9860
J. Phys. Chem. 1996, 100, 9860-9869
Three-Capacitor Model for Surface Potential of Insoluble Monolayers Jordan G. Petrov,*,† Epaminondas E. Polymeropoulos,‡ and Helmuth Mo1 hwald† Max-Planck Institute of Colloids and Interfaces, Rudower Chaussee 5, 12489 Berlin, Germany, and ASTA Medica AG, Weismu¨ llerstr. 45, 60314 Frankfurt, Germany ReceiVed: December 20, 1995; In Final Form: March 21, 1996X
Three three-capacitor model of Demchak and Fort (Demchak, R. J.; Fort, T., Jr. J. Colloid Interface Sci. 1974, 46, 191) that is widely applied to interpret surface potentials of monolayers at water-air interfaces postulates independent contributions of the hydrocarbon chains, polar head groups, and hydration water. We present an experimental verification of this a priori assumption for condensed monolayers of n-heptadecanol and 16-bromohexadecanol. These substances have different terminal CH3CH2 and BrCH2 groups and exhibit as monolayers ∆V potentials and vertical dipole moments that are opposite in sign. Demchak and Fort’s analysis of the head group’s conformation leads to controversial conclusions which question the basic assumptions of the three-capacitor model. Three-dimensional maps of the molecular electrostatic potential (MEP) and the molecular lipophilic potential (MLP) show that the ω-dipoles do not influence the electrostatic potential and hydrophilicity of the head groups of single n-heptadecanol and 16-bromohexadecanol molecules. The models also show that molecular dipole moments are not parallel to the hydrocarbon chains and may, therefore, cause collective (inductive and orientational) polarization leading to different dipole moments and conformations of the head groups of the condensed monolayers under study. These possibilities were examined by means of the interfacial polarity probe 4-heptadecyl-7-hydroxycoumarin embedded in heptadecanol and 16-bromohexadecanol monolayers. Practically the same values of pKi were obtained (pKi ) 7.8 ( 0.1 and 7.9 ( 0.1) in the two matrices, thus indicating the same dipole moment and conformation of the OH-head group and, thus, negligible head group polarization. By relating pKi to the interfacial dielectric constant, values of i ) 65 ( 5 for heptadecanol and 60 ( 5 for 16-bromohexadecanol were obtained, thus showing that ω-dipoles have an almost negligible effect on the dielectric constant of the monolayer-water boundary. The above values for i are in good agreement with other spectroscopic data for monolayers or micelles of neutral surfactants having mono- or polyhydroxy groups.
Introduction Monolayers of amphiphilic substances spread or adsorbed at interfaces exhibit high surface potentials due to anisotropic arrangement of their polar and dipolar groups. Such electrostatic behaviors play an important role for their molecular and supramolecular structure, but the contribution of the particular atomic groups is still far from understood. Analysis of surface potentials of monolayers at the water-air interface most often makes use of the three-capacitor model of Demchak and Fort.1 Following the idea of Davis and Rideal,2 this model considers the change in interfacial potential due to the presence of the monolayer as a sum of three independent terms standing for the contributions of the reoriented water dipoles in the vicinity of the hydrophilic head groups, for the head group region itself, and for the hydrophobic tails oriented toward air. Independent dipole moments and effective dielectric constants are ascribed to these regions. The contribution of the double layer in the aqueous phase is additionally taken into account when the monolayer head groups are charged. In the studies of Zisman and co-workers,3,4 as well as in later studies,5,6 no distinction is made between the terms attributed to the head groups and the subphase, but the two remaining components are also considered to be independent. This assumption, which is basic for both models, is supported by * Corresponding author. On leave of absence from the Institute of Biophysics, Bulgarian Academy of Sciences, Acad. G. Gonchev Str., Block 21, 1113 Sofia, Bulgaria. † Max-Planck Institute of Colloids and Interfaces. ‡ ASTA Medica AG. X Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(95)03794-4 CCC: $12.00
the successful application of Demchak and Fort’s approach to predict the conformation of the polar head groups of a variety of monolayers1,7,8 and to explain the difference in the dipole moments of terphenyl and aliphatic monolayers with the same head groups.1 The same approach is utilized in modeling surface potential-area isotherms9 and is further developed to describe the surface potentials of mixed monolayers.10 When the three-capacitor model is applied to ∆V potentials of monolayers of normal and ω-halogenated fatty acids or amines,3-8 it is assumed that the dipole moments of the head groups µCOOH and µNH2, their degree of ionization, the dielectric constant of the head groups region 2, and the contribution of the hydration water µ1/1 are the same for a given couple of normal and ω-substituted substances. In other words, it is postulated that the acid-base equilibrium and polarity at the monolayer-water boundary is independent of the monolayer-air dipole moment. However, as Demchak and Fort pointed out,1 the values of the local effective dielectric constants determined by their method “incorporate all factors which cause the dipole moment of the monolayer terminal groups to deviate from the values they should have in bulk. These effects include polarization of adjacent film dipoles and substrate molecules, interactions brought about by chain-chain forces, thermal motion, etc. ...Into µ1/1 is incorporated both the polarization and reorientation of the substrate...assumed to be constant for all un-ionized, closepacked insoluble monolayer films.” In some previous investigations11,12 we fluorometrically determined the dissociation constant of the weak amphiphilic acid 4-heptadecyl-7-hydroxycoumarin (HHC) embedded in a neutral monolayer of methyl arachidate at the air-water © 1996 American Chemical Society
