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Fluid Phase Equilibria 363 (2014) 106– 116

Contents lists available at ScienceDirect

Fluid Phase Equilibria

j our na l ho me pa ge: www.elsev ier .com/ locate / f lu id

hermodynamic and aggregation properties of sodium-hexylsulfonate in aqueous solution

aivan Solaimani, Rahmat Sadeghi ∗

epartment of Chemistry, University of Kurdistan, Sanandaj, Iran

r t i c l e i n f o

rticle history:eceived 14 July 2013eceived in revised form 6 November 2013ccepted 8 November 2013vailable online 23 November 2013

eywords:

a b s t r a c t

Thermodynamic and aggregation properties of sodium n-hexylsulfonate (C6H13SO3Na) in aqueous solu-tions have been studied at different temperatures by density, sound velocity, electroconductivity andvapor–liquid equilibria measurements. The critical micelle concentration (CMC), counterion binding ofmicelles and thermodynamics of micellization have been evaluated. From the density and sound velocitydata, the values of the apparent molar volumes and compressibilities, changes in the apparent molarproperties upon micellization and the infinite dilution apparent molar properties of the monomer state

odium n-alkylsulfonateolumetricompressibilityapor–liquid equilibriaicellization

of C6H13SO3Na in the aqueous solutions were determined. Vapor–liquid equilibrium data such as wateractivity, vapor pressure, osmotic coefficient, activity coefficient and Gibbs free energies were obtainedthrough the isopiestic method. A comparison between the mentioned thermodynamic and aggrega-tion properties of C6H13SO3Na in aqueous solutions with those of some other sodium n-alkylsulfonateswere also made and from which the effect of the alkyl chain length of the surfactant on the aggregationparameters were examined.

© 2013 Elsevier B.V. All rights reserved.

. Introduction

Surfactant molecules contain at least one polar group andne hydrophobic nonpolar group and in solutions, above a cer-ain concentration, called the critical micelle concentration (CMC),heir amphiphilic molecules tend to undergo the self associa-ion into ordered structures with different morphologies called

icelles. The micellization of surfactants in aqueous solutions intoicelles, vesicles, or membranes is an important phenomenon

n many industrial, chemical, and pharmaceutical applications.urfactants are classified by their net charge into three main sub-lasses: cationic, anionic, and nonionic. Sodium n-alkylsulfonates typical of a class of conventional anionic surfactants that arehemically more stable compared with sulfate analogs [1]. Nev-rtheless, fewer physicochemical studies of the monomers andhe micelles can be found in the literature compared with thoseor the sodium n-alkylsulfates. Although some limited studiesave revealed aggregation behavior of sodium n-alkylsulfonates

n aqueous solutions [1–21], however the aggregation of sodium

-alkylsulfonates in aqueous solutions has not been studied sys-ematically yet. From both fundamental and applied viewpoints,articular interests are the molecular structure effect on both the

∗ Corresponding author. Tel.: +98 871 6624133; fax: +98 871 6660075.E-mail addresses: rahsadeghi@yahoo.com, rsadeghi@uok.ac.ir (R. Sadeghi).

378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.fluid.2013.11.015

aggregation behavior and the physicochemical properties of theaggregation process. The lack of information, together with theirpotential application has motivated us to investigate the aggrega-tion behavior of sodium n-hexylsulfonate (C6H13SO3Na) in aqueoussolutions. In our previous works, aggregation behavior of surfac-tants sodium n-heptyl sulfonate [22,23], sodium n-pentyl sulfonate[24] and sodium n-dodecyl sulfonate [25] in aqueous solutions atdifferent temperatures have been studied by volumetric, compress-ibility, electroconductivity and vapor–liquid equilibria techniques.In this respect and in continuation of our previous works onthe thermodynamic studies of aggregation behavior of sodium n-alkylsulfonates in aqueous solutions [22–25], and in an attempt toobtain further evidence about the aggregation behavior of a sodiumn-alkylsulfonate, this work is, thus, mainly focused on (i) the studyof the VLE properties of aqueous solutions of C6H13SO3Na at 298.15,308.15 and 318.15 K, (ii) the study of volumetric and compress-ibility properties of aqueous solutions of C6H13SO3Na at 298.15,303.15, 308.15, 313.15 and 318.15 K, (iii) the study of conducto-metric properties of aqueous solutions of C6H13SO3Na at 298.15.Furthermore the obtained data in this work together with thosetaken from the literature for other sodium n-alkylsulfonates wereused to systematic studying of the thermodynamic and aggrega-

tion properties of sodium n-alkylsulfonates in aqueous solutionsand from which the appropriate correlations between the differentthermodynamic or aggregation properties and alkyl chain lengthof the surfactants were obtained.

S. Solaimani, R. Sadeghi / Fluid Phase E

Table 1Physical properties of the used chemicals.

Chemical Source Country Purity (in massfraction %)

Sodium chloride Merck Germany >99.5

2

2

Tcp

2

tmtCr(dtCltaettata

2

a(tTda±Tw

2

idqtoaat

Sodium n-hexylsulfonate Merck Germany >99

. Experimental

.1. Materials

The properties of chemicals used in this work were listed inable 1. All of these chemicals were used without further purifi-ation. The double distilled, deionized water was used for thereparation of the solutions.

.2. Osmotic coefficient measurements

In the present work, the isopiestic method was used to obtainhe osmotic coefficient. The used apparatus consisted of five-leg

anifold attached to round-bottom flasks. Two flasks containedhe standard pure NaCl solutions, two flasks contained the pure6H13SO3Na solutions and the central flask was used as a watereservoir. The apparatus was held in a constant-temperature bathwhose temperature was controlled to within ± 0.05 K) at least 15ays (depend on the molality of C6H13SO3Na) for equilibrium. Fromhe weight of each flask after equilibrium and the initial weight of6H13SO3Na and NaCl, the mass fraction of each solution in equi-

ibrium was calculated. At equilibrium, the chemical potentials ofhe water in each of the solutions in the closed isopiestic systemre identical. Equality of the water chemical potential implies thequality of the water activity. Since the water activity is known forhe standard NaCl solution, it will be known for each solution withinhe isopiestic system. The osmotic coefficients for the standard NaClqueous solutions have been calculated from correlation given inhe literature [26]. The uncertainty in the measurement of waterctivity was estimated to be ±5 × 10−4.

