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Phase Transition in the Adsorbed Layer of Catanionic Surfactants at the Air/Solution Interface Tibor Gila´nyi,* Ro´bert Me´sza´ros, and Imre Varga Department of Colloid Chemistry, Lora´ nd Eo¨ tvo¨ s University, P.O. Box 32, 1518 Budapest, Hungary Received September 27, 1999. In Final Form: December 3, 1999 Dynamic and equilibrium surface tension measurements were performed on aqueous solutions of three symmetric chain catanionic surfactants (dodecyltrimethylammomium dodecyl sulfate, DTA‚DS, decyltrimethylammonium decyl sulfate, DeTA‚DeS, and octyltrimethylammonium octyl sulfate, OTA‚OS). The surface tension of DTA‚DS and DeTA‚DeS solutions shows a peculiar time dependence. Depending on the surfactant concentration, there is a latent period while the surface tension is almost constant followed by a pronounced decrease toward the equilibrium value. The equilibrium surface tension against the logarithm of the surfactant concentration can be characterized by two linear regions. The surface tension of OTA‚OS solutions changes regularly with both the time and concentration as in the case of ordinary surfactant solutions. The dynamic and equilibrium surface tension data were interpreted in terms of a two-dimensional gas/condensed phase transition. A molecular interaction model was developed to describe the adsorption of the catanionic surfactants. In agreement with the experimental observations, the model predicts phase transition in the adsorbed layer of the DTA‚DS and DeTA‚DeS.
Introduction Catanionic surfactants are defined as salts of an amphiphilic anion with an amphiphilic cation.1 The aqueous solutions of the catanionic surfactants show unusual physicochemical properties and phase diagrams. Formation of mixed micelles, unilamellar and multilamellar vesicles, liquid crystals, and other types of structures can be observed in these systems.2-10 An essential feature of the catanionic surfactants is their very strong surface-active character.11,12 The adsorption behavior of these solutions is special since both the cation and anion may be accommodated in a first adsorbed layer and in the diffuse electric double layer as well. There are only a few works in this field, because of the experimental difficulties due to the low solubility of the catanionic surfactants. Recently, Eastoe et al. investigated the surface layer of catanionic surfactant solutions by means of neutron reflection and small angle neutron scattering measurements.13,14 The average area per molecule determined by these methods was found to be in a good agreement with that calculated from surface tension measurements by means of the Gibbs equation. * To whom correspondence should be addressed. (1) Jokela, P.; Jo¨nsson, B.; Sadaghiani, A. S.; Khan, A. Langmuir 1991, 7, 889. (2) Anacker, E. W. J. Colloid Sci. 1953, 8, 402. (3) Packer, A.; Donbrow, M. J. Pharm. Pharmacol. 1963, 15, 317. (4) Balmbra, R. R.; Clunie, J. S.; Goodman, J. F.; Ingram, B. T. J. Colloid Interface Sci. 1973, 42, 226. (5) Jokela, P.; Jo¨nsson, B.; Eichmu¨ller, B.; Fontell, K. Langmuir 1988, 4, 187. (6) Jokela, P.; Jo¨nsson, B.; Khan, A. J. Phys. Chem. 1987, 91, 3291. (7) Khan, A.; Mendonca, C. J. Colloid Interface Sci. 1995, 169, 60. (8) Backlund, S.; Friman, R.; Karlsson, S. Colloids Surf., A 1997, 123, 125. (9) Filipovicvincekovic, N.; Pucic, I.; Popovic, S.; Tomasic, V.; Tezak, D. J. Colloid Interface Sci. 1997, 188, 396. (10) Tomasic, V.; Popovic, S.; Tusekbozic, L.; Filipovic-Vincekovic, N. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1942. (11) Hoyer, H. W.; Marmo, A.; Zoellner, M. J. Phys. Chem. 1961, 65, 1804. (12) Corkill, J. M.; Goodman, J. F.; Ogden, C. P.; Tate, J. R. Proc. R. Soc. London, Part A 1963, 273, 83. (13) Eastoe, J.; Rogueda, P.; Shariatmadari, D.; Heenan, R. Colloids Surf., A 1996, 117, 215. (14) Eastoe, J.; Dalton, J.; Rogueda, P.; Sharpe, D.; Dong, J. Langmuir 1996, 12, 2706.
