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Langmuir 1999, 15, 1716-1724
Static and Dynamic Properties of Calixarene Monolayers at the Air/Water Interface. 1. pH Effects with p-Dioctadecanoylcalix[4]arene Alan R. Esker,† Lan-Hui Zhang,‡ Carl E. Olsen, Kwanghyun No,§ and Hyuk Yu* Department of Chemistry, University of WisconsinsMadison, Madison, Wisconsin 53706 Received January 6, 1997. In Final Form: November 17, 1998
Newly synthesized p-dioctadecanoylcalix[4]arene is shown to form stable monolayers at the air/water interface over a wide pH range (1.8-12). Surface pressure-area isotherms obtained with the Wilhelmy plate technique are used to infer that the molecular packing at the onset of film collapse is consistent with a conelike conformer having all of the phenol oxygens of the calixarenes adsorbed to the interface. Increasing pH leads to a stepwise dissociation to phenoxides and attendant expansion of the monolayer attributable to enhanced electrostatic repulsions among the negatively charged phenoxide polar heads. Analysis of the area per molecule as a function of pH reveals two distinct steps and an intermediate plateau. Considering the presence of two types of chemically inequivalent phenol groups and the potential for intramolecular hydrogen bonding, this behavior was interpreted in terms of acid-base equilibria in which the first step corresponds to an apparent surface pKa,1 ≈ 6.4 while the second step is consistent with an apparent surface pKa,2 ≈ 9.2 (assuming pKa,3, pKa,4 . 12). As for the dynamics of the monolayers, the technique of surface light scattering (SLS) was employed to probe the surface viscoelasticity. Although pH had a dramatic effect on the molecular packing of p-dioctadecanoylcalix[4]arene monolayers, SLS results indicate that all films exhibited the limiting behavior of infinite lateral modulus dynamics when the surface pressure exceeds 1 mN‚m-1, and such behavior is established to be independent of pH. From these findings, it is deduced that the packing of the aromatic rings and long octadecanoyl side chains, rather than electrostatic interactions of the phenoxide headgroups, is responsible for the lateral rigidity of such monolayers.
Introduction Calixarenes are a class of macrocyclic compounds (four to eight phenols connected by methylene links) with conelike three-dimensional structures which resemble chalices, hence the name.1 Since their “re-discovery” in the 1970s, there has been considerable interest in the history, synthesis, host-guest properties, and potential applications of these molecules.2-8 Surprisingly, little systematic attention has been directed to calixarenes at the air/water interface (A/W) despite the uses of phenolformaldehyde resins, which are branched homologues of calixarenes, as surfactants in the recovery of oil from crude oil emulsions,4 and work with ionophoric LangmuirBlodgett (LB) films of crown ethers and porphyrin derivatives transferred from A/W.9 The notable exception to this is a variety of monolayer-forming calixarenes which have been examined with respect to their possible use in * To whom correspondence should be addressed. † Current address: National Institute of Standards and Technology, 100 Bureau Dr., Stop 8542, Gaithersburg, MD 20899-8542. ‡ Current address: Department of Chemistry, Lehigh University, Bethlehem, PA 18015. § Permanent address: Department of Chemistry, Sookmyung Women’s University, Seoul 140-742, Korea. (1) Gutsche, C. D.; Muthukrishnan, R. J. Org. Chem. 1978, 43, 4905. (2) Gutsche, C. D. Acc. Chem. Res. 1983, 16, 161. (3) Gutsche, C. D. In Host-Guest Complex Chemistry Macrocycles; Springer-Verlag: New York, 1985; p 375. (4) Gutsche, C. D. Calixarenes; Stoddart, J. F., Ed.; The Royal Society of Chemistry: Cambridge, 1989. (5) Vicens, J.; Bo¨hmer, V. Calixarenes: A Versatile Class of Macrocyclic Compounds; Kluwer Academic: Boston, 1991. (6) McKervey, A.; Bo¨hmer, V. Chem. Brit. 1992, 28, 724. (7) Bo¨hmer, V.; O’Sullivan, P. TRIP 1993, 1, 267. (8) Bo¨hmer, V. Angew. Chem., Int. Ed. Engl. 1995, 34, 713. (9) Ulman, A. An Introduction to Ultrathin Organic Films: from Langmuir-Blodgett to Self-Assembly; Academic Press: San Diego, 1991.
membrane filters.10-13 These include mercurated compounds,10,11 cross-linkable derivatives,12-16 calix[6]arene and p-tert-butylcalix[6]arene,17 and molecules with ethylene oxide polar headgroups.18 These studies primarily focused on surface pressure-area per molecule (Π-A) isotherms at A/W. Additionally, they have probed how an increasing ring size enhances water evaporation through these perforated monolayers relative to hexadecanol and how ionic and covalent cross-linking (via interfacial polymerization) affects the surface viscosities of these monolayers. A key issue when dealing with monolayer studies is whether the material actually forms a stable monolayer. As calixarenes can be easily modified both at the top and bottom side of the “aromatic basket”, a variety of synthetic options exist to strike a suitable balance between hydrophobic and hydrophilic substituents for stable monolayer formation. Failure to strike a suitable balance leads to materials which dissolve in the aqueous subphase (too hydrophilic) or form aggregates which fail to spread into uniform monolayers at the interface (too hydrophobic). (10) Markowitz, M. A.; Bielski, R.; Regen, S. L. J. Am. Chem. Soc. 1988, 110, 7545. (11) Markowitz, M. A.; Janout, V.; Castner, D. G.; Regen, S. L. J. Am. Chem. Soc. 1989, 111, 8192. (12) Conner, M.; Janout, V.; Regen, S. L. J. Am. Chem. Soc. 1993, 115, 1178. (13) Conner, M. D.; Janout, V.; Kudelka, I.; Dedek, P.; Zhu, J.; Regen, S. L. Langmuir 1993, 9, 2389. (14) Dedek, P.; Janout, V. Regen, S. L. J. Org. Chem. 1993, 58, 6553. (15) Dedek, P.; Webber, A. S.; Janout, V.; Hendel, R. A.; Regen, S. L. Langmuir 1994, 10, 3943. (16) Lee, W.; Hendel, R. A.; Dedek, P.; Janout, V.; Regen, S. L. J. Am. Chem. Soc. 1995, 117, 6793. (17) Markowitz, M. A.; Bielski, R.; Regen, S. L. Langmuir 1989, 5, 276. (18) Conner, M.; Kudelka, I.; Regen, S. L. Langmuir 1991, 7, 982.
