Thermodynamics of Alkali− Metal Cations and Macrocycles (18-Crown

6772

J. Phys. Chem. B 1997, 101, 6772-6779

Thermodynamics of Alkali-Metal Cations and Macrocycles (18-Crown-6, Ethyl p-tert-butylcalix(6)arenehexanoate, Cryptand 222) in Solution and in the Solid State Angela F. Danil de Namor,* Mariel L. Zapata-Ormachea, Olga Jafou, and Nawar Al Rawi Laboratory of Thermochemistry, Department of Chemistry, UniVersity of Surrey, Guildford, Surrey, GU2 5XH, U.K. ReceiVed: February 5, 1997; In Final Form: May 23, 1997X

Stability constants and derived Gibbs energies and enthalpies and entropies of complexation of alkali-metal cations and macrocycles (18-crown-6 and ethyl p-tert-butylcalix(6)arenehexanoate) in benzonitrile at 298.15 K derived from titration calorimetry (macro and micro) are first reported. These data are compared with those previously reported for cryptand 222 and these cations in this solvent. A “peak” selectivity is observed for the complexation of the calix(6)arene ester and alkali metal cations with a monotonic increase in stability from lithium to potassium followed by a decrease from the latter to rubidium. This behavior is analogous to that shown for cation binding involving 18-crown-6 and cryptand 222. Similar to the process of complex formation involving these ligands, that involving the calix(6)arene ester and these metal cations is enthalpy controlled with an exothermic maximum for the potassium cation. Among the ligands considered, thermodynamic data involving cation-calix(6)arene ester interactions are characterized by a lower enthalpic stability (less exothermic) and a more favorable entropy (except for K+) than corresponding data involving cryptand 222 or indeed 18-crown-6. These results are analysed in terms of solute-solvent interactions reflected on the solution thermodynamic data of the free and the complexed electrolytes and the ligand in benzonitrile. Standard enthalpies of solution of macrocycles and their sodium and potassium salts in benzonitrile measured calorimetrically are discussed in relation to (i) corresponding data for the uncomplexed salts and (ii) previously reported data for sodium and potassium cryptate salts in various solvents. Enthalpies of coordination referred to the process in the solid state for eighteen systems involving sodium and potassium coronates, cryptates, and calix(6)arenates are derived and whenever possible these are discussed on the basis of (i) available X-ray crystallographic data and (ii) the anion effect on the coordination process.

Introduction A wide variety of synthetic and natural macrocyclic ligands (L) able to complex alkali-metal cations (M+) are now available. Many efforts have been directed to investigate the thermodynamics of complex formation of these ligands and metal cations (eq 1) in different solvents1 (s) in order to assess the selective behavior of macrocycles for these ionic species.

M+(s) + L(s) f M+L(s)

(1)

L(sol) f L(s)

(3)

MLX(sol) f M+L(s) + X-(s)

(4)

Among synthetic macrocycles, crown ethers,10 cryptands,11 and calixarenes12 have received considerable attention. As far as calixarenes are concerned, functionalization of the phenolic hydrogens has led to a wide range of lower rim derivatives. Among these, ethyl p-tert-butylcalix(6)arenehexanoate, EtCalix(6), 1a, is an interesting ligand since, similar to 18-crown-6,

However, the solvation of the free and the complexed cation (M+L) and the ligand in solution (strongly dependent on the nature of the solvent) plays a crucial role in the complexation process.2,3 Therefore, it is important to obtain information regarding the solution properties of the species participating in the complex formation. The solution thermodynamics of 1:1 electrolytes in various solvents referred to the process involving the solid (sol) and the dissociated species (eq 2)

MX(sol) f M+(s) + X-(s)

(2)

have been reported by various groups.4-9 These data have been used to derive single-ion Gibbs energies ∆tG°, enthalpies ∆tH°, and entropies ∆tS° (on the basis of the Ph4AsPh4B convention)8 for the transfer of cations and anions from a reference solvent, usually water to another. However, solution thermodynamic studies on neutral macrocyclic (nonelectrolytes) (eq 3) and their metal-ion complexes, M+LX- (eq 4) are relatively scarce9,14-17 X

Abstract published in AdVance ACS Abstracts, August 1, 1997.

S1089-5647(97)00459-8 CCC: $14.00

18-C-6, 1b, and cryptand 222, 222, 1c, this derivative is selective for potassium.13 These ligands have distinctive hydrophilic regions. Thus, 18-C-6 is characterized by the presence of a hole and therefore, this ligand is unable to achieve complete encapsulation of the cation upon complexation. Experimental evidence on cryptand 222 indicates that for univalent cations in dipolar aprotic media,14,15 its intramolecular cavity provides a suitable shielding to the cation to the extent that a direct interation between the alkali-metal cation and the solvent is © 1997 American Chemical Society

Alkali-Metal Cations and Macrocycles

J. Phys. Chem. B, Vol. 101, No. 34, 1997 6773

unlikely to occur. The information regarding EtCalix(6) is very limited as to make a definite statement regarding this ligand. The aims of this paper are the following: (i) To characterize thermodynamically using titration calorimetry (macro and micro) the complexation process (eq 1) involving L [EtCalix(6) and 18-C-6] and alkali-metal cations in benzonitrile (PhCN) at 298.15 K and to compare these with corresponding data for 222 and these cations in the same solvent9 and temperature. (ii) To assess the complexation data on the basis of the thermochemical properties of the species participating in the binding process. In doing so, standard enthalpies of solution of these macrocycles and their metal-ion complexes in PhCN are determined by classical calorimetry. (iii) To calculate the enthalpies of coordination, ∆coordH° (eq 5) referred to the process where reactants and product are in the solid state.17

MX(sol) + L(sol) f MLX(sol)

(5)

