J. Phys. Chem. 1992,96, 8631-8639 and the only candidate whose use is questionable, based upon this requirement, is the 16sHo-2,4,-hexanedionate complex. It was concluded that the solvent evaporation technique would be the most usefd method to produce nonporous retentive polyester spheres. Since an organic solvent such as chloroform is able to dissolve the polyesters, it is imperative that the Ln complex have adequate solubility in chloroform in order to be encapsulated in suitable amounts in the spheres. It is apparent that the CHC13 ~ with acetylacetone and ethyl solubility of the ‘ 6 5 Hcomplexes acetoacetate are sufficient for their intention. Although ethyl acetoacetate complexes Ho3+,its higher pK, allows a competing hydrolysis mechanism to occur which greatly reduces the maximum percent 1 6 5 Hcomplexed. ~ From these Observations, it is apparent that acetylacetone is the most effective complexing agent for 1 6 5 Hfor ~ subsequent incorporation of the complex into PLA microspheres. Acknowledgment. This work was supported in part by Grant 1N-163 from the American Cancer Society, Grant Rll-8110671 from the National Science Foundation, and the Commonwealth of Kentucky through the Kentucky EPSCoR Program. The authors also wish to thank Craig S.Pohlod and Mark Kaczor at the University of Illinois TRIGA Reactor and Brad Keck at the University of Missouri Research Reactor (MURR) for sample irradiations.
8631
References and Notes (1) Brown, W. B.; Steinbach, J. F.; Wagner, W. F. J . Inorg. Nucl. Chem.
1960. 13, 119. (2) Grenthe, I.; Fernelius, W. C. J . Am. Chem. SOC.1960, 82, 6258. ( 3 ) Brittain, H. G. Nucl. Med. Biol. 1988, 15, 17. (4) Moeller, T.; Ulrich, W. F. J . Inorg. Nucl. Chem. 1965, 2, 164. (5) Stary, J. The Solvent Extraction of Metal Chelates; Irving, H., Ed.; Macmillan: New York, 1964. (6) Rydberg, J. Ark. Kemi 1955, 9, 95. (7) Wu, J.; Shen, Z . Polym. Chem. 1990, 28, 1995. (8) Mumper, R. J.; Mills, B. J. A.; Ryo, U. Y.; Jay, M. J . Nucl. Med. 1991, 33, 398. (9) Mumper, R. J.; Ryo, U. Y.; Jay, M. J. Nucl. Med. 1991, 32, 2139. (10) Mumper, R. J.; Jay, M. Pharm. Res. 1991, 9, 149. (11) Mumper, R. J.; Jay, M.J . Controlled Release 1992, 28, 193. (12) Mader, W. J. Organic Analysis; Interscience: New York, 1954; Vol. 2. (13) Ehrhardt, G. J.; Day, D. E. Nucl. Med. Biol. 1987, 14, 233. (14) Hosain, F.; Haddon, M. J.; Hosain, H.; Drost, J. K.;Spencer, R. P. Nucl. Med. Biol. 1990, 17, 15 1. (15) Stites, J. G.; McCarty, C. N.; Quill, L. L. J . Am. Chem. SOC.1948, 70, 3142. (16) Rydberg, J. Acta Chem. Scand. 1950,4, 1503. (17) Bjerrum, J. Metal Amine Formation in Aqueous Solution. Theory of the Revmible Step Reactions; Haase: Copenhagen, 1941. (18) Block, B. P.;McIntyre, G. H. J . Am. Chem. SOC.1953, 75, 5667. (19) Izatt, R. M.; et al. J . Phys. Chem. 1955, 59, 170. (20) Moeller, T.; Moss, F. A. J.; Marshall, R. H. J. Am. Chem. Soc. 1955, 77, 3182. (21) Betts, R. H.; Dahlinger, 0. F. Can. J . Sci. 1959, 37, 91.
