J. Phys. Chem. 1987, 91, 2415-2422 saturation may be relaxing to the lattice via proton hyperfine interactions. Independent evidence exists for energy transfer between free radicals and the proton spin system in carbonaceous materials. In coals, the nuclei may be polarized by pumping the free-radical EPR transition and the nuclear Tl and Tz times are of the same order of magnitude as those measured here for electron spin-lattice relaxation.*' Moreover, strong matrix ENDOR lines have been found for the pitches under present discussion.11*z8 Finally, the EPR line shape and saturation behavior also demonstrate the interplay between the static or heterogeneous line broadening by hyperfine interactions and the dynamic or homogeneous line broadening by spin-spin interactions, as the average molecular weight of the pitch increases. In the low molecular weight materials with small radicals, the spins are dilute and the hyperfine interactions are large. These free radicals with their particular nuclear spin states tend toward an overall Gaussian line shape and saturate independently of one another. In high molecular weight materials, the free radicals are more concentrated (27) Wind, R. A.; Duijvestijn, M. J.; Lugt, C. V. D.; Smidt, J.; Vriend, J. In Magneric Resonance. Introduction, Advanced Topics, and Applications ro Fossil Energy; Petrakis, L.; Fraissard, J. P., Eds.; D. Reidel: Dordrecht, The Netherlands, 1984; pp 461-484. (28) Singer, L. S.;Lewis, I. C. Carbon 1984, 22,487.
2415
and the hyperfine interactions are smaller. The free radicals interact with one another, exchange saturation and exhibit more Lorentzian line shapes. The degree of dynamic broadening, as gauged by TZ-l, is observed to increase with molecular weight. Thus, the Portis plots of saturation exhibit a clearly increasing ratio of homogeneous to heterogeneous broadening as molecular weight increases. Although the pitch fractions generally display properties characteristic of a chemically homogeneous material, there is, nevertheless, some evidence of chemical heterogeneity of the pitch fractions. The Portis plots show that the samples comprise radicals with a range of ratios of homogeneous and heterogeneous broadening. The distribution of ratios appears to be widest for the lowest average molecular weight pitches and narrows toward purely homogeneous behavior in the highest average molecular weight pitches. The discrepancy between the average saturation parameters measured by EPR and the selective values measured by the echo method also points out a surprisingly wide range of TITzvalues. Also, the pyridine-soluble fraction of the naphthalene pitch actually displays a range of T , values. Acknowledgment. We gratefully acknowledge the assistance of Dr. Devkumar Mustafi in making the electron spin-echo measurements of T , and T2.
Complexation of Diaza Crown Compounds with Some Alkali Metal Ions in Acetonitrile and in Methanol at 25 OC Alessandro D'Aprano* Institute of Physical Chemistry, University of Palermo, 901 23 Palermo, Italy
and Bianca Sesta Department of Chemistry, "UniuersitB La Sapienza", 00185 Rome, Italy (Received: September 9, 1986)
Conductometric measurements of lithium and potassium picrate in pure methanol, in pure acetonitrile, and in the presence of 1,7,10,16-tetraoxa-4,13-diazacyclooctadecane and N-methyl-N'-dodecyl- 1,7,10,16-tetraoxa-4,13-diazacyclooctadecane macrocyclic ligands have been carried out at 25 ' C . The analysis of the results obtained with the different systems shows that the interaction forces, correlated with the molecular details of ions, solvents; and ligands, are, in most cases, superimposed on the ion-dipole forces acting between cations and macrocyclic cavities to such an extent as to prevent the cation macrocyclic ligand complexation. The effect of side chains attached to the main diazo crown ether ring on the complexation process is also discussed.
Introduction Complexation of alkali metal cations with cyclic polyethers (crown compounds according to Pedersen's' nomenclature) in both aqueous and nonaqueous solvents has recently received increasing interest as shown by the several review articles"' published in the (1) Pedersen, C. J. J . Am. Chem. SOC.1967, 89, 7017. (2) Izzatt, R. M.; Bradshaw, J. S. Nielsen, S.A.; Lamb, J. D.; Christensen, J. J.; Sen, D. Chem. Rev. 1985, 85, 271. (3) Christensen, J. J.; Eatough, D. J.; Izzatt, R. M. Chem. Rev. 1974, 74, 351. (4) Lisegang, G. W.; Eyring, E. M. In Synthetic Multidentate Compounds; Academic: New York, 1978. (5) Lamb, J. D.; Izzatt, R. M.; Christensen, J. J.; Eatough, D. J. In
Coordination Chemistry of Macrocyclic Compounds; Plenum: New York, 1979. ( 6 ) Poonia, N. S.; Bajaj, A. V. Chem. Rev. 1979, 79, 389. (7) De Young, F.; Reinhaudt, D. N. Adu. Phys. Org. Chem. 1980,17,279.
past 15 years. Equilibrium constants, enthalpy changes, entropy changes, rate constants, and activation parameter data on the complexation of cations with a variety of macrocycle compounds are reported. The implications of such a process in industrial and biological fields such as phase transfer,8-10 ion-selective electrodes,' '-I3 membrane separation processes,14chelation therapy,15 and tran(8) Pedersen, C. J. J . Am. Chem. SOC.1967, 89, 2945. (9) Pedersen, C. J.; Frendorff, H. K. Angew. Chem. 1972, 84, 16.
(IO) Landini, D.; Montanari, F.; Parisi, F. M. J . Chem. Soc. Chem. Commun. 1974, 879. (11) Fyles, T. M.; Melik-Diemer, V. A,; Whitfield, D. M. Can. J . Chem. 1981, 59, 1734. (12) Kale, K. K.; Cussler, E. L.; Evans, D. F. J . Phys. Chem. 1980, 85, 593. (13) Shono, T.; Okohara, M.; Ikeda, I.; Kimura, K. Tonura, H. J . Electroanal. Chem. 1982, 132, 99. (14) Hong Qi, 2.; Cussler, E. L. J . Membr. Sci. 1984, 19, 259.