Surface Potential of Insoluble Monolayers interface. An interfacial pKi value was found that was bigger than the bulk pKb of a soluble homologue of the dye in aqueous solution. This pK shift was ascribed to the lower polarity of the head group region, where the chromophore of the amphiphilic dye was presumably located.11-15 Subsequent studies16 have shown that the pKi value at the air-water interface can substantially differ from the pKi of the same dye in the same matrix monolayer but transferred by the Langmuir-Blodgett technique at the solid-water interface. Moreover, positive or negative shifts in pKi were observed depending on whether an anionic or a cationic monolayer was deposited on the hydrophilic glass substrate underneath the dyecontaining neutral methyl arachidate matrix. These shifts were interpreted as resulting from the oppositely oriented dipoles of the ion pairs formed between the surface charges of glass and those of the head groups of the anionic or cationic monolayer. Such an interpretation was inferred by the earlier observation that a monolayer of ω-trifluorostearic acid deposited on the solid substrate underneath the coumarin dye caused opposite pKi shifts depending on the orientation of the ω-dipoles of the ω-trifluorostearic chains.17 All of the above observations imply that remote dipoles have an effect on the acid-base equilibrium and/or polarity at the monolayer-water boundary located at a distance of at least two molecular lengths (5.7 nm) away from them. Although registered at the solid-liquid interface, they question the independence of the surface potential components assumed by the three- or two-capacitor models for monolayers at the airwater phase boundary. In this paper, we examine the existence of these effects, and thus the postulated independence, directly at the air-water interface. Surface potentials, ∆V, of C17H35OH and 16-BrC16H32OH monolayers and ω-dipoles that differ both in magnitude and sign18,19 and pKi of 4-heptadecyl-7hydroxycoumarin embedded in them are studied. The neutral head groups exclude any double layer effect in the aqueous subphase and enable titration of the amphiphilic dye at pHindependent interfacial conditions. The electrically indifferent outer phase (air) rules out the influence of other bulk dipoles or charges. Thus, if the remote ω-dipoles at the monolayerair boundary were to polarize the head groups, affect their conformation and dipole moment, or cause different orientation of hydration water, then different local permittivities and different shifts of pKi should be observed. The same result would be obtained if the ω-dipoles directly change the protonation equilibrium of the strongly polarizable dye chromophore located at the monolayer-water boundary. In both cases a violation of the additivity of the surface potential components, assumed in the three- and two-capacitor models, would be registered. In order to examine the significance of the above effects at the molecular level, three-dimensional computer models of both alcohols were constructed and their dipole moments were calculated. Maps of the local molecular electrostatic potential (MEP) and molecular lipophilic potential (MLP) were obtained that visualize the influence of the ω-dipoles on the local potential distribution and hydrophilicity of the hydroxy head groups. Materials and Methods 4-Heptadecyl-7-hydroxycoumarin (HHC) was purchased from Molecular Probes, USA, and C17H35OH from Merck. 16BrC16H32OH was synthesized by Bayer AG. Monolayers were spread as 1 × 10-3 M chloroform onto 1 × 10-2 M aqueous subsolutions of NaH2PO4 and Na2HPO4 prepared with water from a Milli-Q system. The pH was adjusted with HCl or NaOH. All inorganic substances were products of Merck of analytical grade of purity.
J. Phys. Chem., Vol. 100, No. 23, 1996 9861
Figure 1. Calculational (Y, X) and physical (Y′, X′) coordinate systems applied in the molecular modeling. The gauche and trans conformations of both 16-BrC16H32OH and C17H35OH molecules are plotted atop of each other.
Surface pressure-area and surface potential-area isotherms of the C17H35OH and 16-BrC16H32OH monolayers were recorded in a rectangular Teflon Langmuir trough. A strip of filter paper 2 cm wide served as a wettable Wilhelmy plate to measure surface pressure, and the vibrating plate method was applied for determining ∆V. Accuracy of 0.2 mN/m and 5 mV was characteristic for the two measurements. Subsolution temperature was kept constant within (0.5 °C by a thermostating plate underneath the trough. The experimental setup for recording fluorescence of monolayers has been previously described.11,12 A small dye-to-matrix molecular ratio of 1:400 was used to avoid dye aggregation. As shown earlier this value satisfies the linear dependence of fluorescence intensity on dye concentration in the monolayer.11 This mixture was spread onto the aqueous subsolution, and after following 2 minutes for evaporation of chloroform, the monolayer was compressed to the surface pressure at which the fluorescence was registered. The intensity at 450 nm, corresponding to maximum emission was measured, and its value were reduced by the “blank” intensity of a pure water surface. The dye was exited at 366 nm, where only its anionic form absorbs. Thus, the fluorescence measured was due to the dye anion only. The molecular geometry of the two alcohols was optimized in Vacuo by means of the MNDO20 semiempirical method. We chose this method because it correcly predicts a deeper energy minimum for the trans conformation of ethanol in agreement with ab initio quantum mechanical calculations and microwave spectroscopic data for ethanol vapor.21,22 Application of the other widely used AM1 method23 gives strong energetic preference to the gauche conformation of ethanol, although the optimized angles and interatomic distances are closer to the experimental values. The total dipole moments of heptadecanol and 16-bromohexadecanol as well as their µx, µy, and µz components were calculated assuming all-trans-configuration of their aliphatic chains. For this calculation the MNDO method takes into account not only the point charges but also hybridization effects which can sometimes account for up to 50% of the dipole moment value. The dipole moment components depend on the coordinate system, and for this reason great care should be taken when assigning the position of its origin. We placed the origin at a distance of 0.2 nm from the O-atom, with the positive X-axis directed along the H-H bond of the trans OH-group (Figure 1). A shift by another 0.2 nm does not significantly change
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Figure 2. Maps of the local electrostatic potential (MEP) of the matrix molecules. From left to right: gauche-16-Br-C16H32OH, gauche-C17H35OH, trans-16-Br-C16H32OH, and trans-C17H35OH. The vertical bar in the head groups region scales 0.1 nm.
