Exploiting Micelle-Driven Coordination To Evaluate the Lipophilicity of

1 Jun 2012 - Ligand 1-dodecyl-4,7,10-trimethyl-1,4,7,10-tetraazacyclododecane ... 8.0 × 10. −7 . For less soluble acids, we prepared two solutions ...
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Exploiting Micelle-Driven Coordination To Evaluate the Lipophilicity of Molecules Yuri A. Diaz Fernandez,*,† Luca Pasotti,*,† Piersandro Pallavicini,† and Jose M. Fernandez Hechavarria‡ †

Inorganic Nanochemistry Laboratory (inLab), University of Pavia, viale Taramelli 12, Pavia, Italy Institute for Applied Science and Technology, ave. Salvador Allende y Luaces, Havana, Cuba

‡

S Supporting Information *

ABSTRACT: We present a systematic study based on the calculation of complexation constants between a Zn-complex solubilized in Triton X-100 micellar solutions and a series of linear mono- and dicarboxylic acids, under physiological pH conditions, that allowed the evaluation of the lipophilicity of these molecules. This empirical lipophilicity parameter describes conveniently the partition of organic molecules between hydrophobic microdomains and water. The results can be used to predict the lipophilicity of molecules with similar structure and allows the distinction of intrinsic contributions of the carboxylates and of the methylene groups to the lipophilicity of the molecule.

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INTRODUCTION Lipophilicity expresses the affinity of a molecule for a lipophilic environment.1 It is commonly measured by the tendency of the chosen molecule to distribute in a biphasic system, either liquid−liquid (by determining the partition coefficient in 1octanol/water2) or solid−liquid (retention on reversed-phase high-performance liquid chromatography,3,4 thin-layer chromatography system5). Lipophilicity is relevant in pharmacological studies and in the assessment of the environmental fate and transport of organic chemicals.6 Most pharmaceutical drugs are designed to be lipophilic enough to cross cell membranes with a trans cellular mechanism,7 and the increasing interest in liposomal drug delivery focuses also on the relationship between the lipophilicity of a drug and its ability to cross the liposome wall.8 Octanol−water (or in general water−solvent) partition data have been extensively used to predict biological absorption of molecules; however, there is still a controversial discussion as to whether octanol as an isotropic phase can mimic natural membrane barriers, which are made of ordered and anisotropic lipid−protein membranes.9 As a matter of fact, the octanol− water partition coefficients are often defined for undissociated neutral species,2 despite that many pharmaceutical drugs are weak acids or bases, and generally are in charged forms under physiological conditions.10 Several methods have been developed to complement the classical water−solvent partition method for the characterization of lipophilicity of organic molecules.9 Among these techniques, the partition equilibrium of solutes between micellar pseudo phases and bulk water has been extensively investigated, from both experimental and theoretical approaches.11−51 © 2012 American Chemical Society

The lipophilicity of different kinds of molecules has been investigated exploiting the influence of micellization on the kinetic rate of organic reactions,11,12 the variation of the spectroscopic properties of molecules in different microenvironments,13−15 and the modification of thermodynamic equilibrium in micellar solutions.16−18 From the theoretical point of view, lipophilicity has been parametrized using several molecular descriptors39−41 and correlating different macroscopic properties of the substances.42−46 Quantitative structure−properties relationship (QSAR) studies have revealed that the lipophilicity of molecules could be separated in contributions of the single chemical moieties constituting the molecular structure.47−50 This approach allows the prediction of the lipophilicity of new molecules, on the basis of the experimental data available for well-known molecules, and has found several applications in biological and pharmaceutical sciences.49,50 An interesting experimental approach to quantify the lipophilicity of organic molecules is based on the coordination chemistry in micellar solutions.51 The solubilization of interacting molecular species in microheterogeneous solutions often leads to the emergence of interesting phenomena that have been used to characterized the structure of different micellar systems.52−56 Similarly, the confinement of coordinating donor−acceptor pairs in nanometric domains usually modifies the coordination equilibrium, with respect to bulk conditions.57−68 Received: March 23, 2012 Revised: June 1, 2012 Published: June 1, 2012 9930