Benzonitrile was the solvent chosen because the (i) EtCalix(6) is soluble enough in this solvent and (ii) a phase separation between PhCN and water can be achieved, and therefore, the direct partitioning of electrolytes in this system is feasible. Experimental Part Chemicals. Ethyl p-tert-butylcalix(6)arenehexanoate was synthesized as detailed elsewhere.16 Microanalysis was carried out at the University of Surrey. The found percentages of C (72.59) and H (8.34) are in agreement with the calculated values (C, 72.55; H, 8.12). Sodium perchlorate (99%, Aldrich), potassium iodide (99%, Aldrich), and rubidium tetraphenylboron (95%, Aldrich) were dried under vacuum at 70 °C for several days before use. Benzonitrile (Aldrich) was distilled from P2O5 under reduced pressure.9,17 The middle fraction was collected and redistilled after refluxing the solvent for a few hours. The water content of the solvent checked by Karl Fischer titration was not more than 0.01%. Sodium and potassium complexed salts of 18-C-6 and 222 were prepared as described elsewhere.17 The sodium and potassium tetraphenylboron complexes of EtCalix(6) were prepared by addition of the calixarene ester to an acetonitrile solution containing the appropriate metal cation salt. The mixture was heated at 80 °C until a clear solution was obtained. The solvent was removed using a rotary evaporator. The solid was recrystallized from absolute ethanol and dried for several days under reduced pressure. Solubility Measurements. For these measurements, an excess amount of the calixarene derivative was added to the solvent in order to obtain a saturated solution. The mixtures were left in a thermostat at the required temperature (293.15, 298.15, 303.15, 313.15 ( 0.01 K) for several days until equilibria were attained. Then, known volumes of the saturated solution were taken. The solvent was carefully evaporated. The solid residue was dried until constant weight. All analysis were performed in triplicate. Thermochemical Measurements. Enthalpies of complexation of metal cations and EtCalix[6] were determined by titration microcalorimetry. Microcalorimetric experiments at 298.15 K were carried out using the titration vessel of the 2277 thermal activity monitor (TAM).18,19 The vessel was filled with 2.8 cm3of a solution of calixarene ester (concentration range: (8.9 × 10-5) - (1.0 × 10-3mol dm-3)) and solutions of metal ion salts (concentrations used were (2 × 10-3) - (3.5 × 10-2) mol dm-3 depending on salt solubility) were injected (∼16 injections, 0.015-0.025 cm3 for

each run) from a 0.5 cm3 gas-tight Hamilton syringe, attached to a computer-operated syringe drive at 5-min intervals. Blank experiments were carried out in all cases to account for heat of dilution effects resulting from the addition of the metal-ion salt to the solvent contained in the calorimetric vessel. A dynamic correction based on Tian’s equation18,19 was used to calculate the integrals from the microcalorimetric curve. The reliability of the microcalorimeter was checked by carrying out the standard reactions suggested in the literature.20 The equipment was calibrated chemically by determining the standard enthalpy of complexation of 18-C-6 and Ba2+ in water at 298.15 K. Values for log Ks ) 3.72 ( 0.05 and ∆cH° ) -31.71 ( 0.25 kJ mol-1 were obtained. These are in good agreement with the values (log Ks ) 3.77 ( 0.01, ∆cH° ) -31.42 ( 0.20 kJ mol-1) reported in literature for this system.20 Enthalpies of complexation of metal cations and 18-C-6 in benzonitrile at 298.15 K were measured as described elsewhere.17,18 Determination of Solution Enthalpies. Enthalpies of solution were measured with the Tronac 550 solution calorimeter designed by Christensen and Izatt.21 The accuracy of the equipment was tested by using the standard reaction of THAM [tris(hydroxymethyl)aminomethane] in a 0.1 mol dm-3 aqueous solution of hydrochloric acid suggested by Irving and Wadso¨.22 The value of -29.79 (. 0.5 kJ mol-1 for the standard enthalpy of solution of THAM in HCl at 298.15 K is in close agreement with that reported in the literature (∆sH° ) -29.76 ( 0.02 kJ mol-1) using the same equipment.14 For these measurements, the sealed ampoule containing the compound was placed in the ampoule holder, the reaction vessel was filled with an accurately measured volume of solvent (50 mL), and the system was placed in the thermostated bath. After a period of equilibration (30 min), the ampoule was broken, and the resulting temperature change of the reaction was registered on a chart recorder. After each experiment, electrical calibrations were performed. For the determination of enthalpies of solution of complexes, these were carried out in the presence of small amounts of the ligand in order to ensure that no dissociation of the complex ocurred during these measurements. In all cases corrections were applied to account for the heat of breaking of empty ampoules in the solvent which was experimentally determined (PhCN, -0.04 J; MeCN, 0.15 J). Results and Discussion Thermodynamics of Complexation. Table 1 lists stability constants (log Ks) and derived Gibbs energies ∆cG° and standard enthalpies ∆cH° for the complexation of 18-C-6 and EtCalix(6) with alkali--metal cations (Li+, Na+, K+, and Rb+) in PhCN at 298.15 K. Entropy values ∆cS° were calculated from eq 6.

∆cG° ) ∆cH° - T∆cS°

(6)

Complexation data for 18-C-6 were derived from classical titration calorimetry. However, this technique was not suitable for measurements involving EtCalix(6) given that for these systems smaller heats and slower kinetics were observed than those for the complexation of 18-C-6 and alkali--metal cations in PhCN. Therefore, measurements carried out with EtCalix(6) were performed with the TAM, a microcalorimeter system (thermal power sensitivity is about 1 µW or better) with the capacity of measuring heats associated with slow processes.23 We were unable to obtain data for the complexation of caesium and EtCalix(6) or 18-C-6 in this solvent since salts containing

6774 J. Phys. Chem. B, Vol. 101, No. 34, 1997

Danil de Namor et al.

