J . Phys. Chem. 1984,88, 3605-3607
3605
Diffusion-Controlled Quenching in Solutions at High Pressures W. D. Turley and H. W. Offen* Department of Chemistry and The Marine Science Institute, University of California, Santa Barbara, California 93106 (Received: December 27, 1983; In Final Form: February 3, 1984)
Dynamic quenching of the fluorescence of pyrene and pyrenebutyric acid is studied as a function of pressure (1-300 bar). The pressure dependence of diffusion-controlled quenching, both by electron transfer to m-dicyanobenzene and by oxygen, is accurately described by the inverse relation between encounter rate and solvent viscosity.
Introduction The rate of quenching of an electronically excited molecule M* by a quencher molecule Q in homogeneous solvent is frequently described by the Stern-Volmer kinetic equation
k, = (7-l - rO-l)/[Q] where k, is the observed quenching rate constant, and ro and T are the lifetimes of M* in the absence and presence of quencher at concentration [Q], respectively. The mechanism, particularly in polar solvents, is envisioned to be M*
+ Q = M*.-.Q kd
d-d
k,
products
so that
(3) The observed rate k, equals the encounter rate kd when the forward steps dominate. For this limiting case of diffusional quenching the Stokes-Einstein equation, D = k B T / ( 4 q a ) , leads to the familar expression',2
kd = 8RT/ 20007
(4)
This equation predicts a simple relation between the diffusion rate D, the temperature T, and the viscosity 7. When, as is frequently the case, the calculated kd differs appreciably from the measured k, for encounter-limited reactions, correction terms for size differences of solvent and solute are added to explain the discrepancies.' The purpose of the present work is to test the applicability of eq 4 to bimolecular fluorescence quenching at high pressures. One previous high-pressure study by Brey, Schuster, and Drickamer3concluded that k, and 7 were not simply related as suggested by eq 4. However, self-diffusion studies by Jonas, Hasha, and Hyang4s5have shown for a number of liquids that the quantity D s / T is constant within 10% to pressures of 5 kbar. We have chosen a select number of quenching systems and solvents to discover the limitations, if any, of eq 4 at high pressures.
Experimental Section Purification of the chemicals was accomplished by column chromatography and vacuum sublimation for pyrene, by repeated recrystallization from 100% ethanol for 1-pyrenebutyric acid (PBA), and by double vacuum sublimation for m-dicyanobenzene (m-DCNB). The solvent acetonitrile (Mallinckrodt spectrograde) is dried with MgS04 and freshly distilled before use. The 100% Gold Shield ethanol is used as received. (1) Alwattar, A. H.; Lumb, M. D.; Birks, J. B. "Organic Molecular Photophysics"; Birks, J. B., Ed.; Wiley: London, 1973; Vol. I, Chapter 8. (2) Birks, J. B. "Photophysics of Aromatic Molecules"; Wiley-Interscience: London, 1970. (3) Brey, L. A,; Schuster, G. B.; Drickamer, H. G. J . Chem. Phys. 1977, 67, 5763. (4) Jonas, J.; Hasha, D.; Huang, S. G.J . Chem. Phys. 1979, 71, 3996. (5) Jonas, J.; Hasha, D.; Huang, S . G. J . Phys. Chem. 1980, 84, 109.
0022-3654/84/2088-3605$01.50/0
TABLE I: Quenching Parameters at 1 atm lo-'%
probe pyrene pyrene pyrene PBA
solv CH,CN C2H50H C2H50H HzO
ns
7".
360
404 404 129
quencher m-DCNB rn-DCNB O2 02
M-I S-Y 1.2
0.48 2.8 1.1
lo-'?& M-1 s-1
2.8 0.89 0.89 1.1
The fluorophore concentrations are 10 MMfor pyrene and 100
r M for PBA. Air-saturated solutions of water and ethanol are (ref 6) assumed to contain oxygen concentrations of 2.67 X (ref 7) M, respectively. In the Stern-Volmer and 1.45 X computations (eq 1) the [Q] is corrected for solvent density changes at high The high-pressure optical cell and associated techniques for handling encapsulated solutions have been previously reported.' The pressure is generated on a mobile cart and transmitted by hexane to the sample. The experiments are performed at 23.0 f 0.2 "C in the 0-3-kbar pressure range. The freshly prepared solutions are bubbled with dried and scrubbed nitrogen for 1 h before loading the cell under a nitrogen atmosphere. The luminescence lifetime apparatus has been de~cribed.'~In use is an RCA 8852 photomultiplier tube and a Tektronix 7904 oscilloscope with plug-ins 7A26 and 7B85. The pyrene and PBA fluorescence is excited at 337.1 nm, passed through an 0.8-m grating monochromator, and monitored at 372 and 380 nm, respectively. Graphical analysis of the intensity decay leads to a 3% error in the lifetimes. The pressure effects on lifetime are fully reversible; that is, the 1-atm values agree within 3% before and after taking the sample to 3 kbar.