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Exploiting the micellar-driven coordination effect, we have recently developed a micellar-based fluorescent sensor for the lipophilicity of linear monocarboxylic fatty acids, capable of working at physiological conditions, that is, pH = 7.4,69 a value at which the carboxylate group is deprotonated. In that work, the complex between pyrenecarboxylate (PyCOO−) and a fivecoordinate Zn2+ cation trapped in a lipophilized tetraazamacrocycle is confined in Triton X-100 micelles. The coordinated PyCOO− is intensely fluorescent, but its emission drops when a competing carboxylate enters the micelle and removes PyCOO− from the apical position of the Zn2+ complex. For a chosen carboxylate, the degree of distribution between the water bulk and the micellar pseudo phase is a function of its lipophilicity. As a consequence, the more a carboxylate is lipophilic, the more intense will be the observed fluorescence decrease.69 Later, we demonstrated that a similar approach can be applied also to the evaluation of the lipophilicity of nonsteroidal anti-inflammatory drugs (NSAID, all featuring a single carboxylate group), simply by changing the coordinating fluorophore and the metal cation bound in the macrocyclic ligand.69 In both cases,69,70 only monocarboxylates were investigated. Working on the same micellar approach, now we present a systematic study based on the calculation of complexation constants between a micelle-confined Zn-complex and a series of linear mono and dicarboxylic acids, under physiological pH conditions, which allowed the evaluation of the lipophilicity of these molecules. Moreover, this empirical scale can be also used to predict the lipophilicity of similar molecules, using the additivity of the contributions of chemical moieties constituting the molecular structure.

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Figure 1. Chemical structures of (a) Triton X-100, (b) pyrene carboxylic acid (PyCOOH), (c) generic carboxylic acid, (d) C12Me3Cyclen Zn2+ complex (ZnL2+), and (e) generic dicarboxylic acid.

Progressive additions of 20 μL of standard 0.100 M NaOH were made. The pH was monitored with a double-electrode pH-meter. After each base addition, the pH of the solution was allowed to stabilize. Next, a 3 mL volume of solution was put in a quartz cell, the emission fluorescence spectrum was recorded, and afterward this volume was reintegrated into the bulk solution. The experimental If% versus pH profiles were fitted using a Marquadt−Levenberg Algorithm as described in the Supporting Information, S1. Partition of PyCOO− from Water to Triton X-100 Micelles. The experiment was carried out at a constant concentration of buffer (HEPES 0.05 M, pH = 7.4) and PyCOOH (8 × 10−7 M), varying the concentration of Triton X-100 from 0 to 0.025 M. Two identical solutions (A and B) of 15 mL each, containing Hepes and PyCOOH, were prepared. To one of these solutions (solution A) was added Triton X-100 to reach a concentration of 5 × 10−2 M. Progressive additions of solution A to B were carried out, and the emission fluorescence spectrum was recorded after each addition. Complexation Experiments. The fluorescence intensity of the PyCOO− at pH 7.4 was recorded, at different concentrations of [ZnL]2+, by adding a 1.00 × 10−3 M titrating solution. Titration was carried out in the same way for 10 solutions containing different amount of Triton X-100 from 5 × 10−4 to 2 × 10−2 M. Data obtained for these titrations were elaborated with Hyperquad12 to obtain the formation constant of [PyCOOZnL]1+. Fitting plots at representative concentrations of Triton X-100 are shown in the Supporting Information, S2. Competition Titrations. A concentrated solution of chosen CH3(CH2)nCOOH or HOOC(CH2)nCOOH acid were used to titrate a 30 mL aqueous solution containing HEPES 0.05 M (pH 7.4), Triton X-100 0.01 M, [ZnL]2+ 1.66 × 10−5, and PyCOO− 8.0 × 10−7. For less soluble acids, we prepared two solutions (solutions A and B, 15 mL each) containing buffer, Triton X-100, [ZnL]2+, and PyCOO−, in the same concentrations described above. To solution A, the acid was added to obtain a 1.6 × 10−4 M concentration; progressive addition of the solution A to B was carried out, and the emission fluorescence spectrum was recorded after each addition. Data obtained for these titrations were elaborated with Hyperquad71 to obtain the formation of the constant of [CH3(CH2)nCOOZnL]1+ or [OOC(CH2)nCOOZnL] and [ZnLOOC(CH2)nCOOZnL]2+. Fitting plots for representative carboxylic and dicarboxylic acid are shown in the Supporting Information, S3 and S5. Potentiometric Titrations. Aqueous solutions of 0.05 M of NaNO3 and 0.01 M of Triton X-100, with the carboxylic acid 10−3 M (for less soluble acids 10−4 M), were titrated in the cell of the automatic titrating system, thermostatted at 25 °C and kept under a N2 atmosphere with standard NaOH 0.100 M (0.010 M for less soluble acids). The E° = 394 mV for the hydrogen glass electrode was determined using the Gran method.72 Data obtained for these titrations were elaborated with Hyperquad71 to obtain the protonation