10.1021/la970016b CCC: $18.00 © 1999 American Chemical Society Published on Web 01/30/1999
pH Effects on Calixarene Monolayers
There is some discrepancy in the literature on whether p-tert-butylcalix[n]arenes (n ) 4, 6, or 8) form stable monolayers. One group claims that they do not but that related ester derivatives built off the phenolic oxygen do.19 Additionally, they report that different ring sizes of these derivatives selectively bind univalent cations. More recently, Dei et al.20 have published work showing selective ion binding for “stable” p-tert-butylcalix[6]arene monolayers. However, the isotherms do not agree quantitatively with those by Markowitz et al.17 Additionally, atomic force microscopy has been used to image p-tert-butylcalix[6]arene transferred onto substrates of 1H,1H,2H,2H-perfluorodecyltrichlorosilane by the LB technique.21 To form stable monolayers, the authors reported the use of octadecanol as a cosurfactant. Their work supports a conelike conformation at A/W. Considering the discrepancies observed with the simple calixarenes, it is also useful to examine more complicated structures. Some examples of these are p-octadecylcalix[4]arene22 and p-octadecylbishomooxacalix[4]arene.23 For these two systems, the dissociation of phenol to phenoxide at high pH leads to an increased size of the headgroups through enhanced electrostatic repulsions. For the case of p-octadecylcalix[4]arene, stability again becomes an issue as the authors report that this molecule only forms stable monolayers at a high pH. Taken together, the reports of selective host-guest chemistry and pH sensitivity suggest that calixarenes may be suitable as a model system for membrane-bound receptors, but on monolayers as contrasted to those on bilayer membranes. To test the feasibility of this prospect, a new calixarene compound, p-dioctadecanoylcalix[4]arene, has been prepared. Here, the ability of this molecule to form stable monolayers, verified by surface pressure measurements using the Wilhelmy plate technique, and the surface viscoelastic properties of these films obtained by surface light scattering (SLS) are examined over a wide pH range. In the accompanying report, the effects of various potential ligands to the aromatic basket are examined in detail.24 Experimental Section Materials. p-Dioctadecanoylcalix[4]arene (4) was synthesized as shown in Scheme 1. Structure 1, 5,11,17,23-tetra-tert-butyl25,26,27,28-tetrahydroxycalix[4]arene, was prepared in 52% yield from p-tert-butylphenol and formaldehyde as detailed elsewhere.25 Structure 2, 25,26,27,28-tetrahydroxycalix[4]arene, was synthesized in 74% yield by AlCl3-catalyzed removal of the tertbutyl groups from structure 1, following the published procedure.26 Structure 2 (1.00 g, 2.36 mmol) was dissolved in 60 mL of CHCl3. After refluxing for 2 h, the reaction mixture was poured into 100 mL of 6 M HCl. The organic layer was then separated and washed several times with water, before it was dried over MgSO4. The slightly waxy solid, obtained from the evaporation of CH2Cl2, was boiled with methanol. The methanol-insoluble portion was collected by filtration and was recrystallized from acetone and methanol to afford 3.23 g (92.0% yield) of structure (19) Ishikawa, T.; Kunitake, T.; Matsuda, T.; Otsuka, T.; Shinkai, S. J. Chem. Soc., Chem. Commun. 1989, 736. (20) Dei, L.; Casnati, A.; Nostro, P. Lo; Baglioni, P. Langmuir 1995, 11, 1268. (21) Namba, M.; Sugawara, M.; Bu¨hlmann, P.; Umezawa, Y. Langmuir 1995, 11, 635. (22) Nakamoto, Y.; Kallinowski, G.; Bo¨hmer, V.; Vogt, W. Langmuir 1989, 5, 1116. (23) Asfari, Z.; Bayard, F.; Bo¨hmer, V.; Decoret, C.; Gust, W.-R.; Malthete, J.; Vicens, J.; Vogt, W.; Weber, P. Mol. Cryst. Liq. Cryst. 1990, 187, 335. (24) Zhang, L. H.; Esker, A. R.; No, K.; Yu, H. Langmuir 1999, 15, 1725. (25) No, K. H.; Noh, Y. J. Bull. Korean Chem. Soc. 1986, 7, 314. (26) Gutsche, C. D.; Levine, J. A. J. Am. Chem. Soc. 1982, 104, 2652.
Langmuir, Vol. 15, No. 5, 1999 1717 Scheme 1
3 (25,26,27,28-tetraoctadecanoyloxycalix[4]arene) as a white crystalline solid in the 1,3-alternate conformation: mp 88-90 °C. IR (Nicolet Impact 400 FT-IR spectrometer, KBr): 1750 cm-1. 1H NMR (Varian Gemini 300, CDCl ) δ: 7.02 (s, 12), 3.73 (s, 8), 3 1.58 (t, 8), 1.27 (br s, 120), 0.88 (t, 12). 13C NMR (CDCl3) δ: 171.30 (CdO), 148.89, 133.65, 129.91, 125.46 (Ar), 37.82, 33.03, 32.05, 29.88, 29.80, 29.72, 29.66, 29.49, 24.03, 22.78, 14.17. Anal. C, 80.39; H, 10.81 (Calcd for C100H160O8: C, 80.57; H, 10.84). A solution of structure 3 (2.51 g, 1.69 mmol) in 160 mL of nitrobenzene was treated with 1.98 g (14.8 mmol) of AlCl3 and was stirred for 48 h at room temperature. The reaction was quenched by the addition of water, and the solvent was removed by steam distillation. The resultant solid was then collected, crushed into powder, washed with water, dried, dissolved in chloroform, and decolorized with activated charcoal. The residue, obtained by evaporation of the chloroform, was recrystallized from hexane, leaving 1.13 g (70% yield) of structure 4, 5,17dioctadecanoyl-25,26,27,28-tetrahydroxycalix[4]arene, as a white powder: mp 95-97 °C. IR (KBr): 3300 cm-1 (OH), 1700 (CdO). 1H NMR (CDCl ) δ: 10.2 (br s, 4), 7.73 (s, 4), 7.12 (d, 4), 6.80 (t, 3 2), 4.28 (br s, 4), 3.65 (br s, 4), 2.80 (t, 4), 1.67 (quint, 4), 1.30 (br s, 56), 0.90 (t, 6). 13C NMR (CDCl3) δ: 199.36 (CdO), 153.78, 148.86, 132.01, 130.02, 129.82, 128.69, 128.17, 123.23 (Ar), 38.34, 32.08, 31.75, 29.85, 29.66, 29.56, 29.51, 24.61, 22.81, 14.20 (CH2, CH3). Anal. C, 80.17; H, 9.71 (Calcd for C64H92O6: C, 80.27; H, 9.70). Sodium chloride, sodium tetraborate, sodium dihydrogenphosphate, and hydrochloric acid were purchased from Aldrich with 99.999% purity. Sodium hydroxide was also obtained from Aldrich with 99.99% purity. Sodium chloride and sodium tetraborate were baked at 550 °C for 5 h to eliminate any volatile organic impurities before use. Deionized water obtained by passing distilled water through a Millipore Q2 system was used to prepare the subphases. Monolayer Preparation and Surface Pressure Measurements. Experiments were carried out in a Teflon trough (28.5 × 11.0 × 1.25 cm3) housed in a Plexiglas box. Humid nitrogen gas bubbled through a water trap was gently flowed through the box to maintain high relative humidities (>80%), thereby keeping the sandblasted platinum plate (2.63 × 1.11 × 0.01 cm3) well-
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Table 1. Effect of Atmospheric CO2 on Subphase pH Values subphase
initial pH
final pH
