Langmuir 2004, 20, 10935-10942
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Headgroup and Hydrocarbon Tail Effects on the Surface Tension of Sugar-Based Surfactant Solutions. Atte J. Kumpulainen,* C. Marcus Persson, and Jan Christer Eriksson Department of Chemistry, Surface Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden, and The Institute for Surface Chemistry, P.O. Box 5607 SE-100 44, Stockholm, Sweden Received May 13, 2004. In Final Form: September 17, 2004 Measurements of surface tension isotherms were conducted for water solutions of pure and mixed n-decylβ-D-glucopyranoside (C10-Glu) and n-decyl-β-D-maltopyranoside (C10-Mal) surfactants. By applying the Gibbs surface tension equation, the surface densities of Glu and Mal were derived for different compositions and concentrations. The surface fractions were compared with theoretically calculated values where the headgroups were modeled as hard disks. Satisfactory agreement was found for hard-disk sizes of 22.9 and 11.3 Å2 in the case of a 1:1 mixture. The results of the hard-disk calculations were employed to estimate the configurational free energy of the n-decyl-hydrocarbon chain. The results obtained agree well with previous calculations for the n-dodecyl chain. Comparison with n-dodecyl β-D-maltopyranoside (C12-Mal) indicated a further contribution, with the longer hydrocarbon chain giving rise to a higher surface tension in good agreement with data for hydrocarbon liquids. Furthermore, the interpenetration of the headgroup into the hydrocarbon film was studied by means of comparing surface-tension data for n-decyl- and n-dodecylethylene-oxide-based surfactants and n-decyl- and n-dodecyl-β-D-thiomaltopyranosides (C10-S-Mal and C12-S-Mal, respectively) and -maltopyranosides. It was found that lengthening the tetra(etylene oxide) chain by one segment affects the surface tension only marginally, indicating little interpenetration of the additional ethylene-oxide group into the hydrocarbon film. For the thiomaltosides, however, the corresponding effect was found to be remarkably high.
Introduction The adsorption of a surfactant from bulk solution to an air-water interface is determined by a few free-energy contributions stemming from the hydrocarbon chain and the headgroup. Upon fitting surface tension data for a pure surfactant with some appropriate equation of state, it is difficult, of course, to exactly determine from which part of the molecule a certain contribution to the surfacepressure increase actually arises. For a mixture of two surfactants, however, we can determine the surface fraction of each of the components from the change of the surface tension due to changing the bulk fractions of the surfactants. Moreover, for a mixture of surfactants of equal hydrocarbon chains, the differences in free-energy contributions at equal surface density are only related to differences between the headgroups, as the environment in the hydrocarbon film can be assumed to be the same at a given molecular area. Surface tension measurements were undertaken1 for solutions of mixtures of n-decyl-β-D-glucopyranoside (C10-Glu) and n-decyl-β-D-maltopyranoside (C10-Mal). For C10-Mal and C10-Glu, there is a considerable difference in size between the surfactant headgroups and this causes interesting differences in the adsorption behavior. First, in the dilute Henry range, the surface concentrations measured are identical for C10-Mal and C10-Glu, and hence, the headgroup difference does not contribute at 22 °C. After the transition from the Henry range to the liquidexpanded regime, the larger headgroup (Mal) is initially preferred, but as the extent of adsorption increases, Mal adsorbs less readily than Glu and eventually Mal mol* Author to whom correspondence should be addressed. Phone: +46 8 7909922. Fax: +46 8 208998. E-mail: atte.kumpulainen@ surfchem.kth.se;
[email protected]. (1) Persson, C. M.; Kumpulainen A. J.; Eriksson, J. C. Langmuir 2003, 19, 6110.
ecules are expelled from the surface. We shall analyze the adsorption of these surfactants from solution with the aid of the hard-disk equation of state.2,3 Here we will show that the hard-disk model can account for the headgroup behavior of mixed sugar-based surfactants from solution nearly quantitatively. There are primarily two main contributions to the overall free energy of the monolayer affecting the surface-tension lowering, the mixing of headgroups and the configurational pressure from the hydrocarbon tails. The configurational pressure of dodecyl chains has been theoretically calculated4,5 and used to successfully determine the surface-pressure increase upon surface density increase for both ionic6,7 and nonionic8 surfactants. The configurational surface pressure has been experimentally deduced for an n-decyl-chain.8 The configurational surface pressure was obtained by comparing the surface pressure at equal molecular areas for pure decyl and dodecyl surfactants. However, difficulties in determining the molecular area close to the critical micelle concentration (cmc) can affect the resulting deduced configurational pressure immensely. In this study, we obtain the configurational pressure and free energy by fitting the change in headgroup surface fractions with the well-established hard-disk model. We hereby achieve a stable model able to predict the surface fractions of two components in the surface, and therefore, also the surface pressure arising from the headgroups. Thus, we can also (2) Nilsson, U., Thesis. Lund, Sweden, 1992. (3) Erpenbeck, J. J.; Luban, M. Phys. Rev. A 1985, 32, 2920. (4) Gruen, D. W. R.; Lacey, E. H. B. Surfactants in solution; Mittal, K. L., Lindman, B, Eds.; Plenum Press: New York, 1984; Vol. 1. (5) Szleifer, I.; Ben-Schaul, A.; Gelbart, W. M. J. Phys. Chem. 1990, 94, 5081. (6) Eriksson, J. C.; Ljunggren S. Colloids Surf. 1989, 38, 179. (7) Persson, C. M.; Jonsson, A. P.; Bergstro¨m, M.; Eriksson, J. C. J. Colloid Interface Sci. 2003, 267, 154. (8) Persson, C. M.; Kjellin, U. R. M.; Eriksson, J. C. Langmuir 2003, 19, 8152.