.3. Volumetric measurements

The density and sound velocity of the mixtures were measuredt different temperatures with a digital vibrating-tube analyzerAnton Paar DSA 5000, Austria) with proportional temperature con-rol that kept the samples at working temperature within ±10−3 K.he apparatus was calibrated with double distilled deionized, andegassed water, and dry air at atmospheric pressure. Densitiesnd ultrasonic velocities can be measured to ±10−6 g cm−3 and10−2 m s−1, respectively, under the most favorable conditions.he uncertainties of density and ultrasonic velocity measurementsere ±3 × 10−6 g cm−3 and ±10−1 m s−1, respectively.

.4. Conductometric measurements

Electrical Conductivities were measured by a digital conductiv-ty meter (Metrohm model 712) with a sensitivity of 0.1% and a

ipping-type conductivity cell with platinized electrodes at a fre-uency of 1 MHz. In this method, 10 mL of water was placed in ahermostated (by a Julabo circulating thermostat with a precisionf 0.02 K) double-walled glass container at a certain temperaturend surfactant solution of known concentration was progressivelydded. The conductivity was recorded when its fluctuation was lesshan 1% within 2 min.

quilibria 363 (2014) 106– 116 107

3. Results and discussion

In the present work, three sets of experiments including osmoticcoefficient measurements at 298.15, 308.15 and 318.15 K, conduc-tometric measurements at 298.15 K and density and ultrasoundmeasurements at 298.15, 303.15, 308.15, 313.15 and 318.15 K werecarried out in order to describe thermodynamic properties of binaryaqueous C6H13SO3Na solutions.

3.1. Vapor–liquid equilibria measurements

The water activity or osmotic coefficients are one of the mostimportant thermodynamic properties for the understanding ofthe interactions in aqueous solutions. In addition, the activity isclosely related with the other thermodynamic properties and inthermodynamic modeling, it is the essential variable. Furthermorealthough the concentration dependence of the different thermo-dynamic properties exhibit a change in slope at the concentrationin which micelles are formed, however, the concentration depend-ence of vapor–liquid equilibria properties such as water activityand osmotic coefficient exhibits a more distinct change especiallyin the case of short-chain surfactants. In spite of their importance,in colloidal chemistry, the values of vapor–liquid equilibria prop-erties seem to be rarely determined experimentally, in contrast toelectrolyte solution chemistry or biology.

For a certain C6H13SO3Na solution with molality m which is inisopiestic equilibrium with a sodium chloride solution with molal-ity m∗ and osmotic coefficient ˚*, the osmotic coefficient wasobtained according to:

= �∗˚∗m∗

�m(1)

where �∗ and � are the sums of the stoichiometric numbers ofanions and cations in the reference solution and the solution ofC6H13SO3Na, respectively. ˚* is the osmotic coefficient for aqueoussolution of NaCl with molality m* calculated from the correlationgiven in the literature [26]. From the experimental osmotic coef-ficient data, the activity of water in the surfactant solution andthe vapor pressure of this solution were determined at isopiesticequilibrium molalities, with the help of the following relations:

aw = exp[−Mw�m˚] (2)

ln aw = ln(

p

p◦w

)+ (B◦

w − V ◦w)(p − p◦

w)RT

(3)

where Mw is the molecular weight of the solvent, B◦w is the

second virial coefficient of water vapor, V ◦w is the molar volume

of liquid water, and p◦w is the vapor pressure of pure water.

Experimental data of the osmotic coefficients, water activities andvapor pressures of aqueous C6H13SO3Na solutions are given inTable 2. The experimental water activities, aw, osmotic coefficients,˚, and vapor pressure depressions, p − p◦

w , for binary aqueousC6H13SO3Na solutions are plotted against the molality of surfac-tant, respectively, in Figs. 1–3. In these figures the experimentaldata for aqueous C5H11SO3Na [24], C7H15SO3Na [23], C8H17SO3Na[19] and NaCl [26] solutions are also given. As can be seen theseplots exhibit a change in slope at the concentration in whichmicelles are formed. For m < CMC, the values of both wateractivity and vapor pressure depression of aqueous C5H11SO3Na,C6H13SO3Na, C7H15SO3Na, C8H17SO3Na and NaCl (no micelliza-tion) solutions have similar values. However for the concentrationshigher than CMC, both of water activity and vapor pressure depres-sion are larger than those we expect in the absence of micellization

and at each concentration these quantities follow the orderNaCl < C5H11SO3Na < C6H13SO3Na < C7H15SO3Na < C8H17SO3Na,which is the same trend for the hydrophobic properties of alkylchain of surfactant. In fact, the confinement of a fraction of the

108S.

Solaimani,

R.

Sadeghi /

Fluid Phase

Equilibria 363 (2014) 106– 116

Table 2Isopiestic equilibrium molalities, m, osmotic coefficients, ˚, water cctivities, aw , and vapor pressures, p, of aqueous C6H13SO3Na solutions at different temperatures T.

T = 298.15 K T = 308.15 K T = 318.15 K

m/mol kg−1 m*/mol kg−1 ˚ aw p/kPa m/mol kg−1 m*/mol kg−1 ˚ aw p/kPa m/mol kg−1 m*/mol kg−1 ˚ aw p/kPa