Many more publications deal with the surface behavior of the mixtures of aqueous cationic and anionic surfactant solutions because of the practical application of surfactant mixtures as detergents, dispersants, etc. The composition and some other properties of the mixed monolayers have been characterized by various models based on the regular solution theory and on various adsorption isotherm equations. It can be concluded from these investigations that the 1:1 mixture has extremely strong surface active character compared to that of the individual surfactants.15-22 These mixtures usually show similar behavior to the aqueous solutions of catanionic surfactants, and the influence of the counterions is often negligible.19-21 The equimolar mixtures of symmetric chain cationic and anionic surfactants form an equimolar adsorption layer showing negative deviation from the ideal behavior due to the strong attractive interactions in the monolayer.19-21 Matsuki et al. found that another consequence of these strong interactions may be manifested in a two-dimensional gas/condensed type phase separation in the case of mixtures of decyltrimethylammonium bromide and sodium decyl sulfate solutions.22 In the present work we study experimentally the surface properties of the aqueous solutions of three symmetric chain catanionic surfactants by surface tension measurements and present a molecular interaction model to describe their adsorption and the phase behavior of the adsorbed layer. Experimental Section Materials. For the preparation of the catanionic surfactants, alkyl sulfate and alkyl trimethylammonium salts were used. The sodium dodecyl sulfate, sodium decyl sulfate, and sodium octyl sulfate were produced by Merck (Darmstadt, Germany). These anionic surfactants were recrystallized from a 1:1 mixture (15) Huang, J. B.; Zhao, G. X. Colloid Polym. Sci. 1995, 273, 156. (16) Rodakiewicz-Novak, J. J. Colloid Interface Sci. 1981, 84, 532. (17) Rodakiewicz-Novak, J. J. Colloid Interface Sci. 1982, 85, 586. (18) Rodakiewicz-Novak, J. Colloids Surf. 1983, 6, 143. (19) Go´ralczyk, D. Colloid Polym. Sci. 1994, 272, 204. (20) Go´ralczyk, D. J. Colloid Interface Sci. 1994, 167, 172. (21) Go´ralczyk, D. J. Colloid Interface Sci. 1996, 179, 211. (22) Matsuki, H.; Aratono, M.; Kaneshina, S.; Motomura, K. J. Colloid Interface Sci. 1997, 191, 120.
10.1021/la991266q CCC: $19.00 © 2000 American Chemical Society Published on Web 02/04/2000
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of benzene and ethanol. The dodecyltrimethylammonium bromide, decyltrimethylammonium bromide, and octyltrimethylammonium bromide were purchased from Sigma (Germany). The catanionic surfactants were produced by mixing the anionic and cationic surfactant solutions in 1:1 molar ratio. The precipitate was washed with distilled water until bromide ions could not be detected in the supernatant with silver nitrate. This product was recrystallized twice from acetone. The sodium bromide was an analytical grade product produced by Reanal (Hungary). For the preparation of the aqueous solutions, double distilled water was used. Surface Tension Measurements. The dynamic and equilibrium surface tensions were measured by the drop weight method. Detailed descriptions of the apparatus and technique were published earlier.23 The measurements were carried out at 25.00 ( 0.05 °C in a closed vessel containing the saturated vapor of the measured solution. The surface tension of the water was found equal to 72.2 ( 0.1 mN m-1. The dynamic surface tension measurements were performed by measuring the weight of single drops formed during a time period from 30 s to 40 min. The equilibrium surface tension was determined from the surface tension vs t-1/2 curves by extrapolation (t ) ω).
