3420
J. Phys. Chem. 1991, 95, 3420-3422
Observation of a Llnear Correlatlon between Dimethyl Sulfoxide Solution Reduction Potentlala and Equilibrium Ackllties for Substituted Methylanthracenes M. J. Bausch,* C. Cuadalupe-Fasano, and A. Koohang Department of Chemistry and Biochemistry, Southern Illinois University at Carbondale. Carbondale, Illinois 62901 -4409 (Received: July 31, 1990)
With the aid of cyclic voltammetric techniquesthat utilize a platinum working electrode,we have determined reduction potentials for 15 variously substituted methylanthracenes in dimethyl sulfoxide (DMSO) solution. An excellent correlation is observed between reduction potentials for IO IO-substituted-9-methylanthracenesand absolute DMSO phase C-H acidities for the same IO-substituted-9-methylanthracenes: a plot of Erd vs pK, for these species is linear ( r = 0.989) with slope 0.77. 9-Methylanthracenes in which an anthrylic hydrogen atom has been replaced with SPh, CN, or NO2 substituent deviate from the Ed/pK, correlation established by the IO-substituted-9-methylanthracenes.These results complement published gas-phase results (Fukuda, E.K.; Mclver, R. T. J. Phys. Chem. 1983,87,2993-2995) and allow direct comparison of substituent effects on the stabilities of radical anions and carbanions derived from substituted 9-methylanthracenes when dissolved in DMSO.
Introduction The transfer of a proton from an acid to a base is an example of a seemingly simple chemical reaction. The deprotonation of a neutral acid results in the formation of its monoanionic conjugate base. An oft-examined property of a given acid and its incipient conjugate base is the equilibrium constant [K, in eq 1, where
&
+
HA DMSO DMSOH' + A(1) dimethyl sulfoxide (DMSO) represents solvent] for the transfer of a proton from the acid to the solvent. Several experimental methods have been developed for measuring solution-phase equilibrium acidities.' Solution-phase equilibrium acidity data have been instrumental in countless investigations of the properties and reactivities of acid and anion stabilities and reactivities (e.g., Hammett and Bransted plots), including DMSO studies in which the thermodynamics of proton loss from a given family of acids have been used as models for the kinetics of alkyl group transfer,2 is~merization,~ and electron-transfer reactions,' as well as the thermodynamics of electron-transfer reactions.s Elegant techniques have also been developed that enable examination of the intrinsic (gas phase) acidities of various species.6 Comparison of gas- and solution-phase acidities has enabled much to be learned in the area of solvent effects on proton-transfer reactions.' The transfer of an electron to or from a molecule is another example of a rather simple chemical reaction. Addition of an electron to a neutral molecule results in the formation of a radical anion (eq 2). In solution, electrochemical techniques enable HA le- * HA'(2) determination of the relative ease of electron addition to a given species, while absolute gas-phase electron affinities have been determined with the aid of various spectroscopic techniques.8
