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Micellization of Surfactants in Acetamide Melt S. Dev, K. Gunaseelan, and K. Ismail* Department of Chemistry, North Eastern Hill University, NEHU Campus, Shillong 793 022, India Received November 9, 1999. In Final Form: April 13, 2000 Electrical conductances of solutions of sodium dodecyl sulfate (SDS) and cetylpyridinium chloride (CPC) in acetamide melt were measured at 89 °C as a function of concentration. The dependence of molal conductance of SDS and CPC on concentration has been compared with that of normal electrolytes in acetamide melt. Both SDS and CPC are found to micellize in acetamide melt. A mixed electrolyte model has been used to compute the micellization parameters, viz., critical micelle concentration, aggregation number, and counterion binding constant, from the conductance data. Surface potentials of the micelles were computed by solving the nonlinearized Poisson-Boltzmann equation. The free energy terms for micellization were also evaluated.
Introduction Surfactants form regular micelles in polar nonaqueous solvents including molten salt media. Reports on micellization in molten salt media are, however, very few1-3 because of the poor solubility of surfactants in ionic melts and due to the high working temperatures of ionic melts which cause thermal decomposition of surfactants. Thus, to undertake the study of micellization of ionic surfactants in molten media, it is necessary to select such molten media that the above-mentioned difficulties can be overcome. Acetamide melt has attracted the attention of many molten salt chemists because of its ability to act as an excellent polar solvent and to form room-temperature molten salts on mixing with inorganic salts.4-6 Recently, Akhter3 reported that surfactants do micellize in acetamide melt. In the present work specific conductances of sodium dodecyl sulfate (SDS) and cetylpyridinium chloride (CPC) in acetamide melt were measured at 89 °C with a view to estimate their micellization parameters in this molten medium by using the mixed-electrolyte model reported recently by Shanks and Franses.7 The values of the micellization parameters obtained thus were then used to compute the surface potentials of SDS and CPC micelles in acetamide melt by solving the nonlinearized PoissonBoltzmann equation. For the purpose of comparison, the electrical conductance of NaNO3, a normal electrolyte, in acetamide melt at 89 °C was also measured. Experimental Section SDS (Sigma, 99%) and CPC (SISCO, extra pure grade) were used without further purification. Acetamide (E. Merck) was recrystallized from its solution in doubly distilled acetone whereas * To whom correspondence may be addressed. Fax: 091-364250486. E-mail:
[email protected]. (1) Bloom, H.; Reinsborough, V. C. Aust. J. Chem. 1967, 20, 2583; 1968, 21, 1525; 1969, 22, 519. Reinsborough, V. C.; Valleau, J. P. Aust. J. Chem. 1968, 21, 1, 2905. Reinsborough, V. C., Aust. J. Chem. 1970, 23, 3, 1473. (2) Evans, D. F.; Yamauchi, Y.; Roman, R.; Casassa, E. Z. J. Colloid Interface Sci. 1982, 88, 89. Evans, D. F.; Yamauchi, A.; Wei, G. J.; Bloomfield, V. A. J. Phys. Chem. 1983, 87, 3537. (3) Akhter, M. S. Colloids Surf., A 1995, 99, 255. (4) Narayan, R.; Phani, K. L. N. Molten Salt Techniques; Gale, R. J., Lovering, D. G., Ed.; Plenum Press: New York, 1991. (5) Berchiesi, G.; Farhat, F.; De Argelis, M. J. Mol. Liq. 1992, 54, 103. (6) Nikolic, R.; Ristic, G. J. Solution Chem. 1994, 22, 787. (7) Shanks, P. C.; Franses, E. I. J. Phys. Chem. 1992, 96, 6, 1794.
NaNO3 (SD) was recrystallized from its solution in doubly distilled water. Electrical conductance measurements were made at 1 kHz using a Wayne Kerr B905 Automatic Precision Bridge as described elsewhere.8,9 A dip-type cell of cell constant ) 121.11 m-1 was used. A thermostated oil bath was used to maintain the temperature at 89 °C.