Results The fluorescence lifetime T~ of pyrene and pyrenebutyric acid is shortened reversibly with increasing pressure. For example, the PBA lifetime of 128 ns at 1 atm shortens to 111 ns at 3 kbar and returns to 130 ns upon release of pressure. Figure 1 shows that the pressure decrease of T~ (-17% over 3 kbar) is the same for pyrene in both CH3CN and C 2 H 5 0 Hsolvents. The experimental k, (eq 1) as well as the computed kd (eq 4) at 1 atm for both electron-transfer and oxygen quenching are summarized in Table I. The observed k, and T~ for pyrene are in reasonable agreement with previous reports of related system; 2 ~ 1 4 ~ 1similarly 5 (6) Greenburg, A. E., Comers, J. J., Jenkins, D., Franson, M. A. H., Eds., "Standard Methods for the Examination of Water and Wastewater", 15th ed.; APHA-AWWA-WPCF, American Public Health Association: Washington, DC, 1980; p 392. (7) Kretschmer, C. B.; Nowakowska, J.; Wiebe, R. Ind. Eng. Chem. 1946, 38, 506. (8) Danforth, W. E. Phys. Rev. 1931, 38, 1224. (9) Srinivasan, K. R.; Kay, R. L. J . Solution Chem. 1977, 6, 357. (10) Hamann, S. D. In "Modern Aspects of Electrochemistry"; Conway, B. E., Bockris, J. O'M., Plenum Press: New York, 1974; Vol. 9. (1 1) Offen, H. W.; Turley, W. D. J . Colloid Interface Sci. 1983, 92, 575. (12) Dawson, D. R.; Offen, H. W. Reu. Sci. Instrum. 1980, 51, 1349. (13) Watts, R. J.; Harrington, J. S.;Van Houten, J. J . Am. Chem. SOC. 1977, 99, 2179.
0 1984 American Chemical Society
3606 The Journal of Physical Chemistry, Vola 88, No. 16, 1984
Turley and Offen
EtOH
24.0
-- - _
23.0-
-c
L
I
I O
I
I
20
30
10
20
30
P / kbar
P/kbar
Figure 1. Pressure dependence of the pyrene fluorescence lifetime T~ in ethanol (0, 0 ) and acetonitrile ( 0 , e ) . Data points are taken with
Figure 3. Plot of the logarithm of the experimental quenching rate k, (-) and the calculated diffusion rate kd (---) as a function of pressure. The In k, values are given for pyrene-m-DCNB in CH$N at 4.7 X ( 0 ) and 7.8 X (+) M and in C2H50Hat 4.7 X M (0);for M; and for PBA-02 ~ y r e n e - 0in~C2HSOH( 0 )with [02]= 1.45 X in H 2 0 at 2.7 X (0) and 1.3 X lo-’ (W) M. The latter data set is taken from the dissertation of C. J. Mastrangelo (Diss. Abstr. Int. B 1977, 38, 712).
increasing (open symbols) and decreasing (half-solid symbols) pressures.