0.2861 0.3012 0.971 0.9900 3.137 0.4847 0.4839 0.920 0.9841 5.536 0.3974 0.3957 0.914 0.9870 9.4650.3217 0.3350 0.960 0.9889 3.134 0.5031 0.5020 0.920 0.9835 5.533 0.4457 0.4406 0.907 0.9855 9.4500.3797 0.4028 0.979 0.9867 3.126 0.5675 0.5529 0.899 0.9818 5.524 0.4601 0.4676 0.933 0.9846 9.4420.4364 0.4442 0.940 0.9853 3.122 0.5936 0.5693 0.885 0.9812 5.521 0.5448 0.5238 0.884 0.9828 9.4240.4438 0.4532 0.943 0.9850 3.121 0.6674 0.6298 0.873 0.9792 5.509 0.5499 0.5365 0.897 0.9824 9.4200.4557 0.4712 0.955 0.9844 3.119 0.6836 0.6353 0.860 0.9790 5.508 0.5890 0.5620 0.878 0.9815 9.4120.4721 0.4839 0.947 0.9840 3.118 0.7528 0.6722 0.827 0.9778 5.501 0.6187 0.5785 0.861 0.9810 9.4070.4872 0.4911 0.932 0.9838 3.117 0.7981 0.6907 0.802 0.9772 5.498 0.6339 0.5876 0.853 0.9807 9.4040.4961 0.5165 0.963 0.9829 3.115 0.8735 0.7223 0.767 0.9762 5.492 0.6359 0.5968 0.864 0.9804 9.4010.5165 0.5292 0.948 0.9825 3.113 0.9032 0.7297 0.750 0.9759 5.490 0.6399 0.6096 0.878 0.9800 9.3970.5287 0.5456 0.955 0.9820 3.111 0.9597 0.7372 0.713 0.9757 5.489 0.7074 0.6317 0.823 0.9792 9.3900.5642 0.5675 0.931 0.9812 3.109 0.9686 0.7521 0.721 0.9752 5.486 0.7122 0.6390 0.827 0.9790 9.3880.5936 0.5840 0.911 0.9807 3.107 1.0369 0.7651 0.685 0.9747 5.484 0.7479 0.6722 0.830 0.9779 9.3770.6074 0.6023 0.919 0.9801 3.105 1.0636 0.7689 0.672 0.9746 5.483 0.8080 0.6778 0.774 0.9777 9.3750.6140 0.6059 0.915 0.9800 3.105 1.0674 0.7801 0.679 0.9742 5.481 0.8228 0.6852 0.769 0.9775 9.3730.6173 0.6225 0.935 0.9794 3.103 1.1309 0.7838 0.644 0.9741 5.480 0.8880 0.7204 0.750 0.9763 9.3620.6393 0.6298 0.914 0.9792 3.103 1.1900 0.8007 0.626 0.9735 5.477 0.9061 0.726 0.741 0.9761 9.3600.6627 0.6372 0.892 0.9789 3.102 1.2140 0.8101 0.621 0.9732 5.475 0.9545 0.7427 0.720 0.9755 9.3540.6580 0.6556 0.925 0.9783 3.100 1.2649 0.8251 0.607 0.9727 5.472 1.0759 0.7745 0.667 0.9745 9.3440.7094 0.6722 0.880 0.9778 3.098 1.3199 0.8420 0.594 0.9721 5.469 1.2837 0.8307 0.601 0.9726 9.3260.7687 0.6870 0.831 0.9773 3.096 1.3291 0.8439 0.592 0.9721 5.469 1.4846 0.9006 0.565 0.9703 9.3040.8178 0.7427 0.846 0.9754 3.091 1.3616 0.8552 0.585 0.9717 5.467 1.5003 0.9082 0.563 0.9700 9.3010.9932 0.7614 0.714 0.9748 3.089 1.4149 0.8779 0.579 0.9709 5.462 1.5951 0.9234 0.539 0.9695 9.2961.0045 0.7689 0.713 0.9745 3.088 1.4285 0.8628 0.563 0.9714 5.465 1.7129 0.9825 0.536 0.9675 9.2771.0882 0.7763 0.665 0.9743 3.087 1.4776 0.8741 0.552 0.9710 5.463 1.8570 1.0132 0.510 0.9664 9.2671.2853 0.8420 0.612 0.9720 3.080 1.4828 0.8892 0.560 0.9705 5.460 1.9087 1.0382 0.509 0.9656 9.2591.3449 0.8458 0.588 0.9719 3.080 1.6131 0.9139 0.529 0.9697 5.455 1.9810 1.0652 0.504 0.9647 9.2501.3658 0.8533 0.584 0.9717 3.079 1.7512 0.9405 0.502 0.9688 5.450 2.1125 1.1077 0.492 0.9632 9.2361.4672 0.8760 0.559 0.9709 3.076 1.9511 1.0228 0.492 0.9660 5.435 2.3481 1.1876 0.477 0.9605 9.2091.7710 0.9386 0.497 0.9688 3.070 2.2846 1.1310 0.467 0.9623 5.414 2.4522 1.2327 0.475 0.9589 9.1941.9008 0.9729 0.481 0.9676 3.066 2.9898 1.4014 0.448 0.9529 5.361 2.7030 1.3137 0.461 0.9561 9.1671.9661 0.9825 0.470 0.9673 3.065 3.8080 1.7691 0.453 0.9397 5.286 2.8545 1.3595 0.453 0.9545 9.1522.0898 1.0189 0.459 0.9660 3.061 3.9382 1.8886 0.471 0.9354 5.262 2.9012 1.4135 0.464 0.9526 9.1342.1261 1.0362 0.459 0.9654 3.059 4.3312 2.1020 0.483 0.9275 5.217 3.0697 1.4819 0.462 0.9502 9.1112.3075 1.0845 0.444 0.9638 3.054 3.0224 1.5021 0.476 0.9495 9.1042.6909 1.2151 0.429 0.9592 3.039 3.1310 1.5855 0.487 0.9465 9.0752.7090 1.2485 0.439 0.9581 3.036 3.3050 1.6511 0.482 0.9442 9.0533.1083 1.4155 0.437 0.9522 3.017 3.5243 1.8318 0.507 0.9377 8.990

3.8679 1.9926 0.507 0.9318 8.934

u(aw) = ±5 × 10−4.

S. Solaimani, R. Sadeghi / Fluid Phase Equilibria 363 (2014) 106– 116 109

0.9

0.92

0.94

0.96

0.98

1

a w

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4 5

m / mol.kg-1

a s

Fig. 1. Plot of water activity data, aw , and mole fraction based surfactantactivity, as, against molality of solute, m: ©, C5H11SO3Na + H2O at 298.15 K[24]; �, C6H13SO3Na + H2O at 298.15 K; ×, C6H13SO3Na + H2O at 308.15 K;�

Cm

cisfctasmh

FC×C.

Fig. 3. Plot of vapor pressure depression data, p − p◦w/kPa, against molality of solute,

, C6H13SO3Na + H2O at 318.15 K; �, C7H15SO3Na + H2O at 298.15 K [23]; ♦,8H17SO3Na + H2O at 298.15 K [19]; —, NaCl + H2O at 298.15 K [26]; . . .. . .., supposedonomer solution at 298.15 K.

ounterions to the micellar surface results in an effective loss ofonic charges and therefore the hydration number of monomerictate of surfactant is larger than the hydration number of micellarorm of surfactant and therefore micellization lowers the NaCloncentrations required to achieve a certain water activity andherefore for a certain surfactant concentration, both of waterctivity and vapor pressure depression of micellar solutions of

urfactant are larger than those we expect in the case of supposedonomer solution. The greater the extent of aggregation among

ydrotrope molecules, the lesser will be the number of free

ig. 2. Plot of osmotic coefficient data, , against molality of solute, m: ©,5H11SO3Na + H2O at 298.15 K [24]; �, C6H13SO3Na + H2O at 298.15 K;, C6H13SO3Na + H2O at 308.15 K; �, C6H13SO3Na + H2O at 318.15 K; �,7H15SO3Na + H2O at 298.15 K [23]; ♦, C8H17SO3Na + H2O at 298.15 K [19];

. .. . ., NaCl + H2O at 298.15 K [26].

m: ©, C5H11SO3Na + H2O at 298.15 K [24]; �, C6H13SO3Na + H2O at 298.15 K; �,C7H15SO3Na + H2O at 298.15 K [23]; ♦, C8H17SO3Na + H2O at 298.15 K [19]; . . .. . .,NaCl + H2O at 298.15 K [26].

hydrotrope molecules in the aqueous solution. The decrease in theactivity of water in the presence of short-chain surfactants is morethan that observed in the presence of long-chain surfactants. Closeexamination of the water activity data of the aqueous C6H13SO3Nasolutions at different temperature indicate that the values of aw inthe monomer solutions slightly increase by increasing temperaturehowever that in the micellar solutions decrease as temperatureincreases.