0022-365418712091-2415$01.50/0 0 1987 American Chemical Society
2416
D’Aprano and Sesta
The Journal of Physical Chemistry, VoL 91, No. 9, 1987
TABLE I: Phvsical Prowrties of Solvent at 25
‘c
~~
solvent MeCN MeOH
D
v
36.02 32.63
0.003448 0005445
d 0.7785 0.7866
1O6k0 0.06 0 12
membrane transport phenomenal6’* are part of the reasons that have stimulated such a fruitful area of chemical investigation. Nevertheless, it must be pointed out that although many of the features of the complexation process can be obtained from previous research (for example, the selectivity of the process correlated to the relative size of cation and ligands cavity, the influence of cation solvation, etc.) the understanding of the phenomenon in terms of interaction forces between macrocycle ligands and ions is still incomplete. Most of the previous studies, in fact, have been limited to a qualitative description of the process or have been carried out in oversimplified systems where most of the interactions (solvation, ion pairing, etc.) could be “a priori” excluded. In order to investigate the role of the interaction forces (acting in solution between ions, ion-solvent, ion-ligand, and ligandsolvent) on the cation-macrocyclic ligand complexation process, we present a conductometric investigation of potassium and lithium picrates in the quasi-isodielectric solvents acetonitrile and methanol with and without the presence of 1,7,10,16-tetraoxa-4,13-diazacyclooctadecane and N-methyl-N’-dodecyl-1,7,10,16-tetraoxa4,13-diazacyclooctadecane,ligands having a cavity size able to fit the cations of both electrolytes.
TABLE I 1 Conductance of LiPi and KPi in Pure MeOH and MeCN at 25 OC
MeOH KPi 104c A 2.4429 4.5011 7.0753 9.1880 12.4410 13.4980 14.6500 25.4420
LiPi 104c A
95.26 1.8773 77.70 93.70 3.0582 76.98 92.16 4.5081 76.24 91.13 6.6476 75.48 89.68 9.3012 74.60 89.26 12.4840 73.85 88.81 16.2830 73.03 85.51 20.3790 72.26 25.0430 71.45 27.7360 71.02
MeCN KPi 104~ A 1.7054 155.37 2.7917 153.43 3.7107 152.03 4.7625 150.66 6.2390 148.77 7.6228 147.27 8.8241 145.99 10.0079 144.86 11.2138 143.72 12.3293 142.73 13.407 1 141.84 15.1424 140.42 16.8658 139.09 18.3550 138.02
LiPi 104~ A 1.5670 1 17.44 2.9770 107.77 4.8750 98.66 7.1416 90.79 10.1580 83.10 13.3120 76.99 16.6910 71.94 21.1610 66.74
surements were made in a cell of 100-mL capacity with a cell constant 2.77985 f 0.00005 calibrated by the Lind, Zwolenick, and Fuoss method25using aqueous potassium chloride solutions. The physical properties of MeOH and MeCN, measured at 25 “C, are summarized in Table I where D is the dielectric costant, 17 the viscosity in poise, d the density (g/mL), and ko the solvent conductance in mho cm-’. Dielectric constants were measured at 1 MHz with a Boonton Corporation (Model 75D)bridge and a stainless steel celLz6 The complete description of the apparatus, general technique, and cell Experimental Part calibration were described elsewhere.24 Densities were measured Materials. 1,7,10,16-Tetraoxa-4,13-diazacyclooctadecane (D2) with a vibrating digital densimeter from A. Paar (Model DMA (Merck Kriptofix 22,mol wt = 262.35)was twice recrystallized 60/602). The thermal stability maintained by a suitable temfrom benzene-n-heptane. Traces of solvents were removed by perature controller was better than hO.01 “C as checked with an drying for 24 h under high vacuum. A. Paar (Model DT 100) digital thermometer. Viscosities were N-Methyl-N’-dodecyl-1,7,10,I6-tetraoxa-4,I3-diazacyclooc- measured in a Ubbelohde type viscometer (276.5s water flow tadecane (RD,)(mol wt = 444.53)was synthesized as described time). In order to check the changes in the bulk properties of the solvents caused by the addition of D, or RD, the physical in the l i t e r a t ~ r e . ’ ~ ~ ~ ~ Lithium picrate (LiPi) was synthesized by adding a hot alcoproperties of solutions of D, or RD2 (of about 0.01 mol/L) in holic solution of lithium carbonate to a solution of picric acid in MeCN and in MeOH were measured at 25 “C. The variations in dielectric constants, viscosities, and densities were respectively ethanol. Both products were analytically pure grade. The LiPi was recrystallized three times from ethanol and traces of solvent within 0.1, 0.2,and 0.8% for all the solutions. were removed by drying under vacuum for 48 h at 45 “C. Methods. Different methods have been used for the conducPotassium picrate (KPi) was prepared by neutralizing an altance measurements. For the conductance runs of LiPi and KPi coholic solution of picric acid with potassium hydroxide followed in pure MeCN and MeOH a master solution of these electrolytes was made up by weight in a weight buret. After determination by vacuum evaporation of solvent and recrystallization from methanol. The purity of RD, and of the two picrates was tested of the solvent conductance, a portion of the master solution was by mass spectrometry. weighed from the weight buret into the solvent in the conductance Certified reagent grade acetonitrile (MeCN) and methanol cell to give the starting solution for the conductance run. Further (MeOH) were further purified as previously described.2’,22 The points were obtained by adding successive portions of the master purity and the water content of purified solvents were determined, solution to the cell. The additions of the master solution were according to Hogan,23with the gas-chromatographic technique made as to not exceed the maximum concentration (C,,, = by using the apparatus previously de~cribed.,~ 2D3(10-’) equiv./L. This upper limit is fixed by the range of Apparatus. The resistence of the solutions was measured at validity of the conductance equation,’ used to analyze the data. 1000, 4000,and 10000 H z with a Jones bribge using an oscilAll the solutions were made up by weight and the volume loscope to determine the balance point. The cell was held a t concentrations (c, mol/L) were calculated by the equation: constant temperature in an oil bath equipped with a Leeds and c / m = do - A m Northroup regulator. Temperatures were measured with a platinum resistence thermometer using a Muller bridge. The bath where m is moles of salt per kilogram of solvent, do is the density temperature was 25.000 f 0.003 OC. The conductance meaof the pure solvent, and A is an experimentally determined constant. The conductance runs in MeCN-D2 and MeOH-D2 were performed by using a similar procedure. In this case a solvent mixture of appropriate composition was first prepared by weight (15) Lehn, J. M.; Mantovani, F. Helv. Chim. Acta 1978, 61, 67. (16) Lamb, J. D.; Christensen, J. J.; Izatt, S . R.; Bedke, K.; Astin, M. S . ; in a storage flask. A weighed amount of this solvent mixture was Izzat, R. M. J. Am. Chem. Soc. 1980, 102, 3399. put into the conductance cell in order to determine the solvent (17) Aalmo, K. M.; Krone, J. Acta Chem. Scand. Ser. A 1982, A36, 227. conductance. Another portion was used to prepare the master (18) Tso, W. W.; Fung, W. P. Znorg. Chem. Acta. 1981, 55, 129. solution of KPi or LiPi in the weight buret. The starting solution (19) Cinauini. M.: Montanari. F.; Tundo. P. J . Chem. Soc.. Chem. Commun. i975, j93. point and further points of the conductance run were-obtained (20) Le Mogne, J.; Simon, J. J . Phys. Chem. 1980.84, 170. (21) D’Aprano, A.; Fuoss, R. M. J . Phys. Chem. 1969, 73, 400. (22) DAprano, A. J . Phys. Chem. 1972, 76, 2920. (23) Hogan, J.; Engel, R. E.; Stevenson, H. F. Anal. Chem. 1970, 42, 249. (24) D’Aprano, A,; Donato, I. D.; Caponetti, E. J . Solution Chem. 1979, 8, 135.