0.02 M Na2B4O7 + 0.025 M NaOH 0.0125 M Na2B4O7 + 0.015 M NaOH 0.02 M NaOH + 0.02 M NaCl 0.02 M NaOH + 0.02 M NaCl + N2
8.35 9.76 12.08 12.08
8.33 (4 h) 9.59 (37 h) 11.21 (10 h) 12.05 (10 h)
wetted while simultaneously reducing the effect of carbon dioxide in the air on subphase pH. Table 1 shows the effect that CO2 has on some basic subphases and how the use of N2 prevents this problem. The same nitrogen flow setup was used for all measurements unless specifically noted. About 200 µL of spreading solution with total concentrations of ∼0.1 mg/mL (in HPLC grade chloroform, Aldrich) was spread on the subphase with a Hamilton microsyringe to prepare the monolayer. Surface tensions were measured by the Wilhelmy plate technique with a Cahn electrobalance (model 2000). Values were recorded, and the surface light-scattering measurements were begun once a stable surface tension value was obtained (typically, ∆σs < 0.04 mN‚m-1 over a 5 min period). The surface concentration was controlled by stepwise compression of the Teflon barrier. For some of the SLS measurements, successive additions of the spreading solution were used to control the surface concentration with both approaches yielding the same results. The temperature of the subphase was maintained at 23.0 ( 0.1 °C by circulating thermostatted water from a Lauda bath through a glass coil placed in the bottom of the trough. Surface Light Scattering (SLS). All SLS experiments were performed simultaneously with static surface tension measurements. The SLS experimental setup has been described in detail elsewhere27 and is based on a design by Ha˚rd et al.28 The laser wavelength, λ, the incident angle, θ, and the distance from the interface to the detector, R, were 632.8 nm, 64.4°, and 3.64 m, respectively. The full width at half-maximum intensity of the Gaussian laser beam profile, ∆ui, and the wave vector k were obtained with water as the calibration standard. In this work, the fourth-, fifth-, and sixth-order diffraction spots from the optical grating imaged on the water surface were used to define the scattering angles. The corresponding wave vectors are identified on the graphs for the SLS results (see below).
Figure 1. Π-A isotherms of p-dioctadecanoylcalix[4]arene monolayers with (filled circles) and without (open circles) NBDPE on water at 23 °C. The dashed vertical line at 0.78 nm2‚molecule-1 corresponds to the value predicted by CPK models for calix[4]arenes in a conelike conformation.
Isotherm Studies of Stable Monolayers. In contrast to the finding that p-octadecylcalix[4]arene forms stable monolayers only on basic subphases,22 p-dioctadecanoylcalix[4]arene forms stable monolayers over a wide range of pH. This suggests that the decrease from four octadecyl to two octadecanoyl hydrophobic tail chains results in a favorable shift in the balance between hydrophobic and hydrophilic moieties in p-dioctadecanoylcalix[4]arene which promotes stable monolayer formation. Not only does this switch reduce the hydrophobicity of the molecule but the use of octadecanoyl groups also places carbonyl carbons at the para position on two of the four aromatic rings. Presumably, enhanced resonance stabilization by the carbonyl groups on the rings confers increased acidity, lower pKa values. Chemical dissimilarity or inequivalence among the four phenolic hydrogens must be taken into account when assessing the overall balance of hydrophobic and hydrophilic characters, and for the interpretation of the isotherms, as will be done shortly. Some general features of the isotherm can be gleaned from Figure 1. As seen in the figure, the isotherm on water is rather condensed (maximum static elasticity, s,max ) -A(∂Π/ ∂A)T,max ≈ 80 mN‚m-1) with a limiting area of ≈0.9 nm2‚molecule-1 and a collapse area close to 0.78 nm2‚ molecule-1, the predicted value from Corey-Pauling-
Koetun (CPK) models for a conelike conformation with all of the phenol oxygens adsorbed to the interface.13,22 Such a conformation means that the aromatic rings have a finite tilt angle and the side chains are probably somewhat disordered as they have twice the area seen at closest packing for saturated fatty acid monolayers.29 It also leads to the conclusion that closest packing is controlled by the aromatic baskets rather than the hydrocarbon side chains. The limiting area is also reasonable if one considers that a single molecule of p-octadecylphenol has a reported limiting area of 0.24 nm2‚molecule-1.30 The figure also shows the effect of 1 mol % NBD-PE (1-acyl-2-[12-[(7nitro-2-1,3-benzoxadiazol-4-yl)amino]dodecanoyl]phosphatidylethanolamine) which was included for imaging the monolayers by fluorescence microscopy. However, the only phase behavior observed is the rather unremarkable coexistence between a gaseous film and a more condensed monolayer at dilute surface concentrations where Π hovers around the detection limit, 0 mN‚m-1, very similar to what is observed for phospholipids.31 With the exception of a slight to insignificant increase in the collapse pressure, the addition of NBD-PE does not alter the monolayer properties of p-dioctadecanoylcalix[4]arene. It can be assumed throughout the remainder of this report that all films contain 1 mol % NBD-PE unless otherwise stated. Subphase pH Effects. As noted above, p-dioctadecanoylcalix[4]arene forms stable monolayers over a wide subphase pH range. Isotherms for pH values ranging from 1.8 to 12 are shown in Figure 2. The buffer systems collected in Table 2 were used to maintain both constant pH and ionic strengths (≈0.04 M, except where noted). For subphases with pH values greater than 6, it is also necessary to perform the experiments under a humid nitrogen atmosphere. This prevents pH decreases mediated by carbonic acid arising from the ambient carbon dioxide in the air, and this is confirmed with the data collected in Table 1. The predominant features are increasing collapse pressures (Πc ≈ 8 to ≈ 30 mN‚m-1) and limiting areas (A ≈ 0.9 to ≈1.2 nm2‚molecule-1) as the pH increases from 1.8 to 12. For the most basic subphases (pH > 8), the collapse point was not reached because of long equilibration times and the problems with the low surface tension films overflowing the sides of the trough just after spreading or compression. The expansion of the films is expected on the basis of the reported isotherms for p-octadecylcalix[4]arene22 and p-octadecyl-
(27) Sano, M.; Kawaguchi, M.; Chen, Y.-L.; Skarlupka, R. J.; Chang, T.; Zografi, G.; Yu, H. Rev. Sci. Instrum. 1986, 57, 1158. (28) Ha˚rd, S.; Hamnerius, Y.; Nilsson, O. J. Appl. Phys. 1976, 47, 2433.