TABLE 1: Stability Constants (log Ks) and Derived Standard Gibbs Energies and Enthalpies and Entropies of Complexation of 18-C-6, EtCalix(6), and 222 with Alkali-Metal Cations in Benzonitrile at 298.15 K cation

log Ks

∆cG°/kJ mol-1

Li+ Na+ K+ Rb+

4.74 ( 0.02a 4.89 ( 0.09a (4.75)c 6.11 ( 0.11a (5.76)c 5.84 ( 0.08a (4.89)c

-27.06 ( 0.11 -27.91 ( 0.51 (-27.0) -34.88 ( 0.63 (-32.9) -33.34 ( 0.46 (-27.9)

Li+ Na+ K+ Rb+

4.37 ( 0.05a (3.7)d 5.31 ( 0.04a (3.1)d 6.14 ( 0.04a (5.1)d 4.77 ( 0.04a (4.8)d

-24.95 ( 0.28 (-21.1) -30.31 ( 0.23 (-17.7) -35.05 ( 0.23 (-29.1) -27.23 ( 0.23 (-27.4)

Li+ Na+ K+ Rb+ Cs+

8.66b (6.99)e 11.40b (9.63)e 13.06b (11.01)e 11.00b (9.50)e 6.59b (4.55)e

∆cH°/kJ mol-1 18-C-6 -38.48 ( 0.32a -40.61 ( 0.64a (1.7)c -54.70 ( 0.47a (-17.0)c -50.07 ( 0.41a (-15.0)c EtCalix(6) -21.04 ( 1.32a -29.17 ( 0.74a -47.68 ( 1.30a -29.66 ( 1.33a

-49.43 (-39.84) -65.08 (-54.97) -74.55 (-62.85) -62.79 (-54.23) -37.62 (-25.97)

222 -47.03b (-29.79)e -66.11b (-60.96)e -79.54b (-71.29)e -74.22b (-70.20)e -49.70b (-43.51)e

∆cS°/JK-1 mol-1

∆cfS° f/JK-1 mol-1

-38.3a -42.6a (96.7)c -66.5a (53.4)c -56.1a (43.3)c

-275.9 -261.0 -271.5 -240.6

13.1a 3.8a -42.4a -8.2a

-224.0 -214.6 -247.4 -192.7

8.0b (33.9)e -3.4b (-20.1)e -16.7b (-28.5)e -38.3b (-53.6)e -40.5b (-59.0)e

-229.6b -221.8b -221.7b -222.8b -222.9b

a This work. b References 9 and 17. c Data in MeCN given in ref 38. d Data in MeCN given in ref 13. e Data in MeCN given in ref 9. f Calculated from solvation entropies, ∆solvS° of cations given in refs 9 and 17 and ∆cS° values given in column 5.

this cation are not soluble enough to generate measurable heats with these ligands. In order to compare the complexing ability of 18-C-6 and EtCalix(6) for alkali--metal cations in PhCN relative to 222, thermodynamic data for the complexation of this ligand and these cations in the same solvent previously reported by us9 are included in Table 1. Judging from the log Ks values shown in this table, a common feature of these ligands is their selectivity for the potassium cation. However, among the ligands considered, 222 is able to recognize more selectively the alkali--metal cations in this solvent than either 18-C-6 or EtCalix(6). A quantitative assessment of this statement can be made by considering the stability constant ratio (S ) Ks(K+)/ Ks(M+); M+ ) Li+, Na+, and Rb+) which shows that cryptand 222 is more selective for potassium relative to Li+, Na+, and Rb+ by factors of 2.5 × 104, 4.6 × 101, and 1.1 × 102, respectively. Replacement of 222 by 18-C-6 [S ) 23 (Li+), ) 16.6 (Na+), and ) 1.9 (Rb+)] or indeed EtCalix(6) [S ) 59 (Li+), ) 6.8 (Na+) and ) 23.4 (Rb+)] results in a considerable drop in selectivity. The high stability and selectivity of 222 for alkali--metal cations relative to 18-C-6 and EtCalix(6) reflect the relative rigidity of the former ligand whose cavity is able to recognize more selectively alkali-metal cations than 18-C-6 (hole) or EtCalix(6) (pseudocavity?). An important aspect to consider is the solvent effect on complex stability. As far as 18-C-6 and 222 are concerned, these have been extensively investigated.1, 14-17 This is not the case for EtCalix(6). For this ligand and alkali--metal cations, stability constant data have been only reported in acetonitrile, MeCN13 (see Table 1, values between brackets). Inspection of log Ks values shows that the behavior of EtCalix(6) for alkali-metal cations in benzonitrile is analogous to that of 18-C-6 in MeCN24 and 222 in MeCN14 and PhCN9 in that a “peak selectivity” is observed with a monotonic increase in stability from lithium to potassium followed by a decrease from the latter to rubidium. On these basis, it is difficult to explain the rather anomalous behavior in the log Ks values for this ligand and metal cations in acetonitrile reported in the literature,13 particularly the decrease in stability found in moving from lithium to sodium. The magnitude of stability constants in acetonitrile are well within the scope of titration microcalorimetry, however, attempts made to use this technique for the derivation of thermodynamic data for these systems failed due to the relatively low solubility of this ligand in this solvent (see below). However, the information available seems to indicate that the