(25) Lind, Jr., J.; Zwolenik, J. J.; Fuoss, R. M. J . Phys. Chem. 1961, 65, 999. (26) Lind, Jr., J.; Fuoss, R. M. J . Phys. Chem. 1961, 65, 999. (27) Fuoss, R. M. Proc. Natl. Acad. Sci. (I.S.A. 1980, 7 7 , 34.
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987 2417
Complexation of Diaza Crown Compounds TABLE III: Conductance in MeCN-D2 and in MeOH-D, at 25 O C MeOH MeCN cD%= 52 X 102 X C D ~= 200 X C D ~= 200 X 10 mol/L 10 mol/L lo4 mol/L mol/L KPi LiPi KPi LiPi
three parameters can be obtained by solving the three equations:
104c 3.2916 5.9599 9.3230 12.3230 14.9480 17.7660 20.7040 23.9990
(p = e2/DKT;k2 = n@Nc/125) using a successive approximation method in order to find the values of the parameters which minimize:
A
128.21 126.39 124.41 122.90 121.89 120.71 119.69 118.63
104c 5.1005 9.1253 12.4821 17.8352 23.6701 32.4782 37.3853 46.3866
A
122.34 119.81 118.27 115.74 113.28 109.75 107.90 104.71
104c 9.4346 12.2795 16.3631 21.4071 25.6537 31.2020
A
82.35 81.40 80.27 79.08 78.20 77.19
104~
5.4502 9.8621 15.6205 27.1367 32.3937 37.4890
A
74.60 73.13 71.64 69.50 68.69 68.02
with the same method described above. In the experiments made to determine the effect of addition of D2 or RD2 on the conductance of alkali picrates in MeOH or MeCN, the conductance of the system, initially containing a known amount of electrolyte in pure solvent, was measured. Then known amounts of D2 or RD2 were progressively added to the solutions and the conductances were remeasured after each addition. In order to eliminate the contribution of the D2 (or RD2) to the total conductance, the conductance of these two nonelectrolytes was determined in MeCN and in MeOH.
Results The experimental values of the molar conductance of KPi and LiPi in pure MeOH and MeCN are summarized in Table I1 where A is the molar conductance (ohm-’ cm2 mol-’) and c the concentration of the electrolyte (mol/L). Table I11 summarizes the experimental values of the molar conductance of KPi and LiPi in MeCN-D2 and MeOH-D2. Each run is headed by the solvent composition expressed as mole of D2 per liter of solution. Data shown in Tables I1 and I11 were analyzed by the conductance equation derived by F ~ o s s ~ which ’ - ~ ~ can be put in the symbolic form: A = y(Ao[l - ( A X E / X )
+ AAv + AAH - A n , ] )
(1)
where y is the fraction of solute which contributes to the conductance current, A X E / Xis the part of the relaxation field generated by purely electrostatic interactions between ions, Ahv = Ao(AXv/x) is the part of the relaxation field due to change in the electrophoretic current caused by perturbation potential, AAH, is the Sanding-FeistelN hydrodynamic-hydrodynamic interaction term, A d , is the electrophoretic countercurrent, and A, is the limiting conductance. Details on the derivations of the terms of the symbolic equation have been fully described in ref 27-29. Briefly summarized the equation is essentially based on a new model of “Gurney cospheres centered on ions of charge e and surrounded by a continuum” that replaces the old unrealistic primitive model (rigid charged spheres in a continuum). One of the main features of the new model is that the distance of closest approach of free ions ( R ) is defined as the distance from the reference ion beyond which ions are treated as nonconducting pairs provided that a unique partner can be statistically defined. This allows for the presence of solvent-separated ion pairs in solution. It must be pointed out that R is a property primarily determined by the solvent and the charge of the two ions. Equation 1 is basically a three-parameter equation:
+
A = A(c;A,,KA,R) (A, is the limiting conductance, K A the association constant, and R the cosphere diameter.) Given a set of conductance data (c , A i j = 1, ..., n) covering the concentration range (0 < c < 2D3’(10’7) equiv/L) the above (28) Fuoss, R. M. J . Phys. Chem. 1978, 82, 2427. (29) Fuoss, R. M. J. Phys. Chem. 1975, 79, 525. (30) Sanding, R.; Feistel, R. J. Solution Chem. 1979, 8, 41 1
A = Y@OP - (M/X)- AAel) y = 1 - K,cy2f
In f = - p k / 2 ( 1
+ kR)
Z2 = Zj[Aj(calcd) - Aj(obsd)12/(n - 2)
All the calculations were made on an HP 9835A computer using a Basic translation of the Fortran program kindly supplied by Fuoss. In such a program the free energy change for the pairing process is also calculated by applying Gibbs thermodynamics to the pairing equilibrium and transforming the conductometric association constant to a molality scale.31 The data collected in Table IV show the coDductometric parameters Ao, KA, G, = A G / R T , and R obtained from the above analysis together with the standard deviation (%) between observed and calculated conductivities. In the same table conductance parameters obtained from analysis of the Copland and F u o s (KPi ~ ~ ~in pure MeOH) and Walden and Birr33 (KPi and LiPi in MeCN) data with the new conductance equation are also included. To our knowledge conductometric data on LiPi in pure MeOH do not exist in the literature. As can be observed our data for KPi in pure MeOH are in very good agreement with Copland’s data. The difference in pure MeCN can be ascribed to the low accuracy of the Walden data. In particular the LiPi data are widely scattered; in analyzing these data with the 1980 Fuoss equation, obviously erratic data points were omitted. Table V shows the variation of the specific conductance of MeOH and MeCN with D2 or RD, concentration with M expressed in mol/L. The conductance shown by the nonelectrolytes D2 or RD2 can be attributed to a partial ionization of N H groups and/or to traces of impurities. Tables VI-VI11 summarize the changes in the conductance of KPi and LiPi in MeCN and MeOH caused by the addition of D2 or RD2. Each run is headed by the electrolyte concentration expressed as equiv/L.