Results and Discussion The measured specific conductances, κ, of SDS (concentration range 1.09 × 10-3 to 0.0799 mol kg-1) and CPC (concentration range 1.19 × 10-3 to 0.0899 mol kg-1) at 89 °C in pure acetamide melt were plotted in Figure 1 as a function of solute concentration. On the basis of Figure 1, the values of the critical micelle concentration (cmc) of SDS and CPC in acetamide melt at 89 °C were estimated to be 0.017 and 0.022 mol kg-1, respectively. In Figure 2, on the other hand, the variation of molal conductance10 of SDS and CPC with respect to square root of concentration, c1/2, has been shown. Shown in Figure 2 are also the variations of measured molal conductance of NaNO3 at 89 °C and of reported11 equivalent conductances of KCl, KBr, and KI at 94 °C with c1/2. It may be seen from Figure 2 that in acetamide melt the nature of the variation of molal conductance of surfactants is different from that of molal or equivalent conductance of normal electrolytes. The values of cmc of SDS and CPC estimated from Figure 2 are 0.016 and 0.023 mol kg-1, respectively, which are in agreement with the corresponding values obtained from Figure 1. The cmc value of SDS in acetamide melt estimated in this study is in agreement with the reported3 value at 90 °C. Unlike in water at 25 °C, in acetamide melt at 89 °C the cmc of CPC is greater than the cmc of SDS. A similar trend was reported12,13 in formamide at 50 °C wherein the cmc of SDS is 0.00126 mol dm-3 and that of CPC is 0.012 mol dm-3. Generally, in a solution of an ionic surfactant the change in conductance with concentration is caused by ion-ion (8) Paul, B. C.; Islam, S. S.; Ismail, K. J. Phys. Chem. B 1998, 102, 7807. (9) Chettri, S. K.; Dev, S.; Ismail, K. J. Chem. Eng. Data 1995, 40, 0, 12. (10) Smedley, S. I. The Interpretation of Ionic Conductivity in Liquids; Plenum Press: New York, 1980. (11) Wallace, R. A. J. Phys. Chem. 1971, 75, 5, 2687. (12) Singh, H. N.; Saleem, S. M.; Singh, R. P.; Birdi, K. S. J. Phys. Chem. 1980, 84, 2191. (13) Thomason, M. A.; Bloor, D. M.; Wyn-Jones, E. Langmuir 1992, 8, 2107.
10.1021/la9914662 CCC: $19.00 © 2000 American Chemical Society Published on Web 06/13/2000
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Figure 2. Plots of molal conductance versus (concentration)1/2 for SDS (O), CPC (+), and NaNO3 (0) in acetamide melt at 89 °C. 4, 3, and b indicate plots of the reported (ref 11) equivalent conductances (S cm2 equiv-1) of KCl, KBr, and KI, respectively, versus (concentration/equiv‚dm-3)1/2 in acetamide melt at 94 °C.
Figure 1. Plots of specific conductances versus concentration for SDS and CPC in acetamide melt at 89 °C. For CPC the concentration scale has been shifted to the right side by 20 units.
interactions, ion-solvent interactions, and interaction responsible for micellization. It is an obvious fact that ion-ion and ion-solvent interactions operate in solutions of normal electrolytes. Therefore, to obtain correct values of the micellization parameters from conductance data, it is necessary to account for the three types of interactions appropriately such that micellization parameters are correlated only to interactions responsible for micellization. A similar view was also highlighted by BinanaLimbele and Zana.14 Accordingly, to estimate the micellization parameters of SDS and CPC micelles in acetamide melt from their conductance data, we employed the mixedelectrolyte model reported by Shanks and Franses.7 This model has been successfully used by us8 recently to derive from the conductance data the micellization parameters of SDS in aqueous electrolyte solutions. According to the mixed-electrolyte model, the solution of SDS or CPC in acetamide melt is considered to be a mixture of two electrolytes, viz., a molten solution containing monomers and an equivalent number of counterions (monomer phase) and a molten solution containing micelles and counterions (micellar phase). Both monomer and micellar phases are considered to be electrically neutral. In the micellar phase a neutral micelle (14) Binana-Limbele, W.; Zana, R. Colloid Polym. Sci. 1989, 267, 440.