10.1021/la048815z CCC: $27.50 © 2004 American Chemical Society Published on Web 10/30/2004
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deduce the configurational surface pressure from the n-decyl tail with some accuracy. Knowing the surface fraction, and with a suitable free energy expression for the headgroups in the monolayer, we can determine the behavior of the headgroups and in the end also gain knowledge about the contributions arising from the hydrocarbon chains. The decisive role of the hydrophobicity of a hydrocarbon tail for the adsorption of surfactants is generally recognized, but the detailed aspects of the hydrocarbon chain state in the liquidexpanded (LE) monolayer is still unclear.9,10 In this report, we assume that a coherent hydrocarbon film of liquidlike nature with a constant density is characteristic for the LE state. Herein we define the true LE state from a molecular area lower than 65 Å2, which is considered to be sufficiently high in density to cover the entire surface. Thus, upon increasing the extent of adsorption, the hydrocarbon tail film thickness will necessarily increase. Such a simple model of the hydrocarbon part of the LE monolayer has proven fruitful for the ionic, as well as nonionic, surfactants at the air-water interface.6-8 In this report, we also study aspects of the surfactant adsorption where the interactions between headgroup and hydrocarbon film become interdependent. That is, a strict separation of the free energies for the two parts of the molecule is difficult to make in these cases. For highly hydrophilic headgroups, the subdivision of headgroup and hydrocarbon chain is a good approximation, but with increasing miscibility, the effect of interpenetration of the headgroup becomes noticeable in surface-tension measurements. To make these estimates, it is necessary to compare pairs of similar headgroups with pairs of similar hydrocarbon chains. Here we have chosen n-decyl and n-dodeyl homologues of tetra- and penta(ethylene oxide), and n-decyl and n-dodeyl homologues of β-D-maltopyranoside and β-D-thiomaltopyranoside in order to investigate how small variations in structure determine the monolayer behavior.
(
γ ) γ* - kTΓ∞ ln
)
c +1 k1
(2)
where γ* is a constant, usually set to the surface tension of pure water, γ0, Γ∞ is the surface saturation density, and k1 is an adsorption constant. Theory of Mixed Monolayers. Generally, measurements on binary mixtures of surfactants are important, as such studies enable us to probe into synergistic behaviors. For mixtures of surfactants with equal hydrocarbon tails, only the differences between the headgroups will contribute to the changes, as compared with the pure components. In solutions of C10-Mal and C10-Glu, no synergistic behavior is seen as far as the cmc is concerned, but the total monolayer surface density arising for a certain surfactant concentration is dependent on the bulk fractions of the surfactants. Assuming ideality, the chemical potentials, µ, of the two species in bulk are given by,
µ1 ) µ10 + kT ln(cx1)
(3)
µ2 ) µ20 + kT ln(cx2)
(4)
where µ0 denotes the standard value of the chemical potential and k is the Boltzmann constant, T is the absolute temperature, and c stands for the bulk concentration. As composition variables, we use the total bulk concentration, c, and the bulk surfactant mole fractions, fulfilling x1 + x2)1. At constant temperature the Gibbs surface tension equation reads,
dγ ) -Γ1dµ1 - Γ2dµ2
(5)
where the equimolecular dividing surface for water is being used. At constant bulk fractions eq 5 yields,
Materials and Methods The surface tension was measured with a Kru¨ss K12 tensiometer, employing the Wilhelmy plate method using a platinum plate, sand blasted to ensure a contact angle of 0° at the threephase line. Surface-tension values were obtained from,
F ) 2(LT + LW)γ cos θ + LTLW∆Fgh
Anatrace (Anagrade) were used as received. Trials were made with samples purified in the high-performance surfactant purification apparatus11 and no differences in adsorption could be detected. To fit the surface tension vs concentration, c, data with the purpose to obtain a mathematical representation needed for the calculation of the surface density, we have used polynomials of γ(lnc) and a variant of the Szyszkowski-Langmuir equation,
(1)
where F is the force measured and γ is the surface tension of the liquid-vapor interface,θ is the contact angle at the three-phase line, LT and LW are the thickness and width of the plate, respectively, ∆F is the density difference between the liquid and the vapor phase, g is the gravitational constant, and h is the immersion depth of the plate in the liquid. All surface-tension isotherms were recorded at least three times. The temperature was controlled to (0.2 °C. The water used in the experiments was obtained from a Millipore RiOs-8 and Milli-Q PLUS 185 purification system and finally filtered through a 0.2-µm Millipak filter. The total organic carbon content of the outgoing water was controlled with a Millipore A-10 unit and did not exceed 6 ppb during any of the measurements. n-Decyl-β-D-glucopyranoside was used as received from Sigma (>98% GC). n-decyl-β-D-maltopyranoside, n-decyl-β-D-thiomaltopyranoside and n-dodecyl-β-D-thiomaltopyranoside from (9) Bell, G. R.; Manning-Benson, S.; Bain, C. D. J. Phys. Chem. B 1997, 101, 208. (10) Lu, J. R.; Thomas: R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143.
