J . Phys. Chem. 1985, 89, 3648-3654
3648
Conclusion
t’ght
Solvation coordinate
loose
Figure 10. Schematic potentials of the hydrogen-bonded complexes along solvation coordinate. The potentials I and I1 are for the 1:l and 1:2 complex ions, respectively. The potential for the neutral complex was assumed to be common for both the 1:l and 1:2 complexes.
of the 1:2 complex becomes larger than that of the 1:l complex. The stabilization energy due to the charge interaction, the term used before, corresponds to the decrease of the adiabatic ionization potential and the destabilization energy due to the strain to the excess vibrational energy which the ionic complex produced by the vertical ionization gains. In terms of these potentials, it is easily explained that the neutral complex having strong intermolecular interaction exhibits a broad ionization threshold as seen in Figures 6-8. The adiabatic ionization potentials of the complexes except for the PH-(Ar), complexes are probably located at the energies lower than the onsets of the ionization signals.
The one-color and two-color MPI spectra of various kinds of van der Waals molecules of fluorobenzene and hydrogen-bonded complexes of phenol in a supersonic free jet were reported. The present study clearly showed that the two-color MPI method is a very powerful technique in determining the ionization energy of the complex. The observed ionization potentials of all the complexes studied here are always much smaller than that of the free molecule, and their reduction are in the range of 200-2000 cm-’ (0.025-0.25 eV) for the van der Waals complexes and of 3400-5300 cm-’ (0.42-0.66 eV) for the 1:l hydrogen-bonded complex. As mentioned in the Introduction, in going from the gas to the solution, the ionization potential is known to decrease by 1-3 eV, which is a very large value in comparison with that of the gas-phase complex obtained here. Such a great reduction in the ionization energy in solution is due to the polarization of surrounding solvent molecules, the Coulombic interaction between the ion and photoejected electron trapped in the solvent media, and the trapping stabilization of the photoejected electron. The reduction in the ionization energy of the complex obtained here corresponds to the contribution from the polarization of the surrounding solvent. The results obtained here suggest that the polarization contribution is smaller than the contributions from the Coulombic interaction and the trapping of the photoejected electron existing in solution. In the present study, the binding energies of these complex in the ionic state were not determined. Their direct determination would be expected to provide information on the more detailed intermolecular interaction between the solute cation and solvent, and it is now in progress in our laboratory. Registry No. C6HSF. 462-06-6; Ar, 7440-37-1; HzO, 7732-18-5; CH,CN, 75-05-8; CHC13, 67-66-3; CCI,, 56-23-5; C,HSOH, 108-95-2; C,H,, 71-43-2; CH,OH, 67-56-1; dioxane, 123-91-1.
Hydration Dynamics of Electrons from a Fluorescent Probe Molecule R. A. Moore, J. Lee, and G. W. Robinson* Picosecond and Quantum Radiation Laboratory, Texas Tech University, Lubbock, Texas 79409 (Received: March 25, 1985)
As part of a comprehensive study of electron and proton hydration dynamics, steady-state and picosecond time-resolved experiments have been carried out on the excited state of 6-p-toluidine-2-naphthalenesulfonate(6,2-TNS) in water/alcohol mixed solvent systems. In solvents of sufficiently high water content, temperature-insensitive spontaneous ionization of the intramolecular charge-transfer state of 6,2-TNS occurs following excitation to SI.The presence of water thereby quenches the fluorescence. Used to explain the interesting photophysics is a theoretical scheme that introduces three novel concepts for the study of photochemical quenching, allowing data to be analyzed outside the Stern-Volmer limit. The studies as a function of solvent composition indicate that a special solvent structure consisting of 3-4 water molecules is the electron acceptor and that a significant increase in nonradiative ionization occurs abruptly when this number of water molecules is achieved. A similar solvent structure has been discovered when other molecular precursors of electrons and protons are employed, hinting that a unifying concept may pervade the hydration dynamics of small charged species in water.
I. Introduction Previous studies have indicated that there are large effects on the lifetime, quantum yield, and fluorescence emission maximum of the biological probe molecule 8,l-ANSI and its 6-p-toluidino-2-naphthalenesulfonate (6,2-TNS) when the solvent (1) G. W. Robinson, R. J. Robbins, G. R. Fleming, J. M. Morris, A. E. W. Knight, and R. J. S. Morrison, J . Am. Chem. SOC.,100, 7145 (1978). (2) R. A. Auerbach, J. A. Synowiec, and G. W. Robinson in “Picosecond Phenomena II”, R. M. Hochstrasser, et al., Eds., Springer Verlag, West Berlin, 1980, pp 215-219. (3) G. W. Robinson, R. A. Auerbach, and J. A. Synowiec, Chem. Phys. Lett., 82, 219 (1981).
