Colloids and Surfaces

A: Physicochemical and Engineering Aspects 155 (1999) 405–412

A study of micellization parameters and electrostaticinteractions in micellar solution of sodium dodecyl sulfate

S.S. Shah a,*, Akhtar Saeed b, Q.M. Sharif b

a Department of Chemistry, Quaid-i-Azam Uni6ersity, Islamabad, Pakistanb NCE in Physical Chemistry, Uni6ersity of Peshawar, Peshawar, Pakistan

Received 5 October 1998; accepted 6 January 1999

Abstract

The electrical conductivity of sodium dodecyl sulfate (SDS) in aqueous solution was determined up to aconcentration of 10 times the critical micelle concentration. The effects of solution concentration on the variousinteraction parameters of SDS have been studied. The mass action model was applied to micelle formation tocalculate the micellization parameters: micellization constant, Kc; aggregation number, n ; and number of counterionsper micelle, m. The micellization parameters also made it possible to evaluate the concentration change of monomericsurfactant ion with total surfactant concentration. The Debye–Huckel–Onsager equations have been applied to theexperimental data for aqueous solution of SDS. An average degree of counterion binding to a micelle (m/n) andaggregation number (n) were determined to be 0.72 and 64, respectively. As aggregation number decreasesmonotonously with increase in concentration, this trend has been employed to calculate the electrical conductivity ofthe micelle (lM). © 1999 Elsevier Science B.V. All rights reserved.

Keywords: Micellization; Aggregation number; Micellar size; Sodium dodecyl sulfate; Ionic conductivity; Ionic strength

www.elsevier.nl/locate/colsurfa

1. Introduction

The growing interest in surfactants is mainlydue to their many applications in chemistry, biol-ogy, and pharmacy. Such important roles arerelated to their ability to form aggregate (micelles)when the surfactant concentration in aqueous so-lution exceeds critical micelle concentration(CMC) [1]. Sodium dodecyl sulfate(SDS) is the

ionic surfactant whose micelle formation has beeninvestigated most widely and most profoundlyamong a number of ionic surfactants [2]. How-ever, an electric conductivity of the micelle itselfin aqueous solution still remains unsolved, al-though the physical and electrostatic pictures [3–5] of the micelles have been presented in greatdetail.

A number of problems remain unsolved asregards the properties of aqueous solutions ofsurface active substances, despite their theoreticaland practical importance. For instance, the threemicellization parameters, the micellization con-

* Corresponding author. Tel.: +92-51-829167; fax: +92-51-821397.

E-mail address: ssshah@ch-qau.sdnpk.undp.org (S.S. Shah)

0927-7757/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S0927 -7757 (99 )00021 -7

S.S. Shah et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 405–412406

stant, Kc, the micellization aggregation number, n,and the number of counterions per micelle, m, arequite difficult to determine precisely. This is thereason why micelles have been mostly dealt within a separate phase [6–8]. The purpose of thepresent work is to investigate the micelle contribu-tion to these properties to some extent.

An accurate model of conductivity for micellesolutions should incorporate (i) a means of ac-counting for the interionic interactions, (ii) anobjective definition of the CMC, and (iii) a meansof using all of the available conductivity data totest for consistency. Interionic interactions are ofgreat importance for interpreting data for simpleelectrolytes [9] and must have considerable impactin systems which contain highly chargedaggregates.

Recently, many kinds of newly synthesized am-phiphiles have been in widespread use [10–12]and, therefore, an easy but reliable method todetermine these parameters is quite helpful todevelop and characterize the properties of aggre-gates of these amphiphiles.

In this study, then, the electrical conductivitychange of the SDS solution was analyzed in orderto present the picture of micellar solution fromwhich the electrical conductivity of the micelle canbe evaluated.

2. Experimental

2.1. Materials

SDS, the product of Fluka, was of analyticalgrade and was used without further purification.Water used was distilled twice from alkaline per-manganate solution.

2.2. Conductance measurements

The specific conductance of the surfactant(SDS) was measured on a microprocessor conduc-tivity meter (WTW), LF 2000/C model ofWissenchaftlinch Technische Werkstatten (Ger-many) at 298.2 K.

The conductivity was measured stepwise by in-troducing an aliquot volume of the mother solu-

tion into doubly distilled water. Temperature wascontrolled at 298.2 K. The CMC of the surfactantwas determined from the plots of specific conduc-tivity versus concentration of the surfactantsolution.