( ) ∂γ ∂ln(c)
T,x1,x2
) -kT(Γ1 + Γ2) ) -kTΓ
(6)
where Γ1 and Γ2 are the surface densities of species 1 and 2, and Γ is the total surface density. Supposing the total surfactant concentration, c, to be kept constant, we instead obtain
( ) ∂γ ∂x1
xσ2 xσ1 a ) x2 x1 T,ckT
(7)
where a denotes the area/molecule and xσ1 and xσ2 stand for the surface fractions of components 1 and 2, respectively. Hence, measuring the surface tension as a function of both c and x1 (or x2), we can compute the surface densities of both species. The grand potential expression per molecule for surfactant adsorption in the true LE range as derived by Eriksson and Ljunggren6 reads,
) γa ) γhw(a - a0) + γhaa + conf + pg + mix + trans (8) where γhw is the macroscopic surface tension of the hydrocarbonwater interface, γha the macroscopic surface tension of the hydrocarbon-air interface, and conf the configurational freeenergy function for the hydrocarbon chain, pg is the excess free energy of the headgroup upon transfer to the surface, mix is the (11) Lunkenheimer, K.; Wantke, K.-D. Rev. Sci. Instrum. 1987, 58, 2313.
Headgroup and Tail Effects on Surface Tension
Langmuir, Vol. 20, No. 25, 2004 10937
free-energy function of mixing of the headgroups, trans is the Tanford transfer free energy12 of the hydrocarbon tail from the bulk phase to surface, and a0 is the surface-area shielding from hydrocarbon-water contact due to the headgroup. To represent the headgroup free-energy contributions in the monolayer, we have invoked a version of the hard-disk equation appropriate for two-dimensional mixtures to describe the interactions among the headgroups. Accordingly, for the pure surfactants we have
( (
) )
1HD a1HD a1HD ) ln + kT a - a1HD a - a1HD
(9)
2HD a2HD a2HD ) ln + kT a - a2HD a - a2HD
(10)
where a1HD and a2HDare the areas of disks 1 and 2. We note that the surface-area fractions of components 1 and 2 are equal to φ1σ ) a1HD/a and φ2σ ) a2HD/a, whereas the surface fraction not covered by disks is φwσ ) (a - a1HD)/a for the first case and φwσ ) (a a2HD)/a for the second case. Equations 9 and 10 can be written in the alternative forms,
( (
) )
( ) ( )
1HD a1HD a1HD a ) ln + + ln kT a a - a1HD a - a1HD
(11)
2HD a2HD a2HD a ) ln + + ln kT a a - a2HD a - a2HD
(12)
where the last terms on the right-hand sides represent the ideal free energy of diluting the hard disks from the φ1σ ) 1 and φ2σ ) 1 (infinite dilution) standard states, which are being used here. The first and the second terms account for the entropic repulsion among the hard disks that tend to zero for large values of the surface area, a, per headgroup. Next, we presuppose that the polar headgroups considered are of a similar chemical nature but differ by their size and, furthermore, that the hydrocarbon tails of the surfactants are the same. Hence, for the mixed surfactant film, a number of free-energy contributions will be equal or nearly equal for both components. Toward this background, we can formulate the following Helmholtz energy expression for the headgroup layer
[
( )] [
a1HD 1pg Fσ ) n1σ + ln kT kT a
+ n2σ
()
n1σ ln
( )]
a2HD 2pg + ln kT a
()
x1σ x2σ + n2σ ln + x1 x2
[(
(n1σ + n2σ) ln
+
]
aˆ a + + C (13) a - aˆ a - aˆ
)
where n1σ and n2σ are the number of molecules of components 1 and 2, respectively, in the surface, and C is a constant. In eq 13, the second couple of terms represent the change in mixing free energy upon passing from the solution state to the film state. The last term entailing the average disk area, aˆ ) x1σa1HD + x2σa2HD, constitutes a reasonable mean-field ansatz to account for the hard-disk repulsion in the mixed system. When equilibrium prevails, Fσ for the headgroup layer has to be at a minimum when the total surface area is kept constant. Assuming the headgroup area, a, to be constant means that we can equally well minimize σ ) Fσ/(n1σ + n2σ), i.e.,
[ ()
( )] [
1pg a1HD σ ) x1σ + ln kT kT a σ
x1σ ln