Thermodynamics of Dimerization of NaSCN in Some Acyclic Polyethers Studied by Infrared Spectroscopy P. Firman, M. Xu, Edward M. Eyring, and S. Petrucci* Weber Research Institute and Department of Chemistry, Polytechnic University, Route 1 10, Farmingdale, New York 11 735, and Department of Chemistry, University of Utah, Salt Lake City, Utah 841 12 (Received: November 21, 1991; In Final Form: June 22, 1992)
Infrared spectra (“CN stretch”)of the thiocyanate ion of NaSCN in the solventstetrahydrofuran (THF) and 1,2-dimethoxyethane (DME) are attributed to contact ion pairs in equilibriumwith dimer ion pairs (or quadrupoles). The thermodynamicdimerization constant Kdois obtained from the spectral envelopes in two ways: (1) An apparent dimerization constant Kdapp(ignoring solvent-separated dimers) is calculated, and Kdois obtained through extrapolation to zero electrolyte concentration, with activity coefficients yp = (&aw/Kdo)l/zcalculated by theoretical equations expressing dipole-dipole interactions using a single adjustable parameter d, the dipole-dipole minimum approach distance. (2) A two-step Eigen dimerization scheme is also proposed, and Kdo= Kl(1 K2)is calculated from spectroscopicallydetermined KI and K2 values, achieving fair agreement with &O Calculated by the first method. Ultrasonic relaxation experiments confirm the interpretation of the vibrational spectra by a two-step Eigen scheme. Microwave dielectric relaxation experiments furnish the necessary apparent dipole moment for the Na’NCS ion pair as well as the extrapolated static permittivity of the solutions required for a theoreticalcalculation 2ion-pair activity coefficients. Infrared spectra show the disappearance of contact dimers when the ethereal chain is lengthened from DME to triglyme (TG) and t o tetraglyme (TeG). The above involves going from a bidentate solvating ligand such as DME to a tetradentate ligand such as TG and to pentadentate ligand such as TeG. Thus, when specific interactionsbecome important as in the case of the longer chain ethers, one must be careful not to correlate properties of electrolyte solutions simply with macrQsoopic parameters such as the dielectric permittivity of the solvent. Ultrasonic results confirm the interpretation of the polyethereal systems.
+
Iatroduction Historically, electrical conductance at audio frequencies’ has often been used to calculate the ion-pair formation constant K :. Unfortunately, this method is unsuitable for distinguishing between nonconducting ion pairs and ion-pair dimers. In addition, uncertainties in calculating Ao, the molar conductance at infinite dilution (often estimated in solvents of low permittivity through approximations such as Walden’s rule), cause substantial loss of accuracy in K:. Vibrational spectra offer a potentially powerful alternative. The use of IR methods, in nonaqueous media and at low concentration of electrolyte, appears preferable to Raman techniques (because of the higher sensitivity of IR methods). The use of one of the
normal modes of vibration of the anion has been one of the most effective approaches in both Raman and IR studies (in their respective and complementary possibilities of detecting these modes and their alterations of symmetry upon cation contact).* Unfortunately, one cannot distinguish3 by vibrational spectra free anions from anions associated with cations through even as few as one solvent molecule, the so-called solvent-shared or outersphere ion pairs. The same holds true for distinguishing contact dimer ion pairs (quadrupoles) from solvent-separated pairs? Thus, analysis of spectra, assigning the “contact” band of the envelope to C, (concentration of the bound species) and the “free” band of the envelope to C, (concentration of the free species), leads to = Cb/Ct. a meaningless formation constant,s K PP:
0022-365419212096-8631%03.00/0 0 1992 American Chemical Society
