the �micc
0p (298.15 K) for
DETAC is much more positive (−247.8 J mol−1 K−1).These values can be interpreted in a broader context of the
hydrophobic effect. According to Richards [61–63], the wateraccessible surface areas of a methylene group is 30 Å2 and ofa methyl group, 88 Å2. Thus, the water accessible surface areaof the hydrophobic tails of the surfactants investigated is 358,418 and 478 Å2 for C10, C12 and C14 alkyl chain, respectively.By modelling the micellization process as a transfer of surfac-tant molecules into the micellar phase, �micc
0p can be expressed
in terms of the change of water accessible nonpolar and polarsurface areas [64]
(3)�micc0p = a�Ap + b�Anp,
where �Ap and �Anp stand for the loss of water accessi-ble polar and nonpolar areas. The parameters a = 0.59 ±0.17 J mol−1 K−1 Å−2 and b = −1.34 ± 0.33 J mol−1 K−1 Å−2
are deduced from protein folding [64]. Because the hydrophilicheadgroups of ionic surfactants remain hydrated on micelle for-mation, �micc
0p can be assumed to reflect solely the change in
exposure of the hydrophobic tails to water, that is �Ap = 0.This approach has recently been shown to be successful in de-scribing the heat capacity change on micellization for non-ionicsurfactants [65].
If the whole hydrophobic tail is assumed to be buried onmicellization, the ratio �micc
0p/�Anp takes the values −0.69,
−1.29 and −1.22 J mol−1 K−1 Å−2 for DETAC, DTAC andTTAC respectively. Furthermore, the ratios of �micc
0p to �Anp
for TABs and TTANO3 are about −0.87 ± 0.06, −1.1 ± 0.1,−1.2 ± 0.2 and 1.32 J mol−1 K−1 Å−2 for DETAB, DTAB,TTAB and TTANO3. Except for DETAC and DETAB, thevalues are in reasonable agreement with the value b in Eq. (3),reported by Spolar et al. [64]. It could be assumed thatthe heat capacity change of micellization is directly propor-tional to the removal of water accessible nonpolar surface foralkyltrimethylammonium analogues with longer alkyl chain(with the number of C atoms >10). Based on the values of�micc
0p/�Anp for DETAC and DETAB, there are methylene
groups which are still in contact with water molecules and thus�Anp is smaller than predicted from the structure of the surfac-tant molecule. This assumption is supported by a recent findingthat octyltrimethylammonium bromide (C8 alkyl chain surfac-tant) where per surfactant ion in the micelle between 9 and
14 water molecules should experience a hydrophobic environ-ment [66].
In addition, at a given temperature, �micc0p(DETAC) >
�micc0p(DETAB) (Table 3), which could be explained in the
following way. During the micellization process, the bindingof ions to the micelle reduces the number of water molecules intheir solvation shell, since the ions now share hydration waterwith the headgroups and the dehydration process of counterionis positive. However, as the size of the counterion increases(Br−), it binds more strongly to the headgroups (resulting insmaller β), but it is less hydrated and the number of watermolecules expelled from the headgroups is smaller that for asmaller (more hydrated) counterion. Consequently, the contri-bution from the dehydration of Cl− is more positive and �micc
0p
is less negative than in the case of Br−, as observed experi-mentally. Clearly the interactions between counterion and head-groups are stronger at shorter chain lengths.
Usually �micc0p has been considered as being temperature
independent, which may be a useful approximation over a rela-tively narrow temperature range [3]. However, it is evident thatthis assumption is not valid over a broader temperature range,either for the investigated systems (Table B in supporting ma-terial) or for many other surfactant systems [7,67]. Because ofthe non-linear temperature dependence of �micH
0, the �micc0p
values can be described as linear functions of the temperature
(4)�micc0p = �micc
0p(298.15 K)
(1 − B(T − 298.15 K)
)as proposed by Muller [5]. The coefficient B was estimatedto be 2.4, 5.6 and 5.9 J−1 mol−1 K−2 for DETAC, DTAC andTTAC, and 20.8 for OTAC (from the reported data on �micH
0
[37]). Values between 2.0 and 4.5 J mol−1 K−2 have been re-ported for a series of non-ionic surfactants [7].
A linear relationship between the entropy change and en-thalpy change, called enthalpy–entropy compensation, has beenobserved for the transfer of a variety of small solutes into wa-ter, as well as for the micellization of diverse surfactants [6,53,68,69]. In general, the compensation effect can be described bythe relation
(5)�micH0 = �micH
∗ + Tc�micS0,
where Tc, the so-called compensation temperature, is the slopeof the compensation plot and �micH
∗ is the correspondingintercept. Tc has been proposed as a measure of the “solva-tion” part of the process of micellization (desolvation of thehydrophobic chains) [6,70,71]. �micH
∗ provides informationon the solute–solute interactions and is considered as an indexof the “chemical part” of the micelle formation (aggregation ofthe non-polar chains to form the micellar unit).