(29) Davies, J. T.; Rideal, E. K. Interfacial Phenomena; Academic Press: London, 1961. (30) Adam, K. Proc. R. Soc. 1923, A103, 676. (31) Tamada, K.; Kim, S.; Yu, H. Langmuir 1993, 9, 1545.
Results and Discussion
pH Effects on Calixarene Monolayers
Langmuir, Vol. 15, No. 5, 1999 1719
Figure 2. Π-A isotherms of p-dioctadecanoylcalix[4]arene monolayers with NBD-PE for different subphase pH values (ionic strength I ) 0.04 M, 23 °C). The dashed vertical line at 0.78 nm2‚molecule-1 corresponds to the value predicted by CPK models for calix[4]arenes in a conelike conformation. Table 2. pH Values of Subphase Solutions subphase
pH
0.02 M HCl + 0.02 M NaCl ∼0.01 M HCl 0.04 M NaCl water 0.0205 M NaH2PO4 + 0.0055 M NaOH (I ) 0.03 M) 0.026 M NaH2PO4 + 0.00698 M NaOH 0.019 M NaH2PO4+ 0.0105 M NaOH 0.02 M Na2B4O7 + 0.0328 M HCl 0.02 M Na2B4O7 + 0.025 M HCl 0.0143 M NaH2PO4 + 0.0128 M NaOH 0.02 M Na2B4O7 + 0.0154 M HCl 0.02 M Na2B4O7 0.016 M Na2B4O7 + 0.008 M NaOH 0.0125 M Na2B4O7 + 0.015 M NaOH 0.02 M NaOH + 0.02 M NaCl
1.80 2.00 5.54 5.54 6.58 6.67 7.17 7.95 8.39 8.54 8.74 9.18 9.36 9.72 12.08
bishomooxacalix[4]arene.23 This behavior is consistent with increased electrostatic repulsions among negatively charged phenoxides. By examining a wide range of subphase pH values, there also appears to be a pH independent collapse concentration which is close to the value of 0.78 nm2‚molecule-1 expected for p-dioctadecanoylcalix[4]arene existing at the interface in a conelike conformation. Another noteworthy feature, which will be dealt with in more detail below, is the observation of a large change in the limiting area between pH 5.5 and 6.7, and a second such change between pH 9 and 10. To distinguish between acidity and ionic strength effects, sodium chloride subphases with constant pH values and different ionic strengths were also examined. These are also shown in Figure 2 (0, 0.01, and 0.04 M added NaCl at pH ) 5.5). The sole effect due to the change in ionic strength is a small increase in the collapse pressure. It is worth mentioning that this result is different from the strong and selective expansion that 1 M Na+ ions are reported to induce on a different calix[4]arene monolayer.19 Our initial results with a 10 mM NaCl solution also showed a significantly expanded monolayer with p-dioctadecanoyl-
calix[4]arene. However, once the NaCl was baked at 550 °C for 5 h to remove traces of volatile organic impurities, this effect disappeared altogether. Apparent Surface pKa Values. Accurate pKa values for calixarene derivatives are difficult to obtain because of their insolubility in aqueous systems. Nonetheless, attempts have been made to estimate these values by titrating calixarene systems in organic solvents or organic solvent/water mixtures32-34 and by making soluble calixarenes through the introduction of polar and ionic groups at the position para to the phenolic OH group.35-38 Most though not all studies39 show a significant decrease in pKa of the first acid dissociation in a calixarene molecule relative to the corresponding linear analogue or similarly substituted phenols. Additionally, these systems show large differences in pKa values (as large as 9-10 pKa units) between the first and second dissociations which has also been observed in computer simulations.40 These shifts are commonly attributed to strong intramolecular hydrogen bonding among the phenolic OH groups on the bottom rim of conelike conformations of calix[4]arenes. Considering the existence of two chemically inequivalent types of phenolic protons in p-dioctadecanoylcalix[4]arene as alluded to earlier and the possibility of intramolecular hydrogen bonding, a further examination is called for to deduce apparent surface pKa values. Figure 3 is provided as a starting point for such an analysis of the apparent surface pKa values. In the figure, the area per molecule at Π ) 1, 2, and 5 mN‚m-1 is plotted as a function of pH. The plots show two well-delineated steps separating three plateaus, analogous to a titration curve for a diprotic acid. If one takes into account that p-dioctadecanoylcalix[4]arene molecules carrying different charges will occupy different areas per molecule, then the plots may be qualitatively interpreted as follows: (1) pH 2-5.5, p-dioctadecanoylcalix[4]arene exists in the undissociated state; (2) pH 5.5-7, the dissociation of 1 or 2 phenolic OH groups which is attended by an increase in area per molecule A; (3) pH 7.5-8.4, the transition pH range between the first and second dissociation steps, corresponding to the calixarene molecule carrying a charge of -1 or -2; (4) pH 8.4-10, the second dissociation step also attended by another increase in A; (5) pH 10-12, the asymptotic state of dissociation where p-dioctadecanoylcalix[4]arene carries a charge of -2 to -4. The ambiguity over the number of dissociated phenol OH groups comes from the presence of only two welldefined changes in area per molecule. Two scenarios are considered, the first being that the p-dioctadecanoylphenol moieties have similar pKa values, whereby the first change in area per molecule with respect to pH reflects the dissociation of two protons. Under this scenario, the second transition would correspond to the dissociation of the other two phenol moieties (similar pKa values for both). If, in (32) Araki, K.; Iwamoto, K.; Shinkai, S.; Matsuda, T. Bull. Chem. Soc. Jpn. 1990, 63, 3480. (33) Shinkai, S.; Araki, K.; Kubota, M.; Arimura, T.; Matsuda, T. J. Org. Chem. 1991, 56, 295. (34) Araki, K.; Murakami, H.; Ohseto, F.; Shinkai, S. Chem. Lett. 1992, 539. (35) Shinkai, S. Pure Appl. Chem. 1986, 58, 1523. (36) Shinkai, S.; Araki, K.; Shibata, J.; Tsugawa, D.; Manabe, O. Chem. Lett. 1989, 931. (37) Shinkai, S.; Araki, K.; Grootenhuis, P. D. J.; Reinhoudt, D. N. J. Chem. Soc., Perkin Trans. 2 1991, 1883. (38) Yoshida, I.; Yamamoto, N.; Sagara, F.; Ishii, D.; Ueno, K.; Shinkai, S. Bull. Chem. Soc. Jpn. 1992, 65, 1012. (39) Bo¨hmer, V.; Schade, E.; Vogt, W. Makromol. Chem., Rapid Commun. 1984, 5, 221. (40) Grootenhuis, P. D. J.; Kollman, P. A.; Groenen, L. C.; Reinhoudt, D. N.; van Hummel, G. J.; Ugozzoli, F.; Andreetti, G. D. J. Am. Chem. Soc. 1990, 112, 4165.
