pubs.acs.org/Langmuir © 2010 American Chemical Society
Potentiometric Titrations of Five Synthetic Tetraacids as Models for Indigenous C80 Tetraacids Ola Sundman,*,† Erland L. Nordga˚rd,‡ Brian Grimes,‡ and Johan Sj€oblom‡ †
Department of Chemistry, Umea˚ University, SE 901 87, Umea˚, Sweden and ‡Ugelstad Laboratory, Department of Chemical Engineering, NO 7491, Trondheim, Norway Received June 29, 2009. Revised Manuscript Received December 3, 2009
The acid/base properties, critical micelle concentrations (cmcs), and pH-dependent solubility of five synthetic tetraacids have been studied at several ionic strengths (20-600 mM NaCl) and in the pH range of 1.5-11 using high precision potentiometric titrations, tensiometer measurements, and UV spectroscopy, respectively. The molecular weight of the tetraacids ranged between 478 and 983 g/mol. The potentiometric titration data was evaluated in terms of thermodynamic equilibrium models, developed in the light of relevant solubility data, Langmuir monolayer compressions and cmc of the different tetraacids. The results indicate that for two of the tetraacids, called BP5 and BP7, two chemical forms fully dominate the speciation of the monomers; the insoluble fully protonated form, and the soluble fully deprotonated form. The partly protonated species, only play a very minor role in the speciation of these tetraacids. For the other tetraacids the results are more complicated; for the smallest tetraacid, called BP1, all species seem to play important roles, and for the most hydrophobic, BP10, the formation of micelles and aggregates severely complicates the evaluation of the speciation. For the tetraacid BP3 one of the partly deprotonated forms seems to be important, thus confirming the structure to properties relationship. In spite of the complicated micelle formation chemistry, and although not actually measured, the acid/base properties for the monomers of BP10 were interpreted by means of surface charge densities of the micellar aggregates. The modeling indicates an increase of the aggregation number of the micelle upon acidification, a result of formation of mixed micelles incorporating the fully protonated and deprotonated species. An intrinsic pKa of 5.4 for BP5 was used to model the monomer pKa of BP10, and corresponded well with a monolayer acidity constant pKsa of 5.5 obtained from surface collapse pressures of Langmuir monolayers as a function of pH.
Introduction The problems associated with the occurrence of naphthenic tetraacids in crude oil, e.g. depositions on equipment, have been widely described in literature.1-3 The basic chemistry of these compounds is therefore interesting and economically important, and provides background for investigations. However, the diversity of these naturally occurring molecules, hence forth referred to as indigenous tetraacids or ARN acids, and a complicated and time-consuming purification process, severely complicates the studies of their chemical and physical properties. Therefore, investigations of the chemical properties of these compounds have, to a significant extent, lately been done by means of model compounds. In previous papers, the synthesis3 and some of the physiochemical properties4 of several such synthetic model compounds were studied. An important finding in the latter paper was that, in particular, one of the synthesized compounds, called BP10, showed chemical and physical properties very similar to those of the indigenous tetraacids. The problems associated with ARN acids are mostly predominant at the w/o interface, and understanding the behavior of such compounds in aquatic environment would be advantageous. So far, no thermodynamic modeling studies have been presented with respect to them. In the *Corresponding author. Ola Sundman, Department of Chemistry, Umea˚ University, SE-90187 Umea˚. (1) Brandal, Oe.; Hanneseth, A.-M. D.; Hemmingsen, P. V.; Sj€oblom, J.; Kim, S.; Rodgers, R. P.; Marshall, A. G. J. Dispersion. Sci. Technol. 2006, 27, 295–305. (2) Lutnaes, B. F.; Brandal, O.; Sjoblom, J.; Krane, J. Org. Biomol. Chem. 2006, 4, 616–620. (3) Nordga˚rd, E. L.; Sj€oblom, J. J. Dispersion Sci. Technol. 2008, 29, 1–9. (4) Nordga˚rd, E. L.; Magnusson, H.; Hanneseth, A.-M. D.; Sj€oblom, J. Colloids Surf. A 2009, 340, 99–108.
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present paper, several synthetic tetraacids have been examined by means of high precision potentiometric titrations in order to understand, and to provide input to modeling of the aquatic acid/ base chemistry of these interesting, hydrophobic, compounds. It is commonly accepted that the activity of Hþ at an interface deviates from the aqueous bulk phase activity.5,6 The surface of a micelle can be considered as an interface where the proton activity will change due to the surface charge potential of the micelle, compared to the bulk phase. Studied using indicator dyes solubilized in micelles of varying surface charge have shown that the apparent pKa values for the dyes change compared to their pKa values in aqueous solutions. Depending on the surface charge of the micelle, the apparent pKa value will increase or decrease. As an example, the solubilization of hydroxycoumarin in micelles of SDS, a negatively charged surfactant, increased the pKa value with nearly 3.5 pH units, compared to solubilization in pure water.5 The acid/base properties of dyes will also reflect the acidity constant for the surfactants comprising the micelles. Consequently, titration of a negatively charged surfactant in a micelle may give completely different apparent pKa values than its intrinsic acidity constant at infinite dilution. Tetrameric acids, shown to be surface and interfacially active, can thus be expected to form micelles in aqueous solutions and apparent pKa values different from their intrinsic pKa values. As results, potentiometric pH-titration of a series of tetrameric acids should be interpreted in terms of their cmc values and if they are present in monomeric or micellar state. (5) Fernandez, M. S.; Fromherz, P. J. Phys. Chem. 1977, 81, 1755–1761. (6) Mukerjee, P.; Banerjee, K. J. Phys. Chem. 1964, 68, 3567–3574.
Published on Web 01/06/2010
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Figure 1. Structures of the investigated tetraacids, BP10, BP7, BP5, BP3 and BP1. Also the structure of one of the most dominating indigenous naphthenic C80 tetraacids is shown.