Results and Discussion Dynamic and Equilibrium Surface Tension Data. In Figure 1 the surface tension vs t-1/2 curves are plotted at several concentrations of the DTA‚DS, DeTA‚DeS, and OTA‚OS solutions, respectively. The OTA‚OS solutions show a linear dependence at each concentration in accordance with a diffusion-controlled adsorption kinetics.24-27 In the case of DTA‚DS and DeTA‚DeS, anomalous dynamic behavior can be observed. At smaller concentrations of the investigated concentration range, linear dependence can be seen with surface tension values close to that of pure water. However, above a certain concentration the σ vs t-1/2 curves can be approximated by two linear regions separated by a breakpoint. At the beginning of the adsorption process, the surface tension decreases slightly and after passing a certain time it strongly decreases. At even higher concentrations single linear dependence can be observed again in the investigated time range. In Figure 2 the equilibrium surface tension is plotted against the logarithm of the surfactant concentration. In the case of DTA‚DS and DeTA‚DeS solutions, the experimental curves can be divided into three linear regions with a narrow transitional range between them. In the low concentration range, the surface tension decreases only very slightly with the concentration. Above a welldefined concentration (c*) determined by the intersection of the first two linear sections of the σ vs log c curve, the surface tension strongly decreases. Finally, if the concentration exceeds the solubility of the surfactant, the surface tension becomes constant. Contrary to the longer alkyl chain surfactants, the surface tension of the OTA‚ OS system behaves regularly up to the solubility of the catanionic salt. The equilibrium surface tension was also measured in the presence of 0.1 M sodium bromide. The σ vs log(cγ() curves were the same with or without the excess salt within the experimental error (where the activity coefficient γ( is calculated from the Debye-Hu¨ckel limiting law). This result is in accordance with earlier papers in the literature12,21-22 confirming the equimolar adsorption of the anionic and cationic surfactants into the surface monolayer. (23) Gila´nyi, T.; Stergiopoulos, C.; Wolfram, E. Colloid Polym. Sci. 1976, 254, 1018. (24) Ward, A. F.; Tordai, L. J. Chem. Phys. 1946, 14, 453. (25) Rillaerts, E.; Joos, P. J. Phys. Chem. 1982, 96, 3471. (26) Van de Bogaert, R.; Joos, P. J. Phys. Chem. 1979, 83, 2244. (27) Fainerman, V. D.; Makievski, A. V.; Miller, R. Colloids Surf., A 1994, 87, 61.
Figure 1. Surface tension versus t-1/2 functions of OTA‚OS, DeTA‚DeS, and DTA‚DS solutions at different concentrations. The size of the symbols is commensurable with the standard error of surface tension measurements.
For the quantitative description of the adsorption of catanionic surfactants, the Gibbs equation was applied
-dσ ) Γ+ dµˆ + + Γ- dµˆ -
(1)
where Γ+ and Γ- are the Gibbs relative surface excesses
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Gila´ nyi et al.
Figure 2. Equilibrium surface tension as a function of the logarithm of surfactant concentration for DTA‚DS, DeTA‚DeS, and OTA‚OS solutions.
of the cationic and anionic surfactants (referring to zero excess of water) and µˆ + and µˆ - are the electrochemical potentials of the cations and anions, respectively. Taking into consideration the electroneutrality of the adsorption (Γ+ ) Γ-), eq 1 leads to
-dσ )
Γ+ + Γ(dµˆ + + µˆ -) ) ΓtRT d ln a( 2
Figure 3. Gibbs surface excess of the catanionic surfactants against the concentration of the solution. In the case of DTA‚ DS and DeTA‚DeS the size of the symbols is commensurable to the standard error of the relative surface excess estimated from linear regression. For the OTA‚OS the standard errors were estimated on the basis of polynom regression and denoted by caps.
(2)
where Γt is the total adsorbed amount (which is the sum of the surface excesses of the cations and the anions) and a( is the mean activity of the surfactant solution. The activity was replaced by the mole fraction of the catanionic salts in the investigated concentration ranges. To justify this approximation, we studied the dependence of the solubility product of the catanionic salts as a function of the excess of both the cations and anions. It was found that the solubility products were independent of the surfactant excess from which it can be concluded that the catanionic surfactants in aqueous solution are ordinary strong electrolytes and ion associates do not form in a detectable amount. This is in agreement with the conclusion drawn from electrical conductivity measurements.22,28 In Figure 3 the surface excess isotherms of the three catanionic surfactants derived from eq 2 are shown. The derivatives were calculated from polynoms fitted to the experimental σ vs log c curves. In the case of OTA‚OS, the surface excess isotherm is a monotonically increasing function. The adsorption isotherm of the DTA‚DS and DeTA‚DeS can be divided into two regions with a singularity between them. At a critical concentration (c*) the adsorbed amount abruptly increases with more than an order of magnitude. This indicates a first-order phase transition in the adsorbed layer of the DTA‚DS and DeTA‚ DeS. The phase transition starts at a very small adsorbed amount in a gaslike monolayer and a saturated adsorbed layer develops. In the case of OTA‚OS, phase transition does not take place. In light of these results the anomalous dynamic behavior shown in Figure 1 can also be interpreted. Following the creation of a fresh surface, the adsorbed amount increases (28) Scott, A. B.; Tartar, H. V. J. Am. Chem. Soc. 1943, 65, 698.