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per molecule at a given surface pressure can be written as the sum of the area contributions of each species at the interface: 5
A(Π) )
Figure 3. pH dependence of the area per molecule A, for p-dioctadecanoylcalix[4]arene monolayers with NBD-PE at Π ) 1, 2, and 5 mN‚m-1 (23 °C). All three solid curves correspond to the five-parameter diprotic acid treatment of calixarene described in the text with the parameters summarized in Table 3.
fact, pKa,1 ≈ pKa,2 ≈ 6 and pKa,3 ≈ pKa,4 ≈ 9, this is equivalent to concluding that intramolecular hydrogen bonding is absent or has no significant effect on the acidbase equilibria at the surface. This model is artificial from the standpoint of previous calixarene studies noted above and the fact that pKa values for most polyprotic acids differ by more than 1 unit (∆pKa > 1). For the second and more probable case, one needs to assume that intramolecular hydrogen bonding is significant. Once this is done, the two regions of changing area per molecule only correspond to the dissociation of two p-dioctadecanoylphenol moieties. This would imply that pKa,1 ≈ 6, pKa,2 ≈ 9, and both pKa,3 and pKa,4 . 12. For the following quantitative analysis both scenarios are considered. The appropriate starting point for a quantitative analysis of apparent surface pKa values is to consider the acid-base equilibria and corresponding acid dissociation constants of the four phenolic OH groups. This can be generalized as
H5-nL-n+1 h H4-nL-n + H+ -n
Ka,n )
and +
[H4-nL ][H ] [H5-nL-n+1]
(n ) 1, 2, 3, 4) (1)
where [H5-nL-n+1] and [H4-nL-n] represent surface concentrations of the corresponding species and [H+] is the bulk concentration of hydrogen ions. One important constraint is that the sum of the various calixarene species at the surface is equal to the total surface concentration of the spread material:
[H4L] + [H3L-] + [H2L-2] + [HL-3] + [L-4] ) Γs (2) Using this condition, it is possible to express the mole fraction of each species at the interface, detailed in Appendix A, in terms of [H+] and the acid dissociation constants. To fit the data of Figure 3, it is necessary to make several assumptions. The first of these is the assumption that area additivity holds, whereby the area
xiAi(Π) ∑ i)1
(3)
where index i represents each of the five distinct species in eq 2. Once this is done, eq 3 can be combined with eqs A1-A5 to obtain an expression for A(Π) in terms of pH, Ka,n, and Ai. Unfortunately, this model consists of nine parameters which fails to yield any kind of statistically significant fit. To reduce the number of parameters, a second assumption is made. This is to eliminate two of the four acid dissociation constants by letting Ka,1 ) Ka,2 and Ka,3 ) Ka,4, amounting to a claim that intramolecular hydrogen-bonding effects upon the acid dissociation equilibria are insignificant. As noted above, this assumption is artificial, but leads to the treatment of calixarene as a diprotic acid over the pH range studied here. By so assuming, the data of Figure 3 were fit, and the fitting parameters are collected in Table 3 under the sevenparameter fit. It is clear that the model still has too many parameters considering the large errors on the Ka values. Looking at the parameters, the areas for H4L and H3Lare roughly equal, and the same can be said for the occupied areas of HL-3 and L-4. Thus, the number of parameters can be further reduced by assuming AH4L(Π) ) AH3L-(Π) and AHL-3(Π) ) AL-4(Π). This results in a fiveparameter fit which is also summarized in Table 3. To reiterate, assumptions were made to reduce four acidbase equilibria and five chemical species down to a model consisting of two acid dissociation constants and three spatially, but not necessarily chemically, distinct species in terms of area per molecule. This is nearly equivalent to assuming only two of the four phenol protons on p-dioctadecanoylcalix[4]arene dissociate in the pH range studied. The diprotic acid case is obtained by setting Ka,3 and Ka,4 to 0 (pKa,3 and pKa,4 . 12). Once this is done, fitting the data yields the results shown in Table 3 and in Figure 3 as the solid lines. The only significant difference between the two scenarios, aside from the unrealistic assumptions associated with the tetraprotic calixarene model fits, is that the diprotic acid case shows an ≈1.6x decrease in Ka for the first step while the second step exhibits an ≈1.6x increase in Ka compared to the fiveparameter tetraprotic acid treatment. As seen in Figure 3, the diprotic acid model does an excellent job of fitting all of the features of the experimental data. Looking at the deduced Ka values, it is also helpful to compare these to some appropriately substituted phenols. Representative phenol values exist for 2,6-dimethyl-4acetylphenol (pKa ) 8.22)41 and 2,6-dimethylphenol (pKa ) 10.58).42 The apparent surface pKa values obtained from the five-parameter fit assuming diprotic dissociation are 6.4 and 9.2. These are in reasonable agreement with the bulk values of the corresponding phenols (shifted by 1-2 pKa units). This type of behavior has been reported for both fatty acids and amines at the air/water interface.29,43-48 One key difference is that for fatty acids and amines the shifts are toward neutral pH, making the monolayer less acidic and basic, respectively. In contrast, the apparent pKa values indicate p-dioctadecanoylcalix[4]arene is a stronger acid at the interface than cor(41) Fischer, A.; Leary, G. J.; Topsom, R. D.; Vaughan, J. J. Chem. Soc., Sect. B 1966, 782. (42) Wheland, G. W.; Brownell, R. M.; Mayo, E. C. J. Am. Chem. Soc. 1948, 70, 2492.