2oot
Pyrene / m-DCNB/CH,CN
TABLE 11: Activation Volumes for Quenching $V,*,
Avd‘,
probe auencher solv cm mol-’ cm3 mol-’ pyrene m-DCNB CH3CN 1.7 7.5 pyrene m-DCNB C2H50H 9.4 9.5 8.9 9.5 C2HSOH pyrene O2 PBA 0 2 H2O 1.9 0.8“ “Calculated from a linear fit of viscosity over 3 kbar.
for the fluorophore PBA.I6 The encounter rate kd is calculated from viscosity data” extrapolated to 23.0 OC. In agreement with earlier observations’**the differences between k, and kd are significant: nearly a factor of 3 in either direction for pyrene quenching (k, C kd for “large” quencher molecules and the reverse for “small” 02).The systems chosen for this study are characterized by long and low 7 , so that the transient term in the diffusion equation can be ignored.’ For example, this correction
is about 2% at 1 atm and 4% at 3 kbar for the system pyrenem-DCNB-CH3CN. The application of high pressures diminishes the electrontransfer quenching of pyrene by m-DCNB; the slope dr/dP is seen in Figure 2 to be linear at both concentrations tested. The pressure dependence of r0,1,and [Q] is combined via eq 1 to give k , at different pressures. As illustrated in Figure 3, a plot of In k, vs. P is linear over the 3-kbar pressure range, irrespective of solvent or quencher concentration. For comparison Figure 3 also shows In kdvs. P plots, using literature values for the pressure dependence of the viscosity (eq 4)of acetonitrile,’*J9 e t h a n 0 1 , ’ ~and ~ ~water.’O ~ The small (- 1%) minimum in q(P) for H 2 0 is not visible on the scale of Figure 3. This figure clearly shows a close correlation between the pressure dependence of In k , and In kd. The slopes of the plots in Figure 3 are fitted to a linear equation and related to the activation volume according to the expression AK* = -RT d In ki/dP, where i equals q or d. The results, summarized in Table 11, show excellent agreement between AV,’ and AV,’. The estimated errors are f0.5cm3 mol-’ for m-DCNB as quencher and twice that for oxygen. Thus, the AV,’ calculated for O2 quenching of PBA fluorescence compares in magnitude with some “average” AVd*of activated viscous flow in water. In summary, the pressure dependence of quenching rates tracks well
Weller, A. Isr. J . Chem. 1970, 8, 259. (15) Ware, W. J . Phys. Chem. 1962, 66, 455. (16) Vaughan, W. M.; Weber, G. Biochemistry 1970, 9, 464. (17) “CRC Handbook of Chemistry and Physics”, 58th ed.; CRC Press: Boca Raton, FL, 1977; p F52-57.
(18) Salman, 0. A.; Drickamer, H. G. J . Chem. Phys. 1982, 77, 3329. (19) The n(P) data for CH$N corresponds to 30 OC; it is not expected to be very temperature sensitive. The ethanol viscosity is extrapolated to 23 OC from the published data at 30 and 75 O C . (20) Bridgman, P. W. Proc. A m . Acad. Arts Sci. 1926, 61, 57.
P 1 .o
2 .o
3.0
P / kbar
Figure 2. Pressure dependence of the pyrene fluorescence lifetime in the ( 0 ) and 7.8 X (0)M. Open presence of m-DCNB at 4.7 X and solid symbols refer to increasing and decreasing pressures, respectively.
(14) Rehm, D.;
J. Phys. Chem. 1984, 88, 3607-3611 that of viscosity, despite the large differences between k, and kd at 1 atm (Table I).
Conclusion The well-known systems chosen for the quenching of aromatics by electron transfer or oxygen are diffusion controlled at 1 atm. This study shows that they remain so at high pressures and that the results are simply interpreted by d In k, = -l.O(d In q), as predicted from eq 4 and k, = kd. Instead of the slope of -1 .O the quenching of naphthalene by biacetyl in methylcy~lohexane~ gave the value -0.65. Since the Stokes-Enstein equation is applicable to the self-diffusion of this unsymmetrical solvent molecule at high p r e s s ~ r e sthe , ~ results for this particular quenching system are not attributed to a failure of eq 4 but rather to limitations of the kinetic model used to analyze steady-state, luminescence intensity measurements. Andre et a1.21~22 include static quenching in their
3607
model and found agreement with the experimental results for fluorescence quenching of naphthalene by biacetyl at atmospheric pressure. Irrespective of the differences in molecular sizes and the 1-atm results from eq 1 and 4, this study verifies that for diffusioncontrolled molecular encounters in dense fluids, the pressure dependence of excited-state reactions is predicted from the volume dependence of the solvent viscosity. Thus, pressure studies can be used to establish encounter-limited reaction kinetics.