Figure 4. Surface pressure as a function of the average area per surfactant molecule.
with time due to the diffusion of the surfactant molecules from the bulk solution to the surface layer. The surface tension slightly decreases at first, and when it reaches a critical value (σ*) a new phase appears in the adsorbed layer. Since during the phase transition the surface pressure is constant, the σ vs t-1/2 curves should contain a constant region. This constant part cannot be well detected in the experimental curves because σ* - σo is commensurable with the experimental error. After the development of the condensed phase, the surface tension strongly decreases with further adsorption and tends toward its equilibrium value. With increasing bulk surfactant concentration the diffusion is faster and less time is needed for the full development of the condensed phase. In Figure 4 the surface pressure vs average area per molecule curves are plotted for the investigated catanionic
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headgroups. According to Marcus29 the radii of the hydrated trimethylammonium and sulfate ions are equal to 2.97 and 2.63 Å, respectively, yielding AN ) 31 Å2/molecule for the square lattice. This value is in a good agreement with the experimental one (∼30 Å2/molecule). On the basis of the previous picture, the chemical potential of the catanionic surfactants in the 2D condensed is approximated by the following expression phase µσ,cond ( s 2,aqfoil 2/air µσ,cond ) µ(o + ∆µCH + ∆µCH + ∆µel. (4) ( ( ( (
Figure 5. Schematic representation of the phase equilibrium of the catanionic surfactants at the air/solution interface.
surfactants. In the case of DTA‚DS and DeTA‚DeS at large separation of the molecules in the surface layer the surface pressure slightly increases by decreasing AN. After the critical surface pressure is attained (σo - σ*) the surface pressure remains constantsfirst-order phase transition occurssthen at AN ≈ 30 Å2/molecule it grows to the infinity. In the case of OTA‚OS the surface pressure monotonically increases with decreasing AN and tends to the infinity also at ∼30 Å2/molecule. In this case phase separation cannot be observed. The maximum values of the surface excess or the average area per molecule of the three catanionic surfactants differ slightly, and the average is approximately equal to Γ∞t = 5.5 × 10-6 mol/m2 (∼30 Å2/ molecule). The same saturation adsorption of the catanionic homologues indicate that the hydrophilic headgroups determine the structure of the saturated monolayer. 2D Gas/Condensed Phase Transition. In this section the two-dimensional phase transition of the catanionic surfactants is interpreted by means of a simple molecular interaction model. Let us imagine that a condensed phase and a gaslike phase are in equilibrium in the surface layer of a cataninonic surfactant and they are in equilibrium with the bulk solution (Figure 5). In the case of equimolar adsorption, we can write that N+ ) N- ) N( and Γ+ ) Γ) Γ( ) N(/A, where N+ and N- are the number of the cationic and anionic surfactants and N( is the number of catanionic surfactants in the surface layer. A is the area of the surface layer, Γ+ and Γ- are the surface concentrations of the cationic and anionic surfactants, and Γ( is the surface concentration of catanionic surfactant, which is taken equal to the Gibbs surface excess amount. The mean chemical potential, µ( is defined as
µ( )
µ+ + µ2
(3)
where µ+ and µ- denote the chemical potential of the cations and anions, respectively. 2D Condensed Phase of the Catanionic Surfactants. The calculation of the chemical potential of the catanionic surfactants in the 2D condensed phase requires knowledge of the structure of this phase. It is assumed that the charged hydrated headgroups of the surfactant molecules form an electrically neutral square lattice and their alkyl chains produce a liquidlike oil film. If the hydrated headgroups form a closed-packed square lattice, then the average area per surfactant ion is equal to AN ) (Rcat + Ran)2, where Rcat and Ran are the radii of the hydrated
s is the standard state chemical potential in the where µ(o aqueous solution. The second term in the right-hand side of eq 4 refers to the transfer of an alkyl chain from aqueous solution to liquid alkane phase. This term can be estimated from the solubility of alkanes in water,30 and it is generally calculated from the following expression 2,aqfoil ) (-2.55-1.25nc)kT ∆µCH (
(5)
where nc is the number of methylene groups in the alkyl chain. This expression also takes into account the loss of degrees of freedom for the alkyl chains.31,32 The third term in eq 4 accounts for the interaction of the oil film with the gas phase. This term is approximated as 2/air ) ∆µCH (
(
∂(σA) ∂(2N()
)
T,p
)
σA ) σA( 2N(
(6)