The previously studied model tetraacid, BP10, have been reported to have a very low cmc.4 Since several studies of titration of micelles report a significant difference between the apparent acid/base properties of monomers and micelles,7-9 it was decided that several synthetic compounds, with different critical micelle concentrations (cmcs), would be studied. For this task, the model substances, BP10, BP7, BP5, BP3, and BP1 were chosen, where BP stands for benzophenone, which is the aromatic core, and 10, 7, 5, 3, and 1 stands for the number of carbons in the attached alkyl chain. These five tetraacids (TAs) are shown in Figure 1, where also a proposed structure of the most abundant ingenious tetraacid2 is shown. Potentiometric titrations are preferable performed at constant ionic strengths >100 mM. Such conditions were therefore tested in the present work. However, since the cmcs of the tetrameric acids (TAs) vary with ionic strength, and since the acid/base properties of carboxylic acids are known to depend upon the ionic strength, it was decided that the study should involve also a variation of the ionic strength conditions. Finally, to provide an even more solid foundation for the evaluation of the titration data, several solubility experiments, film compressions and cmc studies were performed.
Experimental Section Chemicals. The chemicals for organic synthesis were all purchased from Sigma-Aldrich, and used without further purification. For the potentiometric titrations all aqueous solutions were prepared from deionized (Milli-Q 185 Plus) and boiled (to remove all gas) water. Dried (180 C overnight) NaCl(s) (AnalaR NORMAPUR) was used to prepare all ionic media. The HCl solutions were prepared from dilute HCl (AnalaR (7) Kanicky, J. R.; Shah, D. O. Langmuir 2003, 19, 2034–2038. (8) Goldsipe, A.; Blankschtein, D. Langmuir 2006, 22, 9894–9904. (9) Dupont-Leclercq, L.; Giroux, S.; Henry, B.; Rubini, P. Langmuir 2007, 23, 10463–10470.
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NORMAPUR), calibrated using dried (80 C overnight) Trizma Base (SIGMA). The dilute NaOH solutions were prepared from a concentrated NaOH solution, filtered through a glass funnel to remove possible contaminants of solid carbonates, and calibrated via titration with dilute HCl(aq) of known concentration. Synthesis. All the synthesis work was preformed at the Ugelstad Laboratory, NTNU, Trondheim, Norway. BP10 was synthesized as described by Nordga˚rd et al.,3 and the BP5 and BP7 material was synthesized according to a similar procedure, where the methyl 11-bromoundecanoate had been replaced with ethyl 6-bromohexanoate and methyl 8-bromooctanoate, respectively. BP1 and BP3 were synthesized via their methyl and ethyl esters, respectively, by reacting 2,20 ,4,40 -tetrahydroxybenzophenone with methyl bromoacetate or ethyl 4-bromobutyrate, in K2CO3/acetone at 65 C for 16-72 h. BP1 and BP3 were obtained by further hydrolysis with NaOH in MeOH:H2O (4:1, 8 h) and acidification with HCl (2M) which precipitated the undissociated TA as a white solid. For use in cmc measurements, the tetrasodium (Na4L(s)) salts of BP5-10 were obtained from the acid form by suspension in a small amount of methanol where the TAs dissolved upon heating. The acids where converted to their tetrasodium salts by adding saturated NaOH in methanol until pH > 12. The salts precipitated upon addition of acetonitrile and were filtered and dried. Cmc Measurements. The cmcs of the TAs were measured using surface tension measurements with a Sigma70 Tensiometer (KSV Instruments, Finland) using a De Nuoy ring probe, at a pH of approximately 11. The TA was added as the Na4L salt, dissolved in 1 mM NaOH with NaCl added to the appropriate [Naþ]. These measurements were all performed at Ugelstad Laboratory, NTNU, Trondheim, Norway. An automatic titration setup was utilized with two titrators (Schott, Titronic); one for addition and one for removal of solution to change the concentration. Both titrators were computer-controlled and 15 points per decade were obtained with a maximal deviation at equilibrium of 0.02 mN/m during three consecutive measurements. The solution was stirred with a magnetic stirrer for 300 s and left to stand for another 300 s before measuring the next point. Langmuir 2010, 26(3), 1619–1629
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It is commonly known that the cmc decreases at increasing salinity and the reason is that addition of salt reduces the electrostatic repulsion between the head groups in the micelle and lowers the energy needed for micellization. Consequently, the cmc will appear at an earlier concentration. A relationship between cmc and salinity has been empirically described by the Corrin-Harkins equation10-12 log cmc ¼ -a þ b log½Naþ tot
ð1Þ
To visualize the data a plot of log(cmc) vs log [Naþ]tot was constructed. Potentiometric Titrations. All titrations were preformed at the Department of Chemistry, Umea˚ University, on the highprecision potentiometric titration equipment, developed at location, and used in several previous papers.13-16 All titrations were performed in an oil bath thermostated at 25 ( 0.1 C and in a thermostated room at 25 ( 1 C. Before and during the titrations all solutions were protected from CO2 contamination using inert N2-gas which was washed through 10% H2SO4(aq) and 10% NaOH(aq). The cell used for the determination of [Hþ] was )
-Ag/AgCl|ionic media (NaCl) solution/suspension in NaCl(aq)|glass electrodeþ
The potential (E, in mV) of this cell is given by eq 2: E ¼ E0 þ
RT ln 10 log½Hþ þ Ej F
ð2Þ
where E0 is an apparatus constant, determined in the initial part of each titration by reacting a dilute HCl-solution with OH-, in 4 to 10 steps, until the acid was nearly neutralized. R in eq 2 is the gas constant, T is the absolute temperature and F is the Faraday constant. Ej is a function of [Hþ], the two junction potentials jac and jalk, and the ionic product of water, Kw, according to eq 3: Ej ¼ jac ½Hþ þ jalk Kw ½Hþ -1
ð3Þ
In eq 3, relevant values for Kw, jac, and jalk were adopted from the literature.17 The equilibrium condition was set to a drift in E less than 0.2 mV/h. After calibration, the tetraacids were added in solid form to a total concentration of approximately 1 mM. Dilute HCl(aq) and NaOH(aq) solutions with corrected ionic strength (NaCl), were used in the acidic direction and the alkaline direction, respectively. Solubility Experiments. The aqueous solubility of the tetraacids, as a function of pH, and at constant ionic strength of 600 mM Na(Cl) was analyzed via batch experiments at the Department of Chemistry, Umea˚ University. The 10 mM solutions of the tetraacids were prepared by dissolving a weighed sample of the tetraacid in an above stoichiometric amount of dilute NaOH(aq) in a volumetric flask, and adding solid NaCl to the appropriate total sodium concentration. The suspended solid material were then dissolved using an ultrasonic bath (Bandelin, Sonorex Digitech). Different amounts of dilute HCl(aq) were added to the samples, which were left on an end-overend rotation test tube holder for 24 h or more. Following this equilibration, the pH of the samples were carefully measured using a combination pH electrode (Orion Ross 8103SC, Thermo Electron Corporation), (10) Corrin, M. L.; Harkins, W. D. J. Am. Chem. Soc. 1947, 69, 683–688. (11) Jacquier, J. C.; Desbene, P. L. J. Chromatogr. A 1996, 743, 307–314. (12) Matsuoka, K.; Suzuki, M.; Honda, C.; Endo, K.; Moroi, Y. Chem. Phys. Lipids 2006, 139, 1–10. (13) Sj€oberg, S.; H€agglund, Y.; Nordin, A.; Ingri, N. Mar. Chem. 1983, 13, 35– 44. € (14) Ohman, L.-O.; Sjoeberg, S. Acta Chem. Scand. 1981, A35, 201–12. (15) Laine, J.; Løvgren, L.; Stenius, P.; Sjøberg, S. Colloids Surf., A 1994, 88, 277–87. € (16) Sundman, O.; Persson, P.; Ohman, L.-O. J. Colloid Interface Sci. 2008, 328, 248–256. (17) Sj€oberg, S.; H€agglund, Y.; Nordin, A.; Ingri, N. Mar. Chem. 1983, 13, 35–44.