MATERIALS AND METHODS

Reagents and Equipment. Triton X-100 (tert-octylphenoxypoly(oxyethylene glycol) with an average of 9−10 oxyethylene units) was purchased from Sigma-Aldrich (average molecular weight = 625). Carboxylic acids were purchased from Sigma-Aldrich and TCI Europe and were used without further purification. HEPES buffer, 4-(2hydroxyethyl)piperazine-1-ethanesulfonic acid, was purchased from Fluka. Dry Zn(CF3SO3)2 was purchased from Fluka and kept in a desiccator. Water was distilled twice, starting from deionized water (prepared with an ionic-exchange apparatus). 1-Pyrenecarboxylic acid was purchased from Sigma-Aldrich. Ligand 1-dodecyl-4,7,10-trimethyl-1,4,7,10-tetraazacyclododecane (C12Me3Cyclen = L) and the Zn2+ complex ([ZnL]2+) had been prepared as described before.69 All chemical structures are represented in Figure 1. Emission spectra were recorded with a Perkin-Elmer LS-50 spectrofluorimeter. In coupled fluorimetric and pH-metric titration of PyCOOH in different media, the excitation wavelength of 365 nm was selected, to minimize the fluorescence emission of PyCOO−. For all of the other experiments discussed below, the excitation wavelength was 340 nm. Potentiometric titration was performed with automatic Titralab TIM900. For the potentiometric determination of apparent protonation constants and the fluorimetric calculation of complexation constants, the Hyperquad software package was used, choosing the appropriate phenomenological models.12 Coupled Fluorimetric and pH-Metric Titration of PyCOOH in Different Media. A concentrated (10−1 M) stock solution of Triton X-100 was prepared in 10 mL of water. Four solutions of 25 mL were prepared, containing 0.05 M NaNO3, 8 × 10−7 PyCOOH, and different amount of the Triton X-100 stock solution: 0, 125 μL (5 × 10−4 M), 750 μL (3 × 10−3 M), and 2.5 mL (10−2 M). Each solution was acidified with 100 μL of 1.00 N standard HNO3, and kept in a thermostatted cell (25 °C) under N2 (atmospheric pressure). 9931