0022-3654/85/2089-3648$01 .50/0
is changed from alcohol to water. The nonradiative rate constant for 6,2-TNS varies from 0.96 X lo8 s-l in methanol (0.67 X lo8 s-l in ethanol) to 169 X lo8 s-l in water. This large increase in the nonradiative rate constant quenches the fluorescence and is accompanied by the appearance of solvated electron ab~orption.~ Other studies have shown that the solvated electron absorption is linear with incident intensity’ and have indicated that the most (4) G . R. Fleming, G. Porter, R. J. Robbins, and J. A. Synowiec, Chem. Phys. Lett., 52, 228 (1977). This work has been criticized [H. Nakamura, et al., Bull. Chem. SOC.Jpn., 55, 1795 (1982)]. One must of course be wary of conclusions based on solvated electron measurements carried out on too slow a time scale.
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 17, 1985 3649
Hydration Dynamics of Electrons likely process reponsible for the fast nonradiative rate in water is spontaneous ionization from the relaxed excited state. The one-photon character of this process is further confirmed by recent studies,6-’0 which have quantitatively tied together data on the excited-state dynamics initiated by Nd3+/glass laser excitation and by dye-laser excitation as well as steady-state fluorescence quantum yield data obtained with extremely weak spectrofluorometer light sources. As in the case of indole, the relaxed excited state of 6,2-TNS must have the propensity to ionize spontaneously in an aqueous medium. In the case of 6,2-TNS, an intramolecular charge-transfer state T’N-S is the relaxed excited state.” The molecular dipoles of water, sensing the negative charge on the naphthalene moiety, reorient to form a special “preformed” structure.2 This local breaking up of the normal liquid structure creates awkward orientations for H-bond formation and facilitates electron solvation with low activation energy. (For indole, a relatively nonpolar molecule in its excited state, an improbable fluctuation of the H-atom configuration with high activation energy is required to bring this about,’* an idea consistent with the proposal of Freeman.I3) In nonaqueous polar solvents,’ the intramolecular charge-transfer state of these ANS derivatives is formed, but little or no ionization occurs. These cases, studied extensively by the Kosower g r o ~ p , ’ ~constitute ,’~ a completely separate set of photophysical data from the ones we are studying. Water is distinct and, just as for acid-base equilibria in aqueous compared with nonaqueous media, requires special consideration.’6 In order to place the above notions on a firmer basis so that a better structural picture of the solvent-assisted ionization process can be formulated, three novel theoretical concepts are introduced in this paper. None of these has been previously used in the description of photochemical quenching. First of all, rates for the exchange of solvent molecules and electron acceptor molecules (Le., quenchers) in the microenvironment are included specifically in the kinetic equations; secondly, a probability matrix method is used to treat compound or cooperative effects when more than a single acceptor molecule plays a role; and finally, the limitation of small acceptor concentration is relaxed, the formalism being valid over the full range 0-100%. This theory is then applied to the 6,2-TNS photophysical data in water/alcohol mixed solvent systems.