+ x2σ
() [ σ
( )]
2pg a2HD + ln kT a
x1 x2 aˆ a + ln + x2σ ln + x1 x2 a - aˆ a - aˆ
(
+
)] + C′ (14)
Differentiation with respect to x2σ now yields the following xσ(a) relation
( ) ( )
a2HD x2σ x1 2pg - 1pg + ln HD + ln + kT x2 x1σ a1 (a2HD - a1HD)(2a - aˆ ) (a - aˆ )2
) 0 (15)
where we may assume that 2pg - 1pg ) -γhw(a2HD - a1HD), i.e., that the shielding effect of the larger headgroup per se causes enrichment of surfactant 2 in the mixed film, provided a2HD > a1HD. For smaller a values, however, the hard-disk repulsion term of eq 14 becomes predominant, resulting in depletion of surfactant 2. In the appendix (see Supporting Information), a more extensive alternative derivation of eq 15 is presented. The derivative of eq 14 with respect to the molecular area at constant chemical potentials and temperature yields the surface pressure contribution from the mixture of hard disks,
( )
1 dσ kT da
T,µ1,µ2
a γHD 1 1 )))kT a φw2 (a - aˆ )2
(16)
where φw is the area fraction not covered by disks. Equation 16 hence does not differ from the regular hard-disk equation of state for one hard disk, apart from the average hard-disk area, aˆ , here replacing the one hard-disk area, aHD. We have used a simple model to express the mixing of the hard disks. However, we need not pay close attention to the exact situation in the surface with regard to mixing of differently sized objects, as the size of the optimal hard disk is very much smaller than the actual molecular area.13,14 Correlation effects due to optimal packing of the disks are only likely to occur approaching the limiting surface coverage, which is 91% for uniform disks. Here the model is only stretched to a hard-disk packing fraction corresponding to around 37%. Since we can obtain the surface fraction for, e.g., a 1:1 mixture, in considerable detail, we can make meaningful comparison with the prediction based on eq 15 with experimental results. The surface tension is the derivative of the excess free energy per molecule of eq 8 with respect to the area/molecule, a, at constant temperature and composition of the bulk solution (and hence also surface composition),
γ)
(∂a∂ )
T,µ1,µ2
) γhw + γha + γconf + γmix
(17)
The configurational pressure due to restricting the hydrocarbon chains configurations in the surface, γconf, is hitherto unknown for the decyl hydrocarbon tail. Determining the optimal hard disks enables us to deduce the configurational surface pressure of the decyl tail, as the surface pressure from the headgroup mixing is obtained by eq 16. To attain the best fit for the range from around 65 to 40 Å2, the hard-disk sizes typically used are 20 and 10 Å2 for pure Mal and Glu respectively.8
Results and Discussion Comparison with Experimental Results on Mixtures of Decyl Surfactants. Isotherms were measured for the pure solutions of C10-Mal and C10-Glu and for mixed solutions containing 90, 80, 65, 50, and 35 mol% C10-Mal 1 at 22 °C. The change in surface tension with bulk fraction at constant total bulk concentration then yields the surface mole fractions according to eq 6. There are large differences in adsorption between pure C10-Mal and pure C10-Glu. C10-Glu adsorbs more readily at nearly all concentrations. (12) Tanford, C. The hydrophobic effect, 2nd ed.; Wiley and Sons: New York, 1980. (13) Mansoori, G. A.; Carnahan, N. F.; Starling, K. E.; Leland, T. W. J. Chem. Phys. 1971, 54, 1523. (14) Manciu, M.; Ruckenstein, E. Colloids Surf., A 2004, 232, 1.
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Figure 1. Surface tension as a function of the bulk fraction of C10-Mal at a constant overall concentration of 0.262 mM. The solid line corresponds to the best-fit second-degree polynomial function.
Kumpulainen et al.
Figure 2. Calculated surface fraction using hard-disk areas of 22.9 and 11.3 Å2 (solid line) and thermodynamical surface fraction (dotted line with squares) of C10-Mal for the 1:1 mixture.