the results (µy changes by less than 1%). The same coordinate system was used for the gauche conformation. Such an origin might slightly differ from the one defining the measured normal dipole moment of the monolayer µ⊥, because of the unspecified extension of the hydration water region. Since the component of the dipole moment along the hydrocarbon chain can be related to the experimental value of µ⊥ we rotated the coordinate system by -56°. In this way the positive Y axis is oriented along the hydrocarbon chain and points to the ω-groups. MEP and MLP display the local electrostatic potential and lipophilicity (pseudo) potential on the solvent accessible surfaces of molecules.24 MEP is determined from the molecular structure and the partial atomic charges. Its local values are defined by the distance function N q i MEP ) ∑ i)1 di
(1)
where qi is the partial atomic charge, di is the distance of the atom i from the given point on the surface, and N is the number of atoms.25 MLP was determined from the atomic lipophilicity contributions26,27 on the basis of the following function:28 N
MLP )
fi‚g(di) ∑ i)1 N
(2)
g(di) ∑ i)1 Here, fi is the partial liophilicity of the atom i, and the distance dependence is given by the Fermi-type function
g(di) )
e-a,b + 1 ea(di-b) + 1
(3)
Although MLP itself has no rigorous physical meaning, it has been demonstrated27 that a reasonable choice of the free parameters (a ) 1.5 and b ) 4.0) can be used to map weighted increment values fi for Crippen’s water/octanol partition coefficient data26,27 onto molecular surfaces. This approach makes a quantitative comparison of lipophilicity possible. Results and Discussion Molecular Models and Dipole Moments. The variation of the free enthalpy of single heptadecanol and 16-bromohexadecanol molecules in Vacuo as a function of dihedral angle of rotation of the O-H bond shows that the gauche and trans conformations having dihedral angles of 70° and 180°, respectively, are most energetically favorable. The second gauce conformation with a dihedral angle of 292° is energetically equivalent to the first one. The minimum of the trans conformation is slightly deeper for both heptadecanol (by 0.54 kJ/mol) and 16-bromohexadecanol (by 0.46 kJ/mol). The barriers of the trans-to-gauche transitions are close to each othe, 1.08 and 1.09 kT for heptadecanol and 16-bromohexadecanol, respectively. The slight energetical preference to the trans conformation is in accordance with quantum mechanical calculations and microwave spectroscopic data for ethanol vapors21,22 but is opposite to the conclusion of Demchak and Fort about n-alkanol monolayers extracted from ∆V data by means of the three-capacitor model.1 However, the preferential conformation of single molecules in Vacuo may differ from the one in a condensed monolayer due to collective polarization or because of the interaction of the head groups with water substrate. Figure 2 presents three-dimensional maps of the local
Surface Potential of Insoluble Monolayers
J. Phys. Chem., Vol. 100, No. 23, 1996 9863
Figure 3. Maps of the local lipophilicity (MLP) of gauche-16-BrC16H32OH, gauche-C17H35OH, trans-16-BrC16H32OH, and trans-C17H35OH (from left to right). The vertical bar in the head groups region scales 0.1 nm.
TABLE 1: Dipole Moments and Dipole Moment Components of the Two Energetically Most Favorable Gauche and Trans Conformations of C17H35OH and 16-BrC16H32OH Molecules Evaluated from Three-Dimensional Molecular Models conformation
µtot (D)
µx (D)
µy (D)
µz (D)
C17H35OH gauche C17H35OH trans 16-BrC16H33OH gauche 16-BrC16H33OH trans
1.51 1.36 1.58 1.74
-0.03 -1.36 0.62 -0.70
1.03 0.01 -0.62 -1.60
1.10 0.06 1.31 0.00
electrostatic potential of the gauche and trans conformations of C17H35OH and 16-brC16H32OH. The numbers at the color code are an indication of the range of the potential change covered by the scale. The MEP’s show that in spite of the different CH3CH2 and BrCH2 terminals the head group regions of the same conformers have almost identical potential distributions. Therefore, the dipole moments of the gauche-hydrophilic heads of C17H35OH and 16-brC16H32OH single molecules or those of the trans-couple are independent of the dipole moments of the CH3-CH2 and Br-CH2 bonds as assumed by the threecapacitor model. However, different dipole moments of the head group regions (and therefore of the region of hydration water) can be expected if opposite gauche and trans conformations preferentially exist in the two monolayers. Figure 3 demonstrates that the lipophilicity of the head group regions of heptadecanol and 16-bromohexadecanol single molecules having the same conformation is independent of the nature of the ω-terminal group of the hydrophobic chain. The close resemblance in the distribution of the lipophilic potentials of the head groups should conform with the similar structures of hydration water in their vicinity, a result which also agrees with Demchak and Fort’s model. Table 1 shows that both C17H35OH conformations have positive µy-components while both 16-BrC16H32OH conformations exhibit negative µy-values. The absolute values of µy of
the gauche and trans conformers differ by about 1 D for each of the two substances. This large difference in the polarity of the head groups strongly suggests that different conformations can be distinguished by interfacial polarity probes. The negligible value of µy of the trans-C17H35OH molecule infers that not this but the gauche conformation prevails in the heptadecanol monolayer exhibiting a significant surface dipole moment (see the next section). The µx- or the µz-components have large values, pointing out that the total dipole moments are not parallel to the chains. This orientation may result in a collective polarization of the adjacent molecules and hydration water, an effect which should be specific for the monolayers under study. Such an effect may refute the conclusions resulting from the models of single molecules and would mean violation of the additivity of the surface potential components assumed by the three-capacitor model. It is usually assumed that the methylene groups do not contribute to the dipole moment of the hydrocarbon chain.1-10 The color variation in the upper and lower parts of the MEPs in Figure 2 show that this is not exactly the case for the substances studied here. The same effect can be seen in Figure 3; the local lipophilicity changes gradually along the molecule so that the methylene groups adjacent to the hydroxyls are more hydrophilic than the others. Surface Pressure-, Surface Potential-, and Dipole Moment-Area Isotherms. Figure 4 shows the surface pressurearea, Π/F, and surface potential-area, ∆V/F, isotherms of monolayers of C17H35OH (curves 1 and 1′) and 16-BrC16H32OH (curves 2 and 2′) spread at 18 °C on 1 × 10-2 M phosphate subsolution with pH 7.5. The heptadecyl alcohol monolayer is stable up to 56 mN/m with a transition between a liquidcondensed and a solid-condensed state at 13 mN/m and 0.203 nm2 (13.2 mN/m and 0.205 nm2 can be read from Figure 14 of ref 29a for the octadecanol monolayer on water at 18.1 °C).