+
( I ) (a) Jaffe, H. H. Chem. Reo. 19!33,53,191-261. (b) Cos,R.A.; Yates, K. Con.1.Chem. 1983.61.2225-2243. ( c ) Bowden, K. Chem. Reu. 1966, 66,119-131. (d) Streitwieser, A.; Hammons, T. H.; Ciffurin, E.; Brauman, J. 1. J. Am. Chem. Soc. 1%7,89, 59-67. (e) Matthews, W.S.; Bares, J. E.;
Bartmess, J.; Bordwell. F. G.; Comforth, F. J.; Drucker, 0.E.; Margolin, Z.; McCallum, G. J.; Vanier, N. R. J. Am. Chem. Soc. 1975,97,7006-7014.(f) Bors, D.A.; Kaufman. M. J.; Streitwieser, A. J . Am. Chem. Soc. 1985,107,
69754982. (2)Bordwell, F. G.;Hughes, D. L. J . Am. Chem. SOC. 1986, 108, 7300-7309. (3)Bordwell. F. G.;Hughes, D. L. J . Am. Chem. SOC.1985, 107, 4737-4744. (4)Bordwell, F. G.;Bausch, M. J. J . Am. Chem. Soc. 1986, 108, 1985-1 988. (5) Bordwell, F. G.; Bausch, M. J. J . Am. Chem. Soc. 1985, 108, 1979-198s. (6)Baimess, J. E.; Mclver, R. T. Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979;Vol. 2, Chapter 11. (7)Taft, R. W.;Bordwell, F. G. Acc. Chem. Res. 1988, 21, 463-469. (8)(a) Smyth, K.C.; Brauman, J. I. J. Chem. Phys. 1972,56, 1132-1 142. (b) Lifshitz, C.; Tieman, R. 0.; Hughes, B. M. J . Chem. Phys. 1973, 59, 3 182-3192,
0022-365419 112095-3420$02.50/0
TABLE I: Dimethyl Sulfoxide Sdutioll Equilibrium Acidity rad Reduction Potential Data for lO-G-9-C'-Methyl.nthrrccws (1) G
H NO1
CHO CN H CN COPh SPh C1 H H Ph H CH3 OCH,
G'
pK,I2
NO, H H OCH, CN
12.7 13.2 16.6 17.415 19.7 20.0" 22.2 25.5 28.2 28.6 30.6 30.8 31.1"
H
H H H SPh OCH, H H H 31.8 H 31.8
ApK,," kcal/mol
25.5 24.5 19.9 19.0 15.9 15.2 12.2 7.7 4.0 3.7 1.0
0.4 (0.0)
-1.0 -1.0
Ed,'' V -0.92 (irr) -0.57 -0.81 -0.83 -1.30 -0.93 -1.13 -1.20 -1.24 (irr) -1.13 (irr) -1.42 -1.47 -1.47 -1.47 -1.45
AEd,13 kcal/mol
12.7 20.8 15.2 14.8 3.9 12.4 7.8 6.2
5.3 7.8 1.2 0.0 (0.0) 0.0 0.5
"Redox" data of these types have proven invaluable in mechanistic investigations of reactions involving single electron t r a n ~ f e r . ~ In gas-phase results, Fukuda and McIver demonstrated that relative electron affinities of substituted nitrobenzenes plot linearly with relative gas-phase acidities of substituted anilines and phenols.I0 Outlined in this paper are results from our examinations of substituent effects on (a) the thermodynamics of DMSO solution deprotonation and (b) DMSO solution reduction potentials for 15 variously substituted 9-methylanthracenes (1). Results
6 1
from these experiments suggest that reduction potentials and equilibrium acidities for 10-substituted-9-methylanthracenesare also linearly related to each other, affording a linear free energy relationship (LFER)that spans 25 kcal/mol. Methods Acidity constants for 1 have been determined by using the Bordwell colorimetric method," a technique that enables collection of absolute pK, data in DMSO solution. Reduction potentials for 1, at a platinum electrode, have been determined with the aid (9)Eberson, L. Acta Chem. S c a d . Ser. B 1984,838,439-459. (IO) Fukuda, E.K.; Mclver, R. T. J . Phys. Chem. 1983.87,2993-2995. (11)Bordwell, F. G.Acc. Chem. Res. 1988, 21, 456-463.