surface fraction.16 For a second-degree polynomial, the following, of course, holds true,
In the Henry range, the adsorption is practically identical for C10-Mal and C10-Glu; however, immediately after the transition from the Henry region, C10-Mal is preferred in the surface for a 1:1 mixture for a brief concentration interval. The most noticeable feature distinguishing C10-Mal and C10-Glu is the size difference between the headgroups; at the cmc, the average molecular area, a, of C10-Glu is 37 Å2, whereas C10-Mal only comes down to 48 Å2. The cmc’s of all solutions are between 2 and 2.2 mM. For the mixed solutions, all average molecular areas at the cmc are between those of C10-Mal and C10-Glu. In the mixed solutions, C10-Mal is evidently initially favored, but as the adsorption increases, the smaller C10-Glu molecule tends to become more favored and the C10-Mal molecule will eventually be expelled from the surface. Interestingly, there is a region of ideal mixing of the surfactants in the surface between approximately 68 and 66 mN/m. This range exhibits an almost constant area/molecule of around 79.5 Å2, for both the pure surfactants and the 1:1 mixture, and very high elasitcity. This particular adsorption regime corresponds to a surface covered by distorted two-dimensional surface micelles, called the granular range.15 Granular ranges are detected for all of the investigated sugar-based surfactants, except for n-dodecyl-β-D-thiomaltopyranoside. For the 1:1 mixture, C10-Mal adsorption reaches a maximum at a bulk concentration of around 0.25 mM. This coincides with an area/molecule for the 1:1 solution of around 48 Å2. For the Mal/Glu mixtures, a straight line or a second-degree polynomial of γ(x) at constant concentration accurately represents the data. Measurements of surface tension as a function of the bulk fraction of Mal at constant bulk concentration of c ) 0.262 mM are displayed in Figure 1. Using these data, eq 6 is readily solved for the 1:1 mixture. If we can accurately determine the surface density for the mixture, we can obtain the surface fractions by the difference between pure C10-Mal and C10-Glu surface tensions at equal concentrations. Accordingly, it is found that a surface fraction of C10-Mal equal to 0.5 is reached at approximately 80 Å2. For the hard disk, the larger cross-section will be favored in this regime due to the higher coverage of hydrocarbon-water interface. We have used second-degree polynomial expressions of γ(x) at constant bulk concentration, c, to evaluate the
where Π ) γ0 - γ is the surface pressure. Calculating the equilibrium hard-disk surface fractions by means of eq 15, we find that a 1:1 mixture of hard disks of sizes 22.9 and 11.3 Å2 yields good agreement with the thermodynamical results of the 1:1 mixture. The maximum error is around 1% from 63 Å2 down to 42 Å2, the area/molecule at the cmc is 40 Å2. The calculated and the thermodynamical surface fractions are compared in Figure 2. Thus, the hard-disk model accounts quite well for the surface pressure at medium densities in the true LE range, a < 65 Å2, but fails at high packing densities. Thus, using these hard-disk sizes, we can predict the surface fractions and, hence, also the surface-tension lowering due to the headgroups in this regime. The difference between harddisk standard states, 2pg - 1pg ) -1.08 kT was found to be reasonably close to the estimated -γhw(a2HD - a1HD)) -1.43 kT. The free energy of the hard disks obtained rather accurately describes the mixing of the headgroups and can thereby be used to deduce an estimate of the second free-energy contribution affecting the surface pressure increase, the configurational free energy of the C10-chain.
(15) Kumpulainen A. J.; Persson, C. M.; Eriksson, J. C. Langmuir, submitted for publication.
(16) Aratono, M.; Villeneuve, M.; Takiue, T.; Ikeda, N.; Iyota, H. J. Colloid Interface Sci. 1998, 200, 161.
γ(x) ) k1x2 + k2x + γGlu k1 + k2 ) ∆γ ) γGlu - γMal (18) For the 1:1 mixture, the choice of a second-degree polynomial then results in the expression,
xMalσ )
2∆γ 2 x (1 - x) + x kTΓ
(19)
Thus, if we accurately can determine the surface density of the 1:1 mixture, and invoking the surface tensions of the pure surfactants, then the surface excess of each one of the two components can in principle be derived with similar accuracy as for the overall surface density. In this way, we get expressions for the variation of the surface fraction as a function of the surface density. Using the approximation, γ0 ) γhw+γha, facilitates the calculation further, and thus eq 17 yields,
-Π ) γconf + γmix
(20)
Headgroup and Tail Effects on Surface Tension
Figure 3. Configurational free energy of decyl chains, experimentally deduced (solid line), and configurational free energy of dodecyl chains, calculated (dotted line). Note that the position of the free energy function of the decyl chain may be shifted by a constant contribution.
Figure 4. Configurational pressure of decyl chains, -γconf(C10), experimentally deduced (solid line), and configurational pressure of dodecyl chains, -γconf(C12), calculated (dotted line).
The configurational free energy contribution from the decyl hydrocarbon chains obtained from the 1:1 mixture is presented and compared with the corresponding calculated configurational free energy for dodecyl chains in Figure 3. The configurational pressure attained is in fair agreement to the obtained function of Persson et al.8 The configurational pressure, presented in Figure 4 is compared with the calculated pressure of dodecyl chains. The configurational pressure can then be used to make predictions of the interactions between headgroups for pure surfactants. We will use the deduced configurational surface pressure to account for decyl surfactants henceforth. Comparison with Pure n-Decyl and n-Dodecyl Surfactants. Surface tension isotherms of C10-Mal, C10-S-Mal, and C10-Glu at 22 °C are presented in Figure 5. The corresponding surface densities are presented in Figure 6. All three surfactants have the same slope of γ(c) in the Henry range but differ markedly after the transition to the LE range.15 The transition occurs at considerably lower concentrations for C10-S-Mal than for C10-Mal and C10-Glu. Also, the cmc of C10-S-Mal is considerably lower than that for C10-Mal and C10-Glu, 0.7, 2.2, and 2 mM, respectively. Surface tension isotherms of C12-Mal and C12-S-Mal at 22 °C are presented in Figure 7. The corresponding surface densities are displayed in Figure 8. From the surfacetension isotherms of C12-Mal and C12-S-Mal, it is clearly
Langmuir, Vol. 20, No. 25, 2004 10939
Figure 5. Surface tension isotherms in the true LE range for C10-Mal, C10-S-Mal, and C10-Glu at 22 °C. C10-Mal is represented by the circles, C10-Glu by the empty squares, and C10-S-Mal by the triangles.