3. Theoretical

The following equilibrium can be given formicelle formation of monodisperse ionic micelles[13].

nS− +mG+ = Mn−n(n−m) (1)

where S−, G+, Mn are surfactant ion, counte-rion, and micelle of aggregation number n, and mis number of counterions per micelle, respectively.From Eq. (1) the micellization constant, Kc, iswritten as

Kc= [Mn ]/([Sn][Gm]) (2)

where [S], [G], and [Mn ], are the correspondingmolar concentrations, respectively, and the elec-troneutrality of solution holds:

[G]− [S]− (n−m)[Mn ]=0 (3)

The mass balance for surfactant ion and counte-rion are respectively expressed as

Ct= [S]+n [Mn ] (4)

Ct= [G]+m [Mn ] (5)

where Ct is the total surfactant concentration.From Eqs. (3)–(5), [S] and [G] are written as:

[S]= (1−n/m)Ct+ (n/m)[G] (6)

[G]= (1−m/n)Ct+ (m/n)[S] (6a)

From the logarithm of Eq. (2), with Eqs. (4) and(6a), one obtains;

ln[S]= − (m/n) ln{(1−m/n)Ct+ (m/n)[S]}

− (1/n) ln Kc+ (1/n) ln{(Ct− [S]/n)} (7)

This equation suggests that the concentrationof each chemical species can be evaluated at asurfactant concentration in combination with Eqs.(4) and (6a), once the three micellization parame-ters, Kc, n, and m, are obtained.

S.S. Shah et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 405–412 407

The value of degree of counterion binding tomicelle (m/n) is evaluated from the ratio of slopesin the conductivity, K, versus concentration, C,above and below the CMC. The micellizationconstant can be derived from the definition of theCMC.

1/Kc=2n(n+m)(CMC)n+m (8)

On the other hand, the molar conductivity of amicelle, lM, with charge (n−m) can be givenfrom the equivalent conductivity [14] as

lM=0.820(n−m)2/rh=a(n−m)2 (9)

where r is a micellar radius and h is solventviscosity.

4. Results and discussion

The changes of specific and equivalent conduc-tivities with total surfactant concentration areshown in Fig. 1. From the kink point, the CMCwas determined as 8.1 mol m−3. The values ofspecific conductivities below and above the CMCare also given in Tables 1 and 2, respectively. Theconcentrations of [Na+] and [DS−] were sepa-rately determined up to 10 times the CMC at298.2 K.

The concentration changes of the two ions withtotal surfactant concentration have been alreadyanalyzed by the mass action model, hence for thepresent study, the values of surfactant ion concen-

Fig. 1. Specific and equivalent conductivity of SDS at 298.2 K.

S.S. Shah et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 405–412408

Table 1Specific conductivity (K), ionic strength (I) with total surfactant concentration (Ct) and the corresponding ionic conductivity (l)changes (premicellar phase at 298.2 K)

I (mol1/2 m−3/2)Ct (mol m−3) lNa+ (10−4 S m2 mol−1)K (10−3 S m−1) lDS− (10−4 S m2 mol−1)

0.7800.609 49.210.401 20.971.190 0.796 1.090 48.85 20.761.744 1.3201.14 48.60 20.61

1.507 48.381.50 20.482.2721.802.777 1.666 48.20 20.37

1.805 48.043.260 20.282.101.929 47.902.38 20.203.723

2.654.166 2.041 47.77 20.122.142 47.65 20.054.591 2.882.236 47.553.12 19.995.000

3.325.392 2.322 47.45 19.932.401 47.36 19.885.769 3.532.476 47.273.71 19.836.132

6.481 2.5453.90 47.19 19.78

tration [DS−] have been read off from Fig.3 ofref. [14]. Then, Eqs. (4) and (6a) were used tocalculate the concentration of micelle [Mn ] andconcentration of counterion [Na+], respectively.The most reliable values for the parameters werefound to be n=64, m=46.7 and log Kc=230 [5].These parameters’ values could perfectly repro-duce the concentration changes of the two ionswith SDS concentration up to 10 times the CMC.These changes are summarized in Table 2.

SDS perfectly dissociates itself in an aqueoussolution below the CMC and the ionic conductiv-ity of Na+ can be given by the following equation[15]:

lNa+ = (50.10−1.141I)/104 (S m2 mol−1)(10)

As L=lNa+ +lDS− is below the CMC, lDS−iseasily evaluated, and can be expressed as

lDS− = (21.49−0.674I)/104 (S m2 mol−1)(11)

The limiting ionic conductivity of surfactant ionlDS−

o (21.49) is obtained by linear regression anal-ysis [16]. The changes of ionic conductivity ofsurfactant ion lDS− with surfactant concentrationabove and below the CMC are shown in Fig. 2.

Now that concentration changes of Na+, DS−

and micelle with surfactant concentration are

known, it is possible to obtain the contribution ofeach chemical species to the equivalent conduc-tance (L) above the CMC.

L=lNa+[Na+]+lDS−[DS−]+lM[Mn ] (12)

Fig. 2. Ionic conductivity of surfactant ion (lDS−) versussquare root concentration of SDS.