0 199 1 American Chemical Society
Reduction Potentials and Equilibrium Acidities of cyclic voltammetric (CV) techniques. Results and Discussion The acidity and reduction potential data for 1 are listed in Table I. Inspection of the acidity data in Table I reveals that the pKis for substituted 9-methylanthracenes are remarkably sensitive to structural changes in the anthracene ring system at carbon 10. For example, in DMSO, 10-nitro-9-methylanthracene is 24.5 kcal/mol more acidic than 9-methylanthracene. The stability of resonance structures that place substantial electron density immediately adjacent to G,such as that drawn in 2, no doubt results
* 0
2
in the observed acidity variations. The acidifying effects due to changes in G (when G’= H) are NO2 > C H O > C N > SPh > CI > Ph > H > CH3 = OCH3.lZb Also apparent from the data in Table I are the similar effects that C N substituents have on the DMSO acidity of 1, whether present in 1 as G (pK, = 20.0) or G’ (pK, = 19.7); similar trends are observed for NOz substituents as well. Finally, close scrutiny of the ApK, data for 9-methylanthracene [G = G’= H; ApK, = (O.O)], lO-cyano-9methylanthracene (G = CN, G’ = H; ApK, = 15.2 kcal/mol), 9-(methoxymethy1)anthracene (G = H, G’= OCH3; ApK, = 1.0 kcal/mol), and 1O-cyano-9-(methoxymethyl)anthracene (G= CN, G’= OCH,; ApK, = 19.0 kcal/mol) reveals that the individual acidifying effects of G = C N and G’= OCH, substituents are synergistic when present in the same molecule.16 Analysis of the redox data in Table I indicate that the reduction potentials for substituted 9-methylanthracenes also display a remarkable sensitivity to structural changes in the anthracene ring system at carbon 10. For example, 10-cyano-9-methylanthracene and IO-nitro-9-methylanthracene are 12.4 and 20.8 kcal/mol easier to reduce than 9-methylanthracene. The ease and reversibility of the electrochemical reductions of many of the anthracenes in Table I are no doubt due to the stability of resonance structures such as that drawn in 3, where substantial electron density at
* G
3 carbon 10 is adjacent to G. When G’= H, the reduction potentials for 1 vary as follows (with 1 where G = NOz easiest to reduce): NO2 > C H O > C N > SPh > CI > Ph = H = CH3 = OCH3. In light of the similarities in the observed substituent effects on the DMSO acidity constants and reduction potentials for (1 2) (a) The pK,’s in Table I are listed in ref 12b, except where noted. (b) Bares. J. E. Ph.D. Thesis, 1976, Northwestern University, Evanston, IL. (1 3) The ApK, data in Table I and in the text are statistically corrected for the differing number of acidic protons present in each of the anthracenes in Table 1. The pK, and redox experiments were conducted at 25 O C , at which temperature I pK, unit and 1 V equal 1.37 and 23.06 kcal/mol, respectively. (14) Electrochemistry conditions: DMSO solvent; 0.1 M Et4N+BF4electrolyte; Pt working and Ag/AgI reference electrodes (ferrocene/ferrocenium = +0.875 V as internal standard); CV 0.1 V/s sweep rate. [l] = ca. 1 mM. Except where indicated as irreversible, in which case the Ed values are the peak potentials for the cathodic waves, the End values in Table I are midpoints of well-defined cathodic and anodic waves (separated by 60-70 mV) that indicate revenibility. (1 5) Bausch, M. J.; Guadalupe, C.; Jirka, G.; Peterson, B.; Selmarten, D. Polycycl. Aromot. Comp., submitted for publication. (16) This synergism is best understood by realizing that the Hammett p values for the parent 9methylanthracenesand 9-(methoxymethyl)anthracenes are likely to be different.
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3421 25
20
c
t
iph
a 4
. Q
0 0 ’
G,O’
A ~
-9
-5
~
0
5
~
10 15 A#$ (kervmol)
~~~
~
20
25
30
Figure 1. DMSO solution AEd values plotted as a function of DMSO solution ApK, values, for variously substituted IO-G-9-G’-methylanthracenes (1).