9864 J. Phys. Chem., Vol. 100, No. 23, 1996
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∆V )
Figure 4. Surface pressure-area π/F and surface potential-area ∆V/F isotherms of monolayers of heptadecanol (curves 1, 1′) and 16bromohexadecanol (curves 2, 2′).
Figure 5. Vertical components of monolayer dipole moment, µ⊥ versus area per molecule, F, for heptadecanol (1) and 16-bromohexadecanol (2). The arrows show the molecular areas at 9 mN/m at which the amphiphilic dye was titrated.
The monolayer of 16-bromohexadecanol is much less stable, collapsing from a liquid-condensed state at 19 mN/m. The surface potential of the heptadecanol monolayer is always positive and reaches a value of +465 mV at a collapse area of 0.185 nm2/molecule. The heterogeneity observed for many substances at large areas per molecule is clearly seen between 0.50 nm2 and 0.30 nm2, where curve 1′ shows irregular increase or decrease in ∆V. The 16-bromohexadecanol monolayer exhibits a smooth variation of surface potential at compression, ∆V becoming increasingly negative and reaching -445 mV at a collapse area per molecule of 0.194 nm2/molecule. The change of the slope at about 0.360 nm2 (where surface pressure starts to increase above zero) indicates abrupt molecular reorientation in the monolayer or hydration water.9 Figure 5 represents the variation under compression of the vertical component µ⊥ of the dipole moment of the two monolayers for areas per molecule F between 0.320 and 0.185 nm2. µ⊥ is calculaed from the Helmholz formula
µ⊥ 0F
(4)
where 0 is the permittivity of vacuum and is the mean permittivity of the monolayer assumed to be one. Both µ⊥/F isotherms do not reach limiting values under compression as is usually observed.1,4 At 0.227 nm2 they pass through extrema that are practically equal but opposite in sign (0.250 D and -0.255 D, respectively) and at 0.200 nm2 reach values of 0.235 D and -0.235 D. A similar decrease of µ⊥ from 0.250 D at 0.222 nm2 to 0.240 D at 0.200 nm2 was registered for eicosanol monolayers by Harkins.29b A nonmonotonous µ⊥/F trend was also observed for octadecyl nitrile monolayers in ref 1. The observed trend of the µ⊥/F isotherms may indicate that both the tilt angle and the head group conformation of the monolayer molecules change simultaneously under compression. For this to be the case the OH-conformation should change in a way leading to a strong decrease in the absolute value of molecular dipole moment. Neglecting collective polarization and the usually small contribution of hydration water, one can conclude from Table 1 that this requirement is fulfilled for a gauche-to-trans transition to C17H35OH and a trans-to-gauche transition of 16-BrC16H32OH monolayers. Thus, at 0.200 nm2/ molecule the conformation of the OH groups of the two monolayers should be different in contrast to the assumptions of the three-capacitor model. The nonmonotonous variation of µ⊥ under compression may arise from the fact that molecular dipole moments are not parallel to the hydrocarbon chains (see Table 1). In this case, the vertical orientation of the molecular dipole moment will not coincide with vertical molecular orientation, and µ⊥ should then reach its extremal value at larger areas per molecule. This possibility does not require changes in the head group conformation under compression and does not contradict the threecapacitor model. Conformation of the Monolayer Head Groups. Demchak and Fort proposed a procedure to predict the conformation of the monolayer head groups from surface potential data. Following this procedure we compared the experimental values of the vertical dipole moment components µ⊥ at 0.200 nm2/ molecule with the values of µ⊥,calc calculated from their main equation based on the three-capacitor model:
µ⊥,calc )
µ1 µ2 µ3 + + 1 2 3
(5)
For µ2 we substituted by the vertical dipole moment components of the gauche, trans, or free rotating conformations of the OH groups and for µ3 by the normal components of the dipole moments of the ω-groups. The values of µ2 (OH-gauche) ) 1.00 D, µ2 (OH-trans) ) -0.63 D, µ2 (OH-free) ) 0.18 D, µ3 (CH3) ) 0.33 D, and µ3 (BrCH2) ) -1.63 D were taken from refs 1 and 7, and the values of µ1/1 ) -0.065 D, 2 ) 6.4, and 3 ) 2.8, obtained for ω-halogenated fatty acids and amines,7,8 were first utilized because these systems are similar to ours. It was found that only the value of µ⊥,calc (C17H35OH-gauche) is close to the experimental value of µ⊥, while the estimates for the trans and free rotating conformers considerably differ from it. This confirms the conclusions of Alexander31 and of Demchak and Fort1 that the gauche conformation preferentially exists in condensed n-alkanol monolayers. However, all calculated values for 16-bromohexadecanol significantly deviate from the experimental result.