8632 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 If the "free" band corresponds to both free anion and solvent-separated ion pairs of respective concentrations Cl and C2 and the 'contact" band to C3, the true formation constant4 is K p = (C3+ C2)/C12,whereas Kp"W = C3/(Cl + C2),. Many literature reports have unfortunately appeared reporting K:PP as a true formation constant. Some authors have even reported AH values calculated from a van't Hoff plot of In K:PP vs 1/T. The situation has recently been ameliorated by a proposal6 to express C, through activity coefficients, namely, expressing a concentration of a "species" defined as existing "at noncontact distances" as an "interaction" affecting K a*. This is the physicist's alternative to a chemist's definition of a loose 'species". The Bjer" association theory7defining as ion pairs ions at distances of up to about 36-47 A in solvents of permittivity c = 6-8 is a relevant example of the above concept. The same ideas hold for a dimerization formation constant Kd, where the solvent-separated ion pairs are expressed through a dipoldipole or ion pair to ion pair activity coefficient. In the former case a plot of In K a p p vs v'Co has been proposed,6 and in the second case a plot of fn Kp"PP vs C has been suggested. This is due to In Y~ being proportional to v'Co according to the DebyeHiicke1 theory (at lower concentration and neglecting y p ,the ion-pair activity coefficient) for the first case and to In y p being proportional to Co (actually to the ion-pair (or dipole) concentration C,, at lower concentrations and according to recent the~ r i e s ,and ~ , ~neglecting the dimer activity coefficient). We therefore decided to use infrared spectra, NaSCN as a model electrolyte and ethers of increasing polydentate oxygen donor ability, to apply the above ideas and calculate the dimerization constant Kdo. (As shown below, the ion-pair formation constant K: appears to be too large in these media for its determination by IR spectrometry.) The aim of this work is to upgrade infrared spectroscopy as one of the modern methods for studying aspects of the thermodynamics of complexation of electrolytes in media of low permittivity. We have also used ancillary relaxation methods such as ultrasonic absorption and microwave relaxation spectrometries to sustain the interpretation of the IR spectra. By elongating the polyethereal chain of the solvent, we have approached true polymeric liquid solutions which are relevant to battery construction.
Experimental Section Equipment and procedures for the infrared,4.I0ultrasonic,'' and microwave dielectric relaxationI2 work have already been described. To achieve better mutual reproducibility and precision of the spectra, BaF2 windowed, sealed infrared cells of thickness 0.1 and 0.03 mm, respectively, were thermostat4 at 25.00 f 0.05 OC, the cell temperature being monitored by a thermistor probe attached to the jacketed cell holder. To THF (Aldrich, Gold Label) were added metallic sodium and benzophenone, and the mixture was stirred until a blue permanent color, indicating the absence of peroxides, was obtained. The liquid was then distilled at atmospheric pressure in an allPyrex apparatus with Teflon sleeves in the ground joints. DME was treated similarly and distilled under reduced pressure in the same distillation apparatus. Triglyme and tetraglyme (Aldrich) were kept over molecular sieves (predried at 400 "C) and then distilled in vacuo. All the distilled liquids were tested for the absence of water by running an IR spectrum in the 3300-3800-cm-' range at high sensitivity (0.1 absorbance unit at full scale). On the basis of absorbance shown in the case of diglyme (50 ppm of water, Fluka), it is estimated that the content of water in the liquids studied was > 1-lo6), the slope of the plot should be given by 4dco x 10-3 slope = 3kT Bpz from which the average apparent value of gpcould be calculated. This plot is shown in Figure 12 (microfilm edition) for the data of NaSCN in TeG. Linear regression of +(e) vs 1/ T gives #(e) = -7.462 + 2.78 X IO3( 1 / T ) with ? = 0.97. Then from the slope esu cm. we calculate the average value 1, = 38.8 x Conclusions The present spectroscopic results could conceivably promote infrared spectrometry to the role of a modem and specific method of measuring dimerization constants, Kd0 once the identity of the species present is ascertained. The problem of the ‘solvent-sep-