1O-G-9-methylanthracenes, comparisons of the acidity and redox data for these species are warranted. The complete set of ApK, and AErd data from Table I are shown in Figure 1. In Figure 1, DMSO solution Md values are plotted as a function of DMSO solution ApK, values for the 15 substituted IO-G-9-G’-methylanthracenes (1). The line drawn in Figure 1 is the least-squares fit for the 10-G-9-methylanthracenes only. The excellent correlation (r = 0.989) for these data spans 25 kcal/mol in relative acidities and is therefore one of the most extensive solution-phase linear free energy relationships that we are aware of. Correlations of electrochemical redox potentials and acidity constants for families of acids have been published previously. For example, reduction potentials for a family of para-substituted benzenearsonic acids have been shown to plot linearly with acidity constants for the same species.” There have also been countless examinations of the relationships between redox potentials for a given series of compounds and Hammett u constants; most of these span 3-5 kcal/mol in acidities and involve comparisons of redox potentials for a given series of compounds (usually in an organic solvent) with aqueous phase-based Hammett u constants. Other demonstrations of linearity between solution-phase reduction potentials and acidity constants for a related series of molecules include that in which a plot of DMSO solution reduction potentials of 44Gphenyl)- 1,2,4-triazoIinediones versus DMSO solution equilibrium acidities of 4-(G-phenyl)urazoles is linear (r = 0.98).’* Additionally, Fukuda and McIver,lo in the gas phase, observed that relative electron affinities of substituted nitrobenzenes plot linearly with relative gas-phase acidities of substituted anilines and phenols. These relationships are linear over a range of ca. 23 kcal/mol and demonstrate that in the gas phase substituents affect the energies of anilide and phenoxide anions in the same ways that they affect the energies of nitrobenzene radical anions.I0 The results presented in this paper suggest the same relationship, in DMSO solution, over a similarly large range, for 10 different
10-substituted-9-methylanthracenes. While the cited gas-phase data enable comparisons of substituent effects on intrinsic phenol and aniline acidities with substituent effects on nitrobenzene electron affinities, the fact that the DMSO solution redox and acid-base data were collected by conducting experiments on the same species (Le., 1) allows direct comparison of the effects of substituents on the stabilities of the radical anions derived from 1 (i.e., 1 + le-) with the effects of those same substituents on the stabilities of the conjugate bases derived from 1 (Le., 1 - 1H+).The linearity observed in Figure 1 (when G is varied in 10-G-9-methylanthracenes)indicates that substituents in the 10-position affect the energies of DMSO solution radical anions and carbanions derived from 9-methylanthracenes in a similar fashion. Our results differ from the gas-phase relationship cited previously in that the slope of the line (17) Breyer B. Ber. Drsch. Chem. Ges. 1938, 71, 163-171. (18) David, B. M.S. Thesis, 1989, Southern Illinois University, Carbondale, IL.
J. Phys. Chem. 1991, 95, 3422-3425
3422
in Figure 1 is 0.77, as opposed to the unit slope observed in the substituted aniline/phenol acidities vs substituted nitrobenzene electron affinities gas-phase plot. We are currently investigating other families of molecules in attempts to better understand the magnitude of the slope in Figure 1. Further inspection of the data in Table I and Figure 1 reveals the presence of three "orphan" points that do not fall on the least-squares line composed of redox and acid-base data collected for IO-G-9-methylanthracenes.Common to these varieties of 1 is that all are substituted at the "a" (G') position rather than the 10 (G) position. In contrast to the similarities in their effects on the DMSO acidities of 1, replacement of hydrogen atoms in 1 with C N (or NO2) at the G and G' positions has markedly different effects on the reduction potentials of 1: while IO-cyano9-methylanthracene is 12.4 kcal/mol easier to reduce than 9methylanthracene, 9-(cyanomethy1)anthracene is only 3.9 kcal/mol easier to reduce than 9-methylanthracene (these values are 20.8 and 12.7 kcal/mol for IO-nitro-9-methylanthracene and 9-(nitromethyl)anthracene). These differences are readily explained by noting the presence of the -CHz- moiety between the
C N (or NOz) substituent and the anthracene ring in 9-(cyanomethy1)anthracene (or 9-(nitromethyl)anthracene): the aliphatic carbon prevents resonance interactions between the CN (or NOz) substituents and the anthracene ring. In summary, DMSO solution reduction potentials for 10-G9-methylanthracenes correlate nicely with DMSO solution equilibrium acidity constants for the same species. The LFER spans 25 kcal/mol, has a slope of 0.77, and complements previously observed gas-phase relationships. 9-Methylanthracenes in which one of the anthrylic hydrogens has been replaced with NOz, CN, or SPh do not fall on the line established by the 10-substituted species. Examinations of the relationships between solution-phase redox potentials and equilibrium acidity constants are continuing in our laboratories. Acknowledgment. We are grateful to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work. We are also grateful to Dr. Jin-Pei Cheng for carrying out some of the preliminary redox experiments.