Discussion Complexation of alkali metal cation with crown compounds depends on several factors related to the specific properties of the ligand, reacting ions, and solvent. Taking into account the possible equilibria that these specific factors can cause we must consider, according to Izzatt et a1.2 the cation-macrocycle complexation process as part of the following Born-Haber cycle: M+
+ x - + s + c ~ Xi +
(M+X-)S
+
Cr
-
(M+CrX-)S
K4
where M+ is the cation; X- is the anion; S is the solvent; (M+)S is the solvated cation; (X-)S is the solvated anion; Cr is the ligand; (M+Cr)S is the solvated metal crown complexes; (M+X-)S is the solvated ion pair, and (M+CrX-)S is the solvated ion pair between the complexed cation and anion. Each of the above equilibria depends specifically on the interaction forces which act in solution between the components and is, therefore, correlated with the characteristic properties (size, charge, dipole moment, polarizability, etc.) of each species. In order to point out the influence of the equilibria associated with K , , K3, K4, and K5 on that associated with ion macrocycle (31) Fuoss, R. M. J . Solution Chem. 1986, I S , 231. (32) Copland, M.; Fuoss, R. M. J . Phys. Chem. 1964, 68, 1177. (33) Walden, P.; Birr, E. J. Z . Phys. Chem. 1924, 144, 269.
2418
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987
D'Aprano and Sesta
TABLE I V Conductance Parameters
R
Gs
u/Ao, %
ref
+ D2
161.08 i 0.03 161.96 f 0.24 134.11 f 0.14
77 f 1 84 f 12 32 f 2
22 f 1 22 f 17 24 f 4
-7.3 -7.4 -6.4
0.01 0.14 0.05
this work 33 this work
+ Dz
135.60 f 0.17 136.66 f 0.37 129.21 f 0.12
1009 f 4 1024 f 64 44 f 1
48 f 7 50 f 54 44 f 1
-9.9 -9.9 -6.7
0.04 0.25 0.05
this work 33 this work
KPi-MeOH KPi-MeOH KPi-MeOH KPi-MeOH KPi-MeOH KPi-MeOH
+ D2
99.44 i 0.04 99.40 f 0.03 99.31 f 0.05 99.30 f 0.04 99.32 f 0.04 89.44 f 0.01
39 f 39f 41 f 42 f 41 f 24 f
2 1 3 2 2 1
12f2 1211 12323 13 f 2 13 f 2 12 f 1
-6.9 -6.9 -6.9 -6.9 -6.9 -6.4
0.03 0.01 0.02 0.01 0.01 0.01
this work 32 32 32 32 this work
LiPi-MeOH LiPi-MeOH
+ D2
80.55 f 0.03 79.49 f 0.06
23 f 1 24 f 1
21 f 1 17 f 2
-6.3 -6.4
0.03 0.03
this work this work
KA
A0
KPi-MeCN KPi-MeCN KPi-MeCN LiPi-MeCN LiPi-MeCN LiPi-MeCN
TABLE V Specific Conductance of MeCN and MeOH Containing D2 or RD2
MeCN
MeOH RD2
D2 104 M
0.0000 3.3042 5.7567 9.1748 13.8370 2 1.2900 32.6110
106k 0.006 0.028 0.037 0.068 0.108 0.201 0.321
104 M 0.0000 1.1973 2.1542 5.3518 9.7966 12.1310 14.48 10
D2 106k 0.006 1.670 2.309 3.963 5.896 6.856 7.747
TABLE VI: Conductance of LiPi and KPi in MeCN as a Function of D, Concentration C~ifi= 7.750 X C ~ i p i= 10.404 X CKfi = 7.784 X lo4 equiv/L lo4 equiv/L lo4 equiv/L ,wD2104 A hfD2 io4 hfD2 io4 A 0.0000 146.90 0.0000 90.46 0.0000 83.15 0.8647 90.59 0.3488 84.05 0.4733 145.89 1.3197 144.30 2.0479 93.74 0.6382 84.78 1.2249 86.26 2.4515 142.19 3.3046 97.49 4.9250 102.14 2.1912 88.84 4.0926 139.21 6.8110 106.54 3.4247 92.15 5.8036 136.42 7.8610 108.43 4.8902 96.12 7.9777 133.70 9.5270 110.59 6.3366 99.86 11.5080 131.89 131.20 8.2265 104.24 18.3760 10.7900 111.85 12.2520 112.80 10.2420 108.01 25.9690 131.15 1 1 1.40 33.7020 131.16 14.2520 113.87 12.8090 TABLE VII: Conductance of LiPi and KPi in MeOH as a Function of D2 Concentration CKpi = 10.340 X io4 equiv/L A MDZ lo4 A M D lo4 ~ h M D io4 ~ 74.50 0.0000 91.24 0.0000 90.78 0.0000 1.7068 92.04 0.8659 90.96 74.55 0.1895 74.58 1.6322 4.3428 92.33 2.2082 91.09 3.4015 91.18 74.49 3.2163 7.2851 92.56 11.0120 92.74 5.7334 91.13 74.38 4.3862 7.4044 91.01 74.32 5.8147 13.8660 92.76 74.20 7.2190 16.4650 92.91 11.7520 90.87 73.68 10.9940 18.9960 92.97 13.5760 90.92 73.69 21.9440 93.08 15.1790 90.90 12.5690 73.69 14.1800 27.1750 93.10 17.4230 90.92 73.68 18.0060 22.6790 90.92
complexation ( K , ) let us discuss separately the results for the different systems investigated in the present work. Potassium Picrate in Acetonitrile. Figure 1 summarizes the conductance of KPi in acetonitrile with and without macrocycle (curves b and a, respectively) as a function of electrolyte concentration. Curve c represents the conductance behavior of a solution of KPi in acetonitrile (at fixed electrolyte concentration) as a function of diaza crown ether concentration.