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Table 1. General Equilibrium Matrix Used in the Simulations and Optimizations of the Simulation Models for the Tetraacidsa Hþ
log β
L4-
phase
þ
0 1 0 soluble H 0 0 1 soluble L4opt 1 1 soluble HL3opt 2 1 soluble H2L2opt 3 1 soluble H3L opt 4 1 solid H4L (s) -pKw -1 0 soluble OHa The β-values indicated by “opt” were optimized for each of the models evaluated.
filled with 0.6 M NaCl and calibrated using a solution of known [Hþ] and by using eq 2. Following this, the solid material was removed by centrifugation and the remaining clear solutions were filtered through 0.20 μm filters before analysis. The amount of remaining TA(aq) in the samples were then finally analyzed by UV measurements (Shimadazu UV-2100) at 322 nm. Langmuir Monolayer Compressions. Surface pressure-area isotherms were recorded using a KSV Langmuir trough (Helsinki, Finland) of effective film area 364 75 mm at ambient temperature. The trough was made of Teflon and the barriers of Delrin. The trough and barriers were thoroughly cleaned with acetone or ethanol, tap water and ultrapure water before use, and by aspirating the surface with a Pasteur pipet connected to a vacuum-aspirator. The surface was assumed pure when the surface pressure of subphase only did not exceed 0.5 mN/m upon full compression. Isotherms were recorded at different pH of the aqueous subphase; pH 2.2 adjusted with 1 M HCl, pH 5.6-5.8 using ultrapure water with a resistivity of at least 18.2 Ω and pH 7 and 8 buffers from Merck. When necessary, additional NaCl was added in order to obtain equal Naþ concentrations for all buffers. BP10 was dissolved in spectrophotometric grade chloroform at a concentration of 0.3 mM. An amount of 40 μL was spread on the subphase with a 50 μL Hamilton syringe. The solvent was allowed to evaporate over 5 min before compression at a barrier speed of 5 mm/min. Premicellar Equilibrium Modeling. When no micelles are formed, the tetraacids can be treated as an ideal tetrameric acid. To model the acid/base properties of these ideal tetrameric acids, the following principle was applied; the system was limited to two components; Hþ and the fully deprotonated tetraacid studied, L4-. Only monomers were allowed to form, and the insoluble tetraacid was considered to be a solid product. All other monomers were considered to be soluble aquatic species, cf. Table 1. A general equation describing the formation of each of these species of a tetraacid can then be written as pHþ þ L4 - h Hp Lp -4
ð4Þ þ
where p is the stoichiometric number of H for each molecule of TA. The general thermodynamic formation constant, β0p,1 for a particular species may then be written as β0 p, 1 ¼
fHp Lp -4 g ½Hp Lp -4 γHp Lp-4 ¼ þ p 4p þ p 4fH g fL g ½H ½L ðγHþ Þ γL4 -
ð5Þ
where γ represents the activity coefficients as described by eqs 6 and 7. fAg ¼ ½AγA log γ ¼ -0:511 3 z
2
! pffiffiffi pffiffiffi I pffiffiffi -0:2 3 I 1þ I
ð6Þ ð7Þ
In eq 7, z denotes the charge of the ion considered, and I is the ionic strength. The activity of solid phases is either 1, if it exists, or 0, if it does not exist. DOI: 10.1021/la902326y
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If a constant ionic strength and temperature is applied, and thus constant activity factors can be assumed, the following expression, eq 8, valid only at a specific ionic strength and temperature can be applied for the soluble species. βp, 1 ¼
½Hp Lp -4 ½Hþ p ½L4 -
ð8Þ
The formation constants, βp,1, can then be used to model the acid/base properties of the TA at the specified conditions. Also, the acid/base model can be used to simulate the speciation and solubility of the TAs. These activity-to-concentration calculations are performed applying the WinSGW software, and the resulting equilibrium model is an activity-scale equilibrium model. By using the principles described above, the general equilibrium matrix presented in Table 1, was considered the simplest model suitable to simulate the systems. For the modeling of the acid/base properties and optimization of the log β values WinSGW18,19 was also applied. To optimize the log β values, rough estimations were tested in the simulation software until a decent fit of the theoretical titration curve to the potentiometric titration data was achieved. When a decent model was achieved, the values were mathematically optimized to describe the data. In the program, the following relation is utilized: SSQ ¼
X ðlog½Hþ exp - log½Hþ calc Þ2 þ
ð9Þ
½COO - H -h þ Kw h -1 ¼ ½TA B
ð10Þ
where H and B are the total concentration (mol/dm3) of protons and tetraacid, respectively. h is the concentration (mol/dm3) of free protons, [Hþ], and Kw is the autoionization product of water at the ionic strength in question. If Z is plotted as a function of -log[Hþ], the degree of deprotonation over the whole pH-interval can easily be overviewed. Although not entirely correct, apparent pKa values, for each of the species, i.e., H4L(s), H3L-, H2L2-, and HL3- can be evaluated as Z = -0.5, -1.5, -2.5, and -3.5 respectively. Postmicellar Modeling. For the experimental conditions described in this work, the concentration of the aggregate (micelle) is taken to be very dilute, such that the interaction between micellar aggregates can be neglected and the concentration of the micelle only determines the size of the electroneutral volume associated with each micelle. Additionally, it is assumed that the electrostatic free energy of the charged micelles does not vary significantly through various important configurations and the configurational entropy of the micelle as well as the average local concentration of acidic groups should depend only on (18) Eriksson, G. Anal. Chim. Acta 1979, 112, 375–383. (19) Karlsson, M.; Lindgren, J. 2000; p The WINSGW software was developed at Department of Inorganic Chemistry, University of Umeå. See http://www.dagger.mine. nu/MAJO/WinSGW_eng.htm for more details. (20) Marcus, R. A. J. Chem. Phys. 1955, 23, 1057–68.