stability of complexes formed between EtCalix(6) and alkali-metal cations is higher in benzonitrile than in acetonitrile. This is essentially the same pattern to that found for 18-C-6 and 222 with these cations and these will be discussed below. An important aspect to consider are the enthalpy and entropy contributions to the Gibbs energy of complexation since these are the first data ever reported on systems involving EtCalix(6). In terms of enthalpies, reasonable linear relationships are obtained when ∆cH° values are plotted against the stability (log Ks) of the metal-ion complexes [correlation coefficients are 0.9921 (18-C-6), 0.9002 [EtCalix(6)], and 0.9080 (cryptand 222)]. Therefore, the complexes are enthalpy stabilized. As the size of the cations increases, and consequently, the solvation energy decreases, the enthalpic stability increases reaching the exothermic peak for potassium in all cases. In terms of entropy, the destabilizing effect is at its maximun for the potassium cation as far as 18-C-6 and EtCalix(6) are concerned. In fact for these two ligands a more favorable enthalpy (more exothermic process) results in a more negative entropy and thus, these data provide good examples of incomplete enthalpy-entropy compensation effects recently discussed by Grunwald and Steel.25 Among the ligands considered, complexation processes involving EtCalix(6) and alkali-metal cations are characterized by a lower enthalpic stability and a more favorable entropy than 18C-6. Ligand desolvation upon complexation may be reflected in the entropy ∆cfS° associated with the process of complexation of the metal cation in the gas phase (g) by the solvated ligand to give the solvated complex (eq 7)

M+(g) + L(s) f M+L(s)

(7)

Details are given in Table 1 for L ) 18-C-6, EtCalix(6), and 222. Entropies of solvation, ∆solvS° for alkali--metal cations are those from the literature.17 The data show that the more positive ∆cfS° found for EtCalix(6) relative to 222 (except for K+, see below) or, indeed, 18-C-6 may indicate a greater desolvation of this ligand upon complexation which leads to an increase in disorder because more free solvent molecules are released. However, there are other factors which contribute to the entropy of complexation of macrocycles and cations in solution, such as the conformational changes that the ligand undergoes upon complexation.26-28 In the case of EtCalix(6) these are striking. Thus, 1H NMR studies in (CDCl2)2 carried

Alkali-Metal Cations and Macrocycles out by Otzuka et. al29 demonstrated that the 1,2,3 alternate conformation found for the free ligand (three neighboring aromatic groups (1,2,3) are inverted with respect to those in 4,5,6 positions) changes to a “cone” conformation in the K+EtCalix(6) complex. Whether or not the conformational changes observed in (CDCl2)2 are the same as those in PhCN remain to be investigated. In an attempt to investigate the solvation properties of the species participating in the complexation process involving EtCalix(6), their standard solution Gibbs energies ∆sG° are now considered. Gibbs Energies of Solution. It is well established that as far as 18-C-6 and 22230 are concerned, cation solvation plays a predominant role in the complexation of these ligands with alkali-metal cations in dipolar aprotic media. Benzonitrile, a poorer solvator for these cations than acetonitrile (positive values are found for the single-ion transfer Gibbs energies, ∆tG° of these cations from MeCN to PhCN based on the Ph4AsPh4B convention at 298.15 K)9 offers a more favorable complexation medium for processes involving 18-C-6 and 222 than acetonitrile (see Table 1). Although this seems to be the case for EtCalix(6) since the stability of the metal-ion complexes of this ligand is higher in PhCN than MeCN, it is important to investigate the effect of these solvents on EtCalix(6). In order to do so, we proceeded with solubility measurements of this ligand in PhCN (1.72 × 10-3 mol dm-3) at 298.15 K. However, we found that the solubility of EtCalix(6) in MeCN is indeed very low, and therefore, we were unable to obtain reliable data in this solvent, and therefore, in qualitative terms, it can be stated that ∆tG° EtCalix(6) from MeCN to PhCN is negative and therefore, this ligand is better solvated in PhCN than in MeCN. We also have qualitative evidence that the solubility of [KEtCalix(6)]ClO4 in PhCN is higher than in MeCN to such an extent that this limitation impeded us from proceeding with the enthalpies of solution of this electrolyte in MeCN. Since the differences in the complexation of EtCalix(6) and metal cations in these solvents are dependent on the transfer Gibbs energies of the free (∆tG° positive) and complexed cations (∆tG° negative) and the ligand (∆tG° negative) from MeCN to PhCN (eq 8),

∆cG°(PhCN) - ∆cG°(MeCN) ) -∆tG°(M )(MeCNfPhCN) - ∆tG°EtCalix(6)(MeCNfPhCN) + +

∆tG°M+EtCalix(6)(MeCNfPhCN) (8) Provided that the log Ks value in MeCN is accurate enough (∆cG° in this solvent are derived from these data), the negative ∆(∆cG°) values found in most cases results from sum of the contributions given by the free and complexed cations which outweighed that of the ligand. Futher insight into the solvation properties of these species may be obtained from enthalpy data, and these are now discussed. Enthalpies of Solution. As stated above, the solubility of EtCalix(6) and its metal-ion complexes in MeCN is relatively low to allow us proceed with the determination of the enthalpies of solution of this compound in this solvent. We also found that, although the solubility of EtCalix(6) in PhCN is good enough as to proceed with calorimetric measurements, the rate of dissolution of this ligand in this solvent is too slow as to perform these experiments accurately since the equipment suitable to us is not designed for slow dissolution processes. Therefore, enthalpy data for this ligand was derived from the van’t Hoff plot of the equilibria data as a function of the temperature. Details are given in Table 2. We are aware that