’
11. Experimental Section 6,2-TNS was obtained from Eastman and recrystallized three times from hot water. Demineralized water, HPLC grade methanol (Fisher Co.), and USP absolute ethanol (US. Industrial Chemicals Co.) were mainly used to prepare the water/alcohol ( 5 ) J. A. Synowiec, Ph.D. Thesis, London, 1978. In nonaqueous solvents, where spontaneous ionization is improbable, to acquire sufficient kinetic energy to escape the local cationic environment, electrons must usually be produced by a two-photon process. (6) J. Lee and G. W. Robinson, J . Chem. Phys., 81, 1203 (1984). References quoted in this publication [D. V. Bent and E. Hayon, J . Am. Chem. SOC.,97,2612 (1975); E. Amouyal, et al., Faraday Discuss. Chem. SOC.,74, 167 (1982)l conclusively show that electrons are produced in the case of indole. The near one-to-one correswndence of our indole results at high temperatures and our results for the ANS derivatives in aqueous solve& reported here and elsewhere (ref 10) leave little doubt that electrons are produced in all these cases as well. (7) G. W. Robinson, J. Lee, and R. A. Moore in “Ultrafast Phenomena IV”, D. H. Auston and K. B. Eisenthal, Eds., Springer-Verlag, West Berlin, 1984, pp 313-316. (8) J. Lee, R. D. Griffith, and G. W. Robinson, J . Chem. Phys., 82, 4920 (1985). (9) J. Lee and G. W. Robinson, J . Phys. Chem., 89, 1872 (1985). (10) J. Lee and G. W. Robinson, J. Am. Chem. Soc., in press. (1 1) See, for example, D. Huppert, H. Kanety, and E. M. Kosower, Faraday Discuss. Chem. Soc., 74, 161 (1982). (12) G. W. Robinson and J. Lee, J. Phys. Chem., to be submitted for publication. This work will be based on a model for H bond dynamics in pure water [G. W. Robinson, J. Lee, K. G. Casey, and D. Statman, Chem. Phys. Lett, in press]. (13) G. R. Freeman, Annu. Rev. Phys. Chem., 34,463 (1983). (14) E. M. Kosower, Acc. Chem. Res., 15, 259 (1982). (15) E. M. Kosower and H. Kanety, J. Am. Chem. Soc., 105,6236 (1983). (16) H. A. Laitinen and W. E. Harris, “Chemical Analysis”, 2nd ed., McGraw-Hill, New York, 1975.
solvent mixtures, 6,2-TNS concentrations being in the range 1 X to 1.5 X M in all experiments. Dissolved oxygen is known to affect the photochemistry of ANS derivatives.” We have found independently in our laboratory (ambient pressure -675 torr) that there is a 12% increase in lifetimes and quantum yields for 6,2-TNS in deoxygenated as compared with nondegassed alcohols. In cases where the solvent has a high water content and the overall rates are high, the O2 effect is minimal. A greaseless glass/Teflon high-vacuum system is ordinarily employed in our laboratory for the purification of samples. The samples can be prepared and studied in their absorption cells under high-vacuum conditions, while avoiding the changes in solvent composition accompanying conventional degassing methods. In spite of the normal dependability of this purification technique, care must be taken for certain samples because of the long solvent distillation times required. For example, it was found that aging 6,2-TNS solutions under room lighting conditions exhibit different spectral and lifetime properties than freshly prepared samples. Thus, to obtain consistent results, a simpler and quicker purification method using a drybox arrangement and solvents deoxygenated prior to mixing had to be resorted to for the 6,2-TNS experiments. Quinine sulfate dihydrate (Baker Ultrex) and sulfuric acid (Fisher Reagent) were used as a standard in the determination of quantum yields.I8 Emission spectra were measured on a Perkin-Elmer MPF-44B spectrofluorometer with a DCSU-2 attachment and modified sample housing. This instrument enables measurement of corrected excitation and emission spectra from nearly 200 to 600 nm, a range that adequately covers the fluorescence of 6,2-TNS in all solvent systems. Absorption spectra were measured on an Aminco DW-2a spectrophotometer. Picosecond time-resolved fluorescence emission spectra were measured by using the 4th harmonic (263.4 nm) of a mode-locked Nd3+/phosphate glass laser for excitation. Coaxial detection geometry was used. Schott cutoff filters selected the emission wavelengths to be observed. The detection system was an Electro-Photonics Photochron I1 UV-sensitive streak camera with an S-20 photocathode. Streak camera signals were intensified with a three-stage EM1 image intensifier and digitized through the use of a PAR optical multichannel analyzer (SIT). A single photon counting apparatus using a synchronized argon ion pumped dye laser was also employed to measure the longer lifetimes in high alcohol content mixtures. In the region of overlap of the two techniques, the results show agreement with the experimental values obtained from the streak camera. A more complete description of both of these experimental systems has been presented e l ~ e w h e r e . * J ~ ~ ~ ~ 111. Theory for Linear Quenching
A charge-transfer process in an excited electronic state is accompaniei by fluorescence quenching of the precursor species. A theoretical scheme for photochemical quenching, including the solvent rearrangement process, was presented in earlier p. a.~ ) e r s : ~ , ~ ~ A A-Q
+ hv, + hv;
+ A*
+
-
---*
A
A* A*-Q
+ hv,
[s(t)]
[~’(t)] [ko]
(1) (2)
(3)
A-Q 4- hv,’ [ k ’ ] (4) A*-Q A* Q =+ A*.*.Q [k,, k,’] (5) Here A refers to the ground state of the probe molecule (6,2-TNS), while A* refers to its excited state. If the probe is surrounded by only inert solvent, A or A* is used to denote the probe. If a (17) W. 0. McClure and G. M. Edelman, Biochemistry, 5, 1908 (1966). (18) J. N. Demas and G. A. Crosby, J . Phys. Chem., 75, 991 (1971). (19) G. W. Robinson, T. A. Caughey, R. A. Auerbach, and P. J. Harman “Multichannel Image Detectors”, Y,Talmi, Ed., American Chemical Society, Washington, DC, 1979, ACS Symp. Ser. No. 102, pp 199-213. (20) R. J. Robbins, G. R. Fleming, G. S. Beddard, G. W. Robinson, P. J. Thistlethwaite, and G. J. Woolfe, J . Am. Chem. Soc., 102, 6271 (1980). (21) G. W. Robinson and W. A. Jalenak, Laser Chem., 3, 163 (1983).