pH Effects on Calixarene Monolayers
Langmuir, Vol. 15, No. 5, 1999 1721
Table 3. Curve-Fitting Results for the Seven- and Five-Parameter Fits seven-parameter fit Π
(mN‚m-1)
1.0
2.0
five-parameter fit 5.0
AH4L(Π) (nm2) AH3L-(Π) (nm2) AH2L-2(Π) (nm2) AHL-3(Π) (nm2) AL-4(Π) (nm2) Ka,1 × 107 ) Ka,2 × 107 Ka,3 × 1010 ) Ka,4 × 1010
0.86 ( 0.01 0.81 ( 0.06 1.05 ( 0.01 1.20 ( 0.18 1.22 ( 0.01 8.1 ( 3.1 4.1 ( 4.3
Tetraprotic Calixarene 0.84 ( 0.05 0.81 ( 0.01 0.79 ( 0.06 0.74 ( 0.05 1.03 ( 0.01 0.98 ( 0.01 1.18 ( 0.18 1.14 ( 0.18 1.20 ( 0.01 1.16 ( 0.01 8.8 ( 3.6 8.6 ( 3.2 4.2 ( 4.4 3.5 ( 3.6
AH4L(Π) (nm2) AH3L-(Π) (nm2) AH2L-2(Π) (nm2) AHL-3(Π) (nm2) AL-4(Π) (nm2) Ka,1 × 107 Ka,2 × 1010 Ka,3 Ka,4
NA NA NA NA NA NA NA NA NA
NA NA NA NA NA NA NA NA NA
a
Diprotic Calixarenea NA NA NA NA NA NA NA NA NA
1.0
2.0
5.0
0.86 ( 0.01 0.86 ( 0.01 1.05 ( 0.01 1.22 ( 0.01 1.22 ( 0.01 6.3 ( 1.5 3.6 ( 0.8
0.84 ( 0.01 0.84 ( 0.01 1.03 ( 0.01 1.20 ( 0.01 1.20 ( 0.01 6.5 ( 1.7 3.6 ( 0.7
0.80 ( 0.01 0.80 ( 0.01 0.98 ( 0.01 1.16 ( 0.01 1.16 ( 0.01 6.2 ( 1.6 3.1 ( 0.6
0.85 ( 0.01 1.05 ( 0.01 1.23 ( 0.01 # # 3.9 ( 1.2 6.0 ( 1.9 / /
0.83 ( 0.01 1.03 ( 0.01 1.21 ( 0.01 # # 4.0 ( 1.3 5.9 ( 1.8 / /
0.79 ( 0.01 0.98 ( 0.01 1.16 ( 0.01 # # 3.8 ( 1.2 5.1 ( 1.4 / /
NA ) not applicable; # ) not determinable; * , 10-12 (assumed). Uncertainties stand for one standard deviation.
respondingly substituted phenols in the bulk. Considering the large increases in acidity of the first dissociating proton already discussed above for calixarenes and their linear analogues, the small shift observed here most likely reflects interfacial factors which diminish the influence of intramolecular hydrogen bonding. Finally, given the small magnitude of these shifts (1-2 pKa units) and the absence of four distinct transistions in Figure 3, the possibility that all four phenol protons are dissociating in two steps corresponding to the two chemically inequivalent phenol protons, although unlikely, cannot be entirely dismissed. Surface Viscoelasticity. As demonstrated above, pH has a tremendous effect on the isotherm of p-dioctadecanoylcalix[4]arene. A parallel study of pH effects on the surface viscoelasticity of the calixarene was also performed using surface light scattering, which probes the frequency and temporal damping characteristics of propagating capillary waves at the air/liquid and liquid/liquid interfaces through an analysis of light scattered by these ripplons via a Doppler effect.49 For pure liquids, the propagation characteristics can be summarized by the following dispersion relations for the frequency, ω0,50 and temporal damping coefficient, R:51 Limit I; pure liquid surface, with σ ) σs
ω0 ) 2πfs )
x (
1 σk3 1 - y-3/4 F 2
)
(4)
)
(5)
and
R ) π∆fs,c )
2ηk2 1 1 - y-1/4 F 2
(
with parameters of the static liquid surface tension ) σ (43) Betts, J. J.; Pethica, B. A. Trans. Faraday Soc. 1956, 52, 1581. (44) Spink J. A. J. Colloid Interface Sci. 1963, 18, 512. (45) Bagg, J.; Haber, M. D.; Gregor, H. P. J. Colloid Interface Sci. 1966, 22, 138. (46) Grundy, M. J.; Richardson, R. M.; Roser, S. J.; Penfold, J.; Ward, R. C. Thin Solid Films 1988, 159, 43. (47) Yazdanian, M.; Yu, H.; Zografi, G. Langmuir 1990, 6, 1093. (48) Yazdanian, M.; Yu, H.; Zografi, G.; Kim, M. W. Langmuir 1992, 8, 630. (49) Langevin, D. Light Scattering by Liquid Surfaces and Complementary Techniques; Marcel Dekker: New York, 1992. (50) Thompson, W. (Lord Kelvin) Philos. Mag. 1871, 42, 368. (51) Stokes, G. G. Cambridge Trans. 1845, 8, 287.
) σs, spatial wave vector ) k, liquid density ) F, steady shear viscosity ) η, and a dimensionless parameter of y ) σF/(4η2k). These equations represent the first-order corrections of the simple theories,50,51 where fs and ∆fs,c correspond to the experimentally accessible frequency shift and corrected full-width at half-maximum intensity of the power spectrum of the Doppler-shifted, scattered light. The latter quantity, ∆fs,c, is related to the experimentally determined full-width at half-maximum intensity, ∆fs, obtained from a Lorentzian fit of the power spectrum, by the following expressions:28
∆fs,c ) ∆fs -
∆fi2 ∆fs
(6)
and
∆fi ) x2
(
)( )
∆ui cos θi Rλ
dω0,k dk
(7)
where ∆ui characterizes the Gaussian beam profile, θi is the incident angle, R is the distance from the interface to the detector, and λ is the wavelength of the laser light. Equations 4-7 can be used to calibrate the instrument with a standard liquid, commonly water, which is verified against other standards. Thus, the instrument was calibrated using water as the standard with subsequent verification by determining σ and η for anisole and ethylbenzoate. The results obtained for these liquids showed maximum deviations of 3% from the literature values. For monolayer-covered surfaces, the motion of the propagating capillary waves is influenced by the viscoelastic behavior of the surface film. This motion is described by the following dispersion equation which accounts for the transverse and longitudinal motion within the film:52
η2(k - m*)2 )
[
η(k + m*) +
][
]
gF ω*F *k2 σ*k2 + η(k + m*) + iω* iω* iω* ik (8)
where g is the gravitational constant though the gravity wave contribution (the third term in the second bracket
1722 Langmuir, Vol. 15, No. 5, 1999
Esker et al.