Surface Potential of Insoluble Monolayers The same calculations were performed with µ1/1 ) 0.040 D, 2 ) 7.6, and 3 ) 5.3 determined by Demchak and Fort1 for monolayers of terphenyl derivatives and octadecyl nitrile and successfully applied to predict the head groups conformation of six classes of aliphatic substances. The use of this set of values confirmed the gauche conformation of heptadecanol and showed predominance of the free rotating conformation in the 16-bromohexadecanol monolayer. Thus, at the same area per molecule, the gauche OH-conformation seems to be characteristic for the heptadecanol monolayer but the free rotating conformation should be predominant in the monolayer of 16bromohexadecanol. This conclusion contradicts the main assumption of the three-capacitor model that the head groups’ conformation and their dipole moment are independent of the ω-groups at the monolayer-air boundary. The above controversy can be formally removed if the value of 3 ) 4.2, estimated from our experimental data in the same way as in refs 1 and 7, is used together with the same values for the other parameters in eq 5. In this way we find with µ1/1 ) -0.065 D, 2 ) 6.4, 3 ) 4.2 that all six estimates of µ⊥,calc disagree with the experimental data for µ⊥. In the second case (µ1/1 ) 0.040 D, 2 ) 7.6, 3 ) 4.2) a good coincidence between calculated and experimental values is found for the gauche conformations of both heptadecanol and 16-bromohexadecanol. All other calculated values are far away from the experimental data. This agreement becomes quantitative if the value of µ1/1 is reduced to 0.025 D, which is consistent with the way Demchak and Fort determined it. It is worth mentioning that the new set of parameters, µ1/1 ) 0.025 D, 2 ) 7.6, and 3 ) 4.2, yields the same conclusions about the head groups’ conformation in all six classes of aliphatic compounds analyzed in ref 1 but also removes the controversy for the monolayers studied here. Our analysis shows that a strict application of Demchak and Fort’s model predicts different conformations for the same head group under the same experimental conditionsstemperature, monolayer density, aqueous subphase. The conclusions are very sensitive to the values of the parameters used; different conformations of the same head group can be predicted by only a small change in the local permittivities of the monolayer. For this reason the reliability of this approach should not be overestimated, and the problem of an independent determination of the head group conformation should be addressed either by spectroscopic methods or in studies of ice nucleation at interfaces.32 Fluorometric Titration of the Coumarin Dye in Heptadecanol and 16-Bromohexadecanol Monolayers. The π/F isotherms in Figure 4 show that at 0.227 nm2/molecule, where µ⊥ of the two monolayers differ maximally, the surface pressure of C17H35OH is very low and the two monolayers are in a different state. For this reason we determined pKi of HHC at a constant surface pressure of 9 mN/m and different areas per molecule (see the arrows in Figure 5). Under these conditions both monolayers are in the same liquid condensed state and µ⊥ ) +0.240 D for heptadecanol and -0.255 D for 16-bromohexadecanol, respectively. Figure 6 shows the pH-dependence of the fluorescence intensity of 4-heptadecyl-7-hydroxycoumarin at 450 nm corresponding to maximum emission of the dye from both matrices. (A study of the fluorescence and excitation spectra of HHC in the same monolayers will be published elsewhere.32) The fluorescence from the 16-BrC16H32OH matrix is systematically weaker than that from the C17H35OH one. This difference seems to be due to the smaller chromophore density in the 16BrC16H32OH monolayer because it can be practically removed
J. Phys. Chem., Vol. 100, No. 23, 1996 9865
Figure 6. Fluorescence intensity of 4-heptadecyl-7-hydroxycoumarin versus pH of the subsolution. Squares correspond to C17H35OH and triangles to 16-BrC16H32OH matrix.
Figure 7. Logarithmic plot of the pH-dependencies of the dissociation constant of the dye according to eq 6. Squares correspond to the C17H35OH and triangles to the 16-BrC16H32OH matrix.