Chemlcal Instabilities and Blfurcatlons in Encillatort S. R. Inamdar, P. Rajani, and B. D. Kulkarni* Division of Chemical Engineering, National Chemical Laboratory, Pune 41 I 008, India (Received: July 6, 1990; In Final Form: October 30, 1990)
The linear stability analysis of the exponential autocatalysis has been carried out to bring out the bifurcation behavior and identify the regions for the occurrence of chemical instabilities. The rich bifurcation behavior shown by this realistic model is presented in detail.
Introduction The present paper considers an alternate form of autocatalysis (Encillator) given as
'..
x-Y-z
analysis of this model has been carried out. Further, on the basis of the properties of Jacobian matrix of the system, the equations for locus of two types of instabilities have been derived. The numerical results for the global stability behavior for these conditions are presented and discussed.
..e'
where the product Y systemically autocatalyzes its own rate of formation through interaction with the rate constant k. This rate form was originally proposed by RaviKumar et al.' mainly to explain the strong nonlinearity, resemblance to Semenov type of law, and analogy to Arrhenius type of rate constant dependence found in certain systems. This rate form has wide applications in several biochemical systems and also in explaining the phenomena in diverse chemical and combustion type of reactions. The exponential autocatalysis has received acceptance as a general model for class of reactiondiffusion systems,2and results obtained by using conventional autocatalysis such as the one used in Brusselator type models compare well with this model system. The exponential autocatalysis has revealed the existence of multiplicity and oscillatory behavior under homogeneous conditions.' More recently, the scheme in the presence of diffusion was analyzed with a view to establish bounds on the steady-state solution^.^ The conditions for the existence of nonuniform solutions in the form of dissipative structures have also been derived analyti~ally,~ and the behavior near the Hopf bifurcation point has been derived by using the reductive perturbation to obtain the description in terms of the Ginzburg-Landau equation.' The global nonuniform patterns and limit cycle have also been constructed by using multi-time-scale analysis.' In the present work the linear stability
* To whom all correspondence should be addressed.
'NCL communication no. 4944.
Linear Stability Analysis The temporal kinetic scheme of the exponential autocatalysis is governed by the following equations dx/dt = xo - x - Da,x exp(ay) (14 dy/dr = yo - y Da,x exp(ay) - D a 9 (1b) The steady-state solutions of these equations are represented as (xs, 0) and can be obtained as xo - xs exp(a8) = -, e = xo + Yo - xs (2) 1 + Da2
+
By use of eq 2, the steady-state equation in terms of 0 can be expressed in the form of a transcendental equation as Daleae-
XO
xo
+ yo - 0(l + Da2) + 1 = 0
(3)
To obtain the conditions for the Occurrence of chemical instabilities, we write the Jacobian matrix of the system in eq l as
~
)
- Daleue -axsDaleao Da I eae -(1 + Da2) + axSDaleue
-1
A=(
(4)
~~
( I ) RaviKumar, V.; Kulkrani, B. D.; Doraiswamy, L. K. AIChE J . 1984, 30, 649. (2) Bar Eli, K. J . Phys. Chem. 1984, 88, 3616. (3) Inamdar, S. R. Ph.D. Thesis, University of Poona, 1990.
0022-3654/91/2095-3422$02.50/0 0 1991 American Chemical Society