of the form MAn(1-β) is considered to ionize to give 1 mol of anionic (Mn(1-β)-) or cationic (Mn(1-β)+) micelle and n(1 - β) mol of counterions (A+ or A-). n and β are the aggregation number and counterion binding constant of a micelle, respectively. The molar conductivity of SDS or CPC in acetamide melt, Λ, can therefore be written as
Λ ) Λ1mPmono + Λ1micPmic
(1)
where Λ1m is the molar conductivity of surfactant in the monomer phase when it is in the monomer form and Λ1mic is the molar conductivity of surfactant in the micellar phase when it is in the micellar form. Pmono and Pmic are the fractions of the total surfactant molecules which exist in the monomer and micellar forms, respectively. Λ1mic is related to the molar conductivity of micelle, Λnm, by the relation, Λ1mic ) Λnm/n. The molar conductivities are related to the respective equivalent conductivities as Λ1m ) Λ1eq and Λnm ) Λneqn(1 - β), where Λ1eq is the equivalent conductivity of surfactant in the monomer form and Λneq is the equivalent conductivity of micelle. The P terms can be evaluated as Pmono ) c0/ct and Pmic ) (ct - c0)/ct ) ncn/ct, where c0 is the cmc, ct is the total concentration of the surfactant, and cn is the molar concentration of micelle. Thus eq 1 becomes
Λ ) Λ1eqc0/ct + Λneqn(1 - β)cn/ct
(2)
On accounting for the effect of ion-ion interactions on electrical conductivity by the Debye-Hu¨ckel-Onsager equation, eq 2 becomes
Λ ) [Λ01 - A1I1/2/(1 + B0a1)]c0/ct + [Λ0n - AnI1/2/(1 + B0an)]n(1 - β)cn/ct (3)
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Table 1. Computed Values of the Parameters of Micellization of SDS and CPC in Acetamide Melt and of Conductance Equation 3 at 89 °C parameter
SDS
CPC
c0 ( 0.001/mol kg-1 n(5 β ( 0.005 104Λ01/S m2 equiv-1 104λ01/S m2 equiv-1 104λ0c/S m2 equiv-1 104Λ0n/S m2 equiv-1 104λ0n/S m2 equiv-1 r1/nm rc/nm rn/nm A1 An 104 std dev in k/S m-1 Ψ ( 5/mV ∆G°m/kJ mol-1 ∆G°el/kJ mol-1 ∆G°hy/kJ mol-1
0.017 30 0.463 26.15 10.35 15.80 69.52 53.72 0.437 0.286 1.358 36.84 396.66 4.18 -121 -35.62 11.67 -47.29
0.022 20 0.428 31.72 9.47 22.25 62.13 39.88 0.478 0.203 1.300 38.21 269.28 4.68 110 -33.68 10.61 -44.29
I ) ct
(4)
Ai ) {2.801 × 106|z+z-|qΛ0i/[(T)3/2(1 + q1/2)]} + {41.25(|z+| + |z-|)/[η(T)1/2]} (5) q ) [|z+z-| (λ0+ + λ0-)]/[(|z+| + |z-|) (|z+| λ0- + |z-| λ0+)] (6) In the above eqs 4-6, kB is the Boltzmann constant, T is the absolute temperature, is the dielectric constant of acetamide melt, e0 is the elementary charge, and η is the viscosity of acetamide melt. λ0+ and λ0- are the limiting ionic equivalent conductivities of cationic and anionic species of effective charges z+ and z-, respectively. In this model the dependence of n on surfactant concentration and the polydispersity of micelles have been ignored. To compute the values of co, n, and β using eq 3, the values of r1 (radius of the surfactant monomer), rn (radius of the micelle), rc (radius of the counterion), a1, an, A1, An, Λ01, Λ0n, λ0+, λ0-, and I are required to be determined first. r1 in angstroms was calculated from the relation
r1 ) [(3/4π)(27.4 + 26.9nc)]1/3
(7)
where nc is the number of carbon atoms per hydrocarbon chain of the surfactant used.15 Presuming the micelle to be spherical in shape, rn was computed from the relation rn ) n1/3r1. The limiting ionic equivalent conductivity of anionic or cationic surfactant monomer was computed using the Stokes-Einstein relation
λ01 ) z1e0F/6πηr1
at
I ) c0 + 0.5n(1 - β)2cn
In eq 3 ais and Λ0is correspond to effective ionic sizes and limiting equivalent conductivities, respectively, of monomer (i ) 1) and micelle (i ) n). I is the ionic strength and