104 M 0.0000 2.2960 4.4215 7.2610 15.4550 31.1830 41.5910
RD2 104 M 0.0000 2.0373 3.8606 6.2796 9.5035 22.312 36.012
106k 0.116 3.474 4.907 6.390 9.380 15.988 16.781
Vi.iDf
I
1 6 0 k 160
106k 0.116 3.2811 4.542 5.833 7.096 10.372 12.654 102 I
@ 0
2
6
4
A 140
120 120
'""
b 0
2 2
4
VT
I02
e 2
6
o
8
Figure 1. Conductance of potassium picrate in: pure acetonitrile (curve a) and acetonitrile + D2 mixtures (cD2= 52 X lom4mol/L) (curve b). Conductance of a solution of KPi in acetonitrile (cKpi= 7.784 X lo4 equiv/L) as a function of Dz concentration (top scale) (curve c).
An inspection of the figure shows the following features: (1) The conductance of potassium picrate in pure acetonitrile (curve a) is drammatically decreased (up to 18%) by the presence of the macrocycle ligand (curve b). (2) As the concentration of diaza crown ether increases (as in the experiment represented by the curve c) the conductance of a solution of KPi in pure acetonitrile a t fixed ionic strength gradually decreases, approaching the conductance of the solution of KPi in CH3CN D2 mixtures having the same electrolyte concentration. In addition, the slope of the curve changes drastically in a region where the ratio CKpi/CD,is equal to 1. All these features are clearly related to the overall process of the cycle considered above. In order to clarify the contribution of the five equilibria to the overall process let us consider separately each of them in relation to the specific properties of the component of the system under study. We consider first the equilibria associated with ion pair processes. As shown in Table IV the association constant is 77 for the ion pair between uncomplexed potassium and picrate ion and
+
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987 2419
Complexation of Diaza Crown Compounds
TABLE VIII: Conductance of LiPi and KPi in MeOH and MeOH as a Function of RD2 Concentration MeCN MeOH CLiti= 10.463 X lo4 C m = 7.784 X lo4 CLi, = 11.560 X lo4 C,, = 12.506 X lo4 equiv/L equiv/L equiv/L equiv/L A 84.14 83.69 84.04 84.76 86.13 88.28 91.32 95.73 100.70 102.40 102.40 102.40
MRD2 lo4 0.0000 0.6727 1.7386 2.6140 3.8223 5.2429 6.8817 8.8227 10.7750 12.9870 15.3230 17.3280
M R D 10' ~ 0.0000 0.2404 0.9764 2.2867 4.1888 6.4486 8.8814 11.7570 15.3 160 19.2310
A 146.91 145.32 141.40 135.19 126.40 116.51 108.90 107.50 106.10 104.82
32 for the ion pairing between macrocycle-cation complex and the anion. The smaller value obtained for the latter process is easily understood if we consider the weakness of the cation charge caused by the macrocyclic ring. In spite of such differences, ion pair association can be considered, as a first approximation, to be of the same order of magnitude and in any case moderately small. This assumption corresponds to considering that the equilibria associated with 4 , K4, and K5scarcely influence the equilibria associated with K1 and K2. We consider next the solvation equilibrium ( K l ) . Acetonitrile molecules are fairly small and have a dipole moment of 3.51 D.34 When an electrolyte is dissolved in such a solvent, we can expect that the dipolar molecules near the ions must be oriented by the ionic field. Considering that the potential energy of an acetonitrile molecule in contact with a potassium ion is 4 kT (as calculated by assuming the dipole as point dipole located at the nitrogen atom and from the estimated distances using Hirschfelder model), we can consider the potassium ion in acetonitrile as a solvated species. From the above consideration we can therefore assume that the overall process acting in a solution containing KPi, MeCN, and D2 is simply triggered by the equilibrium (M+)S + (X-)S
+ C r == (M+Cr)S + (X-)S
K = 1[M'CrS] [ X S ] / [M+S] [Cr] [X-SI 1 = I[M+CrSI / W+SI[Crl I (2) The equivalent conductance A, measured at fixed ionic strength as a function of the macrocycle concentration MD (as in the experiment represented in curve c) was computed as 105 k / c where k is the specific conductance at a given value of MD2 and c is the electrolyte concentration. It can be easily shown that in such a situation A, is the weighted average of the various species present, namely XI = XPi-s,Az = XK+S, and A3 = A p C R S CY(XI
+ A,) + (1
+ XI)
- ..)(A3
(3)
where CY is the fraction of the uncomplexed cation (the free (K+)S). By defining x = [(K+Cr)S]; c - x = [(K+)S] CY
= (c - x)/c = 1 - x / c
(4)
Substituting (4) into (3) yields A, = A
- (x/c)AX
+
where A = XI X2 is the equivalent conductance of the solution at MD2 = 0 and AA = A2 - A3 is the difference in conductance of the potassium ion solvated by acetonitrile molecules and complexed by the macrocyclic ligand. ~~
~
(34) Lewis, G.; Smyth, C.