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constant. Fitting plots for representative dicarboxylic acids are shown in the Supporting Information, S4. Quantum Chemistry Calculations. The bonding energy of the carboxylates (from formic to hexadecanoic acid) in the apical position of [ZnL]2+ has been estimated using MOPAC 2007 and Avogadro 1.0 software packages. We have used a model macrocycle structure, having four methyl substituents, to reduce the number of optimizing coordinates, and archive shorter calculation times. The initial geometry was previously optimized using a molecular mechanics routine (Avogadro) with the MM+ potential. The optimal geometry and energy for [ZnL]2+, for the isolated carboxylic acids and for the adducts with [ZnL]2+, were obtained using the PM6 semiempirical Hamiltonian combined with restricted Hartree−Fock procedures (MOPAC). The bonding energy was calculated as the difference between the energy of the adduct and the energy values of the isolated molecules in vacuum. A similar procedure was adopted to calculate the bonding energy of dicarboxylates (from oxalate to octadecanoate), toward one and two [ZnL]2+ coordination centers. In all cases, the starting conformation of the alkyl chain was set fully extended, and all of the atomic coordinates were optimized to find minimal-energy conformation.

only formed in poorly solvating environments, like Triton X100 micelle interior.69 Therefore, complexation between carboxylates and [ZnL]2+ should be considered an intramicellar process. In this Article, the micellar solution is considered as a microheterogeneous system formed by two different pseudophases: the bulk solution and the micellar pseudophase.73 In this phenomenological model, the penetration of a given carboxylate (RCOO−) inside the micelles can be treated as a classical partition equilibrium, considering that at the equilibrium the chemical potential in the bulk solution (μb) is equal to the chemical potential in the micellar pseudo phase (μm). The last parameter, μm, depends on the average local concentration of RCOO− inside each micelle, and cannot be determined by a direct straightforward measurement. A reasonable strategy to estimate the penetration of a solute in the micellar pseudo phase is to correlate the local concentration with a macroscopic measurable parameter (i.e., the apparent macroscopic [ZnL]2+−RCOO− complexation constant). As a matter of fact, considering the equilibrium condition μb = μm for each species, it is possible to define an apparent [ZnL]2+− RCOO− complexation constant that includes both the effect of partitioning and the effect of the RCOO− complexation processes in the apical position of [ZnL]2+. For further discussion, this apparent complexation constant should not be confused with the intrinsic local complexation constant that takes into account only the Gibbs free energy exchange involved in the formation of the complex. The pseudo phase approach also allows the treatment of these intrinsic local complexation constants as being independent of the partitioning of the species between the two environments (Scheme 1). If we consider the formation of the complex between [ZnL]2+ and the carboxylates RCOO− inside the micelles, it is possible to write the equilibrium constant, taking into consideration the average local concentration of a species X, Cm(X), and the activity coefficients, γm(X), inside the micelle:

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RESULTS AND DISCUSSION 1. Theoretical Basis. The sensing system studied in this Article exploits a multicomponent self-assembling in Triton X100 micelles, according to the strategy developed by our group69 (Scheme 1). Under the employed work conditions, the Scheme 1. Partition and Intramicellar Complexation Equilibria for Monocarboxylates and [LZn]2+a

k

RCOO−(m) + [ZnL]2 +(m) =m [RCOOZnL]2 +(m) k m(RCOO−) =

am(X) =

(1)

am([RCOOZnL]+ ) am(RCOO−)am([ZnL]2 + )

(2)

γm(X)Cm(X) Cm,0

(3)

In eq 3, we have assumed a hypothetical standard state for the solute in the micellar pseudo phase, having a standard concentration Cm,0. Assuming the dilute regime (i.e., for low occupancy numbers of solutes inside the micelles), the activity coefficient can be considered independent of the number of solutes per micelle and hence can be enclosed inside an apparent equilibrium constant in the micellar pseudo phase, k⧧m, which for simplicity also contains the Cm,0 terms:

a

The relative number of solutes per micelle in this scheme is not scaled to the real conditions. For further details, please see the Supporting Information.

macroscopic concentration of [ZnL]2+ is ∼100-fold larger than the macroscopic concentration of PyCOO−. Accordingly, some micelles contain only [ZnL]2+, and some others [ZnL]2+ and PyCOO−. In the complex, the Zn2+ cation is five-coordinated with a square-pyramidal geometry, holding a water molecule in the apical position, unless PyCOO− is present. In the latter case, the carboxylate group coordinates Zn2+ and PyCOO− increases considerably its fluorescence intensity. Previously, it has been demonstrated that the complex [PyCOOZnL]+ can be

k m⧧(RCOO−) =

Cm([RCOOZnL]+ ) Cm(RCOO−)Cm([ZnL]2 +

(4)