B0 ) [8πNAe02/(103kBT)]1/2I1/2
substituting for λ0c. The properties of the acetamide melt at 89 °C used in the computation are η ) 0.0181 P and ) 61.9.11 The limiting equivalent conductivity of micelle, λ0n, was also calculated using eq 8 by substituting for zn the value n(1 - β). Once λ0n was calculated, An and Λ0n were determined easily. a1 and an were evaluated by adding rc to r1 and rn, respectively. Shanks and Franses7 have used different models for the calculation of I required in the data fitting. We found that in the present case I computed from the expression7,8
(8)
where F is the Faraday constant. It may be noted that z1 ) 1. The limiting ionic equivalent conductivity of the counterion, λ0c, was then obtained by subtracting λ01 from the experimentally determined value of Λ01 (Table 1). The radius of the counterion, rc, in acetamide melt was then determined from the Stokes-Einstein relation after (15) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley-Interscience: New York, 1973.
ct e c0 at
ct > c0
(9)
provides a relatively better fit of the conductivity data to eq 3. In eq 9 for I suggested by Shanks and Franses,7 the contribution to I from free counterions present in the micellar phase has been reduced arbitrarily by a factor of (1 - β). For the data fitting we used the same procedure described earlier.8 The results of the data fitting are given in Table 1. It may be noted that the values of cmc of SDS and CPC obtained from the data fitting are in agreement with the cmc values obtained from Figures 1 and 2. Furthermore, it may be pointed out that unreasonable values for n and β were obtained from the data fitting when the contribution from the ionic micelles were taken into account in the calculation of I.7,8 Thus, on the basis of the mixed-electrolyte model it appears that micelles contribute to the conductivity but not to the effective ionic strength, which is in accordance with the observation reported in the earlier studies also.7,8,16-18 After the values of cmc, n, and β were derived from the conductance data in the manner described above, the surface potentials,Ψ, of the ionic micelles of SDS and CPC in acetamide melt were also computed by solving numerically the nonlinearized Poisson-Boltzmann equation in spherical symmetry.8 This equation is of the form
d2y/dx2 ) (ey - e-y)/2x4
(10)
where y ) e0Ψr/kBT and x ) (Br)-1. Ψr is the electrostatic potential at a distance r from the center of the spherical micelle. The boundary conditions used are
y f 0 as x f 0 dy/dx ) 4πFre0/(BkBTx2) at r ) rn
(11)
where B ) [ 8ΠNAe02c0/(103kBT ]1/2 and Fr is the surface charge density at a distance r from the center of the reference micelle. The micellar surface charge density was calculated from the expression
Fr(at r ) rn) ) e0n(1 - β)/(4πrn2)
(12)
The computation method used for the numerical analysis of eq 10 is the same described by us earlier.8 In this method the micelle concentration is presumed to be infinitely dilute. The values of Ψ of SDS and CPC micelles computed thus are given in Table 1. The values of n and β of SDS and CPC in acetamide melt (Table 1) are found to be lower than those in aqueous medium.7,8,19 To explain the lower value of n of SDS and (16) Marra, J.; Hair, M. L. J. Colloid Interface Sci. 1989, 128, 511. (17) Pashley, R. M,; Ninham, B. W. J. Phys. Chem. 1987, 91, 1, 1901. (18) Burehfield, T. E.; Wooley, E. M. J. Phys. Chem. 1984, 88, 2149. (19) Molinero, T.; Sierra, M. L.; Valiente, M.; Rodenas, E. J. Chem. Soc., Faraday Trans. 1996, 92, 59.