Fig. 2 shows that the values of the osmotic coefficient, �,decrease by increasing the alkyl chain length of the surfactant. Theosmotic coefficient isotherms have been intersected in a certainconcentration and the osmotic coefficients for the correspondingconcentration are independent of temperature. As shown in Fig. 2,in the low surfactant concentration region, the measured values of� decrease by increasing temperature; while, for the high surfac-tant concentration region, the measured values of � increase withthe increase in temperature.

The experimental osmotic coefficient is related to the meanmolal activity coefficient of surfactant, �±, at molality m′ by therelation

ln �± = ˚′ − 1 +∫ m′

0

( − 1)d(ln m) (4)

where ˚′ is the osmotic coefficient of the solution at molality m′.The variation of �± with the surfactant concentration is shownin Fig. 4. As can be seen, similar to the osmotic coefficient thevalues of the �± decrease by increasing the alkyl chain lengthof the surfactant. For the low surfactant concentration region,the values of �± decrease by increasing temperature; while, forthe high surfactant concentration region, the calculated valuesof �± are independent of temperature. Calculated water activ-ity coefficients, �w(= aw/xw), of aqueous solutions of C6H13SO3Naalong with those of C5H11SO3Na, C7H15SO3Na and C8H17SO3Na arepresented as a function of surfactant molality in Fig. 5. The wateractivity coefficients are independent of the surfactant concentra-tion up to the CMC and at concentrations higher than the CMC, thevalues of the water activity coefficient increase as a result of the

micelle formation. For concentrations higher than the CMC, �w > 1(positive deviations from ideal-solution behavior) which indicatesthat the solvent–solvent interactions are more favorable than themicelle–solvent interactions. As can be seen, the values of the �w

110 S. Solaimani, R. Sadeghi / Fluid Phase Equilibria 363 (2014) 106– 116

Fig. 4. Plot of mean molal activity coefficient of surfactant, �± , against molal-i2C

itbtt

tmmimaicctp

Fm2�

Fig. 6. Variation of the free energy of micellization, �Gmic (solid lines), �Gmicw

(dashed lines) and �Gmics (dotted lines), as a function of surfactant molality, m, for

CnH2n+1SO3Na + H2O system at 298.15 K: ©, C5H11SO3Na + H2O (calculated from the

ty of solute, m: ©, C5H11SO3Na + H2O at 298.15 K [24]; �, C6H13SO3Na + H2O at98.15 K; ×, C6H13SO3Na + H2O at 308.15 K; �, C6H13SO3Na + H2O at 318.15 K; �,7H15SO3Na + H2O at 298.15 K [23]; ♦, C8H17SO3Na + H2O at 298.15 K [19].

ncrease by increasing the alkyl chain length of the surfactant. Forhe low surfactant concentration region, the values of �w increasey increasing temperature; while, for the high surfactant concen-ration region, the calculated values of �w decrease by increasingemperature.

The equation �G◦mic = RT(2 − ˇ) ln CMC (where R and T have

heir usual meaning, and is the degree of ionization of theicelles) has widely been used to determine the free energy oficellization of the 1:1 conventional long-chain ionic surfactants

n aqueous solution [27]. Long-chain ionic surfactants have diluteicellar aqueous solutions and therefore in deriving this equation,

ctivities have been taken equal to concentrations and intermicellarnteractions have been neglected. However in the case of the short-

hain surfactants which have the high CMC values, the activitiesan not be taken equal to concentration and therefore this equa-ion can not be used for the determination of �G◦

mic. In Fig. 1 thelots of mole fraction based surfactant activity against molality are

ig. 5. Plot of water activity coefficient, �w , against molality of solute,: ©, C5H11SO3Na + H2O at 298.15 K [24]; �, C6H13SO3Na + H2O at

98.15 K; × C6H13SO3Na + H2O at 308.15 K; �, C6H13SO3Na + H2O at 318.15 K;, C7H15SO3Na + H2O at 298.15 K [23]; ♦, C8H17SO3Na + H2O at 298.15 K [19].

data given in ref. [24]); �, C6H13SO3Na + H2O; ×, C7H15SO3Na + H2O (calculated fromthe data given in Ref. [23]); ♦, C8H17SO3Na + H2O (calculated from the data given inRef. [19]).

also given. As can be seen the plots are linear for m < CMC and theirconcentration dependence exhibits a change in slope at the con-centration in which micelles are formed. The dotted lines in Fig. 1shows the activities of components in the supposed monomer solu-tions. For m > CMC, the free energy of transfer of 55.51 mol of waterand m moles of surfactant from the supposed monomer solutionsto the real micellar solutions, �Gmic

w and �Gmics can be obtained as:

�Gmicw = 55.51(�mic

w − �monw ) (5a)

�Gmics = m(�mic

s − �mons ) (5b)

where � is the chemical potential, and subscripts w and s standfor water and surfactant, respectively. �mic

iand �mon

iare chemical

potential of component i in the micellar and supposed monomersolutions, respectively. From the relation for the chemical poten-tial of water and surfactant (�w = �◦

w + RT ln �wxw and �s = �◦s +

�RT ln �±ms) and if we assume the similar standard state in themicellar and supposed monomer solutions we have

�Gmicw = 55.51RT ln

�micw (T, P, x)

�monw (T, P, x)

(6a)

�Gmics = �mRT ln

�mic± (T, P, x)�mon± (T, P, x)

(6b)