The enthalpy–entropy compensation plots are linear and al-most parallel (Fig. C in supporting material). The same behav-iour has been found for homologous alkyltrimethylammoniumbromides [6]. Values of Tc and �micH
∗ values are listed in Ta-ble 3, together with some literature values.
Lumry and Rajender [72] showed that Tc values lie in a nar-row range between 250 and 350 K; for a variety of processesinvolving aqueous solutions of small molecules and in biolog-ical systems near 298.15 K. Moreover, Lumry’s law has been
294 T.-M. Perger, M. Bešter-Rogac / Journal of Colloid and Interface Science 313 (2007) 288–295
summarized by stating that, for processes dominated by hydra-tion, a value Tc ∼= 280 K should be assumed [70,72].
An early re-examination of the literature data for a group ofionic surfactants [73] showed that �micH
0 and �micS0 values
are significantly correlated, with an average value of the com-pensation temperature Tc of 315 K. A value of Tc of 308 K forionic surfactants was later suggested [6], but Tc around 280 Kfor TTAB in aqueous solution has recently been found [19].
The data obtained here, Tc = 240 K for DETAC and Tc ≈260 K for DTAC and TTAC, support this latest value for TTAB[19] and are in reasonable agreement with Lumry’s law.
When the alkyl chain length is increased by one methyleneunit, the value of �micH
∗ decreases by ∼3.9 kJ mol−1, whichis the value obtained for the homologous alkyltrimethylammo-nium bromides [6], although the values of �micH
∗ for TABsare considerably lower.
4. Conclusions
The micellization behaviour of the cationic surfactants DE-TAC, DTAC and TTAC in aqueous solution has been investi-gated by conductivity measurements over the temperature rangeof 278.15–318.15 K. The data obtained are compared with re-ported data for other alkyltrimethylammonium analogues anddiscussed in terms of the influence of the counterion and alkylchain length on the thermodynamic functions of micellization.
The critical micelle concentration (cmc) and enthalpy of mi-cellization (�micH
0) decrease in the order Cl− > Br− ≈ NO−3
at a given temperature and chain length. This decrease is asso-ciated with the increase of counterion binding (≡ 1 − β). Theelectrostatic repulsion between ionic headgroups, which pre-vents the aggregation, is progressively screened, with weaklyhydrated (larger) counterions approaching the micelle surfacecloser than smaller (heavily hydrated) counterions. In the firstcase, the process of micelle formation is less endothermic andthe molecules associate at lower concentrations. The cmc, plot-ted versus temperature, reaches a minimum, while the enthalpyof micellization passes through zero.
The use of the pseudo-phase separation model shows that thevariation of enthalpy and entropy of micellization compensateeach other and the free Gibbs energy of micellization (�micG
0)is only slightly dependent on counterion and temperature. Thefree energy of micellization is more negative for surfactantswith longer alkyl chain length and with larger counterions.
The heat capacities of micellization �micc0p of DETAC,
DTAC and TTAC in aqueous solution have been shown to behighly negative. They are in reasonable accord with the amountof non-polar solvent accessible surface area that is buried onmicellization, indicating that, in decyltrimethylammonium sur-factants, some methylene groups in the micelle core may be stillin contact with water molecules. The magnitude of �micc
0p in-
creases with increase in temperature, with longer alkyl chainlength and with size of the counterion.
The heat capacity change upon micellization is shown tobe directly proportional to the loss of water accessible nonpo-lar surface area, which is itself dependent on the alkyl chainlength. Presumably, for alkyltrimethylammonium surfactants
with shorter chain lengths, the nonpolar area is smaller, as esti-mated by Richard [61–63], and some methylene groups are stillin contact with water molecules. The effect of the nature of thecounterion on the heat capacity could be ascribed to the degreeof its hydration (and thus the contribution of dehydration whenions share the hydration water with headgroups).
Finally, it should be pointed out that the effect of counterionis not limited to an electrostatic effect only but it also influencesaggregate size and aggregation numbers. In this light completethermodynamic studies of micellization of ionic surfactants thatinvolve temperature dependence of �micc
0p in combination with
the corresponding structural studies may provide enough infor-mation for molecular interpretation of micellization.
Acknowledgments
Financial support by the Slovenian Research Agency throughGrants No. P1-0201 and J1-6653 is gratefully acknowledged.
Supporting material
The online version of this article contains additional support-ing material.
Please visit DOI: 10.1016/j.jcis.2007.04.043.
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