Supplementary Material Available: Infrared parameters for the Gaussian-Lorentzian product functions (eq 1) used to decompose the “CN stretch” spectral envelope of the electrolyte NaSCN (Table I); ultrasonic relaxation parameters related to the Debye function for two relaxation processes (Table 111); results of linear regression of S vs C, and P vs C for NaSCN in 1,ZDME and for S vs dCoand P vs d C , for NaiCN in tetraglyme (Table IV); dielectric relaxation parameters and specific conductivities for NaSCN in DME and in tetraglyme (Table V); ultrasonic absorption spectrum for NaSCN in DME (Figure 7); and Battcher plot for NaSCN in tetraglyme (Figure 12) (8 pages). Ordering information is given on any current masthead page. References and Notes (1) Fuoss, R. M.; Accascina, F. Elecrrolyte Conductance; Interscience: New York. 1959. (2) Irish, D. E. In Ionic Interactiom; Petrucci, S., Ed.; Academic Press: New York, 1971; Vol 11. (31 Irish. D. E.; Tang, - S.Y.; Talts, H.;Petrucci, S. J . Phvs. Chem. 1979, 83,‘3268. (4) Saar, D.; Petrucci, S. J . Phys. Chem. 1986, 90, 3326. ( 5 ) Edgell, W. Purdue University, private communication, 1980. ( 6 ) Chabanel. M. Pure Appl. Chem. 1990, 62, 35. (7) Bjerrum, N. K . Dan. Vidensk. Selsk. Mar.-Fys. Medd 1926, 7 , 1. (8) Xu,M.; Obeid, N.; Eyring, E. M.; Petrucci, S.J . Phys. Chem. 1989, 93, 989. (9) Petrucci, S.;Eyring, E. M. J . Phys. Chem. 1991, 95, 1?31. (10) Firman, P.; Marchetti, A.; Xu, M.; Eyring, E. M.; Petrucci, S . J . Phys. Chem. 1991, 95, 7055. (11) Echegoyen, L.;Gokel, G. W.; Kim, M. S.; Eyring, E. M.; Petrucci, S. J . Phys. Chem. 1987, 91, 3854 and previous literature cited therein. (12) Xu,M.; Eyring, E. M.; Petrucci, S.J . Phys. Chem. 1986, 90, 6125 and previous literature cited therein. (13) For a discussion of this function, see: Inoue, N.; Xu,M.; Petrucci, S. J . Phys. Chem. 1987, 91, 4628. Maaser, H. E.; Xu, M.; Hemmes, P.; Petrucci, S.J. Phys. Chem. 1987,91, 3047. (14) (a) Paoli, D.; Lupn, M.; Chabanel, M. Spectrochim. Acta, Part A 1978, 34, 1087. (b) Menard, C. Doctoral Thesis, University of Nantes, France, 1973. (c) Chabanel, M.; Wang, 2.J . Phys. Chem. 1984,88, 1441. (15) (a) Irish, D. E.; Tang, S. Y.; Talts, H.; Petrucci, S.J . Phys. Chem. 1979,83,3268. (b) Buckingham, A. D. Proc. R. SOC.London 1958, A248, 169. (16) P o p , A. Michigan State University, private communication, 1987. (17) (a) Farber, H.;Petrucci, S.J . Phys. Chem. 1975, 79, 1221. (b) F = [(2! - 2)/(2c + l)]d, with a the radius of the cavity containing at its center the dipole of moment and polarizability up. (c) Farber, H.; Petrucci, S. J . Phys. Chem. 1976, 327. (18) Maaser, H.E.; Delsignore, M.; Newstein, M.: Petrucci, S. J . Phys. Chem. 1984,88, 5100. (19) Nttcher, C. F. Theory of Electrical Polarization; Elsevier: Amsterdam, 1973. (20) Saar, D.; Brauner, J.; Farber, H.; Petrucci, S. Ado. Mol. Relax. Interact. Processes 1980, 16, 263. (21) Delsignore, M.; Maaser, H. E.; Petrucci, S. J. Phys. Chem. 1984,88, 2405. (22) Delsignore, M.; Farber, H.; Petrucci, S.J . Phys. Chem. 1985, 89, 4968. (23) Farber, H.;Petrucci, S. In The Chemical Physics of Soluarion; Dogonadze, R., et al., Eds.; Elsevier: Amsterdam, 1986; Part E, Chapter 9. (24) Eigen, M.; Winkler, R. M. In Neurosciences: Second Study Program; Schmidt, F. O., Ed.; Rockefeller University Press: New York, 1970; p 585. (25) Farber, H.; Petrucci, S.In Physical Chemistry of Solvation; Dogonadze, R. R.,et al., Eds.; Elsevier: Amsterdam, 1986; Part B,Chapter 8 and literature cited therein. Hill, N. In Dielectric Properties and Molecular Behavior; Hill, N., et. al.. Eds.; Van Nostrand: London, 1969.
s’o,