on the right-hand side of eq 8) is shown to be negligible, the complex lateral modulus * ) d + iω*κ, consisting of the dynamic dilational elasticity d and its corresponding surface viscosity κ, the transverse modulus σ* ) σd + iω*µ, consisting of the dynamic surface tension σd and the transverse viscosity µ, the complex frequency ω* ) ω0 + iR ) 2πfs + iπ∆fs,c and the complex wave vector, m* ) (k2 + iω*F/η)1/2, Re(m*) > 0. In addition to the pure liquid limit, designated as Limit I above, there are two other important limits for liquid surfaces covered by viscoelastic monolayers. One of them is the case of a purely elastic surface film (µ and κ ) 0). The most interesting consequence of this limit is the occurrence of a maximum damping coefficient which occurs at intermediate elasticity values (d/σs ≈ 0.17, κ and µ ) 0 mN‚s‚m-1 for the surface concentrations examined here) assuming the static surface tension is equal to its dynamic counterpart, σ ) σs ) σd. Such a result was first predicted by Dorrenstein and expressions for the frequency shift and maximum damping coefficient under these conditions are given as54,55 Limit II; * finite, µ ) 0 and κ ) 0
ω0 ) 2πfs )
x (
σk3 10 1 - y-9/16 F 17
)
Figure 4. fs-Π for p-dioctadecanoylcalix[4]arene monolayers without NBD-PE on 0.01 M HCl (circles, pH ≈ 2), water (triangles, pH ≈ 5.5), 0.001 M Na2B4O7 (squares, pH ≈ 8), and 0.01 M NaOH (diamonds, pH ≈ 11-12) for three wave vectors at 23 °C. The dotted curves represent Limit I (pure liquid limit) obtained from eq 4, while the solid curves, calculated from eq 11, correspond to Limit III (infinite lateral modulus dynamics).
(9)
and
R ) π∆fs,c )
( )(
x2 ση2k7 2 F3
1/4
1+
)
4 -5/32 y 11
(10)
The other significant limit for viscoelastic behavior described by the dispersion equation, as applied to the rigid monolayers of p-dioctadecanoylcalix[4]arene, corresponds to * f ∞ (infinite lateral modulus), µ ) 0 for Π > ≈1 mN‚m-1. Under these conditions, analogous equations to eqs 4 and 5 or 9 and 10 are given as53,54 Limit III; * f ∞ and µ ) 0
ω0 ) 2πfs )
x (
1 σk3 1 - y-1/4 F 4
)
(11)
and
R ) π∆fs,c )
( )(
x2 ση2k7 4 F3
1/4
1 1 + y-1/4 2
)
(12)
Experimentally determined fs and ∆fs,c values as a function of the static surface pressure Π on four different subphases at three different wave vectors are shown in Figures 4 and 5, respectively. The limiting behaviors of eqs 4, 5, and 9-12 are also indicated on the plots. As should be expected, pure liquid dynamics are observed in the limit of Π f 0. There is also an intermediate region where values fall between the limits of infinite lateral modulus dynamics and pure liquid dynamics. This corresponds to a partially covered surface consisting of patches of p-dioctadecanoylcalix[4]arene in coexistence with bare or sparsely covered surface, possibly surface gaseous film, whereby the observed signal represents an area average over the length scale of the capillary waves (52) Lucassen-Reynders, E. H.; Lucassen, J. Adv. Colloid Interface Sci. 1969, 2, 347. (53) Reynolds, O. Brit. Ass. Rept. 1880 (cited in ref 60). (54) Esker, A. R. Ph.D. Thesis, University of WisconsinsMadison, Madison, WI, 1996. (55) Dorrenstein, R. Koninkl. Ned. Akad. Wetenshap. Proc. 1951, B54, 260, 350.
Figure 5. ∆fs,c-Π for p-dioctadecanoylcalix[4]arene monolayers without NBD-PE on 0.01 M HCl (circles, pH ≈ 2), water (triangles, pH ≈ 5.5), 0.001 M Na2B4O7 (squares, pH ≈ 8), and 0.01 M NaOH (diamonds, pH ≈ 11-12) for three wave vectors at 23 °C. The dotted, solid, and dashed curves correspond, respectively, to Limit I (pure liquid limit), Limit III (infinite lateral modulus dynamics), and Limit II (maximum damping coefficient for a perfectly elastic surface film according to eq 10).
probed.56,57 As soon as Π exceeds ≈1 mN‚m-1, a very rigid film is formed with dynamics approaching the limit of an infinite lateral modulus with a negligible transverse viscosity, µ ) 0. This figure also shows frequency independence over the range of wave vectors used here. This manifests itself in the departure from the limit of the maximum damping coefficient of a perfectly elastic surface film. Figure 6 is provided to show that small amounts of NBD-PE mixed in the monolayers and NaCl in the subphase have no significant effect on the viscoelastic behavior. It is clear from the data that Na+ as the counterions to the calixarene phenoxides have no detectable effect on the viscoelastic properties of the monolayers. This is expected in view of the small effect observed on the isotherms displayed in Figure 2. (56) Lee, K.-Y.; Chou, T.; Chung, D. S.; Mazur, E. J. Phys. Chem. 1993, 97, 12876. (57) Wang, Q.; Feder, A.; Mazur, E. J. Phys. Chem. 1994, 98, 12720.
pH Effects on Calixarene Monolayers
Figure 6. fs and ∆fs,c vs Π for p-dioctadecanoylcalix[4]arene monolayers with NBD-PE on 0.01 M HCl (pH ≈ 2), water, and 0.04 M NaCl (pH ≈ 5.5), and 0.02 M Na2B4O7 + 0.025 M HCl (pH ) 8.39) for k ) 328 cm-1 at 23 °C. The dotted and solid curves in the upper frame correspond to Limit I and Limit III, respectively, and the dashed, solid, and dotted curves in the lower frame represent Limit II, Limit III and Limit I, respectively.
Figure 7. ∆fs,c,eq vs fs,eq for p-dioctadecanoylcalix[4]arene monolayers without NBD-PE on water at 23 °C. The open triangles correspond to the data for Π < 1 mN‚m-1, while the filled triangles correspond to the data for Π > 1 mN‚m-1. The open circles correspond to data for poly(vinyl acetate). The solid and dashed curves correspond to constant dynamic dilational elasticity, d, and surface viscosity, κ, at the reference state (water, 25 °C and k ) 324 cm-1), respectively. The roman numerals I, II, and III indicate, respectively, the limits of pure liquid dynamics, the maximum damping for a perfectly elastic surface film, and infinite lateral modulus dynamics. The data points represent average values of three wave vectors. Error bars of (0.5% on fs,eq and (5% on ∆fs,c,eq have been omitted for clarity.