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N d2 Φ 2dΦ F X zi e ¥ Φ þ z C exp i i dr2 r dr εεo i ¼1 kT
ð11Þ
In eq 11, r is the radial direction, Φ denotes the electrostatic potential, ε represents the relative static dielectric constant, εo is the permittivity of free space, F denotes the Faraday constant, N represents the number of charged species in the liquid phase and zi (i = 1, 2, ..., N) is the charge number of ionic species i, C¥ i (i = 1, 2, ..., N) denotes the concentration of species i at a distance far the charged surface where dΦ/dr = Φ = 0 and P away from ¥ i=1,N zi Ci = 0, e represents the charge of an electron, k is the Boltzmann constant, and T denotes the absolute temperature. Assuming that the protonated and dissociated groups are uniformly distributed across the surface of the spherical model micelle, and that the solution is electrically neutral at the boundary of the volume element, the boundary conditions of eq 11 can be expressed as follows: at r ¼ Rm ,
dΦ σs 1 Remnag ¼ ¼ εεo dr εεo 4πR2m
ð12Þ
dΦ ¼0 dr
ð13Þ
at r ¼ Rv ,
þ
In this equation -log[H ]exp is the measured -log[H ], i.e., in principle the pH, in the experimental point from the potentiometric titration, and -log[Hþ]calc is the respective calculated value from the ideal model. The log β values in the models are optimized by iteration until the smallest sum of error squares possible is achieved. Each system, at the specified ionic strength, is then optimized to the data. Z Plots. The data from the potentiometric titrations are illustrated in the form of Z-plots, where Z is defined as the average number of protons adsorbed to each molecule of acid, (TA). This definition is shown in eq 10. Z ¼ -
a configurational variable, h.20 Consequently, the electrostatic potential in each sub volume associated with a micelle can be described by the Poisson-Boltzmann equation.20,21 Assuming that the micelle can be described as a charged sphere, the Poisson-Boltzmann equation can be expressed as follows:
In eqs 12 and 13, Rm denotes the radius of the model spherical micelle, Rv is the radius of the volume of solution associated with each micelle (for all practical purposes involved in this work, Rv can be taken as any arbitrarily large value such that dΦ/dr = Φ = 0 at r = Rv due to the fact that the micelles can be considered to be near infinite dilution at the cmc), σs is the surface charge density of the model spherical micelle, R represents the degree of dissociation of the acidic surface groups, nag is the aggregation number of the micelle, and m denotes the total number of acidic groups on each surfactant in the micelle. For a given degree of dissociation, eqs 11-13 are solved numerically by the method of orthogonal collocation on spectral elements22 to obtain the spatial profile of the electrostatic potential, Φ. Once the functional form of the electrostatic potential, Φ, is know, the titration curve of a polyelectrolyte titrated with HCl can be determined from the following equation:20 Δμ0 pKa ¼ þ 2:3kT
R
Φjr ¼Rm σs dA þ pKa0 2:3mRkT
ð14Þ
In eq 14, Δμ0 represents the difference of the chemical potential of the neutralized and un-neutralized acidic groups, and pK0a denotes the intrinsic acid constant which is defined as the apparent pKa at the limit of zero degree of dissociation (pK0a = limRf0 pKa(R)).23 The space charge density, Fcd, in the ionic solution surrounding the spherical model micelle is given by eq 15. Fcd ¼
zi e zi Ci¥ F exp Φ kT i ¼1
N X
ð15Þ
Equations 14 and 15 can be employed along with the solution to eqs 11-13 in order to determine the appropriate value of the (21) Gunnarsson, G.; J€onsson, B.; Wennerstr€om, H. J. Phys. Chem. 1980, 84, 3114–21. (22) Grimes, B. A. Ph.D. Thesis, University of Missouri-Rolla: Rolla, MO, 2002. (23) Sonnefeld, J.; Vogelsberger, W.; Rudakoff, G. Chem. Phys. Lett. 1991, 176, 309–14.
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Figure 2. (a) Surface pressure-area isotherms of Langmuir monolayers of BP10 at different aqueous pH with [Naþ] = 0.1 M, and (b) surface collapse pressure versus the final aqueous pH. The collapse pressures are taken where the horizontal breaks occur and the lines have been fitted to eq 16 with the following data for BP10: ω = 300 A˚2, T = 298 K, πZH = 11.7, πZNa = 17, and pKsa= 5.5.
aggregation number, nag, required to fit an experimental titration curve. In this work, this is carried out for BP10.