~~
~
~
~~~
~
P.J . Chem. Phys. 1939, 7, 1085.
30
lo4 0.0000 0.4993 1.5084 3.4119 6.4429 10.41 10 15.3250 19.1440 22.2780 25.9110 29.3540 36.6840
MRD2
A 89.84 87.69 86.20 82.85 77.94 72.88 69.01 67.74 67.31 66.99 66.98 67.03
/
.-20
>
10
Kz
The concentrations of the species are related through the mass action law:
A,
A 74.09 73.43 72.94 72.96 73.01 72.97 72.96 72.95 72.89 72.99 73.54 73.86
MRDZlo4 0.0000 0.5253 0.8471 1.2761 1.9077 2.7618 3.9841 5.7132 7.7874 9.9994 12.6750 16.2830
c Figure 2. Percentage decrease in the conductance of KPi in acetonitrile (cui = 7.784 X lo4 equiv/L produced by D2 (0)and RDz (0)as a
function of diaza crown ether concentration. Combining (5) with (2) and setting [(A - A,)/A] 100 = y we obtain y = 100K(AA/A)[Cr] (6) which calls for a linear relationship between y and the macrocycle concentration [Cr]. As shown in Figure 2 our experimental results are in full agreement with eq 6 at least in the concentration range 0 < MD2 < 7.8 X lo4 equil/L, where the electrolyte is in e x w s with respect to the diaza crown ether ligand. The change in the slope observed for macrocycle concentration higher than the electrolyte concentration can be easily rationalized by considering that in absence of free (K+)S the addition of the ligand is no longer able to change the conductance of the solution. = 1 indicates, in addition, that 1:l The distinct break at cm/cD2 complexes are formed. In Figure 2 the relative change of the conductance of KPi in pure acetonitrile by addition of the bulky RD2 is also reported. As can be noted the trend is similar to that described before, the increase in the slope being related to the higher value of AA due to the bulkiness of K+RD2 complexes. Lithium Picrate in Acetonitrile. Curves a and b of Figure 3 represent the conductance of LiPi in pure acetonitrile and in acetonitrile-diaza crown ether mixtures, respectively. Contrary to the behavior observed with KPi in the same solvent systems,
D’Aprano and Sesta
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987
2420
vi4 ,,.lo2
I 0
h
TABLE IX: Stability Constant of Alkali Metal Cations and 18C6
2
Complexes in Isodielectric Methanol and Acetonitrile
4
I
loa K i
ligand 18C6
cation Na+ K+
cs+
a
MeOH
MeCN
4.5’
4.8b
6.2c
5.8‘ 4.40
>4d
Reference 36. Reference 37. Reference 38. dReference 39.
A 100 90
.
A
80 I-
60
\
‘t
I 0
0
I
2
2
I
4
fi*loz
I
4
6
Figure 3. Conductance of lithium picrate in pure acetonitrile (curve a) and acetonitrile D2mixtures ( C D ~= 102 X lo4 mol/L) (curve b).
+
Conductance of solutions of LiPi in acetonitrile (cLiti= 7.750 X lo4 equiv/L) (curve c); (cLipi= 10.404 X lo4 equiv/L) (curve d); (cLiti= 10.436 X lo4 equiv/L) (curve e) as a function of D2 (top scales) or RD2 concentration (inside bottom scale). the presence of the macrocyclic ligand increases the conductance of LiPi. This finding is fully confirmed by the experiments (represented by the curves c, d, and e) where the conductance of a solution containing a fixed concentration of LiPi in pure acetonitrile was remeasured after the addition of different amounts of D2 or RD2. Evidently, the increase in conductance observed under these conditions cannot be explained by the simple complexation equilibrium since the cation complexation, if it occurs, produces in any case a decrease of ionic conductance. The solution of this puzzle is easy if we consider that, unlike KPi, LiPi in acetonitrile is quite highly associated to ion pairs ( K A = 1000). In such a case, therefore, the coupled equilibrium for ion pairing (M+)S
+ (X-)S * (M+X-)S
K5
and for cation complexation (M+)S + (X-)S
+ C r * (M+Cr)S + (X-)S
K2 must be considered to describe the overall process. (The small values of the association constant ( K A = 40) obtained for the ion pairing between macrocyclic-cation complex and anion allow us to consider that the equilibria associated with K3 and K4scarcely influence the overall process.) Due to a lack of information about K2 a rigorous treatment of the problem is quite difficult. From a phenomenological point of view the experimental results of LiPi in acetonitrile diaza crown ether mixtures can be rationalized by assuming K2 > K5.With such an assumption the increase in conductance is due mainly to the increase of the ionic strength as a consequence of the dissociation of nonconducting ion pair caused by the complexation process. Potassium Picrate in Methanol. Complexes of alkali metal cations with macrocyclic ligands are found to be mostly of 1:l stoichiometry. The “ion in the hole” model proposed for such complexes assumes that the cation is held in the hole of the polyether ring by ion-dipole force^.'^^^ (35) Frensdorff, H. K. J . Am. Chem. SOC.1971, 93, 600.
Figure 4. Conductance of potassium picrate in pure methanol (curve a). Conductance of solutions of KPi in methanol (cKp,= 9.054 X equiv/L) (curve b); (cm = 10.197 = lo4 equiv/L) (curve c); (cKpi= 12.506 X lo4 equiv/L) (curved) as a function of D2 (top scales) or RD2 concentration (inside bottom scale).