The calculated values of the free energy of micellization areshown in Fig. 6. This procedure was also applied for the VLE datareported for C5H11SO3Na [24], C7H15SO3Na [23] and C8H17SO3Na[19] and the corresponding free energy of micellization are alsoshown in Fig. 6. The calculated values of �Gmic

w and �Gmics indicate

that for concentrations higher than the CMC, water molecules andsurfactant ions respectively become less and more stable by mice-llization and therefore the behavior of surfactant is the derivingforce for the micelle formation. The values of �Gmic

s were large andnegative so that although the calculated �Gmic

w values are positivebut the calculated free energies of micellization �Gmic(= �Gmic

s +�Gmic

w ) have negative values. Increasing the chemical potential ofwater upon micellization indicate that the surfactant–water inter-

actions in the supposed monomer solutions are stronger than thosein the corresponding real micellar solutions. As can be seen, the val-ues of the free energies of micellization become more negative byincreasing the alkyl chain length of the surfactant. Table 4 shows

S. Solaimani, R. Sadeghi / Fluid Phase Equilibria 363 (2014) 106– 116 111

132

134

136

138

140

142

144

0.01 0.1 1 10

V φ/

cm

3.m

ol-1

-0.07

-0.05

-0.03

-0.01

0.01

0.03

0.01 0.1 1 10

m / mol.kg-1

Kφ

/ cm

3. M

pa

-1.m

ol- 1

Fa×

ts

3

ppmtsvt

V

K

wwasc

tCotrv

133

135

137

139

141

143

145

0 0.5 1 1.5 2

V φ,Μ

/ cm

3.m

ol-1

-0.07

-0.05

-0.03

-0.01

0.01

0.03

0.05

0 0.5 1 1.5 2

m / mol.kg-1

Kφ ,

Μ/

cm

3.M

pa

-1.m

ol-1

Fig. 8. Apparent molar volume and isentropic compressibility of C6H13SO3Na in

ig. 7. Apparent molar volume and isentropic compressibility of C6H13SO3Na inqueous solutions against surfactant molality (log scale) at different temperatures:, 298.15 K; �, 303.15 K; �, 308.15 K; �, 313.15 K; ♦, 318.15 K.

he values of CMC obtained from the intersection of the apparentlytraight lines of m against m.

.2. Volumetric measurements

Two important thermodynamic parameters characterizing thehysical state of the micelle is apparent molar volume and com-ressibility, which can be obtained from density and sound velocityeasurements. Experimental data of density and sound velocity for

he investigated system are given in Table 3. The experimental den-ity and sound velocity data allowed us to calculate apparent molarolume, V� , and apparent molar isentropic compressibility, K� , ofhe surfactant through the following equations:

� = M

d− 1000(d − d0)

mdd0(7)

� = Ms

d− 1000 (ds0 − d0s)

mdd0(8)

here d is the density of a solution of molality m, M is the moleculareight of the surfactant, d0 is the density of the solvent. s0 and s

re the coefficients of isentropic compressibility of the solvent andolution, respectively. Isentropic compressibility �s (MPa)−1 is cal-ulate from sound velocity, u, and density data as

s = 1000du2

(9)

The apparent molar volumes at different temperatures are plot-ed against surfactant molality (log scale) for aqueous solutions of6H13SO3Na in Fig. 7. The apparent molar volumes slightly depend

n concentration up to the CMC and at concentrations higher thanhe CMC, the value of the apparent molar volume increases as aesult of the micelle formation. Variation of the apparent molarolume upon aggregation can result from the contribution of three

the monomeric and micellar forms in aqueous solutions against surfactant molalityat different temperatures: ×, 298.15 K; �, 303.15 K; �, 308.15 K; �, 313.15 K; ♦,318.15 K.

different processes [28] (i) the liberation of structured water aroundthe hydrocarbon tail, (ii) the electrostatic repulsion between thehead groups of the surfactant, (iii) the release of water moleculesfrom the counter-ion upon binding to the micelles.

The variations of K� as a function of the molality of C6H13SO3Na(log scale) in aqueous solutions are also shown in Fig. 7. Similar tothe apparent molar volume, the value of K� is nearly constant at lowconcentration of surfactant. At higher concentrations micelle for-mation results in the increase of the value of K� . The negative valuesof K� for low concentration of surfactant are attributed to the strongattractive interactions due to the hydration of ions. By increas-ing concentration of surfactant and micelle formation, because ofthe release of water molecules from the counter-ion upon bindingto the micelles, some water molecules are released into the bulk,thereby making the medium more compressible. The values of CMCobtained from the intersection of the apparently straight lines ofthe apparent molar properties against m (log scale) are given inTable 5 and as an example these plots for C6H13SO3Na in aqueoussolutions at different temperatures have been shown in Fig. 7. Thevalues of the apparent molar isentropic compressibility increase(more positive) by increasing the alkyl chain length of surfactant.

The values of volume and compressibility changes associatedwith micellization processes have also been determined accordingto Gianni et al. [29] procedure. For this purpose the values of theapparent molar properties for the micellar forms of the surfactantwere calculated using the following relation [29]:

�,M = �m − �,m(CMC) × CMCm − CMC

(10)

where Y = V or K, �,M is the apparent molar properties of the sur-

factant in the micellar form and �,m(CMC) is the apparent molarproperty of the surfactant in its monomeric form calculated at CMC.Fig. 8 shows the apparent molar properties of the monomeric (cal-culated through Eqs. (7) and (8)) and micellar (calculated through

112 S. Solaimani, R. Sadeghi / Fluid Phase Equilibria 363 (2014) 106– 116

Table 3Experimental density d/(g·cm−3) and sound velocity u/(m·s−1) of aqueous solutions of C6H13SO3Na(s) at atmospheric pressure and different temperatures.

m/mol kg−1 T = 298.15 K T = 303.15 K T = 308.15 K T = 313.15 K T = 318.15 K

d/(g cm−3) u/(m s−1) d/(g cm−3) u/(m s−1) d/(g cm−3) u/(m s−1) d/(g cm−3) u/(m s−1) d/(g cm−3) u/(m s−1)