Results Monolayer Dissociation Constant. A convenient way to obtain an estimate of the dissociation of a surface active naphthenic acid when present at an interface is by use of the Langmuir trough technique. A monolayer of the surfactant to be studied is spread on an aqueous phase, and the film is compressed by two moving barriers. The surface pressure, π, is recorded and when the pressure suddenly drops or remains constant after a steady increase, the film has most likely collapsed. Havre et al. have shown that it is possible to obtain a monolayer acidity constant, Ksa, for a naphthenic model monoacid, 5β(H)-cholanic acid, by correlating the surface collapse pressure to the aqueous pH under formation of sodium naphthenates.24 Assuming the same partial molecular area of the acid and the soap, (ωZH = ωZNa = ω), the collapse pressure of the monolayer, πc,m, can be found in eq 16, πc, m
2 ! -πc, ZH ω kT 4 ½Hþ kT ln e ¼ ω Kas þ ½Hþ ! # -πc, ZNaω Kas kT e þ Kas þ ½Hþ
ð16Þ
It was investigated if this relationship could also be used to find apparent monolayer acidity constant for BP10. Figure 2a shows the isotherms obtained for BP10 as a function of pH and [Na]þ = 0.1 M. Surface collapse pressures obtained from Figure 2a together with a plot of the fitted curve according to eq 16 is given in Figure 2b. The fitting of the theoretical curve to the experimental values gives pKsa = 5.5 for BP10. The highest collapse point was found at pH 8 due to enhanced water solubility at higher pH and, assuming that the collapse point at pH 8 is close to the maximum collapse pressure, the data fits quite well to eq 16. However, the equation is dependent on similar partial molecular area of acid and soap. This can normally be found from where the increase in pressure sets in, but for BP10 this was difficult to obtain. Therefore, the limiting area, obtained by extrapolation of the linear part (24) Havre, T. E.; Ese, M.-H.; Sj€oblom, J.; Blokhus, A. M. Colloid Polym. Sci. 2002, 280, 647–652.
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Figure 3. Solubility of the studied TAs as a function of -log [Hþ] at 600 mM Na(Cl).The symbols represent data recorded for (2) BP10, (1) BP7, ([) F BP5, (f) BP3, and () BP1. The lines represent the solubility as predicted by the acid/base models presented in the Supporting Information, for BP7 (solid line) BP5 (dashed-dotted line), BP3 (dashed line) BP1 (dotted line) respectively. The total concentration of the respective tetraacid was 3.33 mM in all experiments and simulations.
of the pressure increase may be a better approach in this case. For BP10 these areas were found to be located around 300 A˚2 at pH < 7, and this value has been used in the fitting process. The dissociation data for BP10 resembles what was found for 5β(H)-cholanic acid, i.e., pKsa= 5.65.24 However, the methodology of surface collapse pressure will not take into account the aqueous bulk phase behavior of surface active compounds, such as the influence of the solubility of all species and micellization. A thermodynamic evaluation through the whole sequence, from dissolution of solid material to monomers in solution, possible via micellization, is necessary to understand the acid/base chemistry of these fairly complex molecules. The next sections will consequently deal with the acid/base behavior from a bulk phase perspective including factors like solubility and micellization. It will later be shown however that the monolayer acidity constant obtained for BP10 is comparable to the intrinsic acidity constant for BP5, a less hydrophobic tetraacid. Solubility of Synthetic Tetraacids. The solubility of the tetraacids was studied in 600 mM NaCl ionic medium. This medium was chosen since the problems caused by the indigenous tetraacids often occur in quite saline waters, i.e., seawater. DOI: 10.1021/la902326y
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Figure 4. Surface tension versus concentration obtained by tensiometer measurements at pH ≈ 11. The data for (a) BP10, (b) BP7, and (c) BP5 at different ionic strengths. The cmc values have been obtained by visual consideration where the slope intersects the constant surface tension value after cmc. (d) Corrin-Harkins plot of log cmc vs log [Na]tot for BP10, BP7, and BP5. The solid lines were fitted with linear regression and the parameters are given in Table 2. Table 2. Cmc Data Obtained for BP10-5 as a Function of NaCl Added and Parameters in the Corrin-Harkins Equation Fitted to the Experimental Cmc Data, at pH ≈ 11, as a Function of [Naþ]tot cmc [M] compound
20 mM NaCl
100 mM NaCl
200 mM NaCl
600 mM NaCl
BP10 2.2 10-5 5.1 10-6 3.8 10-6 5.9 10-7 1.5 10-3 7.0 10-4 1.4 10-4 BP7 4.1 10-3 2.0 10-2 1.6 10-2 8.4 10-3 BP5a a The cmc of BP5 at 20 mM NaCl was too high to be measured with the available amount of compound.
The results, shown in Figure 3, show that the solubility of the different TAs, as a function of -log [Hþ], show similar type of behavior, but at different -log[Hþ]. Interesting to see in Figure 3 is that the acid/base models evaluated from the potentiometric titrations given later, and presented in the Supporting Information, accurately predict the solubility. A rapid increase in solubility with -log[Hþ] can, for all tetraacids, be seen in a narrow -log[Hþ] interval. This interval is shifted upward with the length of the alkyl chain, and this goes in good agreement with all the data in this study. It is likely that the solubility of BP10 does follow the same simple pattern as the solubility of BP1-BP7, i.e., as the sum of deprotonated molecules, but we have not been able to model this solubility. Critical Micelle Concentrations. Critical micelle concentrations of the different acids were studied at different ionic strengths. The results, according to the tensiometer technique used, are presented in Figure 4a-d and Table 2. The parameters in eq 1 fitted to the experimental data for BP10, BP7, and BP5 are 1624 DOI: 10.1021/la902326y
a
b
R2
6.33 4.07 2.21
-1.03 -1.23 -0.69
0.9559 0.9905 1.0000
also given in Table 2. The cmcs of BP1 and BP3 were found to be too high to be interesting. From the data the cmc can be estimated at a given salinity. These results confirm that the alkyl chain length have a very significant impact on the cmc of the tetraacids, as can be expected. From parts a and d of Figure 4, it was concluded that the cmc for BP10 precluded titrations of BP10 monomers in any Na(Cl) medium. Titrating on a micellar system will complicate the thermodynamic behavior and interpretation of the system. The use of the other tetraacids was necessary for studying the acid/ base properties of tetraacid monomers. It was thus considered a good approach to use the titration data for BP5 and BP7 to understand the properties of monomeric BP10. Acid/Base Properties of TA Monomers. To understand the acid/base chemistry of the tetraacids, it is important to differentiate between the acid/base properties of the TA monomers from that of aggregated TA. The cmc of BP10 was early on determined to be too low to allow for this. The cmcs of BP5, BP3, Langmuir 2010, 26(3), 1619–1629
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Figure 5. Z-plot for BP5. The symbols represent data recorded at (9) 20 mM, (2) H 50 mM, (f)100 mM, and (() 600 mM Na(Cl) ionic strengths, respectively. The dotted, dashed-dotted, dashed and solid lines represent the respective acid/base models, as presented in the Supporting Information.