Figure 6. Adsorption isotherms in the true LE range for C10-Mal, C10-S-Mal and C10-Glu. C10-Mal is represented by the solid line with squares, C10-S-Mal by the solid line, and C10-Glu by the dotted line with the highest adsorption.
Figure 7. Surface tension isotherms for C12-Mal and C12-S-Mal. C12-Mal is represented by the squares and C12-S-Mal by the triangles.
seen that there are considerable differences in the adsorption of the two surfactants. In the Henry range, the slopes of γ(c) are the same but the transition to the LE monolayer is different. For C12-S-Mal, the adsorption very rapidly increasessat a surface tension of 69 mN/m, the area/molecule is already lower than 50 Å2sand at the cmc, the molecular area is around 46 Å2. For C12-Mal, the adsorption is more gradual. When applying the obtained configurational surface pressure for the decyl tails, we can compare with the
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Figure 8. Adsorption isotherms for C12-Mal and C12-S-Mal. C12-S-Mal, represented by the solid line with squares, adsorbs much more readily at equal concentration than does C12-Mal, which is represented by the solid line.
dodecyl tails where the function is known. Here we find that there is a discrepancy between the C12-Mal, with the configurational surface pressure determined by Gruen et al., and the C10-Mal, with the experimentally deduced configurational surface pressure. This, however, can be explained by the use of the approximation, γ0 ) γhw + γha, which is valid for comparison between equal hydrocarbon chains, but similar to the hydrocarbon liquids, we have an apparent increase in the surface tension for the longer hydrocarbon chain. This means that if we compare decyl and dodecyl homologues we should expect to find a higher surface tension, or lower surface pressure, for the C12 than for the C10 chain at equal molecular areas. If we compare the two surfactant homologues at equal molecular areas, the contributions from the headgroup are assumed to be identical and thus we can compare the two surfactants with respect to the difference in macroscopic surface tensions. Hence, we find that the optimal solution for the difference in macroscopic surface tensions is a 1.7 mN/m higher surface tension for the dodecyl chain than for the decyl chain. For liquid dodecane, the surface tension is 1.8 mN/m higher than for liquid decane,17,18 which is comparable with the achieved difference in macroscopic surface tension. We can also estimate the increase in macroscopic surface tension upon replacement of a decyl with a dodecyl chain from the demixing effect of methyl and methylene groups in the monolayer on the basis of the molecular volumes of these segments, recognizing that the methyl has a volume twice the size of the methylene group.12 This expression is based on the partial free mixing of the chain segments, that is, there are “frozen” segments closest to the water phase,8
-
γCH2-CH3 kT
)
1 d∆SCH2-CH3 dn 1 n dn ) - ln (21) k dn da 2 2 + n da
(
)
where ∆S is the mixing entropy per chain and n is the number of methylene groups participating in the mixing with a single methyl group. For dn/da ) 1/(10 Å2) and n ) 4 for C10 and 6 for C12, a surface-pressure difference of 2.3 mN/m between the C12 and the C10 chain is obtained. Using a simple one-state hard-disk model to describe the Mal headgroup results in rather poor agreement with the measurements; to improve the model, we will assume that there are two states of adsorption for the headgroup (17) Handbook of Chemistry and Physics, 78th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1997. (18) Goebel, A.; Lunkenheimer, K. Langmuir 1997, 13, 369
Figure 9. Residual contributions to the surface pressure for C10-Mal (dotted lines) and C12-Mal (drawn lines) using a onestate hard-disk model of size 21 Å2 in conjunction with -γconf and adding 1.7 mN/m to the C12-Mal fitting function (lines with squares), and a two-state model of sizes 32 and 14 Å2 in conjunction with -γconf and adding 1.7 mN/m to the C12-Mal fitting function (plain lines). The two-state hard-disk model clearly yields a better description of the headgroup interactions, with less than 0.2 mN/m error from 63 to 51 Å2.