0.02667 0.998494 1501.14 0.997074 1513.06 0.995436 1523.38 0.993602 1532.18 0.991581 1539.490.03202 0.998788 1501.97 0.997366 1513.82 0.995724 1524.10 0.993886 1532.84 0.991860 1540.110.04556 0.999525 1504.01 0.998089 1515.73 0.996437 1525.85 0.994589 1534.48 0.992555 1541.610.05359 0.999957 1505.18 0.998514 1516.82 0.996855 1526.88 0.995000 1535.42 0.992963 1542.490.08092 1.001431 1509.23 0.999966 1520.57 0.998286 1530.36 0.996410 1538.63 0.994356 1545.470.16438 1.005810 1520.83 1.004270 1531.40 1.002525 1540.35 1.000591 1547.84 0.998481 1553.930.27909 1.011665 1536.12 1.010024 1545.45 1.008188 1553.25 1.006167 1559.68 1.003977 1564.770.39859 1.017543 1550.74 1.015797 1558.80 1.013861 1565.44 1.011752 1570.73 1.009477 1574.770.46241 1.020692 1558.06 1.018884 1565.41 1.016892 1571.35 1.014730 1576.02 1.012408 1579.460.52594 1.023592 1564.28 1.021722 1570.89 1.019678 1576.19 1.017465 1580.26 1.015100 1583.190.59132 1.026518 1569.63 1.024586 1575.47 1.022485 1580.11 1.020223 1583.63 1.017814 1586.060.65978 1.029273 1573.31 1.027281 1578.49 1.025127 1582.60 1.022820 1585.68 1.020375 1587.770.74928 1.033076 1576.00 1.031011 1580.57 1.028797 1584.18 1.026435 1586.89 1.023942 1588.650.87038 1.037833 1577.16 1.035695 1581.30 1.033413 1584.53 1.030997 1586.85 1.028451 1588.241.08965 1.045507 1577.88 1.043262 1581.33 1.040886 1583.86 1.038384 1585.49 1.035762 1586.231.33443 1.053595 1578.43 1.051238 1580.98 1.048766 1582.61 1.046175 1583.35 1.043474 1583.251.77539 1.066854 1579.16 1.064320 1579.91 1.061684 1579.80 1.058946 1578.89 1.056111 1577.22

u(d) = ±3 × 10−6 g cm−3 and u(u) = ±10−1 m s−1.

Table 4The values of the critical micelle concentration, CMC, for CnH2n+1SO3Na in aqueous solutions at 298.15 K obtained from the osmotic coefficient data.

C5H11SO3Na C6H13SO3Na C7H15SO3Na C8H17SO3Na

CMC/mol kg−1 1.366 0.689, 0.734a, 0.693b 0.380 0.188

EtoaaTp

TV

a 308.15 K.b 318.15 K.

q. (10)) forms of C6H13SO3Na in aqueous solutions at differentemperatures. The difference between the apparent molar propertyf the monomer (�,m) and the micelle (�,M), both extrapolatedt the CMC, yields the corresponding property change (�mic )

ssociated with the micellization reaction which are also given inable 5. In Table 5 the values of the infinite dilution apparent molarroperties of the monomeric form of surfactants, ◦

�,m, have also

able 5olume and compressibility data for the micellization of CnH2n+1SO3Na in water at differe

T/K CMC/mol kg−1 V ◦�,m

/cm3mol−1 �Vmic/cm3 mol−1 V ◦�,m

/cm3 mol−

C5H11SO3Naa

288.15 0.978 115.733 4.555 0.2054

293.15 0.961 116.743 4.440 0.1904

298.15 0.941 117.659 4.334 0.1759

303.15 0.925 118.476 4.200 0.1618

308.15 0.906 119.257 4.080 0.1482

313.15 0.890 119.982 3.954 0.1351

C6H13SO3Na298.15 0.571 133.670 4.814 0.1995

303.15 0.559 134.597 4.583 0.1882

308.15 0.545 135.591 4.408 0.1772

313.15 0.539 136.373 4.206 0.1667

318.15 0.530 137.218 4.043 0.1564

C7H15SO3Nab

288.15 0.345 146.584 5.960 0.2719

293.15 0.330 147.947 5.277 0.2532

298.15 0.323 149.110 5.019 0.2352

303.15 0.319 150.256 4.763 0.2178

308.15 0.312 151.318 4.524 0.2009

C12H25SO3Nac

288.15 0.011 224.134 11.545 0.5621

293.15 0.010 226.692 10.918 0.5250

298.15 0.010 229.296 10.403 0.4891

303.15 0.010 231.748 9.623 0.4545

308.15 0.010 233.921 9.071 0.4209

313.15 0.010 235.848 8.381 0.3884

a Calculated from the data given in Ref. [24].b Calculated from the data given in Ref. [22].c Calculated from the data given in Ref. [25].

been given. This procedure was also applied for the volumetric datareported for C5H11SO3Na [24], C7H15SO3Na [22] and C12H25SO3Na[25] and the corresponding parameters are also given in Table 5.The values of �micV and �micK decrease with increasing tempera-

ture, as observed for sodium perfluoroheptanoate [30] and lithiumperfluoroheptanoate [29], due to the larger increase with temper-ature of the property of the monomer in both cases. Furthermore

nt temperature and atmospheric pressure.

1 K−1 CMC/mol kg−1 K◦�,m

/cm3 MPa−1 mol−1 �Vmic/cm3 MPa−1 mol−1

0.768 −0.0735 0.04370.770 −0.0642 0.04030.764 −0.0554 0.03810.764 −0.0483 0.03580.764 −0.0419 0.03390.772 −0.0367 0.0318

0.500 −0.0614 0.04610.490 −0.0525 0.04370.485 −0.0450 0.04110.483 −0.0383 0.03850.481 −0.0324 0.0362

0.328 −0.0846 0.07350.318 −0.0695 0.06740.309 −0.0574 0.06210.303 −0.0475 0.05730.297 −0.0390 0.0530

0.011 −0.1872 0.16980.010 −0.0627 0.16060.010 −0.0256 0.15340.010 −0.0066 0.12440.010 0.0095 0.11580.010 0.0062 0.1065

S. Solaimani, R. Sadeghi / Fluid Phase Equilibria 363 (2014) 106– 116 113

110

130

150

170

190

210

230

250

3 5 7 9 11 13

n c

V φ,m

0/

cm

3.m

ol-1

-2

-1.7

-1.4

-1.1

-0.8

-0.5

3 5 7 9 11 13

ln( E

φ ,m

0/1

cm

3·m

ol-1

·K-1

)

1.2

1.6

2

2.4

3 5 7 9 11 13

n c

ln(∆

micV

/ 1

cm

3·m

ol-1

)

-3.5

-3.1

-2.7

-2.3

-1.9

-1.5

3 5 7 9 11 13

ln(∆

micK

/ 1

cm

3·M

Pa

-1·m

ol-1

)

cK wit

tata

E

TTviahtihbmlCec

F

wvc(nst

n c

Fig. 9. Variations of V ◦�,m

, ln �micV, ln E◦�,m

, and ln �mi

he obtained values of �micV and �micK increase by increasing thelkyl chain length of the surfactant. The parameter that measureshe variation of volume with temperature is the infinite dilutionpparent molar expansibility which can be obtained by

◦�,m =

(∂V ◦

�,m

∂T

)P

(11)

he E◦�,m

values at different temperatures are also given inable 5. From Table 5, we note that E◦