Figure 6. Z-plot for BP3. The symbols represent data recorded at (9) 20 mM, (f)100 mM, and ([) 600 mM ionic strengths, respectively. The dotted, dashed and solid lines represent the respective acid/base models, as presented in the Supporting Information.
and BP1, however, were high enough to enable potentiometric titrations of the monomers at all ionic strengths of interest. The cmc of BP7 was found to be ∼4 mM in 20 mM Na(Cl) and ∼0.14 mM in 600 mM Na(Cl). By using a total concentration of ∼1 mM, it was thus possible to titrate BP7 both above and below the cmc depending on the salinity. In Figure 5 all the potentiometric titration data recorded for BP5 is shown. From this figure it can be seen that the acid/base properties of BP5 show a dependence of ionic strength (20600 mM Na(Cl)), but that the shape of the titration curve is unchanged. The steep and constant slope of the titration curve is indicative of a solid phase in equilibrium with only one soluble species. The slope itself can not predict the identity of this species, but combined with the observation that the experimental points and the theoretical model levels out at Z ≈-4, the soluble species can be identified as the fully deprotonated L4- species. As an example, the proposed speciation, in 600 mM Na(Cl), as a function of -log [Hþ] is shown in Figure 9a and illustrates this. For the tetraacid with slightly shorter alkyl chains, BP3, similar, but not exactly the same, properties could be observed. The data Langmuir 2010, 26(3), 1619–1629
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Figure 7. Z-plot for BP1. The symbols represent data recorded at (9) 20 mM, (f)100 mM, and ([) 600 mM ionic strengths, respectively. The dotted, dashed and solid lines represent the respective models, as presented in the Supporting Information.
Figure 8. Z-plot for BP7. The symbols represent data recorded at (9) 20 mM ionic strength. The dotted line represents the evaluated model, as presented in the Supporting Information.
presented in Figure 6 illustrates this; also here the deprotonation gives rise to a steep curve, indicative on a solid in equilibrium with the deprotonated forms. Nevertheless, a difference in the shape of the titration curves can be seen at Z j -2, and this is believed to originate from a relatively stable HL3- ion, illustrated in Figure 9b. For BP1, quite different properties were observed; when the data in Figure 5 - 6 are compared with the respective data in Figure 7 the most obvious differences are the slope of the titration curve and the position in -log [Hþ] of the deprotonation (“pKa values”). The steep curves in Figures 4 and 5 are due to the existence of a solid phase, in equilibrium with the fully deprotonated aqueous species. The solid phase of BP1 is not stable -log[Hþ] above 2, and therefore other species must be responsible for the buffering effect above this -log[Hþ] value. The interpretation of the data is that stepwise release of protons, making all intermediate species important, describing the acid/base properties of this molecule. As a result, the distribution diagram, cf. Figure 9, for BP1 is quite different from that of the other TAs. The equilibrium model predicts that all species give an important contribution to the speciation of BP1, while for BP5 only the solid form, H4L(s), and the fully deprotonated form, L4-, contribute significantly to the speciation. Presented in Figure 8 are the data recorded, and the optimized acid/base model for BP7 at 20 mM Na(Cl) (below the cmc). In this DOI: 10.1021/la902326y
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Figure 9. Distribution diagram of (a) BP5, (b) BP3, (c) BP1, and (d) BP7. The lines are constructed according to the equilibrium models evaluated at 600 mM NaCl medium. The model for BP7 is extrapolated from 20 mM, using eqs 7 and 8. The equilibrium calculations were preformed with a total tetraacid concentration of 1 mM.
figure also a model extrapolated, using eqs 7 and 8, to 600 mM (where the acid/base properties of the monomers could not be measured) is presented. The shape of the titration curve of BP7 below the cmc is similar to BP5, but with a higher apparent pKa. The model lines in Figures 5-9 are the result of optimized equilibrium models. The formation constants and the log β values used can be found in the Supporting Information. Titration of TAs above the Cmc. In contrast to the titration curves shown in Figures 5-8, all the results from titrations of BP10, and the titrations of BP7 at 600 mM, where the total concentration is above the cmcs, are divided into two different type of curves; virgin titration curves, i.e., curves resulting from the first dissolution of the TA, and precipitation titration curves. The latter is resulting from titration of dissolved tetraacid at high -log [Hþ] in the acidic direction. The “splitting” phenomenon, the hysteresis, is visualized in Figure 10, where data from such titrations are shown. The dissolution curves show how the solid consumes OH- ions, while the precipitation curves show the stepwise precipitation of solid material from micelles upon lowering the pH. The latter kind of data was used for the evaluations of micelle formation In Figure 11, dissolution data for BP10 recorded at several ionic strengths are illustrated simultaneously, these curves illustrate how the solid material buffer the -log[Hþ] as it consumes OH- ions and establishes an equilibrium with micelles. The corresponding illustration of the precipitation of BP10 is shown in Figure 12. 1626 DOI: 10.1021/la902326y
Figure 10. Z-plot for BP10 and BP7 above their respective cmcs. Comparison between titration data recorded for (9) dissolution and (b) precipitation of BP10 and (2) dissolution and () precipitation of BP7 The total concentration of BP10 was 0.5-1.5 mM and the data were recorded at 600 mM Na(Cl) ionic medium. The data for BP7 was also recorded in 600 mM Na(Cl) and the total concentration of BP7 was 0.5-1 mM.
Since the cmc of BP10 is very low, almost all deprotonated tetraacid will immediately form micelles. A hypothesis is that these micelles, by means of the hydrophobic effect, interact with the remaining solid, thereby stabilizing the solid, fully protonated, Langmuir 2010, 26(3), 1619–1629
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Figure 13. Comparison of the experimentally measured backFigure 11. Z-plot for the dissolution of BP10, above the cmc (approx 1 mM). The symbols represent data recorded at ([) 20 mM, (2) 50 mM, (f) 100 mM, and (9) 600 mM ionic strengths, respectively.