when dividing the fluorescence intensity by the density of the matrix Γ ) 1/F. The degree of dissociation of the dye chromophore was evaluated from the ratio I/Imas of the fluorescence intensity I at a given pH and the plateau value Imax achieved in the strongly alkaline region.11-17 Figure 7 shows the plot of lg (R/(1 - R)) versus pH, which should be linear for a monobasic acid such as HHC:
lg (R/(1 - R)) ) pH - pKi
(6)
The values of pKi determined at lg (R/(1 - R)) ) 0 are pKi ) 7.8 ( 0.1 for heptadecanol and 7.9 ( 0.1 for 16-bromohexadecanol, respectively. The first value agrees with pKi ) 7.75 obtained previously11 for eicosanol monolayers at 30 mN/m and 0.193 nm2 per matrix molecule. Titration of HHC in heptadecanol under the same condition yields pKi ) 7.7, thus showing that pKi is practically independent of the matrix monolayer density when the latter changes between 0.193 and 0.204 nm2. The coincidence of the interfacial pKi values obtained for the normal and ω-halogenated alcanol monolayers means that the acid-base equilibrium of the hydrophilic dye chromophore, located in the head group region, is unaffected by the difference in the ω-dipoles of the monolayer matrices. It also points out that the hydroxy groups of heptadecanol and 16-bromohexadecanol monolayers have the same conformation and dipole
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TABLE 2: Comparison of the Values of the Interfacial Dielectric Constant Determined from pKi of 4-Heptadecyl-7-hydroxycoumarin Applied as Interfacial Polarity Probe in Neutral Spread and Deposited Monolayers and Micellesa system
matrix substance
HHC in spread monolayers
eicosanol methyl arachidate
HHC in spread monolayers
heptadecanol 16-bromohexadecanol
HHC in monolayers deposited on silanated glass
methyl stearate methyl arachidate
HHC in micelles
Triton X 100 Triton X 100 C12E8 DM DM/C12E8 DM/DC ≈ 1:1 Triton X 100
HAC in micelles
titration parameter
interfacial dielectric constant
ref
I450nm I450nm I450nm I450nm I450nm I450nm I450nm A375nm A375nm A375nm A375nm A375nm I450nm
65 45 65 60 39 34 32 35 35 60 60-35 57 32
11 11, 12 this work this work 13 16 14 14 35a 35a 35a 35a 14
a Abbreviations: Triton X 100 ) poly(oxyethylene) isooctylphenyl ether; C E ) n-dodecyl octaoxyethylene glycol monoether; DM ) n-dodecyl 12 8 β-D-maltoside; DC ) n-dodecyl β-D-cellobioside; DM/C12E8 ) mixtures of different molar ratios; DM/DC ≈ 1:1 almost equimolar mixture of DM and DC; HAC ) 4-heptadecyl-7-aminocoumarin.
moments; i.e., they are also independent on the different monolayer-air dipole moments. This result indicates that the nonmonotonous trend of the µ⊥/F isotherms obtained here does not result from conformational changes in the monolayer head groups opposing the decrease in molecular tilt angle under compression. It most probably reflects the different orientation of molecular dipole moments and of the hydrocarbon chains illustrated by Table 1. This difference causes a maximal vertical dipole moment component as a nonvertical orientation of the hydrocarbon chains. Dielectric Permittivity at the Monolayer-Water Boundary and Location of the Dye Chromophore. Both values of pKi obtained here are shifted by 0.2 and 0.3 units from the bulk pKb ) 7.6 determined by Chen33 for the soluble homologue of the same dye, 4-methyl-7-hydroxycoumarin (MHC), dissolved in the same phosphate buffer used in the present investigation. This literature value of pKb is most appropriate for comparison with our data because of the effect35b of the composition of the aqueous phase on pK. Furthermore, this value was confirmed by three independent titrations registering the absorption of the anionic form and the fluorescence of the neutral and anionic forms excited at different wavelengths. We ascribed these shifts to lower interfacial dielectric constant and applied the approach of Fernandez and Fromherz14 to determine i (for details see refs 14 and 15). It assumes that the mean solvent characteristics of the interfacial region can be mimicked by mixtures of dioxane and water so that pKi of HHC at a neutral interface (uncharged monolayer or a micelle) can be related to pKbd-w. The dissociation constant of the soluble dye in water, pKbw, served as a reference for both the interfacial titration and the one in dioxane-water mixtures. Thus, the values of (pKi - pKbw), calculated with pKbw ) 7.6, were used to interpolate the dependence (pKbd-w - pKbw) versus from ref 14 that yielded i ) 65 ( 5 for heptadecanol and 60 ( 5 for 16-bromohexadecanol, respectively. Although different from the bulk dielectric constant of water, the two interfacial values practically coincide with each other; i.e., proves to be independent of the ω-dipole moments of the monolayers under study. Table 2 compares our values for i with other data obtained from pKi of HHC for different neutral monolayers or micelles11-15,34,35a. It is interesting to note that i for eicosanol, heptadecanol, 16-bromohexadecanol, n-dodecyl β-D-maltoside (DM), and n-dodecyl β-D-cellobioside (DC), i.e., for monolayers and micelles with hydroxy head groups, lie in a narrow range between 57 and 65. Lower interfacial dielectric constants (32-
45) were obtained for the relatively less hydrophilic ether and ester head groups. This grouping of the results demonstrates how sensitive the dye pKi is toward differences in the neutral head groups and/or hydration water. The same conclusion follows from the gradual transition of i in mixed DM/C12E8 micelles from 1 ) 60, characteristic for the sugar head groups of DM, to i ) 35 that is typical for the ethoxy head groups of C12E8 (cf. Figure 7, ref 35a). However, all values of i, shown in Table 2, significantly exceed the values of 2 ) 7.6, 6.4, 4.2, 1.8, 1.6, estimated by Demchak and Fort’s procedure when applied to different spread or adsorbed monolayers.36 This difference raises the question: which local dielectric constant is determined spectroscopically? The one for the head group region, 2, the one for the hydration water, 1, or an average of the two? The discrepancy between the two sets of values may be due to the location of OH group of the HHC-chromophore in the monolayer. Molecular models show that the effective chromophore cross-section is significantly bigger than the one of the dye hydrocarbon chain so that the chromophore might squeeze (partially or entirely) out of the head groups region toward water when the matrix monolayer is compressed. The lipophilicity maps of the dye and matrix molecules (Figure 8) infer a thermodynamic reason that should oppose such an immersion. Because the chromophore is considerably more lipophilic than the OH groups of the matrix it will possess better “floatability” and could elevate the adjacent alcohol molecules above their mean position in the monolayer. This speculative picture is inferred by the MLP models but should be rigorously examined by means of molecular dynamics simulations. An estimate of the extreme situation corresponding to a chromophore that is entirely submerged in the aqueous phase locates the acidic OH group of the dye at a distance of about 0.5 nm underneath the head groups of the matrix monolayer. The models in Figure 8 illustrate a probably more realistic picture in which the immersion depth is approximately 0.2 nm. However, because of the thermal motion, any specific location of the chromophore should only be regarded as a statistical average in the vertical direction. X-ray reflectivity investigations37 pointed out that such an “uncertainty” in the position of the head groups of phospholipid monolayers in the liquid condensed state has an amplitude of about 0.3 nm. Similar “smeared out” monolayer-water boundaries were also found by molecular dynamics simulations of monolayers of insoluble fatty acids.38,39
Surface Potential of Insoluble Monolayers
J. Phys. Chem., Vol. 100, No. 23, 1996 9867
Figure 8. Lipophilicity-hydrophilicty model of a condensed monolayer of C17H35OH containing 4-heptadecyl-7-hydroxycoumarin. Left: a frontal view. Right: a side view. The vertical bar in the head groups region scales 0.1 nm.