described by two hard disks. One state covers the hydrocarbon-water interface more efficiently but in turn generates greater repulsive contributions between the headgroups, whereas the second state would cover the hydrocarbon-water interface less efficiently but with less headgroup repulsion. Using eq 15, we can calculate the surface fractions of two hard-disk states with these properties. Since conf is known for the dodecyl chain, we can estimate the free energy of the headgroups for C12-Mal. The free energy in excess of our best-fit hard disk can then be compared with the improvement in the description of the headgroup using a two-state hard-disk model. The best-fit sizes for the two hard disks are 32 and 14 Å2. The residual surface pressure apart from the bestfit hard-disk one-state (21 Å2) and two-state (32 and 14 Å2) models and hydrocarbon configurational pressure for C10-Mal and for C12-Mal (where 1.7 mN/m has been added to eliminate the macroscopic contribution) are displayed in Figure 9. Thus, the two-state hard-disk model explains the longrange repulsion between the headgroups, which was unresolved by the one-state model. This indicates a slight polymeric contribution to the Mal headgroup. A large disk represents a headgroup adopting a specific orientation to donate hydrated water to the contact between water and hydrocarbon chains with the entropic gain in concurrent release of free water. The smaller hard disk then represents the headgroup directed away from the surface. In Figure 10, surface pressure as a function of molecular area for C10-Mal, C10-Glu and the 1:1 mixture is displayed using the hard-disk model and the experimentally deduced -γconf(C10). The surface-pressure increase for the Mal headgroup is well accounted for by a two-state hard-disk model using disk areas of 32 and 14 Å2; for C10-Glu, a hard-disk area of 11.8 Å2 yields a fair representation of the headgroup and for the 1:1 mixture hard disks of 22.9 and 11.3 Å2, of course, yields the correct behavior. We did not use the two-state model to describe the headgroup behavior for the Mal headgroup in the mixture, as this would complicate the model beyond the scope of this paper and would not necessarily produce a better prediction. Partial Interpenetration of the Headgroup into the Hydrocarbon Phase. Ethylene Oxides. With these predictions, it seems one can make estimates of the
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Figure 10. Surface pressure for C10-Mal (with the highest area/molecule), C10-Glu (with the lowest area/molecule), and the 1:1 mixture are represented by thick solid lines. The functions to fit the surface-pressure increase, represented by slim lines with symbols are, for C10-Mal, a two-state hard-disk model with hard-disk sizes of 32 and 14 Å2 in conjunction with -γconf(C10), for C10-Glu, a hard-disk model with hard disk 11.8 Å2 in conjunction with -γconf(C10), and for the 1:1 mixture, two hard disks of sizes 22.9 and 11.3 Å2 in conjunction with -γconf(C10).
adsorption of nearly any surfactant, but one must bear in mind that we have made a strict separation of the headgroup and the hydrocarbon layer. This is a good approximation for highly hydrophilic headgroups. For surfactants where the headgroup would have a preferential partitioning in the hydrocarbon film, we expect to see different behavior. Accurate measurements of equilibrium surface tension have been made on the decyl and dodecyl homologues of tetra(ethylene oxide),8 EO4, and penta(ethylene oxide), EO5. If we compare between these surfactants with respect to the difference in surface pressure between the C10-EO5 and C10-EO4 at equal molecular areas, we expect to get a measure of the effect of the lengthening of the ethylene-oxide chain by one segment with no contributions from the hydrocarbon phase. The following procedure was implemented to determine the effect of headgroup interpenetration; X and Y denote two different headgroups,
γC12-Y - γC12-X - (γC10-Y - γC10-X) ) γint
(22)
where γint is calculated at equal molecular areas for all components. For strictly separable contributions between headgroup and hydrocarbon phase in similarity to eq 8, γint ) 0. Accordingly the surface pressure difference between C12-EO5 and C12-EO4 at equal molecular areas is then expected to be exactly the same as that between C10-EO5 and C10-EO4. However, there is a difference in surface pressure between the pairs of C12- and C10-EO’s under these conditions, which is around 0.63 mN/m for an extended interval and increases rapidly at closer packing, see Figure 11. The sole contribution explaining the surfacepressure difference is at the hydrocarbon-water interface with respect to the net interaction difference between the longer and the shorter hydrocarbon chain and the longer and the shorter ethylene-oxide chain. These effects are very difficult to account for in our model, eq 8, since we assume that it is a liquidlike structureless hydrocarbon film of similar densities with totally separable contributions from the headgroup. The effect of the partial interpenetration is stronger for the shorter chain, and the effect on the surface tension probably will weaken the longer the headgroup chain is. Such effects have been
Figure 11. Surface pressure difference due to preferential interpenetration (γint) of the ethylene-oxide headgroup.
Figure 12. Surface pressure difference due to preferential interpenetration (γint) of the thiomaltoside and maltoside headgroup.
studied by means of neutron reflection techniques.10 It was found that the ethylene-oxide chains of four units or shorter tend to stretch to their full length, whereas headgroups of five units or longer on average do not extend to their full length, indicating that polymeric behavior of the shorter chains is weak. Maltosides and Thiomaltosides. For comparison with the results of C12-Mal and C10-Mal, we also studied the behavior of the homologue pair of C10-S-Mal and C12-S-Mal. Here the differences are of much greater proportions than for the ethylene-oxide-based surfactants. At equal molecular areas, the difference is at most close to 20 mN/m. The effect can in principle only be related to the difference in interactions between a decyl and a dodecyl hydrocarbon film and a sulfur or an oxygen atom in close proximity, noting that the contribution of lateral van der Waals attraction of sulfur does not contribute to the difference studied, as it is deducted when comparing with the same headgroup at equal molecular areas. We can make a similar comparison between the S-Mal pair and the Mal pair as for the ethylene-based surfactants. For the decyl pair, the difference in surface tension at equal molecular areas is rather small, around 6.5 mN/m at most, and diminishing toward the cmc. For the dodecyl pair, on the other hand, we find that the difference in surface tension at equal molecular areas increases to 19.5 mN/m at 49 Å2 and then diminishes toward the cmc. The difference in surface tension between this dodecyl and the decyl pair is presented in Figure 12. As previously stated, the Mal headgroup might have a few discrete states accessible for the headgroup that, depending on the local
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the thiomaltoside-maltoside pairs, the interpretation is not as straightforward. Probably the sulfur will intermingle with the hydrocarbon chains to a greater extent than the oxygen, but this also affects the headgroup very strongly, forcing it to adopt a different configuration in the dodecyl-thiomaltoside case. Conclusions
Figure 13. Surface pressure in the true LE range for C10-S-Mal, dotted line with squares, C12-S-Mal, solid line with squares, C10-Mal, dotted line, and C12-Mal, solid line.