We can define the macroscopic concentration of a species solubilized in the micellar pseudo phase, CM(X), as the number of moles inside the micelles divided by the macroscopic volume of the solution (V): 9932

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Scheme 2. Partition and Intramicellar Complexation Equilibra for Bicarboxylates and [LZn]2+a

a

The relative number of solutes per micelle in this scheme is not scaled to the real conditions. For further details, please see the Supporting Information.

CM(X) =

Cm(X)vm = Cm(X)φ V

KM(RCOO−) =

(5)

where vm is the volume of the micellar pseudo phase and φ is the volume fraction of the micelles. At the same time, we can define the fraction of a solute X inside the micelle (f(X)) as the ratio between the macroscopic concentration inside the micelle and the total macroscopic concentration for each species, C(X): f (X) =

CM(X) C(X)

C([RCOOZnL]+ C(RCOO−)C([ZnL]2 + )

KM(RCOO−) = k m⧧(RCOO−)

f (RCOO−)f ([ZnL]2 + ) φf ([RCOOZnL]+ )

(7)

(8)

It is important to stress that this macroscopic equilibrium constant KM contains concentration-dependent terms, and it is not a real thermodynamics constant, but an apparent equilibrium constant, which can be determined experimentally under given conditions. Therefore, eq 8 relates a microscopic uncertain magnitude (k⧧m) with the macroscopically determinable equilibrium constant KM, the value of which depends on the experimental conditions. According to eq 8, if [ZnL]2+ and [RCOOZnL]+ are completely included in the micelles (i.e., f([ZnL]2+) = 1, f([RCOOZnL]+) = 1), the macroscopic complexation constant is expected to be proportional to the fraction of carboxylate solubilized in the micellar pseudo phase only. For homologous molecules with the same coordination capacity at a given concentration of surfactant (i.e., assuming the term k⧧m(X)/φ is constant), this leads to:

(6)

It is important to notice that f(X) is not a proper partition coefficient, but a distribution fraction, because it is related to the total macroscopic concentration of the species. The advantage of using directly the distribution fraction, instead of the partition coefficient, relays on the experimental difficulties to determine the volume of the micellar pseudo phase. (Further discussion on the relationship between the distribution fraction and the partition coefficient can be found in the Supporting Information.) We can also define a macroscopic equilibrium constant, considering the macroscopic total concentrations of the species. This constant can be related to a hypothetical equilibrium similar to the process described by eq 1 but considering the total concentration of the solutes in the whole system and avoiding the subindexes that indicate intramicellar species (see the next sections for further discussion). Using eqs 4−6, this macroscopic equilibrium constant can be written in terms of the total concentration as follows:

KM(RCOO−) =

k m⧧(RCOO−) f (RCOO−) φ

(9)

The most interesting feature of eq 9 is that the apparent macroscopic constant KM can be determined experimentally for a series of carboxylates, increasing their lipophilicity up to the total inclusion in the micelles (f(RCOO−) = 1), without considerably altering the coordination capacity toward the 9933

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[ZnL]2+. By means of this, the value of the proportionality constant can be determined experimentally straightforward: k m⧧(RCOO−) = φ