In spite of the inexact knowledge of the location of the chromophore, the result of the fluorometric titration shows that the dielectric constant of hydration water, 3, is independent of the ω-dipole moments of the monolayer substances. This, plus the fact that heptadecanol and 16-bromohexadecanol monolayers have the same OH-group conformations, imply that the permittivity of the head groups, 2, is also independent of the polarity at the monolayer-air boundary since different values of 2 should yield different values of 3. Relation to Other Investigations and Validity Range of Our Results. It is often argued that the strength of the electrostatic field outside the ω-dipoles is zero, so that they cannot polarize the head groups. This conclusion could follow from the expression40 for the potential created by an infinite plane of point dipoles with dipole moments µ3 and surface density Γ ) 1/F in a medium with constant permittivity :
∆V )
µ3 2F
(7)
This expression, showing that ∆V is independent of the distance from the infinite plane, may be valid within the region of the hydrocarbon chains. However, in the head group and hydration water regions, where the local dielectric constant increases from 2 to 78 (bulk hydrocarbon and water values), the field strength should be non-zero with a magnitude and a sign depending on the ω-dipoles at the monolayer-air boundary. The existence of a variable dipole field in the interfacial region of a neutral biomembrane has been theoretically elaborated, and it has been shown that it could be responsible for its specific permittivity and binding affinity toward hydrophobic anions and cations.41 An experimental result similar to ours was obtained by Bernett and Zisman,3 who investigated monolayers of partially fluorinated fatty acids. They found that the values of the monolayerair dipole moment, µ3, “are nearly constant at each pH regardless of the length of fluorocarbon chain segment or hydrocarbon segment” and concluded that “any contributions to this dipole moment arising from any effect due to the polarization of water dipoles must be minor.” Our results show a negligible effect
in the opposite direction, namely, that different values of µ3 do not cause a significant difference in µ1/1, µ2, and 2 of the monolayers. Some literature data show that the surface potential of condensed monolayers increases with chain length at constant area per molecule. This dependence could be due to the mutual polarization of the molecules in the monolayer, which should be proportional to their length. Kuchhal, Katti, and Biswas42 observed such a linear elevation of ∆V for monolayers of C16, C18, C20, and C22 alcohols at three different temperatures. A linear variation of the contact potential with chain length was also registered by Evans and Ulman43 for C6 to C22 alkyl-thiol monolayers adsorbed on gold. Harkins and Fisher44 found a nonlinear increase in ∆V for undissociated fatty acid monolayers with chain lengths from C12 to C18 and a higher potential for the C16 alcohol monolayer than the C14 one. Hu¨hnerfuss45 reported a similar nonlinear increase in ∆V for methyl esters of C14, C16, and C22 fatty acids. On the other hand, Adam, Danielli, and Harding46 have found no difference in ∆V for monolayers of C16 and C18 alcohols. These results imply that the conclusion we have drawn from our work, namely, that the influence of the ω-dipoles at the monolayer-air boundary on the head groups polarity is negligible, may be rather specific. The different trend of the ∆V dependence on chain length observed in refs 42-45 could indicate that the carboxyl and methyl ester head groups of fatty acid and ester monolayers become polarized, whereas the OH groups of n-alkanol monolayers do not. Table 3 qualitatively supports this explanation. It compares the average polarizabilities of some head groups which were estimated from the linear plots of the average molecular polarizability47 versus hydrocarbon chain length of normal alkanes and their derivatives in the gaseous phase. It shows that the polarizability of -COOH is twice and that of -COOCH3 three times as big as the one of the OH group. On the other hand, the OH group in the condensed monolayers studied here may be able to rotate freely because its crosssection is smaller than the one of the hydrocarbon chain. This possibility and the same head group conformation found
9868 J. Phys. Chem., Vol. 100, No. 23, 1996 TABLE 3: Average Polarizabilities of Different Functional Groups Estimated from the Linear Dependencies of the Molecular Polarizabilities, r, in the Gaseous Phase47 on Molecular Length, L functional group
avg polarizability (cm3 × 10-24)
estimation from the R (L) dependence for:
-NH2 -OH -COOH -COOCH3 H 2O
1.30 1.47 3.38 4.7 1.45
n-alkylamines alkanols n-fatty acids acetic acid esters direct measurement
experimentally for the heptadecanol and 16-bromohexadecanol monolayers lead to a conclusion that different ω-dipoles do not alter the head group conformation. Application of monolayers with large hydrophilic heads (COOH, COOCH3), where the inductive polarizability is more significant, will be confronted with the problem of steric hindrance of the conformational changes which makes the orientational polarization of the head groups impossible. No specific polarization (inductive or orientational) of hydration water, caused by the difference in the dipoles of the terminal groups CH3CH2 and BrCH2, was found in our work. This should be true for all condensed monolayers of long chain amphiphilic compounds since in this study the strong BrCH2 dipole was located possibly close to the hydration water region, i.e., at the end of the almost shortest C16 hydrocarbon chain that can be studied (alcohols with chains shorter than C14 do not form insoluble monolayers). The identity of the pKi