An alternative way to represent the results is to adopt an analysis scheme first used by Ha˚rd and Neuman.58 For this method, frequency-independent data from multiple wave vectors can be placed on a single plot of ∆fs,c,eq versus fs,eq. This is illustrated in Figure 7, for p-dioctadecanoylcalix[4]arene films using water as the subphase (pH ≈ 5.5), for the same data included on the plots shown in Figures 4 and 5. Essentially identical profiles are observed for the other subphases. To create the plot, d and κ are calculated from the experimentally determined fs, ∆fs,c, k, and σs, and known values of F and η, with the (58) Ha˚rd, S.; Neuman, R. D. J. Colloid Interface Sci. 1987, 120, 15.
Langmuir, Vol. 15, No. 5, 1999 1723
assumption of µ ) 0. Next, the equivalent values of fs,eq and ∆fs,c,eq for a reference surface (water, 25 °C) are calculated by inputting the same values of d and κ, together with kref ) 324 cm-1, σs,ref ) 71.97 mN‚m-1, Fref ) 997 kg‚m-3, ηref ) 0.894 mPa‚s, and µref ) 0. Considering the observation of frequency independence, values of fs,eq and ∆fs,c,eq for different wave vectors are averaged on the plot and errors can be estimated as (0.5% for fs,eq and 5% for ∆fs,c,eq. Also included on this plot are solid and dashed curves, corresponding to different values of d and κ for the reference surface. From this plot it is clear that p-dioctadecanoylcalix[4]arene forms very rigid films for Π > ≈1 mN‚m-1 (filled symbols). For this material, the surface viscoelastic parameters are large (d > 50 mN‚m-1, κ > 50 × 10-5 mN‚s‚m-1) and approach the infinite limit within experimental error. For comparison, the profile for an almost purely elastic monolayer of poly(vinyl acetate) is also shown in Figure 7 as a reference. The scatter of values between the pure liquid limit, I, and the infinite lateral modulus, III, for Π < 1 mN‚m-1 (open symbols) is consistent with area averaging the coalescing condensed p-dioctadecanoylcalix[4]arene patches which coexist with gaseous film. These condensed patches have very large viscoelastic parameters which suppress the resonant coupling between transverse and longitudinal motion. As noted above, this suppresses the damping coefficient which is maximal for perfectly elastic surface films with moderate elasticities, II (d/σs ≈ 0.17, κ and µ ) 0 mN‚s‚m-1). These results are consistent with the expected conelike conformation of the calixarene molecules at A/W. The absence of any pH effect indicates that it is the packing of the aromatic rings and long hydrocarbon chains rather than headgroup interactions which are the most important factors influencing the viscoelastic properties of p-dioctadecanoylcalix[4]arene obtainable by SLS. This interpretation is also consistent with reported s values for p-tert-butylcalix[6]arene20 and it is anticipated that this result can be generalized for all calixarene monolayers in the absence of long flexible hydrophilic headgroups. Conclusions Stable monolayers of p-dioctadecanoylcalix[4]arene exhibit substantial changes in molecular packing because of the enhanced electrostatic repulsions accompanying the stepwise dissociation of the phenol groups. These changes in area per molecule with increasing pH can be modeled in terms of two apparent surface pKa values and three chemical species with unique areas per molecule. This most likely corresponds to the dissociation of only two phenolic protons with pKa,1 ) 6.4, pKa,2 ) 9.2, and pKa,3 and pKa,4 . 12. In contrast to the isotherm results, pH-dependent SLS studies of surface viscoelasticity showed no detectable differences, as all films approach the limit of infinite lateral modulus dynamics. This implies aromatic ring and side chain packing rather than electrostatic headgroup interactions are the predominant factors responsible for the rigid films observed here. Considering the importance of pH in ligand-binding applications of calixarenes or their use in modeling of biological systems, additional isotherm studies are warranted. In particular, the synthesis of calixarene molecules containing different nonionic groups with varying electronwithdrawing strengths at each of the para positions would be useful in sorting out how many protons dissociate. Such a system could also demonstrate whether pH-dependent isotherm studies of calixarene molecules can be used as
1724 Langmuir, Vol. 15, No. 5, 1999
Esker et al.
a reliable method to probe pKa values in these generally insoluble materials. Acknowledgment. This research is supported in part by an NSF grant (DMR 92-03289), Eastman Kodak, and the Helfaer Endowment Fund. A.R.E. was supported in part by a National Research Service Award 5 T32 GM08349 from the National Institute of General Medical Sciences and the Henkel Corporation 1994-1995 Research Fellowship in Colloid and Surface Chemistry. K.N. is grateful to the Organic Chemistry Research Center (OCRC) for their support.
xH2L-2 )
Ka,3Ka,4 Ka,3 [H+]2 [H+] + +1+ + + Ka,1Ka,2 Ka,2 [H ] [H+]2
xH3L- )
[H+] Ka,2 Ka,3 Ka,3Ka,4 [H+] [H+]2 + +1+ + + Ka,1Ka,2 Ka,2 [H ] [H+]2
Ka,3Ka,4 Ka,3 [H ] [H ] + +1+ + + Ka,1Ka,2 Ka,2 [H ] [H+]2
(A3)
xHL-3 )
[H+] Ka,3Ka,4 Ka,3 [H+]2 [H+] + +1+ + + Ka,1Ka,2 Ka,2 [H ] [H+]2
(A4)
and
Ka,3Ka,4
Using the condition specified by eq 2 for the surface mass balance containing un-ionized calix[4]arene with four anionic species, it is possible to express the mole fraction of each species at the interface in terms of only [H+] and the acid dissociation constants:
xH4L )
+
Ka,3
Appendix
[H+]2 Ka,1Ka,2
1 + 2
(A1)
xL-4 )
[H+]2 Ka,3Ka,4 Ka,3 [H+]2 [H+] + +1+ + + Ka,1Ka,2 Ka,2 [H ] [H+]2
(A5)
To fit the data of Figure 3, it is necessary to make several assumptions. The first of these is the assumption that area additivity holds, whereby the area per molecule at a given surface pressure can be written as the sum of the area contributions of each species at the interface:
A(Π) ) xH4LAH4L(Π) + xH3L-AH3L-(Π) + xH2L-2AH2L-2(Π) + xHL-3AHL-3(Π) + xL-4AL-4(Π) (A6) (A2)
which is expressed in shorthand as eq 3. LA970016B