conditions, will be prevalent in varying fractions. Measurements of the average headgroup configuration of C12-Mal in micelles reveal a slight tilt of the headgroup.19 Equally, surface-force measurements on C10-Mal and C10-Glu indicate less than full extension of the Mal headgroup.20 For C12-S-Mal, the headgroup will probably very quickly adopt the state that leads to less headgroup crowding and thus we see that C12-Mal has a significantly higher increase in surface pressure in the range from 65 to 49 Å2, where for C12-Mal, we expect to find a state covering the hydrocarbon-water interface efficiently and in turn generating rather high repulsive contributions. The surface pressure isotherms of C12-S-Mal, C10-S-Mal, C12-Mal, and C10-Mal in the true LE range are displayed in Figure 13. Notably, the substitution from oxygen to sulfur in the linkage between the headgroup and the hydrocarbon tail has severe effects on the headgroup configurations. The reason for the effect can only be found in the contact between the hydrocarbon chains and water. The sulfur atom linking the headgroup and the hydrocarbon chain will more preferably enter in the dodecyl film than the oxygen, thereby forcing the headgroup into a particular state away from the dodecyl hydrocarbon tail phase. The effects due to the preferential partial interpenetration of the headgroup clearly represent the nontriviality of the interface (formed upon surfactant adsorption) where hydrocarbon chains, water, and headgroups mix. In conclusion, considering the free energy contributions from the headgroup and the hydrocarbon film as separable for C12- and C10-Mal, C10-Glu, and the mixtures of C10-Mal and C10-Glu, then clearly we cannot completely separate the contributions for the ethylene-oxide-based surfactants, and in particular, not for the thiomaltoside surfactants, due to the partial interpenetration of the headgroup into the hydrocarbon film. Notably, also the interpenetration generates very different responses, namely for the ethylene-oxide headgroup which is partially miscible in the hydrocarbon film. This will generate a slightly larger surface-pressure increase for the decyl pair where greater interpenetration is found than for the dodecyl pair. For (19) Dupuy, C.; Auvray, X.; Petipas, C.; Rico-Lattes, I.; Lattes, A. Langmuir 1997, 13, 3. (20) Persson, C. M.; Kumpulainen A. J. Colloids Surf., A 2004, 233, 43
By applying the hard-disk model to surface-tension measurements, we can predict the surface fraction in mixtures of n-decyl-maltopyranoside and glucopyranoside. This enables us to study the aspects of the surface tension lowering apart from the headgroup interactions. This results in an estimate of the change of configurational free energy for the n-decyl-hydrocarbon chains, similar to the calculated results of Gruen et al. for n-dodecyl chains. The configurational pressure of the n-decyl-hydrocarbon chains furthermore enables us to calculate the apparent increase in macroscopic surface tension for longer hydrocarbon chains. We obtain a 1.7 mN/m decrease in surface pressure at equal surface densities for the dodecyl hydrocarbon phase over the decyl hydrocarbon phase. A two-state hard-disk model describes the behavior of the maltopyranoside headgroup in the LE regime. The larger disk is favored at larger molecular areas due to the better coverage of the hydrocarbon-water interface, whereas the smaller hard-disk prevails as interactions in the monolayer start increasing with decreasing molecular area. This model has a straightforward physical interpretation. Since the maltoside headgroup contains two glucose units, the glucose unit furthest away from the surface probably will orient in a manner to reduce the free energy cost of the hydrocarbon-water interface by donation of hydrated water with the concurrent release of free water to mix with the bulk. This headgroup state will simultaneously generate high repulsive interactions whereby it becomes less favorable with increasing adsorption. Hence, the headgroup will assume a different orientation with the second glucose unit directed away from the interface, which reduces repulsion. Analysis of surface tension data for pairs of decyl and dodecyl homologues revealed that there are contributions to the surface tension for nonionic surfactants that are due to the partial interpenetration of the headgroup into the hydrocarbon phase. For ethylene-oxide surfactants, the results indicate some degree of interpenetration. This can be explained by the partial miscibility of the ethylene oxide in the hydrocarbon phase, which is more pronounced for the shorter headgroup chain. For the thiomaltoside headgroup, the interpenetration effect was much stronger for the longer hydrocarbon chain. Here the interpenetration of sulfur probably forces the headgroup, with very low miscibility in the hydrocarbon phase, into adopting a different spatial orientation, which leads to lower headgroup interactions in comparison to the maltoside headgroup. Acknowledgment. A.J.K. acknowledges the financial support of VR (The Swedish Research Council). Supporting Information Available: More-extensive alternative derivation of eq 15. This material is available free of charge via the Internet at http://pubs.acs.org. LA048815Z