J. Phys. Chem. B, Vol. 101, No. 34, 1997 6775 TABLE 2: Solubility of EtCalix(6) in Benzonitrile at Various Temperatures T/K

solubility/mol dm-3

293.15 298.15 303.15 313.15

1.63 × 10-2 1.72 × 10-2 1.80 × 10-2 1.86 × 10-2

calorimetry provides more reliable enthalpy data compared with the van’t Hoff method due to the limitations of the latter. However, recent comparative studies31 carried out by us with a series of calixarene amino derivatives showed that for neutral species (nonelectrolytes), the ∆sH values derived from van’t Hoff’s method are in reasonable agreement with those measured calorimetrically. As far as sodium and potassium calix(6)arenate salts are concerned, among the compounds isolated, [NaEtCalix(6)]Ph4B and [KEtCalix(6)]Ph4B are the most suitable ones to perform calorimetric measurements due to their solubility and fast dissolution rate in PhCN. For comparison purposes, we proceeded with the determination of ∆sH° for [Na18-C-6]Ph4B, [K18-C-6]Ph4B, and [Na222]Ph4B in this solvent at 298.15 K. Table 3 reports the enthalpies of solution of these electrolytes in PhCN measured calorimetrically at different concentrations c. For cases where no appreciable changes in ∆sH were found with c, the standard enthalpy of solution, ∆sH° was taken as the average value of the various measurements. For systems where ∆sH values are dependent on the concentration, the standard enthalpy, ∆sH° is the value at c ) 0 from a plot of ∆sH against c1/2. Also included in Table 3 are the enthalpies of solution of 18-C-6 in PhCN as well as data for [Na18-C-6]ClO4 in PhCN. In order to discuss these data relative to those for the uncomplexed electrolytes, ∆sH° values for the free and complexed electrolytes and for the ligands are listed in Table 4. Data for the NaPh4B, KPh4B, NaClO4, KClO4, and cryptand 222 are those from the literature.8,9 The enthalpy of solution (eq 9) results from the contributions of the crystal lattice enthalpy, ∆clH° (endothermic process) and the solvation enthalpy (exothermic process) ∆solvH°:

∆sH° ) ∆clH° + ∆solvH°

(9)

Depending on which of these two processes predominate, ∆sH° can be exothermic or endothermic. As far as 18-C-6 and 222 are concerned, ∆clH° are approximately the same.32,33 Therefore, from the results shown in Table 4, it follows that the 18-C-6 molecule as a whole is slightly better solvated in benzonitrile than in 222. As far as cryptand 222 is concerned, except for water, ∆sH° values in methanol and dipolar aprotic solvents (N,N-dimethylformamide, DMF, dimethylsulphoxide, Me2SO, MeCN, propylene carbonate, PC, nitromethane, CH3NO2, and PhCN) are practically the same and these have been previously discussed.9,14,15,30 Endothermic processes are also observed for the dissolution of 18-C-6 in methanol (∆sH° ) 34.60 kJ mol-1),34 PC (∆sH° ) 24.3 kJ mol-1),24 and DMF (∆sH° ) 34.7 kJ mol-1).24 In fact, these data, particularly the value in PC, are very close to those reported in Table 4 for PhCN but differ significantly from the ∆sH° value of -5.2 kJ mol-1 reported for 18-C-6 in MeCN.24 Although it is known from (i) X-ray crystallography36,37 that in the solid state two molecules of MeCN interact with 18-C-6 through a methyl group and from (ii) microwave relaxation techniques and infrared results38 that this interaction is likely to take place between the methyl hydrogen and the ethereal oxygen, the enthalpy value obtained for the dissolution of this ligand in PhCN provides further experimental evidence that the methyl group may be the active site of interaction of MeCN with 18-

∆sH° ) 25.57 ( 0.23 kJ mol-1

TABLE 4: Standard Enthalpies of Solution of Sodium and Potassium Salts, and of Macrocycles [18-C-6, EtCalix(6), and 222] and Their Sodium- and Potassium-Complexed Salts in Benzonitrile at 298.15 K

∆sH° ) -20.72 ( 0.82a kJ mol-1

25.49 25.31 25.43 25.83 25.80 -22.81 -23.78 -22.62 -25.11 -24.94 -24.61 1.55 × 10-4 1.90 × 10-4 2.46 × 10-4 3.28 × 10-4 4.40 × 10-4 5.50 × 10-4

1.33 × 10-3 3.24 × 10-3 5.35 × 10-3 7.84 × 10-3 9.11 × 10-3

∆sH° ) 1.14 ( 0.33a kJ mol-1

2.90 4.21 4.17 4.71 4.44 6.22 8.29 × 10-4 2.11 × 10-3 2.53 × 10-3 2.95 × 10-3 3.84 × 10-3 6.18 × 10-3

Extrapolated value at c ) 0. b Average value. a

∆sH° ) -19.77 ( 0.83b kJ mol-1

∆sH° ) 19.74 ( 1.10a kJ mol-1

1.04 × 10-3 -8.12 1.59 × 10-3 -7.01 2.60 × 10-3 -7.95 3.03 × 10-3 -7.20 -3 5.03 × 10 -7.59 5.51 × 10-3 -8.19 6.45 × 10-3 -7.53 ∆sH° ) -7.65 ( 0.45b kJ mol-1 19.96 18.22 18.09 16.75 18.47 4.12 × 10-4 7.17 × 10-4 8.77 × 10-4 2.51 × 10-3 3.44 × 10-3 -20.75 -18.90 -20.60 -19.15 -20.14 -19.06 2.60 × 10-4 3.89 × 10-4 4.58 × 10-4 6.27 × 10-4 8.78 × 10-4 9.74 × 10-4 5.14 4.13 2.73 2.41 1.88 3.14 × 10-4 5.14 × 10-4 8.43 × 10-4 1.03 × 10-3 1.72 × 10-3

∆sH° ) 7.27 ( 0.47a kJ mol-1

∆sH/ kJ mol-1 18-C-6

c/ mol dm-3 ∆sH/ kJ mol-1

[KEtCalix(6)]Ph4B

c/ mol dm-3 ∆sH/ kJ mol-1

[K18-C-6]Ph4B

c/ mol dm-3 ∆sH/ kJ mol-1

[Na18-C-6]ClO4

c/ mol dm-3 ∆sH/ kJ mol-1

[Na222]Ph4B

c/ mol dm-3 ∆sH/ kJ mol-1 c/ mol dm-3 ∆sH/ kJ mol-1

[NaEtCalix(6)]Ph4B

Danil de Namor et al.