where A( is the average area per surfactant ion (31 Å2/ molecule) and σ = 22 mN m-1 is the liquid alkane/air surface tension. The last term in eq 4 is the electrostatic contribution to the standard free energy change
∆µel. ( )
(
)
∂(Ulat + Ucap) ∂(2N()
(7)
T,p
where Ulat is the lattice energy of the square lattice calculated by assuming that the center of the hydrated headgroups are in the same plane. However, several experimental results suggest that the centers of the charged headgroups are not in the same plane.33 Ucap is the energy of a capacitor which is necessary to take apart the planes of the oppositely charged headgroups from each other to a distance which is equal to the difference between the hydrated radii of the sulfate and the trimethylammonium ions. The lattice energy was calculated by summing the attractive and repulsive Coulomb interaction energies of a probe ion with the rest of the ions in an infinite lattice.34,35 It can be shown that the contribution due to the electrostatic energy of a plane square lattice is equal to (29) Marcus, Y. Ion Properties, 1th ed.; Marcel Dekker: New York, 1997; Chapter 12. (30) Abraham, M. H. J. Chem. Soc., Faraday Trans. 1 1984, 80, 153. (31) Ruckenstein, E.; Huber, G.; Hoffman, H. Langmuir 1987, 3, 382. (32) Nagarajan, R.; Ruckenstein, E. J. J. Colloid Interface Sci. 1979, 71, 580. (33) Dragcevic, D.; Bujan, M.; Grahek, Z.; Filopovic-Vincekovic Colloid Polym. Sci. 1995, 273, 967. (34) Feynman, R. P.; Leighton, R. B.; Sands, M. The Feynman Lectures on Physics; Addison-Wesley: Reading, MA, 1964; Vol. 2, Chapter 8. (35) Israelachvili, J. Intermolecular & Surface Forces, 2nd ed.; Academic Press: London, 1991; Chapter 1.
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( ) ∂(Ulat) ∂(2N()
)
T,p
Gila´ nyi et al.
Ulat q2 ) -1.615 2N( 8πroa
(8)
where q is the charge of the ions, o is the permittivity of vacuum, r the relative permittivity of the medium, and a is the sum of the hydrated radii of the sulfate and trimethylammonium ions. The relative permittivity was taken to be equal to that of the water (r ) 80). The standard chemical potential contribution due to the energy of a capacitor can be calculated as
( ) ( ∂(Ucap) ∂(2N()
)
T,p
)
∂(Q2/C) ∂(2N()
) T,p
e2Γ(δ 2ro
(9)
where δ is the distance between the condenser plates that was taken equal to 0.34 Å from the difference between the radii of the hydrated headgroups. C ) roA/δ is the electrical capacitance, Q denotes the charge of the condenser plates, and e is the elementary charge. It is important to note that the chemical potential of the catanionic surfactants having the same headgroups differ only in the hydrophobic contribution (eq 5) since the rest of the energy terms (eqs 6-9) depend only on the type of the headgroups. 2D Gaslike Phase of the Catanionic Surfactants. The mean chemical potential of a catanionic surfactant in the gaslike phase, µσ,g ( , is approximated as follows σ,g µσ,g ( ) µ(o + kT ln
(
)
Γ( ) Γo - 2Γ( σ,g + kT ln µ(o
(
)
Θ (10) 2(1 - Θ)
σ,g is the standard chemical potential in the where µ(o gaslike phase and the second term is due to the surface entropy of mixing. Γo denotes the total number of the surface sites, and Θ denotes the surface coverage. In eq 10 the interactions between the adsorbed molecules are neglected; consequently, it can be used at very small surface coverage. The standard chemical potential of the 2D gas is approximated as
σ,g s 2,aqfgas 2/water ) µ(o + ∆µCH + ∆µCH µ(o ( (
(11)
where the second term is the free energy change accompanying the transfer of an alkyl chain from the bulk solution to the adsorbed gaslike phase. This term can be calculated from the solubility data of alkane vapors30 2,aqfgas ) (-4.83 - 0.3nc)kT ∆µCH (
(12)
The third term in the right-hand side of eq 11 takes into account that the alkyl chains may interact with the water surface. To estimate the alkyl chain/water interaction, it is supposed that the methylene groups of an alkyl chain are accommodated in a hemisphere with the radius of the extended alkyl chain. We also suppose that the methylene groups are independent from each other. In such a system a methylene group can occupy two kinds of states: it can be either in contact with the water surface or in the air. The interaction energy of a methylene group being in the air is taken to be zero while the interaction energy between the water surface and a methylene group is approximated with E1 ) (σow - σw)ACH2 ) -1.07kT/CH2 where σow (=50 mN m-1) is the oil/water interfacial tension, σw ()72 mN m-1) is the surface tension of water, and ACH2 ()20 Å2) denotes
Figure 6. Chemical potential against the surface coverage for DTA‚DS, DeTA‚DeS, and OTA‚OS in the 2D gas state (µσ,g ( s µ(o ) (curves 1, 2, and 3, respectively) and the chemical s potential in the condensed phase (µσ,con - µ(o ) (horizontal lines ( 1′, 2′, and 3′, respectively.)