Figure 12. Z-plot for the precipitation of BP10, above the cmc (approx 1 mM). The symbols represent data recorded at ([) 20 mM, (2) 50 mM, (f)100 mM, and (9) 600 mM ionic strength, respectively.
species. At Z r 3, it can be hypothesized that most of the material is found in micelles form, i.e., micelles in acid/base equilibrium with other micelles. In this region the titration curve is not only reversible but also the data from four different ionic strengths (20-600 mM) are overlapping, cf. Figures 11 and 12. When the system then is back-titrated the deprotonated form is stabilized due to formation of mixed micelles incorporating all species including solid material. It is clear that there is a significant difference between the acid/ base properties of BP10 at 20 and 600 mM Na(Cl). The data recorded in 50 and 100 mM Na(Cl) are, however, overlapping and almost indistinguishable. The phenomenon responsible for this is, however, not possible to model using any simple equilibrium model, and is explored using micelle formation theory. Modeling of Experimental Data by Formation of Micelles. By utilizing the methodology described in the Experimental Section, an approach using surface charge densities and aggregation numbers to model the acid/base behavior in a micellar system has been carried out for BP10. In Figure 13, the theoretical prediction of the precipitation-titration curve for BP10 in a 20 mM NaCl solution at 20 C is plotted versus the experimental data. As a first level of approximation, the value Langmuir 2010, 26(3), 1619–1629
titration curve for BP10 to the theoretical prediction made with eq 14. The values of nag and Δμ0 were adjusted to fit the experimental data.
of the micelle radius, Rm, was taken to be the length of an extended 10 carbon chain. The total length from the carboxyl carbon to the phenolic oxygen was estimated by geometrical considerations and using the length of a C-C bond of 1.54 A˚2. Furthermore, the value of the intrinsic acid constant, pK0a, was estimated to be approximately 5.4 (from the titration curve of monomeric BP5). This corresponds well to the monolayer acididy constant (pKsa = 5.5) for BP10 obtained from eq 16 and Figure 2b. The value of Δμ0 that was found to best represent the experimental data was 8.0. It can be clearly seen from Figure 13 that a micelle having an aggregation number, nag, with a value of 60 provides a good fit with the experimental data from Z = -4 to Z = -2. Once the value of Z ≈ -2, the value of the aggregation number, nag, that provides a good fit to the experimental data is about 102. This sudden change in the value of the aggregation number, nag, seems to indicate that once the value of Z ≈ -2, the acid may be starting to precipitate or form mixed micelles composed of protonated and deprotonated species. The total electrostatic repulsion in the micelle would decrease and promote micellar growth. It should be noted that due to the small radius of the micelle, the behavior of eq 14 is extremely sensitive to changes in the value of nag and hence changes in the micelle radius. In addition, it is assumed that the TA is formed as a spherical micelle with all four chains directed to the micellar surface. An arrangement with two of the four chains sticking into the micelle interior would yield a higher micellar radius, affecting the modeling. The possibility that the molecules aggregate into a cylindrical shaped micelle with the aromatic cores lying flat on each other can neither be excluded. Consequently, the results in Figure 13 should be interpreted cautiously and suggests that the micelle size, shape and value of nag should be experimentally determined in future work.
Discussion Of the studied materials, it is clear that BP10, previously shown to have physiochemical properties similar to indigenous tetraacids, is the most interesting model tetraacid from an industrial perspective. It is nonetheless interesting to study a series of similar compounds in order to fully unfold the complexity of the chemistry involved. A major problem with potentiometric titrations on BP10 is its low cmc, and the resulting low monomer concentration, even at quite low ionic strengths. This must be overcome, and the use of a series of tetraacids, with a range of cmcs over several orders of magnitude, was considered a good DOI: 10.1021/la902326y
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Figure 14. Apparent pKa of BP3-10 at 0.5-1 mM concentration, defined as the -log[Hþ] at Z = -2, in 20-600 mM NaCl as a function of the number of carbons in the alkyl chain length. The “missing” data point for BP7 at 100 mM was due to insufficient material for further potentiometric titrations. The lines illustrate the linear relationship.
approach to this problem. The five different molecules investigated showed upon quite different apparent acid/base properties, and it is from the data obvious that the formation of micelles significantly affects the apparent acid/base properties of the molecules. Thus, it is clear that the most interesting area is the micelle formation area, and that the focus of further studies should be in the area where micelles are formed. It is also clear that an attempt to understand the physiochemical properties with respect to the formation of micelles, e.g., aggregation numbers and type of micelles, would be of interest, and therefore such calculations were preformed. An apparent pKa value can be defined as the -log[Hþ] at which 50% of the carboxylic groups are deprotonated. Thus, an obvious observation is that the apparent pKa values of the carboxylate groups increase with the alkyl chain length. This is in good agreement with previous observations.7,9 In the work by Kanicky and Shah,7 it is observed that the apparent pKa for long chain carboxylic acids, are significantly higher than for short chain carboxylic acids. A linear relationship between the chain length of the carboxylic acids and the apparent pKa was postulated, and the authors assigned this effect to premicellar aggregation and to the formation of micelles. As is seen in Figure 14, this is also the case for the tetraacids studied here. Although the linear relationship is not obvious for the data collected at the lowest ionic strenght, it is very clear at higher ionic strength. This behavior is therefore confirmed also for a series of tetraacids, thus providing new knowledge. Since the TAs with longer alkyl chains tend to have a much stronger driving force for the aggregation, Figure 14 clearly illustrates the significant influence from the formation of aggregates on the apparent acid/base properties. The difference in speciation behavior between monomers of BP7, BP5, BP3, and BP1, shown in Figure 9, is probably due to several factors. For BP1, all species tend to give an important contribution to the speciation, while for BP7 and BP5 only the solid, H4L(s), and the fully deprotonated species, L4-, contribute significantly. For BP3 the HL3-(aq) ion also seems important. The observed phenomenon is likely due to the alkyl chain length and molecular size; the short inner molecular distances in BP1 makes the charge from one of the carboxylic acids affects the deprotonation of the others, which is not the case with BP7 and BP5. 1628 DOI: 10.1021/la902326y
