Thermodynamics of Disproportionation of Radical Anions
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978 1371
Thermodynamics of Disproportionation of Radical Anions. The Effect of Counterions and Solvents F. Jachimowicz, H. C. Wang, G. Levin, and M. Szwarc' Department of Chemistry, State University College of Environmental Science and Forestry, Syracuse, New York 132 10 (Received January 3, 1978) Publication costs assisted by the National Science Foundation
The previously described technique has been used in thermodynamic studies of disproportionation of radical anions of perylene and tetracene. The pertinent heats and entropies of disproportionation were determined for the Li', Na+, K+, and Cs+ salts in tetrahydrofuran (THF) and in dimethoxyethane (DME). The peculiar behavior of the sodium salts in THF was confirmed and attributed to the desolvation of Na+ ions which retain their solvation in the radical-anion-cation pairs, but lose it on aggregation with dianions. In DME both the sodium and the potassium salts behave like the sodium salt in THF. The higher solvating power of the bidentate DME allows even the K+ ion to retain its solvation shell in the pair but not in the dianion aggregate. The above technique was applied in thermodynamic studies of electron transfer process, sodium trans-stilbenide + anthracene F! trans-stilbene + sodium anthracenide. Heat and entropy of this reaction were determined. A simple technique described' in a previous publication from this laboratory allows us to study thermodynamics of disproportionation of radical anions and the effect of cations on the respective AH"'s and AS"'s. The effect of cation's nature on AS" is particularly illuminating and thought provoking. This work was expanded now to two systems, perylene and tetracene in two solvents tetrahydrofuran and dimethoxyethane. The results and their interpretation are reported in this communication. They refer to reactions described by the equation 2A-.,Cat' ~t A + A2-,2Cat+
Experimental Section T h e details of the technique used in this investigation are given in the earlier publication.' In essence, it is a potentiometric technique. One measures the potential difference between two electrodes, one immersed in a 50:50 solution of the parent hydrocarbon and its radical anion and the other in a 50:50 solution of the radical anion and its dianion. Bulbs containing these solutions are linked through a liquid junction and the whole unit is placed in a thermostat that allows one to vary up and down the temperature from -55 to -25 "C. The potential difference between the electrodes is measured with voltmeter of infinite resistance, its scale allowing us to read its value to 0.1 mV. The resistance of the apparatus is in the range of 50 Mohm. The measured potential is reproducible; the same reading is recorded when after changing the temperature we return to its original value. Moreover, the potential remains constant a t any fixed temperature a t least for 1 h. The purification of tetrahydrofuran (THF) and dimethoxyethane (DME) was performed on a high-vacuum line using the procedure2 well known by now. Perylene, tetracene, anthracene, and trans-stilbene acquired from Aldrich Co. were crystallized and vacuum sublimed before being used. Alkali metals (mirrors for Na, K, and Cs) were used as reducing agents. The solutions of radical-anion pairs or dianion aggregates were kept a t concentrations of lo-* to M. The fraction of free radical anions in those solutions was reduced to a negligible value by dissolving in them a readily dissociated salt (tetraphenyl boride or triphenyl cyanoboride) sharing a common cation with the studied radical-anion pairs. 0022-3654/78/2082-1371$01 .OO/O
Such salts were typically at M concentration and they served also as the electrolytes in the liquid junction. The potential of the liquid junction was assumed to be negligible, and surely its temperature change imperceptibly affected the temperature dependence of the measured potential difference.
Results and Discussion The device described above measures the potential difference corresponding to the free energy change of the reaction 2A-.,Cat+(at some fixed low concentration) z A t A2-,2Cat+(at the same concentration and in the same solvent) It is difficult to prepare solutions of A and A-.,Cat+ or A-.,Cat+ and A2-,2Cat+a t exactly 50:50 proportion. Any small deviation of the composition from the desired proportion requires a correcting factor (RTIF) In (C,/C,) which is small since C1 = C2. The results pertaining to the disproportionation of salts of perylene and tetracene radical anions are presented in - t2,0vs. T o r -log Figures 1-10 in the form of plots of Kdispr = (t1,o - tz,o)/O.O59T/273 vs. 1/T. For any temperature the slopes of those curves at the appropriate point give the values of AS" or AH", respectively, pertaining to that temperature. The unavoidable uncertainties in the values of the independently determined slopes lead to minor discrepancies between &isp* calculated directly from q , O - t2,o and that computed from the relation AH" - TAS". Let us stress that the experimental points determine curves and not straight lines, although the curvature is small for some systems. The straight lines shown in the figures correspond to the slopes a t the extreme temperatures and provide an indication to what extent ASo or AH" is temperature dependent. Temperature dependence of AS" and AH", manifested by the observed curvatures, arise from the unequalities ACJT # 0 and AC, # 0. This is not surprising because the degree of solvation of the reagents and products does depend on temperature. Our findings are summarized in Table I listing the respective values of AH",AS", and Kdispra t 25 "C, if not stated to the contrary. Trends in the observed entities arising from changes of the nature of counterions and solvents were similar for the perylene and tetracene 0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No. 12, 7978
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Flgure 5. Plot of tzO - c10 vs. T(closed circles) and log Kdlspr vs. 1/ T (open circles) for sodium tetracenide in THF.