values of HHC in the two matrix monolayers shows that different ω-dipole moments do not affect the acid-base equilibrium of the dye chromophore, whose polarizability is 13 times as big as the one for the OH group. (Calculation of the average polarizabilities of 4-methyl-7hydroxycoumarin and phenol, performed with the MNDO method included in the program Vamp,48 yields values of 19.3 × 10-24 cm3 and 11.7 × 10-24 cm3, respectively. The latter one is very close to the experimental value 11.1 × 10-24 cm3, thus giving confidence in this estimation.) Therefore, this conclusion could be safely applied to all monolayers having less polarizable acidic or basic head groups, such as, e.g., RNH2, RCOOH, RC6H4NH2, RC6H4OH, RC6H4COOH, etc. The results presented in this work are in agreement with some of the assumptions of the three-capacitor model but at the same time contradict other assumptions. The negligible effect of collective polarization established here support Demchak and Fort’s assumption1 that “distortions, in the monolayers,of bond and molecular dipole moments are small enough to make extrapolation of bulk data to monolayers feasible.” The values of the interfacial dielectric constant i for the normal and ω-halogenated alcanol monolayers, which are practically the same, agree with the statement that “the local dielectric constants 2 and 3 have independent physical significance.” The controversial conclusions regarding the head groups’ conformation of heptadecanol and 16-bromohexadecanol monolayers and the sensitivity of these conclusions to small variations in the values of the local dielectric constants contradicts the assumption that “2 and 3 are independent on the nature of the film forming molecules”. The separation of the spectroscopically determined values of the interfacial dielectric constant in groups of substances having the same or very similar neutral head groups (Table 2) questions the assumption that “the effect of different monolayers on the substrate contribution to µ⊥ is the same”. The same conclusion follows from the gradual transition of i in mixed DM/C12E8 micelles from i ) 60, characteristic for the sugar head groups of n-dodecyl β-D-maltoside (DM), to i
Petrov et al. ) 35, which is typical for the ethoxy heads of the n-dodecyl octaoxyethylene glycol monoether (C12E8). Conclusions Computed maps of the molecular electrostatic and molecular lipophilic potentials show that the different ω-dipoles of heptadecanol and 16-bromohexadecanol do not affect the potential and hydrophilicity of the head groups of single molecules in Vacuo. MNDO semiempirical quantum mechanical calculations predict the same (trans) preferential conformation for the OH groups and practically equal depths of the energetic minima and heights of the energy barriers for the conformational transitions of single molecules of heptadecanol and 16-bromohexadecanol. The coincidence of the interfacial pKi values obtained for the normal and ω-halogenated alcohol monolayers shows the following: The acid-base equilibrium of the hydrophilic chromophore of the dye, located in the head groups region, is unaffected by the difference in the ω-dipoles of the monolayer matrices. In spite of the differences in ω-dipoles of the monolayers studied the dielectric constant at the monolayer-water boundary is practically the same. The hydroxy groups of heptadecanol and 16-bromohexadecanol monolayers possess the same conformation and dipole moments. This should be the gauche conformation, because the negligible µy-component of the molecular dipole moment of the trans heptadecanol contradicts to the significant experimental value of µ⊥ found. Since for both heptadecanol and 16-bromohexadecanol molecules in Vacuo the trans energetic minima are deeper one can conclude that the aqueous substrate plays a determining role for the conformation of the head groups in the condensed monolayers under study. A comparison of the results of the molecular modeling with the experimental data from fluorometric titrations shows the absence of both molecular and collective polarization due to the ω-dipoles. In accordance with the assumption of the threecapacitor model they do not affect the acid-base equilibrium, conformation, dipole moment, and dielectric constant of the head groups and dipole moment and orientation of hydration water. Application of the three-capacitor model to our data in analyzing the head groups’ conformation according to the procedure proposed by Demchak and Fort infers that heptadecanol and 16-bromohexadecanol monolayers should posses different OH group conformations at the same temperature, area per molecule, and on the same aqueous substrate. This conclusion is not only unreasonable but also self-contradictory since the three-capacitor model postulates an independence of the head groups’ conformation on the ω-dipole moments of the monolayer. Moreover, small changes in the values of the parameters µ1/1, 2, and 3 lead to the prediction of different head group conformations or fail to predict any conformation at all including the one which allows the OH group to rotate freely. Because of this controversy and sensitivity, we believe it is justified to pose the question whether it is suitable to apply common µ1/1, 2, and 3 values even to similar substances such as n- and ω-halogenated fatty acids, amines, and alcohols (cf. refs 1, 7, 8, and this study). Acknowledgment. The experimental part of this study was performed at the Max-Planck Institute of Biophysical Chemistry in Go¨ttingen, in the laboratory of Prof. D. Mo¨bius, while the interpretation of the results on the basis of the molecular models and the preparation of the paper was done at the Max-Planck Institute of Colloids and Interfaces in Berlin. J.G.P. gratefully
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