Given the pure electrostatic character of this interaction we would expect that a given cation (fixed ion size) and a macrocyclic ligand (fixed hole) should have the same binding constant in chemically different solvents that have the same macroscopic dielectric constant. Although this so-called “isodielectric rule” holds quite well for many systems (see Table IX where the stability constant of alkali metal cations and 1,4,7,10,13,16-hexaoxacyclooctadecane (18C6) complexes in quasi-isodielectric methanol ( D = 32.66) and acetonitrile (D= 36.06) are reported), numerous violations, involving solvating power, cation size, etc., have been recently described.2 The conductometric behavior of KPi in the MeOH-D2 system depicted by curves b and c of Figure 4 represents another example of the isodielectric rule violation if we compare such behavior with that previously described for the KPi-MeCN-D2system (Figure 1). Comparison of Figure 4 and Figure 1 shows, in fact, that the addition of the macrocyclic ligand to the KPi solutions in MeOH does not change the total conductance of the system as the polyether does in KPi-MeCN solutions. Since as already pointed out a complexation process always gives a decrease in ionic conductance, the constancy of the total conductance of the KPi solution in MeOH by the addition of D2 indicates that complexation of K+ cations practically does not occur in such a system. Because, as shown in Table IX, K+-18C6 complexes have practically the same stability constant in MeOH and in MeCN, we cannot ascribe to the different solvating power of these two solvents the reason why the quite stable K+D2complexes in MeCN (log k = 4.3240*41)are not formed in methanol solut&m. In addition, the small ion pairing association constant (see Table IV) found for KPi in methanol ( K A = 39) excludes the influence of (36) Luo, G. H.; Shen, M. C.; Zhuge, X.M.; Dai, A. B.; Lu, G.Y.; Hu, H.W. Acta Chem. Sinica 1983. 41. 877. (37) Nakamura, T.; Yumoto, Y.’ Y.;Izutsu, K. Bull. Chem. SOC.Jpn. 1982. 55. 1850.
G8) Takeda, Y . Bull. Chem. SOC.Jpn. 1983, 56, 866.
(39) Mei, E.; Popov, A. I.; Dye, J. L. J . Phys. Chem. 1977, 81, 1677. (40) Kulstad, S.;Malmster, L. A. J . Inorg. Nucl. Chem. 1980, 42, 573. (41) Kolthoff, T. M.; Chantooni, M. K. J . A n d . Chem. 1980, 52, 1039.
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987
Complexation of Diaza Crown Compounds
ligand
structure
coAo2 co O
W
3
20-
10
-
6
fiD2'1024
1
h
t 0
2
4
fi.102
6
8
Figure 6. Conductance of lithium picrate in pure methanol (curve a). Conductance of solutions of LiPi in methanol (cylpl = 10.197 X equiv/L) (curve b); ( c ~ =, ~11.560 X lo4 equiv/L) (curve c) as a function of D2 or RD2 concentration (top scales).
-
*
1
80
O'
L o 0 W
-
2
0
1.4
15
6
4
J
1.4
25
fiRDiD2
I
hole size, A 1.3-1.4
2
0
TABLE X Structures and Hole Size of lSC6, D2, and RD2 Ligands
2421
/
iKpi
1
0 10 20 C.10t 30 Figure 5. Percentage decrease in the conductance of KPi in methanol (CKti= 12.506 X lo4 equiv/L) produced by D2 as a function of diaza crown ether concentration. the ion pair equilibrium on the complexation process. Table X summarizes some of the features of the 18C6, Dz, and RD, ligands. As can be noted despite the three ligands having practically the same hole size, they differ by the presence of N H groups able to form hydrogen bonds with MeOH. Under these circumstances we can reasonably assume that the D, molecules added to the KPi-MeOH solution will take part in the solvent's structure through the equilibrium:
+
n(D2) (MeOH), (D2MeOH),+, instead of participating in the complexation equilibria described by the Born-Haber cycle. If the above interpretation is correct we would expect that the substitution of the hydrogen of the imino groups of the D, with alkyl chains would give ligands able to complex potassium ion in methanol as does the 18C6. The decrease in the conductance of KPi in MeOH caused by the addition of RD, (see curve d of Figure 4) together with y = [(A - A,)/A]lOO (eq 6) vs. RD, concentration behavior shown in Figure 5 (quite similar to that obtained for KPi-RD2-MeCN system reported in Figure 2) are in total agreement with our interpretation. Lithium Picrate in Methanol. As shown in Figure 6 addition of D, to the LiPi-MeOH solution produces effects quite similar to that observed in the KPi-MeOH system. The smaller decrease of the total conductance caused by the addition of RD, with respect to the KPi-MeOH-RD, system can be ascribed to the high solvation of Li' ion. As pointed out by Izzatt et aL2 in fact, the energy required for the desolvation of lithium ion in methanol is
too high to be compensated for the complexation step of the Born-Haber cycle. The analysis of the different effects on the conductance of lithium and potassium picrate in MeCN and MeOH caused by the addition of diaza crown ether ligands so far investigated has clearly pointed out how these effects strongly depend on ion-ligand, ion-ion, ionsdvent, and solvent-ligand interactions that take place in different systems. These are correlated to the specific properties (i.e. size, polarizability, dipole moment, structure, hydrogen bonding, etc.) of the substances involved in such systems. In order to have a deeper understanding of these interaction forces let us consider the conductometric parameters obtained from the conductance measurements of lithium and potassium picrate in MeCN-D, and MeOH-D, mixtures. From an inspection of the data reported in Table IV we note that while the conductometric parameters (Ao,KA, and Gs) for a given electrolyte (KPi or LiPi) change on passing from pure acetonitrile to an acetonitrile D2 mixture, they remain practically constant on passing from methanol to a methanol + D2 mixture. The finding is as expected considering that, in agreement with the previous analysis, the appreciable complexation of Li+ and K+ cations with Dz in acetonitrile practically does not occur in methanol. Concerning the MeCN and MeCN + Dz systems we also note that the quite different conductometric parameters (in particular K A and Gs) for the two electrolytes in pure acetonitrile becomes very similar in the MeCN D2 mixture. This can be easily understood if we consider that in the presence of a suitable amount of diaza crown ether all the cations can be considered complexed so that the measured conductance is due only to the conductance of the anions and M+Cr cations. Under these circumstances the short- and long-range interactions governing the total conductance must be expected to have practically the same size given the similarity in the size of the complexed lithium and potassium cations. In order to obtain information on the radii that represent the spheres which are hydrodynamically equivalent to the ions, let us consider the Stokes radii R, calculated as
+
+
R, = Fe/180nXo7 = (0.819/ho7)10-8
Using the values Xo- = 46.9 for the picrate anion in pure methanol obtained by Copland and Fuoss3, combining their conductometric data with the Gordon's transference data42-43 for = 84.8 for sodium and potassium chloride in methanol and io+ the potassium cation in pure acetonitrile as reported by Della Monica et we obtain the ionic limiting conductance sum(42) Butler, J. B.; Schikk, H. I.; Gordon, A. R.J . Chem. Phys. 1951, 19, 724. (43) Davies, J. A,; Kay, R. L. Gordon, A. R.J . Chem. Phys. 1951,19,749.