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Figure 6. Plot of tz0- el,, vs. T(open circles) and log Kdlspr vs. 1 / T (closed circles) for sodium tetracenide in DME.
systems. This might be expected because the size and electron affinities of those hydrocarbons are comparable. For example, the solution electron affinities of their sodium salts, referred to biphenyl as a 0, are 0.97 and 1.08 V, respectively, in THF. The mutually supporting observations revealed by the data collected in Table I may serve as evidence of the reliability of our procedure. On the whole, the disproportionation of tetracene radical anions is slightly larger than that of perylene radical anions. Following the discussion outlined in the previous publication1 we shall focus our attention on the values of
the respective ASo%. Their variations presumably reflect the extent of desolvation of cations resulting from the conversion of cation-radical anion pairs into aggregates of dianions with two cations. It has been pointed out previously1 that lithium cations in perylene-.,Li+ pairs dissolved in T H F are fully solvated. This conclusion is supported by the conductance ~ t u d i e s .Apparently ~ their degree of solvation is not markedly diminished when the solvated Li+ ions become associated with the more basic dianions, because their smallness results in a tenacious retention of their solvation shell even on the aggregation
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
Thermodynamics of Disproportionation of Radical Anions
1373
TABLE I Temporange: C
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(y]xIOa/aK-' 400-
Cation
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-
Tetracene AH" /kcal mol-' A S " leu
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Perylene
AH" /kcal mol-' AS"leu
-
Solvent
- (Ez,o-El,ol/.V
1:
1M I0
9
400 -logK
8
1374
The Journal of Physical Chemistry, Vol. 82,
No. 72, 1978
a t least, partially desolvated. This could explain the results. Very large values of AS" were observed in the disproportionation of the sodium salts. The results obtained for the tetracene system confirm the previously reported findings' pertaining to the perylene system. Since the radius of Na+ ions is larger than that of Li+, the tightness of its solvation shell is reduced. Consequently these ions may still retain their solvation shell in the weakly interacting cation-radical anion pairs, but some desolvation does take place in the strongly associated aggregates of dianion with two cations. This accounts for the strikingly large AS". The results obtained for sodium salts in DME fit now our expectation. The bidentate nature of DME results in a somewhat smaller entropy gain on desolvation of Na+ ions solvated by DME than in a comparable process involving T H F ligands. The respective ASO's, although still relatively large, are therefore smaller in DME than in T H F and the decrease in entropy of disproportionation leads to a substantially smaller disproportionation constant. Conductance studies of potassium salts in T H F indicate that this larger cation is only slightly solvated by that ~ o l v e n t . ~Subsequently, the disproportionation of potassium salts should not lead to large increase in entropy because little remains to be desolvated. Our expectation, fully confirmed for the perylene salts by the previously reported results, is further supported by the results of the present study of the tetracene system. However, even K+ ions could be appreciably solvated by the bidentate DME, and hence the K+-DME system resembles Na+-THF system, the disproportionation is associated with large entropy increase. Finally, the extent of solvation of the largest Cs+ ions apparently remains low in T H F as well as in DME, and indeed the low AS" observed for those salts in both solvents confirms our conclusion. T h e data obtained for AH"'s are less informative. Disproportionation increases the energy of the system, since the two electrons initially located in orbitals of two separated radical anions are crowded into one orbital. This substantially increases the electron-electron repulsion. Desolvation of the cations further increases the energy of the system, because desolvation is an endothermic process. However, the Coulombic cation-anion interaction increases as the cations become associated with the doubly charged dianions, and this effect decreases the energy of the system. The final result of these opposing factors is difficult to gauge. Only a few studies reported in the literature are concerned with the temperature dependence of disproportionation of radical anion^.^.^ Evans and his associates5-' reported negative or, a t most, very small positive entropy changes occurring in the disproportionation of radical anions derived from quinones, azo compounds, and Schiff bases. The reasons for the negative AS" were not discussed in their papers, and we are puzzled by their findings. Positive S o ' s of disproportionation were reported by S t e v e n s ~ nwho ~ ? ~studied radical anions of cyclooctatetraene (Cot) and of some related systems in hexamethylphosphoric triamide. In those publications Stevenson treated the investigated systems as if they were composed of free ions. However, although the cationradical anion pairs are virtually fully dissociated in hexamethylphosphoric triamide, HMPA, the dianions may be partially associated with cations, e.g. Cot2- + Cat+ ;rt, Cot2-,Cat+
K,
Cot denoting cyclooctatetraene. Hence, Stevenson's ob-
Szwarc et al. I 250
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Figure 11. Plot of A€ (open circles) vs. Tand log K, vs. l/T(closed circles) for the electron transfer from sodium trans-stilbenide to anthracene in THF.