�,mvalues have a positive

alue and increase with decreasing temperature and increas-ng alkyl chain length of surfactant. Positive expansibility is

characteristic property of aqueous solutions of hydrophobicydration. On heating, due to the increase of their motion,he hydrophilic tails increase their size. This produces a slightncrease of the V ◦

�,mand so E◦

�,mwould be positive. In fact

ydrophobic hydration increases with increasing number of car-on atoms in the alkyl chain and therefore the E◦

�,mvalues become

ore positive by increasing alkyl chain length. The variations ofn V ◦

�,m, ln �micV, E◦

�,m, and ln �micK with the alkyl chain length of

nH2n+1SO3Na at 298.15 K are shown in Fig. 9. The linear depend-nce of V ◦

�,m, ln �micV, ln E◦

�,m, K◦

�,mand ln �micK on the number of

arbon atoms in the chain, nc, can be represented by the expression:

= a + bnc (12)

here F = V ◦�,m

, ln �micV, ln E◦�,m

, K◦�,m

or ln �micK . The obtainedalues of the coefficients a and b are given in Table 6. In thease of V ◦

�,m, a represents sum of the infinite dilution apparent

or partial) molar volume of the hypothetical zero chain length-alkylsulfonate anion (nc = 0) and Na+ and the slope of b repre-ents the contribution per methyene group in the alkyl chain ofhe sulfonate anion to the infinite dilution apparent (or partial)

n c

h the alkyl chain length of CnH2n+1SO3Na at 298.15 K.

molar volume of the surfactants. Table 6 shows that at 298.15 Kthe increment in volume due to addition of −CH2− group is of theorder of 15.953 cm3 mol−1. It is more significant to compare theV0

CH2values in aqueous solutions because of the clearer distinc-

tion that occurs in the volumetric properties of various moleculespresent in this state. Millero et al. [31], have collected partialmolal volumes for various functional groups at infinite dilution inwater at 298.15 K. They reported the values of 16.1, 15.9, 14.8, 14.1and 13.8 cm3 mol−1 for V0

CH2in different compounds. By subtrac-

ting from V ◦�,m

the corresponding conventional values for Na+ ion,

(−1.21 cm3 mol−1 [32]), we get the conventional value of V ◦�,m

forn-alkylsulfonate anion (38.999 + 15.953nc).

The results of sound velocity measurements at 298.15 and308.15 K for C5H11SO3Na [24], C6H13SO3Na, C7H15SO3Na [22] andC12H25SO3Na [25] in aqueous solutions are shown in Fig. 10. As canbe seen a very clear change is observed in the slopes of the twostraight lines to which experimental u values can be fit in the pre-and postmicellar ranges. The intersection of these straight linesaffords the value of the CMC of the system. The more importantbehavior of the plots of sound velocity against molality of surfactantis the intersection of sound velocities isotherms of aqueous solu-tions. This phenomenon has also been observed in aqueous watersoluble polymers, electrolyte, and ionic liquid solutions. Further-more although for the monomer solutions the values of u increaseby increasing the alkyl chain length of the surfactant, however thereverse trend was observed in the case of micellar solutions.

Fig. 11 shows the temperature and concentration dependenceof s for aqueous CnH2n+1SO3Na solutions. Similar to the other ther-

modynamic properties these plots show two linear segments withthe intersection at the CMC. The linear regions may be assignedto monomeric and micellar forms. For the monomeric state ofCnH2n+1SO3Na, the values of s decrease sharply with increasing

114 S. Solaimani, R. Sadeghi / Fluid Phase Equilibria 363 (2014) 106– 116

Table 6Coefficients of equation 12 for different properties of aqueous CnH2n+1SO3Na solutions at 298.15 K and atmospheric pressure.

V ◦�,m

ln�micV lnE◦�,m

K◦�,m

ln�micK

a b a b a b a b a b

8

ssttitotc

F(C

Fa[

37.7895 15.9526 0.7890 0.1279 −2.4823

urfactant concentration. However, for the micellar form of theurfactant, the isentropic compressibility of CnH2n+1SO3Na solu-ions decreases very slightly with surfactant concentration. Similaro the sound velocities isotherms, the isentropic compressibilitiessotherms have been intersected in a certain concentration andhis concentration increases by increasing the alkyl chain length

f the surfactant. Furthermore although for the monomer solu-ions the values of s decrease very slightly by increasing the alkylhain length of the surfactant, however in the micellar solutions

1480

1520

1560

1600

1640

0 1 2 3

m / mol.kg-1

u/

m. s

-1

ig. 10. Plot of sound velocity, u, against molality of surfactant, m, at 298.15solid lines) and 308.15 K (dotted lines) for aqueous CnH2n+1SO3Na solutions: ©,5H11SO3Na [24]; �, C6H13SO3Na; × C7H15SO3Na [22]; �, C12H25SO3Na [25].

3.4

3.6

3.8

4

4.2

4.4

4.6

0 1 2 3

10

4κ s

/ M

Pa-1

-1

-0.8

-0.6

-0.4

-0.2

0

0 1 2 3

m / mol.kg-1

10

4(κ

s-κ s

0)

/ M

Pa-1

ig. 11. Plot of s and s − s0 against molality of surfactant, m, at 298.15 (solid lines)nd 308.15 K (dotted lines) for aqueous CnH2n+1SO3Na solutions: ©, C5H11SO3Na24]; �, C6H13SO3Na; ×, C7H15SO3Na [22]; �, C12H25SO3Na [25].

0.1472 −0.0872 0.0050 −4.2334 0.197

the values of s increase by increasing the alkyl chain length of thesurfactant. The isentropic compressibility of aqueous solutions canbe considered as the sum of two contributions, s (solvent intrin-sic) and s (solute intrinsic). The values of s of pure CnH2n+1SO3Naincrease with the increase in temperature. However at the temper-atures investigated in this study, the isentropic compressibility ofwater decreases with temperature. In dilute solutions the s (sol-vent intrinsic) is the dominant contribution to the total value of s

and the measured values of s decrease by increasing temperature(similar to the solvent). However for concentrated CnH2n+1SO3Nasolutions, the s (solute intrinsic) is the dominant contributionto the total value of s and therefore, the measured values of s

increase with the increase in temperature (similar to the pureCnH2n+1SO3Na). The all isentropic compressibility isotherm pairsintersect each other at a certain surfactant concentration and theconverging concentration shifts to lower surfactant concentrationas sum of two temperatures increases. In fact the intersection ofisentropic compressibility isotherms is caused from the differenttemperature behavior of isentropic compressibility of pure waterand pure surfactant and as can be seen from Fig. 11, by subtractingfrom s the corresponding conventional value for pure water, weget s − s0 isotherms which do not intersect each other and similarto the pure surfactant the values of s − s0 increase by increasingtemperature in the whole surfactant concentration range. Howeverthe trend of s − s0 with the alkyl chain length of the surfactantis similar to that of s. In fact the hydration number of monomericstate of surfactant is larger than the hydration number of micellarform of surfactant and therefore, for m < CMC concentration region,the concentration dependence of s is more negative than those forthe m > CMC concentration region. Although, the isentropic com-pressibility of pure CnH2n+1SO3Na increases by increasing the alkylchain length of surfactant (since it is reasonable to assume thatany free volume within the intrinsic volume of large anion such asC12H25SO3