J . Phys. Chem. 1987, 91, 2422-2428
2422
TABLE XI: Limiting Ionic Conductance Xo+ and Stokes Radii R , Values for Lithium and Potassium Ions in Acetonitrile and Methanol with and without Diaza Crown Ether'
[M+SI [M'S] [M+CrS]
ff=
+
cations
solvent
and combining eq 7 with eq 2 we obtain:
MeCN MeCN + D,
io+ 84.8 57.8
R,
K+ K+
2.0 4.1
LY
Li+ Li+
MeCN MeCN
+ D,
59.3 52.9
4.0 4.5
K+ K+
MeOH MeOH
+ D2
52.6 42.5
2.9 3.5
Li+ Li+
MeOH MeOH
+ D,
33.7 32.6
4.5 4.6
RD2 RD2 RD,
salt
KPi KPi KPi LiPi
solvent MeCN MeCN MeOH MeOH
Combination of eq 8 and eq 3 gives Ap
Ahl+x-I AM+X- AM+CrX- AM+CrX- log k2 146.90 146.91 89.84 74.20
130.86 104.19 65.98 70.20
1.123 1.410 1.362 1.055
+ 1)2- 4K2[X-S])'12 - K2([Cr] [X-Sl) + 1)/(2K,[X-SI) (8)
TABLE XII: Equivalent Conductivities and Stability Constants for Diaza Crown Ether-Cation Complexes in MeCN and MeOH
ligand D,
= (f(K2([Cr]- [X-SI)
(7)
4.47 4.43 4.21 3.25
marized in the first column of Table XI. In the second column the Stokes radii calculated from the A,,+ values are also reported. Table XI data show that, in complete agreement with the results so far analyzed, the Stokes radius of the lithium cation in pure acetonitrile is almost twice as big as that of the potassium ion. While in the presence of diaza crown ether, these two cations assume almost the same ion size. We consider next the stability constants of K+D2, K+RD2,and Li+RD2complexes. As pointed out by Evans et al.,45when ion pair association and/or ligand-solvent interactions are negligible, the measurements of the apparent equivalent conductance as a function of ligand concentration (as in the experiments represented in Tables VI-VIII) is sufficient to determine the ligand-cation association constant K2. According to the procedure previously described45setting the fraction of uncomplexed cation a as (44) Della Monica, M.; Ceglie, A,; Agostiniani, A. Efecrrochem. Acta 1984, 29, 161. (45) Evans, D. F.; Wellington, S. L. Nudis, J. A.; Cussler, E. L. J . Solution Chem. 1972, 1, 499.
= f([Crl,K2,AM+CrX-)
from which the two unknowns, K2 and AM+CrX-,may be obtained by a nonlinear least-squares analysis. Data from Tables VI and VI11 analyzed in such way give the results summarized in Table XII. The ratios AM+x-/AM+c~Xreported in Table XI1 represent a measure of the decreased mobilities of the complexes. As can be seen these ratios for a given cation in a fixed solvent depend on the bulkiness of the ligand, while for a given cation and a fixed ligand they depend on the solvation power of the solvent. The values of the stability constants (log K 2 ) obtained in all the systems are large and for KCD2in MeCN are in qualitative agreement with those reported earlier.41,42As far as the complexation of the potassium ion with D2 or RD2 in both MeCN and MeOH we observe that the stability constant values are independent of the chemical characteristic of both ligands and solvents. This finding, in full agreement with the "isodielectric rule", confirms our previous analysis and indicates that the electrostatic ion-dipole forces, depending to the macroscopic dielectric constant of the solvents and on the dipole moment of the ligands, are the strongest factors in the complexation process in such a system. It must be pointed out that although these results seem to support the selectivity of the ligand (fixed hole and dipole moment) for a given cation (fixed size and charge density), the absence of complexation found for the K+ ion and D2 in methanol signal the caution required in applying the selectivity rule without considering polyethersolvent interactions or other interactions able to modify the charge density of the bare cations and/or the net dipole moment of the ligands. The stability constant for K+RD2 in MeOH, an order of magnitude greater than Li+RD2, is another example of altered selectivity caused in such a case by the decrease of the charge density of the lithium ion through the solvation process. Registry No. LiPi, 18390-55-1; KPi, 573-83-1.
The Problem of Perturbation Molecular Orbital Aromaticity Estimates Kathleen Anne Durkin and Richard Francis Langler* Department of Chemistry, Florida Institute of Technology, Melbourne, Florida 32901 -6988 (Received: February 5, 1986)
The Dewar-Dougherty approach to aromaticity estimates, based on approximateperturbation molecular orbital (PMO) estimated Dewar resonance energies, is shown to be unreliable. Difficulties are particularly serious for cyclic molecules containing 4n ?r electrons. A proposed modification of the Dewar-Dougherty method is shown to furnish more reasonable estimates of Dewar resonance energies.
Introduction Perturbation molecular orbital (PMO) theory is a well-established approach in dealing with chemical reactions. probably the *Author to whom all inquiries should be
addressed.
0022-3654/87/2091-2422$01 SO/O
best known example is Fukui's frontier molecular orbital approach to Orbital Problems.' The PMO approach can also be employed to anticipate structural features in molecules with ( I ) Fukui, K. Acc. Chem. Res. 1971, 4, 57.
0 1987 American Chemical Society