lim

f (RCOO−) → 1

KM(RCOO−) = KMlim

2. Intrinsic Coordination Capacity of Carboxylates toward [ZnL]2+. The basic hypothesis behind eqs 11, 12, and 16 is that carboxylates have identical intrinsic coordination strength inside the micelle, irrespective of the length of the alkyl chain. Unfortunately, the values of microscopic coordination magnitudes are not experimentally available. An indirect proof of this fact could be obtained experimentally considering that the pKa values for the homologue series of linear carboxylates in dioxane−water mixture change in less than 0.2 logarithmic units, going from acetic to hexadecanoic acids.69 These data suggest that alkyl-chain inductive effects do not considerably modify the acid−base properties of the carboxylic group in mixed aqueous−organic solvents. Considering the Lewis theory, the basicity of these molecules could be related to the availability of the electron pairs on the carboxylic group,74 and therefore indirectly with their coordinative capacity. Nevertheless, these data are not sufficient to demonstrate the equivalency of all of the members of a homologue series of carboxylates, and therefore we relayed theoretical calculations to find further evidence. To investigate the intrinsic coordinative strength of carboxylates toward [ZnL]2+, we performed quantum mechanical simulations using a PM6 semiempirical Hamiltonian to estimate the bonding energy of carboxylates in the apical position of [ZnL]2+. This semiempirical method is an improvement of the former PM3 Hamiltonian, which solves many of its limitations.75 The theoretical bonding energy can be intuitively related to the free energy exchange after coordination. Neglecting the entropy and expansion work contributions, this energy describes the thermodynamic tendency to form the coordinative bond under experimental conditions and can be calculated by the difference between the total energy values for the adduct and the total energy for isolated molecules in vacuum. Despite that this approximation seems very rough, it could be valid in poor solvating environments, such as the interior of nonionic micelles of Triton X-100.51 For monocarboxylates, the calculated bonding energies toward [ZnL]2+ do not considerably change, by varying the length of the alkyl chain from n = 0 to n = 16 (Figure 2). Furthermore, we found no dependence of the bonding energy due to the conformation of the alkyl chain. These data suggest that the intrinsic coordination capacity of monocarboxylates is

(10)

Hence, eq 9 can be written in its definitive form: KM(RCOO−) = KMlimf (RCOO−)

(11)

This equation provides a direct experimental path to estimate f(RCOO−), that is, the actual penetration capacity of certain carboxylate inside the more hydrophobic micellar pseudo phase that is determined by its lipophilicity. Using eq 11, we can build an empirical thermodynamic scale of lipophilicity, that is, a scale based on the determination of macroscopic coordination constants of homologous coordinating molecules partitioning between the bulk solution and the micellar aggregates. The formulation developed above for monocarboxylates can be extended to bicarboxylates, R(COO)22−. The first complexation step for one of the two −COO− groups, forming [R(COO)2ZnL], see Scheme 2, is described by a set of equations similar to eqs 1−11. Therefore, the first protonation constant in this case can be also written: lim KM,1(R(COO)22 − ) = KM,1 f (R(COO)22 − )

(12)

The second complexation step is described by eq 13 (see also Scheme 2): 2+ [R(COO)2 (ZnL)](m) + [ZnL](m) k m,2

2+ = [R(COO)2 (ZnL)2 ](m)

(13)

A treatment similar to that used for the first protonation step leads to the expressions of the second macroscopic constant, KM,2: KM,2(R(COO)22 − ) =

C([R(COO)2 (ZnL)2 ]2 + ) C([R(COO)2 (ZnL)])C([ZnL]2 + ) (14)

KM,2(R(COO)22 − ) = k m⧧(RCOO−)

f ([R(COO)2 (ZnL)])f ([ZnL]2 + ) φf ([R(COO)2 (ZnL)2 ]2 + )

(15)

2+

If we consider [ZnL] being fully included inside the micelles, we are implicitly assuming that the neutral [R(COO)2(ZnL)] and the charged but more lipophilic [R(COO)2(ZnL)2]2+ (in our case, it contains the two dodecyl chains of the two [LZn]2+ complexes) will be also fully solubilized in the micellar pseudo phase (Scheme 2). This leads to the result that the second macroscopic coordination constant has the same value for all members of a homologous series: ⧧ k m,2

φ

lim = KM,2(R(COO)22 − ) = KM,2

(16)

Hence, for bicarboxylates, provided the assumptions made here are valid, the first coordination constant also gives the direct experimental path to calculate the inclusion fraction in the micelles according to eq 12, while the second coordination constant remains constant as the lipophilicity of the carboxylate increases.