compound

∆sH°/kJ mol-1

NaPh4B [Na18-C-6]Ph4B [NaEtCalix(6)]Ph4B [Na222]Ph4B KPh4B [K18-C-6]Ph4B [KEtCalix(6)]Ph4B [K222]Ph4B NaClO4 [Na18-C-6]ClO4 KClO4 [K18-C-6]ClO4 18-C-6 EtCalix(6) 222

-44.73a 7.27b -19.77b 19.74b 10.25a 1.14b -20.72b 22.15c -10.42a -7.65b 21.93a 10.72b 25.57b 4.96d 31.63c

a From ref 8. b From Table 3 (this work). c Reference 9. d This work (see text).

c/ mol dm-3

[Na18-C-6]Ph4B

TABLE 3: Enthalpies of Solution of 18-C-6 and Sodium and Potassium Macrocycles [18-C-6, EtCalix(6), and 222] Tetraphenylborates and Perchlorates in Benzonitrile at 298.15 K

6776 J. Phys. Chem. B, Vol. 101, No. 34, 1997

C-6 since in moving from MeCN to PhCN; the thermochemical behavior of this ligand in the latter solvent is quite similar to that observed in other nonaqueous solvents where specific ligand-solvent interactions are not known to occur. As far as EtCalix(6) is concerned, availability of ∆sG° (15.78 kJ mol-1) and ∆sH (4.96 kJ mol-1) allows the calculation of the entropy of solution (∆sS ) -36.3 J K-1 mol-1) of this ligand in PhCN at 298.15 K. This behavior is quite different from that observed for 222 and 18-C-6 (which are known to be weakly solvated in this solvent) to the extent that the dissolution of these ligands is characterized by a lower enthalpic stability (more endothermic) than that found for EtCalix(6) and to the extent that these processes are entropy driven. These results seem to suggest that EtCalix(6) is more solvated in PhCN than 18-C-6 or 222, and this would contribute to the lower enthalpic stability and more positive entropies observed in the complexation of EtCalix(6) and Li+, Na+, K+ and Rb+ in this solvent relative to the same process involving 18-C-6 (see Table 1). As far as the electrolytes are concerned, the most striking changes found are those for NaPh4B (exothermic) relative to [Na222]Ph4B (endothermic). These data imply that, while for the former electrolyte, the solvation process predominates, this is certainly not the case for the latter. To a lesser extent, this is also observed for [Na18C6]Ph4B. However, the enthalpic stability of [NaEtCalix(6)]Ph4B, although lower relative to the uncomplexed salt, is higher than that of the ligand. One may be inclined to suggest that these data reflect the shielding effect of the ligand for the cation in the sequence 222 > 18-C-6 > EtCalix(6). However, this may not be necessarily the case for [NaEtCalix(6)] since its conformation is likely to differ significantly from EtCalix(6) to the extent that the complexed cation could be better preorganized to interact with the solvent than the free ligand. Regarding standard enthalpies of potassium containing electrolytes in benzonitrile, the thermochemical behavior of [K222]Ph4B, [K18-C-6]Ph4B, [K222]ClO4, and [K18-C-6]ClO4 in this solvent relative to their uncomplexed electrolytes9 follows the same pattern as that observed for sodium. A notable exception of this behavior is that shown for [KEtCalix(6)]Ph4B since, unlike KPh4B (endothermic), the dissolution of this electrolyte in PhCN is exothermic. Analogous examples of this behavior are found in the solution enthalpy data of free and complexed cryptate salts in water relative to other solvents (Table 5). Thus, the more endothermic character of the dissolution of alkali--metal cryptates in nonaqueous solvents relative to the

Alkali-Metal Cations and Macrocycles

J. Phys. Chem. B, Vol. 101, No. 34, 1997 6777

TABLE 5: Enthalpies of Solution of Alkali-Metal and Alkali-Metal Cryptate Salts and Cryptand 222 in Various Solvents at 298.15 K ∆sH°/kJ mol-1 compound

H 2O

a

MeOH

DMF

Me2SO

MeCN

PC

MeNO2

-43.51a 30.89e

NaPh4B [Na222]Ph4B NaI [Na222]I NaClO4 [Na222]ClO4 NaBr [Na222]Br KPh4B [K222}Ph4B KI [K222]I KPi [K222]Pi KClO4 [K222]ClO4 KBr [K222]Br KCl [K222]Cl [222]

-7.53a -1.63b

-0.42a -14.06b

b

-29.70a 19.41b -10.88a 37.82b -17.15a 14.81b

20.50a 5.60b

-0.42a 20.75b

50.62a 13.76b 21.76a -13.05b 17.15a -18.70b -24.73b

29.32a 28.45b 7.11a 8.58b 6.69a 7.66b 33.51b

c

d

-19.67a 20.04c -33.89a 6.35c 8.20a 33.93c -9.62a 7.82c

-7.11a 28.70c -27.20a 7.40c 15.19a 36.32c -3.35a 12.51c

6.27a 24.77c -9.62a 9.52c 23.39a 35.02c 10.50a 13.60c

2.93a 26.90c -4.18a 18.12c 26.86a 32.17c 14.22a 15.10c

18.95c 31.38c -0.75c 12.05c 34.77c 33.39c 17.95c 11.46c

34.55a

35.60d

32.93d

34.47a

31.42d

e

Reference 8. Reference 33. Reference 9. Reference 14. This work, see text.