− is greater than that in small anion such as C5H11SO3−),

however, the value of s for monomer solutions of CnH2n+1SO3Nadecreases very slightly with n. But at higher surfactant concentra-tions where s (solute intrinsic) is the dominant contribution to thetotal value of s, the isentropic compressibility of aqueous solutionsof CnH2n+1SO3Na (similar to those of pure CnH2n+1SO3Na) increaseswith increasing the alkyl chain length of surfactant. Decreasing ofs for monomer solutions of CnH2n+1SO3Na with increasing alkylchain length may be attributed to this fact that for long alkyl chainsurfactant, the penetration of the solvent molecules into the intra-ionic free space of surfactant is larger than those for short alkylchain surfactants.

A well known property for determination of CMC of surfactantsin aqueous solutions is electrical conductivity. Experimental dataof electrical conductivity at 298.15 K for the investigated systemare given in Table 7. Once micelles are formed, the specific conduc-tivity of aqueous surfactant solutions undergoes an abrupt changein molarity dependence. By linearly extending the portions of thelines before and after breaks, we determined the CMC for sur-factants C5H11SO3Na [24], C6H13SO3Na (this work), C7H15SO3Na[22], C8H17SO3Na [19], C10H21SO3Na [1] and C12H25SO3Na [25] in

aqueous solutions at 298.15 K. The CMC was observed to decreasesubstantially with increasing alkyl chain length of the surfac-tant (Fig. 12). It was also found that there is a linear relationbetween lnCMC and the number of carbon atoms in the chain,

S. Solaimani, R. Sadeghi / Fluid Phase Equilibria 363 (2014) 106– 116 115

Table 7Experimental specific electroconductivity /(mS cm−1) of aqueous solutions of C6H13SO3Na(s) at 298.15 K and atmospheric pressure.

C/mol dm−3 /mS cm−1 C/mol dm−3 /mS cm−1 C/mol dm−3 /mS cm−1 C/mol dm−3 /mS cm−1

0.39380 16.91 0.51708 19.42 0.63310 21.62 0.81310 24.240.40620 17.16 0.52771 19.64 0.64995 21.90 0.83244 24.510.41519 17.35 0.53810 19.84 0.66727 22.11 0.85696 24.850.43125 17.69 0.54641 19.99 0.68564 22.40 0.86989 25.020.44068 17.88 0.55384 20.09 0.69705 22.56 0.88939 25.290.44944 18.07 0.56314 20.38 0.71536 22.85 0.91559 25.630.46072 18.29 0.57173 20.54 0.73797 23.19 0.93208 25.830.47196 18.52 0.58562 20.80 0.76302 23.54 0.95809 26.160.48821 18.85 0.60294 21.11 0.77861 23.77 0.99667 26.630.50097 19.12 0.61902 21.39 0.79755 24.02 1.05416 27.31

u() = ±0.02 mS cm−1.

Fas

ncldiourmC

4

CemoiTti0cvc

[

[

[[[[

[

[

[

[

[

[

ig. 12. Plot of critical micelle concentration, CMC, and degree of counterion associ-tion of micelle, ˛, against the number of carbon atoms in the chain, nc, for aqueousolutions of CnH2n+1SO3Na at 298.15 K: ©, CMC; �, ˛.

c, (ln(CMC/1 mol dm−3) = 3.6334–0.6856 nc with the coefficient oforrelation, R = 0.9997). Furthermore the ratio of the slopes of theines above and below the CMC in the isotherms of specific con-uctivity versus surfactant molarity was taken as the degree of

onization of the micelles, ˇ. The alkyl chain length dependencef the degree of counterion association of micelle (= 1 − ˇ) val-es for the investigated systems shows the typical U-shaped form,eaching a minimum at nc = 7 (Fig. 12). This behavior indicates thaticelles of smallest aggregation number are formed in the case of

7H15SO3Na.

. Conclusion

The micellization behavior of the anionic surfactant6H13SO3Na in water has been investigated by vapor–liquidquilibria, volumetric, compressibility, and conductivity measure-ents at different temperatures. The concentration dependence

f the all investigated thermodynamic properties exhibit a changen slope at the concentration in which micelles are formed.he obtained values of CMC depend on the type of the usedhermodynamic property. The values of CMC for C6H13SO3Nan aqueous solutions at 298.15 K were obtained as 0.699, 0.689,

.582, 0.571, 0.543 and 0.500 mol kg−1 respectively from theonductivity, osmotic coefficient, sound velocity, apparent molarolume, isentropic compressibility, and apparent molar isentropicompressibility properties. The obtained positive values of �Gmic

w

[

[[[

and negative values of �Gmics indicate that for concentrations

higher than the CMC, water molecules and surfactant ionsrespectively become less and more stable by micellization andtherefore the behavior of surfactant is the deriving force for themicelle formation. Volumetric and compressibility data havebeen used to obtain the values of the changes in the apparentmolar properties upon micellization (�micV and �micK) and theinfinite dilution apparent molar properties of the monomer stateof surfactant in aqueous solutions (V ◦

�,m, K◦

�,mand E◦

�,m). From the

data obtained in this work and those reported in the literaturewe have carried out the systematic studies of some thermody-namic and aggregation properties of aqueous solutions of sodiumn-alkylsulfonate. Linear relations were obtained between lnCMC,V ◦

�,m, ln �micV, ln E◦

�,m, K◦

�,mand ln �micK and the number of

carbon atoms in the alkyl chain of surfactant CnH2n+1SO3Na. Itwas found that the calculated Gibbs free energy of micellizationbecomes more negative by increasing the alkyl chain length ofthe surfactant and also the values of �micV, �micK, V ◦

�,mand E◦

�,m

increase by increasing the alkyl chain length of the surfactant.

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