servations provide only an apparent equilibrium constant,
Kobsd= [total Cot2-][Cot]/[Co-.]*,with
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)
where K - refers to the disproportionation of free ions 2Cot-. T', c o t
+ Cot'-
Such an association was reported in his later p~b1ication.l~ The Cot dianions were found to be appreciably associated with K+ but not Na+ ions in HMPA. The lithium system was not investigated. In view of these findings the thermodynamic parameters r e p ~ r t e dfor ~ ?the ~ potassium system have to be recalculated, whereas the data for the sodium system seem to be correct.
Application of Potentiometric Technique in Studies of Thermodynamics Of Electron-Transfer Processes The technique described here could be utilized in thermodynamic studies of electron transfer process, yielding the pertinent AH"'s and ASO's. An example of such a study is presented here. An equimolar T H F solution of anthracene and sodium anthracenide was kept in one bulb of the apparatus depicted in Figure 1 of ref 1,while an equimolar solution of trans-stilbene and sodium trans-stilbenide was kept in the other bulb. The potential difference was measured over a large range of temperatures. The results were reproducible and the measured potentials were constant for about 1 h a t any fixed temperature. The results are presented in Figure 11. The plots of At0 vs. T o r log K,, vs. 1/T are linear, their slopes giving AHo = -6.4 kcal/mol and AS" = -3.7 eu refer to the reaction Ktr
trans-stilbene-.,Na++ anthracene e trans-stilbene + anthracene-.,Na+
taking place in T H F . Thus, K,, is found to be 8.5 X lo3 a t 25 "C. We have now the previously unavailable data needed for calculation of the disproportionation constant of sodium cis-stilbenide in THF. The result gives 1 2, much smaller than the previous estimate." The above method of determining AHO's and ASo's of electron-transfer reaction is an extension of the technique originally developed by Hoijtink" and, after some modifications, used in earlier studies12 carried out in this laboratory.
QuasielasticLight Scattering from Micellar Solutions
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
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(6) A. G. Evans, J. C. Evans, and E. H. Godden, J . Chem. SOC. 6 ,546 (1969). (7) A. G. Evans, J. C. Evans, P. J. Ems, C. L. James, and P. J. Pomery, J. Chem. SOC. B , 1484 (1971). (8) 0. R. Stevenson and J. G. Conceptcion,J . Phys. Chem., 76, 2176 (1972). (9) G. R. Stevenson and J. G. Conceptcion, J . Am. Chem. SOC.,95, 5692 (1973). (10) F. Jachimowicz, G. Levin, and M. Szwarc, J. Am. Chem. SOC.,99, 5977 (1977). (11) G. J. Hoijtink, E. De Boer, P. H. Van der Meij, and W. P. Weijland, R e d . Trav. Chim. Paw-Bas. 75. 487 (1956). (12) J. Jagur-Grodzinski,M: Feld, S. L.'Yang,'and M. Szwarc, J . Phys. Chem., 69, 628 (1965). (13) G. R. Stevenson and I. Ocasio, J. Am. Chem. Soc., 98, 890 (1976).