free salts, in most cases, breaks down in water (the opposite trend is observed) where hydrogen bond formation between this solvent and the donor atoms of 222 in its free (ligand) or complexed state (electrolyte) takes place.9,39-41 We, therefore, conclude that [KEtCalix(6)]Ph4B may interact strongly with the solvent, and if so, this may be partially responsible for the greater loss of entropy observed in the complexation of K+ with EtCalix(6) in PhCN relative to that involving this cation and 222 in this solvent. Indeed, except for this system, the data shown in Table 1 reflect that ∆cS° values for EtCalix(6) are more favorable than those observed for 18-C-6 and to a lesser extent 222. It is quite clear from the above discussion that enthalpies of solution of the ligand and the free and the complexed cation provide valuable insight into the factors which contribute to the binding of metal cations and these ligands. In addition, availability of solution and complexation data allows the calculation of the enthalpy of coordination ∆coordH° of alkali-metal cations salts and these ligands (eq 5) referred to reactants and product in the solid state and these are now discussed. Enthalpies of Coordination. From ∆cH° values for the metal cation (M+ ) Na+ or K+) and the appropriate ligand [L ) 18-C-6, EtCalix(6), and 222] given in Table 1 and ∆sH° of the corresponding free (M+ + X-) and complexed (M+L + X-) electrolytes in PhCN (s) (Table 4), ∆coordH° are calculated using (eq 10):

∆coordH° ) ∆sH°(M+ + X-)(s) + ∆sH°(L)(s) + ∆cH°(s) -

TABLE 6: Enthalpies of Coordination ∆coordH°, of Sodium and Potassium Coronates (18-C-6), Calix(6)arenates [EtCalix(6)], and Cryptate (222) Salts at 298.15 K ∆coordH°/kJ mol-1

system Ba

[Na18-C-6]Ph4 [Na18-C-6]ClO4a [NaEtCalix(6)]Ph4Ba [Na222]Ph4Ba average value [Na222]Ib average value [Na222]ClO4b [Na222]Brb average value [K18-C-6]Ph4Ba [K18-C-6]ClO4a [KEtCalix(6)]Ph4Ba [K222]Ph4Ba,b average value [K222]Ib average value [K222]Pib average value [K222]ClO4b average value [K222]Brb average value [K222]Clb average value

-67.04 -17.81 -49.17 -98.95, -102.43 -100.69 -62.51; -60.24 -61.37 -59.83 -42.97; -43.09 -43.03 -20.02 -17.92 -11.72 -59.81, -60.47, -61.38, -56.86, -61.38, -61.34 -60.21 ( 1.76 -58.20, -58.95, -61.00, -60.17, -57.50, -59.71, -61.71 -59.60 ( 1.50 -46.49, -46.70, -49.99, -42.72, -47.53 -46.69 ( 2.62 -36.24, -36.91, -38.20, -41.43, -41.46, -38.29, -42.42 -39.28 ( 2.46 -38.29, -39.25 -38.77 -37.25, -38.75 -38.00

∆sH°(M+L + X-)(s) (10)

a This work. b From ∆ H° values in Table 5 and ∆ H° values in the s c various solvents (see text).

Coordination data for Na+ and K+222 salts containing different anions (X- ) I-, picrate Pi-, Br-, and Cl-) were calculated from ∆sH° values for 222 and free and complexed electrolytes in the various solvents given in Table 5 and ∆cH° (kJ mol-1) for 222 and Na+ (H2O, -31.88; MeOH, -44.64) and K+ (H2O, -48.37; MeOH, -71.29; DMF, -55.31; Me2SO, -61.17; PC, -71.88; MeCN, -71.29, MeNO2, -80.33) previously reported.9,14,15,35 Details are given in Table 6. The relatively high enthalpic stability found for the coordination of NaPh4B and 222 from data in benzonitrile led us to check the reliability of the ∆coordH° value for this system by carrying

out experimental work in another solvent. Thus, we measured the enthalpy of solution of [Na+222]Ph4B- in MeCN at 298.15 K as a function of the electrolyte concentration (range: (2.66 × 10-4) - (3.43 × 10-3) mol dm-3). A ∆sH° value of 30.89 ( 1.49 kJ mol-1 (average of six measurements) was obtained. This value was combined with corresponding data for NaPh4B (∆sH° ) -43.84 kJ mol-1),8 cryptand 222 (Table 5)9, and the ∆cH° value for Na+ and 222 (see text above) in the same solvent at 298.15 K. As reflected in Table 6, good agreement is found between ∆coordH° for this system derived from these two solvents. In fact, this statement can be extended to the various