Figure 2. Bonding energy of mono- and bicarboxylates toward [ZnL]2+ complex as a function of the length of the alkyl chain; calculated using the semiempirical Hamiltonian PM6. 9934

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Figure 3. Fluorescence spectra of PyCOOH at different pH values in (a) water and (b) Triton X-100 10−2 M. Thick lines evidence the spectra of limiting forms and are taken at pH 2.4 (PyCOOH) and 7.4 (PyCOO−).

erable different moving from water to the micellar environment.76−79 The fluorescence spectrum of PyCOOH in water is broad and has a single maximum around 415 nm (Figure 3a). Conversely, in micellar solutions of Triton X-100, the spectrum is considerably blue-shifted, and a fine structure can be observed with two maxima at 392 and 412 nm, respectively (Figure 3b). Experiments carried out at pH 2.4 with increasing Triton X-100 concentration show that this fine structure appears just above the cmc of Triton X-100 and does not change on further surfactant addition (data not shown). Thus, we can reasonably conclude that the protonated form of PyCOOH is completely included inside the micelles, as can be expected for a neutral hydrophobic molecule. On the other hand, using the variation of fluorescence intensity as a function of the pH (Supporting Information, S1), we calculated the apparent pKa values (Table 1). These change

equivalent, and therefore the theoretical consideration leading to eq 11 can be considered valid. For bicarboxylates, we obtained two qualitatively different results when considering the 1:1 and the 1:2 adducts (Figure 2). The bonding energy release from coordinating one bicarboxylic acid to one [ZnL]2+ molecule (1:1 adduct) smoothly decreases as the alkyl chain length increases, up to 4 methylene groups, then drops and smoothly reaches a plateau (see Figure 2). This interesting result can be understood observing the optimized geometry of the adducts formed (see the Supporting Information, S6 for details). For the smaller members of the series of bicarboxylates, a scorpion-like structure was observed, displaying a close interaction between the second carboxylic group and the Zn2+ complex. Indeed, irrespective of that the initial conformation of the alkyl chain was fully extended, the second carboxylic moiety twisted toward the metal center. This trend was observed up to 4 methylene groups in the alkyl chain. For the larger members of the series, the interaction was probably not sufficient to overcome the conformational barriers, and the full-extended alkyl-chain conformation was obtained. Reasonably, when the alkyl chain becomes large enough, this two-center interaction vanished, and the bonding energy reaches a plateau for the 1:1 complex. On the other hand, when the 2:1 complex was investigated, only the full-extended conformation was obtained for all of the members of the series, probably due to the electrostatic repulsion of the two charged metal centers. In this case, the interaction vanished when the number of methyl groups is higher than 5. We can conclude from these data that the intrinsic coordination capacity of the members of the homologous series of monocarboxylates is equivalent, independently of the number of carbon atoms of the chain, while for bicarboxylates, the coordination capacity homologates when the number of carbons atoms of the alkyl chain is sufficiently large (more than 5 spacing CH2 groups). Hence, under these conditions, the theoretical hypotheses leading to eqs 12 and 16 are valid, and the phenomenological framework presented in the previous section can be applied. 3. Distribution of Pyrene Carboxylate. In micellar solutions of Triton X-100, the carboxylate and the protonated forms of pyrene carboxylic acid could be distributed between the micelles and the bulk solution. The distribution modifies the fluorescence and the acid/base properties of these moieties, because polarity, hydration, and micro viscosity are consid-

Table 1. Protonation Constants (Ka) of PyCOOH in Different Mediaa pKa water Triton Triton Triton Triton a

X-100 X-100 X-100 X-100

5 3 1 2

× × × ×

10−4 10−3 10−2 10−2

M M M M

3.59 4.80 5.37 5.50 5.51

Standard deviation