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These TAs both act closely to the behavior of four different separate ideal monoprotic carboxylic acids. For the intermediate, BP3, the species with 3 negative charges attracts the last remaining Hþ enough to stabilize this species over a significant -log[Hþ] interval, which also is what could be expected from interpolating the knowledge from BP1 and BP5. Furthermore, the deprotonation of the solid BP1 occurs at a very much lower -log [Hþ] than what is the case of BP3-10. This is likely partly due to the inductive effect from the neighboring oxygen atoms, pulling the negative charge toward the ketone group of the benzophenone core and stabilizing the negatively charged anions. Also, possible formation of intermolecular hydrogen bonding, for the partly deprotonated species, could contribute to this significantly increased acidity. A similar situation is seen if benzene 1,2-dioxydiacetic acid, with a first pKa ≈ 2.6,25,26 is compared to phenoxyacetic acid, pKa ≈ 3.0.27,28 Dupont-Leclercq et al.9 illustrated that the apparent pKa of a fatty acid depend highly on the amount of micelles available. This could thus possible explain the peculiar slope of the Z-plots for the micellar systems. And, since the tendency to form micelles are greatly dependent on the ionic medium present, cf. Figures 11 and 12, the ionic strength-dependent shape of the Z-plots could possibly also be explained, because added salt reduces the electrostatic repulsion and the surface charge of the micelle. Moreover, the formation of micelles is most likely responsible for solubilizing the partly deprotonated species, thus also effecting the shape of the titration curve. When first discovering this unique class of surfactants which is responsible for calcium naphthenate deposits, potentiometric titrations of ARN in an organic solvent mixture was carried out together with commercially available mono- and diacids.29 The titration showed in fact only one dissociation step comparable to the observed aqueous behavior of BP7 and BP5 and the monolayer measurement for BP10. From oilfield observations it is estimated that pKaARN ∼ 6,30 again resembling BP5. However, the concentration of ARN in crude oil is in most cases around 1 ppm (∼10-6 mol/dm3) which may very possible be below the cmc of ARN. And, since the cmc varies with the salinity of the produced water, which may differ from oilfield to oilfield, this can give varying estimations of pKaARN, and, to our knowledge, limited data of direct determinations of the pKaARN can be found in the literature. Furthermore, to be able to perform a potentiometric titration, the concentration of the acid studied has to be around or above approximately 0.5 mM in order to maintain sufficient sensitivity for the cell. Thus, performing potentiometric titration experiments using isolated indigenous tetraacids, around or above the cmc, would yield apparent pKa values significantly deviating from field observations. Combined, this could be the reason for limited data for this compound class. A higher apparent pKa value can be seen for BP7 compared to BP5. As can be seen in Figure 4, the increase of equilibrium surface tension below the cmc for these tetraacids is quite slow. This might indicate premicellar aggregation when approaching the cmc. This aggregation affects the deprotonation of BP7 in (25) Suzuki, K.; Hattori, T.; Yamasaki, K. J. Inorg. Nucl. Chem. 1968, 30, 161– 66. (26) Hasegawa, Y.; Choppin, G. R. Langmuir 1977, 16, 2931–2934. (27) Suzuki, K.; Yamasaki, K. J. Inorg. Nucl. Chem. 1962, 24, 1093–1103. (28) Pettit, L. D.; Royston, A.; Sherring, C.; Whewell, R. J. J. Chem. Soc. B. 1968, 588–90. (29) Baugh, T. D.; Grande, K. V.; Mediaas, H.; Vinstad, J. E.; Wolf, N. O. SPE/ IADC 93011. The discovery of high molecular weight naphthenic acids (ARN acids) responsible for calcium naphthenate deposits. In SPE 7th International Symposium on Oilfield Scale; Aberdeen, 2004; SPE, Richardson. (30) Brocart, B.; Bourrel, M.; Hurtevent, C.; Volle, J.-L.; Escoffier, B. J. Dispersion. Sci. Technol. 2007, 28, 331–337.
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this concentration range, increasing the apparent pKa also below the cmc. Synthesis of ARN itself or shorter-chained ARN molecules is a very difficult task. In addition, the purity of the isolated ARN acid may vary.4 Both these problems are however circumvented by using the model tetraacids in this study, and for BP5 it is a good correlation between the potentiometric titrations and the apparent pKaARN from field observations.
Conclusions It was early concluded that the cmc of BP10 did not allow potentiometric titrations of the monomers of this tetraacid. Therefore, several other tetraacids were developed and investigated. The model tetraacids with long alkyl chain length basically show only one protonation step, while the model tetraacids with short alkyl chain length show more than one protonation step. The strange titration curves for the tetraacids, when titrated above their cmcs, strongly indicate the importance of micelle formation for the acid/base properties of large tetraacids, that estimated intrinsic pKa values in some cases must be used for modeling, and that model compounds sometimes can be used for this purpose. For BP10 it is interesting to see that the pKa estimated from Langmuir monolayer films coincide with the intrinsic pKa for the BP5 model compound, which was shown to be present in a monomeric state. Moreover we show that the
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apparent pKa values at 20 mM Na(Cl) show a linear dependence on the alkyl chain length, which must be correlated to premicellar aggregation. Finally, we show that an accurate estimation of the acid/base properties of the BP10 micelles could be achieved via modeling based on the electrostatic potential of the micelles and assumed geometries of the micelle. The modeling indicated an apparent increase of the micelle aggregation number when protonating the tetraacid in the micelle. This increase could be due to solubilization of the protonated species in the micellar environment. Acknowledgment. The authors thank the JIP consortium, consisting of AkzoNobel, Baker Petrolite, BP, Champion Technologies, Chevron, Clariant Oil Services, ConcoPhillips, Shell Global Soulutions, Statoil ASA, Talisman Energy and Total, for major financial support of the present work. Further the Research Council of Norway is acknowledged for partly funding the work preformed at NTNU. Professors Staffan € Sj€ oberg and Lars-Olof Ohman (Umea˚ University) are very greatly acknowledged for valuable scientific discussions throughout the whole course of the present work. Supporting Information Available: Table giving the thermodynamic data used in Figure 7. This material is available free of charge via the Internet at http://pubs.acs.org.
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