6778 J. Phys. Chem. B, Vol. 101, No. 34, 1997 coordination data reported in this table for sodium and potassium cryptate salts since these have been derived from a wide variety of data in different solvents. Such agreement is indicative of the accuracy of solution and complexation enthalpies so far reported on these systems. The most remarkable feature of these data is the higher enthalpic stability observed in the coordination process of systems involving Na+L [L ) 18-C-6, EtCalix(6), and 222] and the Ph4B- anion relative to KLPh4B. There have been no reports in the literature on X-ray crystallographic studies of alkali-metal complexes of these ligands containing this particular anion. However, as far as 18-C-6 is concerned, remarkable differences are found in the crystal structures of [K18-C6]SCN26 relative to [Na18-C-6]SCN.27 For the former, an almost perfect D3 symmetry where the cation sits in the center of the hole and satisfies its coordinating requirements with the six oxygen atoms of the ligand is found. Cation-anion interactions are reported to be weak. X-ray crystallographic studies on [K18-C-6]ClO4 have shown42 that again the metal cation is coordinated to the oxygen atoms of the crown and to two perchlorate anions, but unlike [K18-C-6]SCN, the cation is slightly away from the plane. The relatively close ∆coordH° values for [K18-C-6]Ph4B and [K18-C-6]ClO4 seem to indicate that the strength of interaction between the complexed cation and Ph4B- must be approximately the same as that for ClO4-. Quite a different picture emerges from the solid state structure of [Na18-C-6]SCN where the cation is found to be coordinated in an irregular pentagonal pyramidal arrangement with the six oxygen atoms of the ligand (five on the plane and one out the plane) and a water molecule. The latter interacts with the SCNanion through hydrogen bond formation. There are several factors which may contribute to the higher enthalpic stability of [Na+18-C-6]Ph4B- relative to [Na+18-C-6]ClO4- and [K+18-C-6]Ph4B-, such as the following: (i) In the absence of water, the bonding requirement of the sodium cation may be best satisfied by the anion of highest polarizability [Ph4B- > ClO4-] or indeed the Ph4B- anion attracts the cation to itself out of the center of the crown. In fact, this has been observed in the solid structures of [K+18-C-6] containing ethanoethanoate43 or picrate anions and to a lesser extent, perchlorate (discussed above). It seems reasonable to suggest that these effects are likely to be more pronounced for metal ion-coronand complexes containing smaller cations than K+. (ii) The structural arrangement of [Na+18-C-6] favors interactions between the hydrophobic regions of the ligand and the Ph4B- anion. This may also apply to [Na+222], since upon complexation with sodium (a smaller cation than K+) the ligand undergoes some strain to accommodate this cation. As far as cryptands are concerned, structural studies relevant to this research are those concerning with the crystal structure of [K+222]I- 44 and [Na+222]I-.45 In both cases, the cation is located in the intramolecular cavity coordinated only to the ligand through the oxygen (six) and nitrogen (two) atoms, and therefore, this study reveals that there is no direct interaction between the enclosed cation and the anion. This is consistent with the similar values obtained for ∆coordH° for these systems shown in Table 6. However, inspection of Table 6 shows considerable differences in the coordination data and suggest that the interaction of potassium and sodium cryptate, and high polarizability anions in the solid state is selective since the exothermic character of the coordination process decreases in the following sequence,

Ph4B- = I- > Pi- > ClO4- = Br- = Clwhile for [Na+222]X-, the following trend is observed:

Danil de Namor et al.

Ph4B- > I- > Br- = ClAvailability of polarizability data for a few anions [iodide (6.43 Å), perchlorate (5.09 Å), and bromide (4.16 Å)]33 appears to suggest that there is a trend between coordination enthalpies and anion polarizabilities and these should be further investigated. Final Remarks From the above discussion it is concluded that, although most investigations in the field of solution chemistry involving calixarenes are mainly concerned with complex stability as a mean of assessing the selective recognition of these ligands for the metal cations or neutral species, a detailed thermodynamic characterization of the binding process requires enthalpy and entropy data, since these parameters provide further insights on these processes. This paper not only demonstrates that thermochemical data for the free and complexed electrolytes and the ligand are suitable reporters of solute-solvent interactions but it also makes use of these data for the derivation of enthalpies associated with processes in the solid state. In recent years, attention has been focused on molecular simulation studies on calix(4)arene derivatives and their complexes with neutral and cationic species in the gas phase and in solution. However, in order to test the relevance of such studies accurate thermodynamic data are required. There are examples in the literature in which it has been claimed that the selectivity predicted from simulation studies is in accord with experimental data. However, the poor quality of the data hardly justifies such claims.46 It may be correctly argued that thermodynamics does not provide structural information, on the other hand, any model proposed must fit the experimental thermodynamic data. We are not aware of molecular simulation studies on EtCalix(6) and metal cations either in the gas phase or in solution. To our knowledge no simulation studies have been carried out on the anion effect on the coordination of cryptands and metal cations in the solid state. It is hoped that the information provided in this paper encourages further computer modeling developments involving these systems; particularly in the solid state where the anion effect appears to be quite significant. Acknowledgment. We thank the Engineering and Physical Science Research Council (EPSRC) for the grant provided under Contract GP/K28510. References and Notes (1) Izatt, R. M.; Bradshaw, J. S.; Pawlak, K.; Bruening, R. L.; Tarbet, B. J. Chem. ReV. 1992, 92, 1261. (2) Danil de Namor, A. F. Pure Appl. Chem. 1993, 65, 193. (3) Danil de Namor, A. F.; Wang, J.; Gomez Orellana, I.; Sueros Velarde, F. J.; Pacheco Tanaka, D. A. J. Inclusion Phenom. Mol. Recognit. Chem. 1994, 19, 371. (4) Marcus, Y. Ion Solvation; Wiley: Chichester, 1985. (5) Burgess, J. Metal Ions in Solution; Ellis Horwood: Chichester, 1978. (6) Cox, B. G.; Waghorne, W. E. Chem. Soc. ReV. 1980, 9, 381. (7) Johnsson, M.; Persson, I. Inorg. Chim. Acta 1987, 127, 15. (8) Cox, B. G.; Hedwig, G. R.; Parker, A. J.; Watts, D. W. Aust. J. Chem. 1974, 27, 477. (9) Danil de Namor, A. F.; Ghousseini, L. J. Chem. Soc.; Faraday Trans. 1986, 82, 3275. Danil de Namor, A. F.; Berroa de Ponce, H. J. Chem. Soc., Faraday Trans. 1 1988, 84, 1671. Danil de Namor, A. F.; Hill, T.; Walker, R. A. C; Contreras Viguria, E.; Berroa de Ponce, H. J. Chem. Soc., Faraday Trans. 1 1988, 84, 255. (10) Pedersen, C. J. J. Am. Chem. Soc. 1967, 89, 2495. (11) Lehn, J. M. Struct. Bonding (Berlin) 1973, 16, 1.

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