Acknowledgment. The financial support of our studies by the National Science Foundation is gratefully acknowledged. References and Notes (1) H. C. Wang, G. Levin, and M. Szwarc, J. Am. Chem. Soc., 99, 5056
(1977). (2) M. Szwarc, "Carbanions, Living Polymers, and Electron Transfer Processes",Wiley-Interscience, New York, N.Y., 1968. (3) C. Carvajal, K. J. Tolle, J. Smid, and M. Szwarc, J. Am. Chem. Soc., 87, 5548 (1965). (4) P. Chang, R. V. Slates,and M. Szwarc, J. Phys. Chem., 70, 3180 (1966). (5) A. G. Evans and J. C. Evans, J . Chem. SOC. B , 271 (1966).
Deduction of Micellar Shape from Angular Dissymmetry Measurements of Light Scattered from Aqueous Sodium Dodecyl Sulfate Solutions at High Sodium Chloride Concentrations Charles Y. Young,' Paul J. Mlssel, Norman A. Mazer, George B. Benedek, Department of Physics, Center for Materials Science and Engineering, and Harvard-MIT Program in Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139
and Martin C. Carey Department of Medicine, Harvard Medical School, Division of Gastroenterology, Peter Bent Brigham Hospital and Harvard-MIT Program in Health Sciences and Technology, Boston, Massachusetts 021 15 (Received January 30, 1978) Publication costs assisted by the National Science Foundation
From measurements of the angular dissymmetry and autocorrelation function of laser light scattered from 2 g/dL aqueous solutions of sodium dodecyl sulfate (SDS) in 0.6 M NaCl, we have deduced both the mean radius of gyration, R,, and mean hydrodynamic radius, R h , of SDS micelles over a wide temperature range (15-85 "C) including the supercooled region below the critical micellar temperature (cmt). Above 40 "C, values of the angular dissymmetry function, d(O), defined as the ratio of scattered intensities Z(0)/Z(180° - 0) (30" 5 0 5 go"), are less than 1.05 implying that R, is smaller than 100 A. Below 40 "C, d(0) values increase appreciably as the temperature is lowered and R, is found to increase from 121 8, at 30 "C to 380 A at 15.7 "C, indicating a substantial growth of micellar size. This growth is also reflected by an increase in the R h values from 101 to 195 A. A deduction of micellar shape is made by comparing the measured dependence of R, on R h with theoretical calculations, assuming either spherical, disklike or rodlike micellar growth. The data are found to be in excellent agreement with the predictions based on a rodlike micellar shape, a finding which confirms the previous conclusion of Mazer et al.
Introduction In a previous study, we employed quasielastic light scattering spectroscopy (QLS) to investigate the size and shape of sodium dodecyl sulfate (SDS) micelles formed in aqueous NaCl solutions a t detergent concentrations well above the critical micellar concentration (cmc).'~2In the presence of 0.6 M NaCl, the mean hydrodynamic radius of the micelles, R h , was found to increase dramatically from a minimum value of 25 8, a t high temperatures ( 4 5 "C) to 168 8, a t 18 "C, a temperature at which the micellar phase was supercooled several degrees below the critical micellar temperature (cmt = 25 "C in 0.6 M NaCl). From the dependence of the scattered light intensity measured at a fixed angle on R , we further concluded that the increase in micellar size was consistent with growth of the micelles from a minimum spherical shape of hydrated
* Correspondence and Reprint Requests should be addressed to Charles Y. Young, MIT 13-2018, Cambridge Mass. 02139. 0022-3654/78/2082-1375$01 .OO/O
radius 25 8, into long prolate elliposids (rods) having a semiminor axis of 25 A. In light of existing controversies as to whether the shape of large nonspherical micelles is rodlike or d i ~ k l i k ewe ,~~ considered that additional experimental information on the shape of the large SDS micelles would be useful. In addition to measurements of R h , another quantity which may be used to characterize the size and shape of micelles is the mean radius of gyration, R,, which can be deduced from the angular dissymmetry of the scattered light intensity. For a given value of R h , R , will have different values for particles of different shape. Thus different relationships will exist between R h and R , depending on the shape of the micelles. Hence, measurements of both quantities can be employed to distinguish between the possible shapes of large micelles. In this paper, we report experiments in which R h and R g of SDS micelles are measured in 2 g/dL solutions a t various temperatures (15-85 "C) in 0.6 M NaCl. These 0 1978 American Chemical Society