Acknowledgment. We greatly appreciate the generosity of Professor Watts in providing access to his laboratory and lifetime instrumentation and the financial support of the Department of Chemistry and the Marine Science Institute. Registry No. PBA, 3443-45-6; rn-DCNB, 626-17-5; pyrene, 129-00-0; oxygen, 7782-44-7.
(21) Andre, J. C.; Brouchy, M.; Niclause, M. C. R. Hebd. Seances Acad. (22) Andre, J. C.; Niclause, M.; Wave, W. R. Chem. Phys. 1978,28,371.
Sci., Ser. C 1975, 281, 421.
Protonic Counterpart of Electronegativity as an Organizing Principle for Acidity and Basicity Lawrence L. Lohr Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (Received: January 30, 1984)
The concept of a charge-dependentelectronegativity is extended to protons by the use of a polynomial representationof molecular energies as a function of the number of protons and the number of electrons. Coefficients in the polynomial are determined by finite first and second differences of known energies, with the polynomial then being used to predict other energies. The relationshipsprovide an organizing principle for gas-phase acidity and basicity data by expressing succinctly the interdependence of the energies of proton-transfer and electron-transfer reactions. Application is made to the energetics of strongly hydrogen-bonded systems.
I. Introduction We have recently carried out a series of a b initio theoretical investigations of the gas-phase acidities’ and b a s i c i t i e ~of ~ ,group ~ 5 compounds, with particular emphasis on molecules containing phosphorus-carbon and arsenic-carbon multiple bonds. Comparisons were made to the acidities and basicities of related saturated molecules and of analogous unsaturated and saturated nitrogen-containing molecules. From these comparisons a number of trends were noted, not just in the individual acidities (anion proton affinities) or basicities (neutral molecule proton affinities) but also in their sum, a quantity which is the protonic counterpart of the sum of the ionization energy and electron affinity of a molecule to which the Mulliken electronegativity is proportional. It is the purpose of the present investigation to explore more fully the concept of a protonic counterpart of electronegativity, which we shall call “protofelicity”, and to develop a unified approach to electronegativity and protofelicity which will serve as an organizing principle for experimental (or theoretical) data and as an extrapolative device for estimating otherwise unknown molecular energies. The electronegativity xe of a chemical species, atomic or molecular, has been defined4as the negative of the electronic chemical potential F , the latter being the derivative of the energy E with
respect to the number of electrons Ne in the species with the external potential being held fixed. While we recognize that Ne for an isolated species is a discrete rather than the continuous variable implied by discussion of a deri~ative,~ it is convenient to regard Ne as continuous, particularly in applications to atoms or fragments which are a part of an extended system. It has been noted6 that the energy of an atom or molecule may be. represented as a polynomial function of the number of electrons Ne, with a quadratic approximation providing an adequate representation as long as the successive removals of electrons involve the same type of orbital, as in successive 2p ionizations of a neon atom. A quadratic energy expression implies6 an electronegativity xc which is linearly dependent upon Ne, with xe for the chosen reference species, usually a neutral, being the Mulliken electronegativity (IE EA)/2, where IE and EA are the ionization energy and electron affinity, respectively, of the reference species. The quantity -(IE - EA) then represents the rate of change of xe with respect to Ne. The concept of a charge-dependent electronegativity is one which we wish to extend to protons, following the non-Born-Oppenheimer general formalism of Capitani et al.’ The further concept that if two or more species of generally different electronegativity xejoin to form a composite species there results a common new electronegativity has been expressed many
(1) Lohr, L. L.; Ponas, S . H. J . Phys. Chem., in press. ( 2 ) Lohr, L. L.; Schlegel, H. B.; Morokuma, K. J . Phys. Chem. 1984,88, 1981. (3) Lohr, L. L.; Scheiner, A. S. J. Mol. Struct. THEOCHEM, in press. (4) Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 68, 3801.
( 5 ) For a recent discussion of derivative discontinuities, see: Perdew, J. P.; Parr, R. G.; Levy, M.; Balduz, J. L., Jr. Phys. Reo. Lett. 1982, 49, 1691. (6) For example: Iczkowski, R. P.; Margrave, J. L. J . Am. Chem. SOC. 1961, 83, 3547. (7) Capitani, J. F.; Nalewajski, R. F.; Parr, R. G. J . Chem. Phys. 1982, 76, 568.
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0 1984 American Chemical Society