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Table 2Specific conductivity (K), concentration changes of counterion [Na+], surfactant ion [DS−], micelle [Mn ] and ionic strength (I) with total surfactant concentration (Ct)and the corresponding ionic conductivity (l) changes (micellar phase at 298.2 K)

[Na+] [DS−] I lNa+ lDS− lMCt K [Mn ](mol m−3) (10−4 S m2 mol−1)(10−3 S m−1) (S m2 mol−1)(mol m−3) (mol m3)(mol m−3)(mol m−3) (10−4 S m2 mol−1)

44.46 18.16 0.3740.110 24.387.018.926.1014.070.238 43.80 42.55 17.02 0.2357.6021.58 10.45 6.33

41.82 16.59 0.21452.708.15 11.1224.90 0.2956.0267.669.53 40.72 15.94 0.21412.43 5.62 0.39330.82

0.519 86.80 39.47 15.21 0.19538.28 11.36 14.00 5.0138.8442.50 14.8312.29 0.19515.04 4.87 0.587 97.5338.05 14.37 0.176111.5247.95 13.53 0.6784.5116.25

126.9114.79 37.25 13.89 0.15817.61 4.15 0.77853.95139.0015.83 36.65 13.54 0.15818.83 4.00 0.85758.85

36.17 13.26 0.142149.000.92262.94 3.8819.8416.6867.93 35.5717.64 12.91 0.14221.07 3.71 1.003 162.00

35.14 12.65 0.124171.873.69 1.06671.93 18.49 22.13182.3019.22 34.69 12.38 0.10923.25 3.65 1.13276.16

1.197 192.49 34.26 12.13 0.09519.6780.23 24.32 3.61

S.S. Shah et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 405–412410

where Eqs. (10) and (11) were applied to thesolutions above the CMC and the contribution ofcharged micelle was taken into account to calcu-late the ionic strength. For evaluation of ionicstrength, we have applied a 3D model [17] as thismodel includes the contribution of all chargedspecies in the solution.

I=12

%m

i=1

CiZi2=

12(Ci+Cm

+)+12dCnn2(1−b)2

(13)

where Ci is the total surfactant concentration, Cm+

is the concentration of counterion, Cn is the con-centration of micelle, n is aggregation number, d

is a shielding factor to account for the fact thatthe micelles contribute to the ionic strength and b

is the counterion binding parameter equivalent tom/n.

In the 3D model, the contribution of the mi-celles is more significant over the other species inthe solution than the previous models [17], yield-ing only smaller ionic strengths. This is becausethe micelle contributions are taken to be zero inprevious models. When micelle contributions toconductivity and the interionic interactions areincluded in the 3D model, the ionic strengthabove the CMC increases to a level much higherthan that for an equal concentration of 1:1 elec-trolytes. This increase is due to the significantcontributions of the micelles which are treated asan [n(1−b)]:1 electrolyte (see Eq. (13)). The ionicstrength values with surfactant concentration areshown in Fig. 3.

The Einstein–Stokes equation (Eq. (14)) can beapplied to the relation between the ionic conduc-tivity of micelle with the charge Z of −17.3 andits radius r, when a moving particle is larger insize compared with the surrounding solventmolecules.

lM= �Z �F2/6pNhr (14)

where F is Faraday’s constant, N is Avogadro’snumber, and h is the viscosity coefficient of sol-vent. The radius of the micelle, calculated fromthe values of ionic conductivities of micelles givenin Table 2, is found to be between 0.10 and 0.14nm. This is a too small value to be accepted. Onthe other hand, the radius of micelle was evalu-

Fig. 3. Ionic strength (I) of surfactant solution versus the totalconcentration of SDS.

ated to be 2.53 nm from its diffusion coefficient[18]. This radius is longer than the full length ofDS− ion, and the 2.07 nm evaluated by Tanford[1]. This anamolous behavior can be explained bythe fact that micelles move about with manysolvent molecules and with counterions aroundthem in the form of ionic atmosphere.

In micelle formation, the monomer packingdepends on geometric parameters such as micelleradius, r, chain monomer volume, 6, maximumlength that the chain can assume(critical chainlength), and the interfacial area per monomer, a(see Fig. 4). For spherical micelles, simple geome-try is used to calculate micelle radius [19] byfollowing the equations

N=4pr3/36 (15)

a=4pr2/n (16)

Tanford [1] has related the monomer chainvolume (in A, 3) to the number of carbon atoms, nc,of the alkyl chain, as in Eq. (17).

S.S. Shah et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 405–412 411

Fig. 4. Schematic representation of an idealized sphericalmicelle.

Fig. 5. Ionic conductivity of micelle (lM) versus surfactantconcentration.

From the graph it is clear that lM values de-crease monotonously with concentration of SDS,similar to the aggregation number (n). These mi-nor but contributing factors will help us to inves-tigate further into the interionic interactions andthe micelle formation of other surfactantsolutions.

Acknowledgements

The laboratory facilities provided to one of us(QMS) by Prof. Dr M. Saleem, Chairman, De-partment of Chemistry and the financial grant ofthe Quaid-i-Azam University, Islamabad aregratefully acknowledged.

References

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S.S. Shah et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 405–412412

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