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CPC in acetamide melt, we calculated the free energy change of ionic micelle formation per mole of monomer, ∆G°m, using the expression2,8,20,21
∆G°m ) RT(1 + β) ln xcmc
(13)
where R is the gas constant and xcmc is the cmc in mole fraction unit. ∆G°m has been considered to be comprised of electrostatic free energy, ∆G°el, and hydrophobic free energy, ∆G°hy, terms and is represented as8,22,23
∆G°m ) ∆G°el + ∆G°hy
(14)
Values of ∆G°el for SDS and CPC in acetamide melt were obtained using the computed values of Ψ since ∆G°el ) FΨ. Once ∆G°el values were calculated, the values of ∆G°hy were easily determined from eq 14. The computed values of the three free energy terms for SDS and CPC in acetamide melt are given in Table 1. ∆G°el represents the work done against a repulsive electrostatic force and hence is always a positive term, whereas ∆G°hy represents the free energy of transfer of a hydrocarbon chain from the molten acetamide medium to the interior of a regular micelle and is a negative term. The values of ∆G°m, ∆G°el, and ∆G°hy for SDS and CPC in aqueous medium at 25 °C are -37.48, 13.60, and -51.08 kJ mol-1 and -47.91, 9.26, (20) Paul, B. C.; Ismail, K. Bull. Chem. Soc. Jpn. 1993, 66, 703. (21) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561. (22) Emerson, M. F.; Holtzer, A. J. Phys. Chem. 1965, 69, 9, 3718. (23) Mukerjee, P. J. Phys. Chem. 1969, 73, 3, 2054.
and -57.17 kJ mol-1, respectively.8,19,24 By comparing the values of the free energy terms of SDS and CPC in molten acetamide and aqueous media, it is apparent that the values of ∆G°hy are less negative in acetamide melt which may be due to the reduced solvophobic interactions since acetamide is more lipophilic than water. This, in turn, may be responsible for causing lower values of n for these surfactants in acetamide melt. Furthermore, the ability of a solvent to force surfactants to form micelles is quantified sometimes in terms of its cohesive energy density reported by the term De ) γ/V1/3, where γ is the surface tension of the solvent and V its molar volume.14,25 For micellization to occur in a particular solvent it was reported that the value of De for the solvent is required to be above 1.0-1.1 J m-3. Hydrogen bonding capability of a solvent has not been shown to be a necessary condition for micellization.14 For acetamide melt De ≈ 1.0 J m-3 at 89 °C (which is comparable to the value of formic acid at 25 °C) whereas for water De ) 2.75 J m-3 at 25 °C. Thus, lower value of De for acetamide melt may also be responsible for the lower values of n observed in this molten solvent. Acknowledgment. K.G. acknowledges the award of Senior Research Fellowship to him by the CSIR, New Delhi. LA9914662 (24) Healy, T. W.; Drummond, C. J.; Grieser, F.; Murray, B. S. Langmuir 1990, 6, 506. (25) Ramadan, M.; Evans, D. F.; Lumry R.; Philson, S. J. Phys. Chem. 1985, 89, 3405.