the cross sectional area of a methylene group. By application of the Boltzmann statistics the distribution of the methylene groups between the two energy levels can be calculated. On the basis of these assumptions the standard chemical potential contributions due to the alkyl chain/water surface interaction are -3.44, -3.63, and -3.78 kT for surfactants containing 8, 10, and 12 methylene groups, respectively. Phase Behavior of the Adsorbed Layer. Comparing the chemical potentials of the gaslike and condensed phases, the 2D phase behavior of a catanionic surfactant can be predicted. The chemical potential referred to the s standard state in the solution (µσ,g ( - µ(o) was calculated from eqs 10-12 and plotted against the surface coverage for the three catanionic surfactants in the 2D gas state s - µ(o ) values for the (Figure 6, curves 1-3). The (µσ,cond ( 2D condensed phase calculated according to eqs 4-9 are plotted with dotted horizontal lines (Figure 6, curves 1′3′) (note that they are not a function of the surface coverage). As can be seen in Figure 6, at small surface coverage the gaslike phases of the catanionic surfactants are favorable compared to the condensed ones. By increasing the surface coverage first in the case of the DTA‚DS, then in the case of the DeTA‚DeS the chemical potential of the 2D gas phase intersects the chemical potential of the 2D condensed phase indicating the occurrence of a phase transition. On the other hand in the case of OTA‚OS, the chemical potential of the gaslike phase is smaller than that of the condensed phase at surface coverage even as high as 0.3. Since the model used for the gaslike phase neglects the lateral interactions among the surfactant molecules, the calculated chemical potential becomes overestimated with increasing surface coverage. This suggests that in the case of OTA‚OS, the chemical potential of the gaslike phase does not intersect the chemical potential of the condensed phase; consequently, phase transition cannot occur. The above qualitative predictions are in good agreement with the surface characteristics of the investigated symmetric chain catanionic surfactants supporting the described physical model. A quantitative test of the model is the comparison of the calculated and measured standard free energy changes.
Phase Transition in the Adsorbed Layer
To determine the free energy change of the surfactant for its transition between the 2D gas phase and the bulk solution (or 2D condensed phase), the adsorbed amount in the gas phase should be precisely measured. Since below c* the extent of surface tension lowering is commensurable with the experimental error, the derivative of the σ vs log c function is rather inaccurate. Therefore it is better to base this comparison on the transition of the surfactant from the bulk solution to the 2D condensed phase because c* is an experimentally well determinable parameter from which the respective free energy changes can be calculated. s - µ(o ) values are -14.2 and -16.7 The theoretical (µσ,cond ( kT while the experimental ones are -15.4 and -17.9 kT for DeTA‚DeS and DTA‚DS, respectively. The difference between the experimental and theoretical standard free energy change is 1.2 kT in the case of both catanionic surfactants. This discrepancy can be attributed to a small error in the oil/air interaction energy (eq 6) or the use of the bulk water permittivity in the electrostatic contribution term (eq 7). The model gives an opportunity for the prediction of the surface phase behavior of other kind of surfactant solutions. In general it can be stated that the longer alkyl chain and larger attractive interactions make the 2D phase transition more favorable. In the case of individual ionic
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surfactants the repulsive interactions among the headgroups increase the chemical potential of the 2D condensed phase in such an extent that phase separation cannot occur. In the case of nonionic surfactants, the absence of the attractive interactions among the headgroups also makes the phase transition unfavorable. However, according to the model the chemical potential of the condensed phase can be reduced compared to the gaslike phase by increasing the alkyl chain length of the surfactant molecules. In the case of those ionic and nonionic surfactants that have a long enough alkyl chain, the 2D phase transition can also be expected. In the case of water-soluble ionic and nonionic surfactants, such a phase transition cannot be observed. However, in accordance with the expectations on spread surface films of some long chain nonionic and ionic surfactants, the 2D phase transition can be observed36 indicating that in these cases the hydrophobic driving force is large enough for the compensation of the absence of the attractive interactions among the headgroups. LA991266Q (36) Schick, M. J. In Surfactant Science Series; Schick, M. J., Ed.; Marcel Dekker: New York, 1967; Vol 1, Chapter 14.