3650 The Journal of Physical Chemistry, Vol. 89, No. 17, 1985
quencher resides at the probe’s “active site”, the notation is A-Q or A*-Q. As will be clear from the discussion in the next section, this kinetics scheme is wholly valid for the case where the active site can accommodate only a single quencher molecule, thus the terminology linear quenching. The linear quenching theory can also apply accurately to the case where the active site accommodates more than one quencher but where the quencher concentration is sufficiently small that the probability of having more than one quencher molecule at the active site is negligible. This is the usual realm of application of photochemical quenching theory and leads to conventional Stern-Volmer behavior.22 Experiments show that water acts as a quencher for 6,2-TNS while alcohol is an inert solvent. It is known23that u, = u: but that u, > vel, for A N S derivatives in polar media. Processes with forward and reverse rate constants k2 and k i reflect the exchange of an inert solvent and a quencher molecule. Processes with rate constants ko and k l include the emission of light as well as all nonradiative processes. The process kl, as it relates to 6,2-TNS, consists of at least four distinct substeps, which may be schematically represented by the following. A*...Q + Act... Q ACt*-Q
-+
A%.Q
4
A+...Q...e-
+ hu,‘
(7)
A+...Q...e-
[kel
(8)
A...Q
[ka]
(9)
-P
The first of these substeps is known’ to be immeasurably fast by use of Nd3+/glass laser pulses (55 ps). The second and third substeps combine to give the rate constant k , = kd k,, where k,,’ is the sum of the “intramolecular” rate constants, those for radiation, internal conversion, and intersystem crossing, from the configuration Aci-.Q. The third substep eq 8 is sufficiently irreversible to act as an efficient quenching step. Energy relaxation involving the solvent accounts for this irreversibility. The energy relaxation step in hydration dynamics has been shown to be accompanied by loss of 0-H vibrational energy.9 It is this third substep that distinguishes water from other polar solvents. Because of the slowness of the required solvent reorientations for larger polar molecules,” this substep is slowed to a point where ionization can no longer compete with the intramolecular processes denoted by k,’. The rate of charge recombination, the fourth substep, is not known but is probably fairly fast, ?lo9 s-l. Some threshold electrons may diffuse away (dissociate) ‘from the parent cation to form ordinary (relatively long-lived) solvated electron^.^ We consider charge recombination and charge dissociation to be secondary effects that do not perturb the rate of decay of the complex Act-.Q. The latter is the rate we measure in all of our experiments, either directly or through quantum yield determinations. Letting x and y denote the time-dependent concentrations of A* and A*-Q, respectively, leads to the following coupled rate equations
+
dx/dt = ~ ( t+) k,’y - ( k ,
+k2)~
dy/dt = ~ ’ ( t+) k 2 -~ (k1
(10)
(22) N . J. Turro, ‘Molecular Photochemistry”, Benjamin, New York, 1967, pp 93-95. (23) C. J. Seliskar and L. Brand, J . Am. Chem. Soc., 93, 5405, 5414 (1971). (24) G . A. Kenney-Wallace and C. D. Jonah, Chem. Phys. Left.,39, 596 (1976); G . A. Kenney-Wallace in “Photoselective Chemistry”, Part 2, J. Jortner, Ed., Wiley, New York, 1981, pp 535-577; D. Huppert, G . A. Kenney-Wallace, and P. M. Rentzepis (HKR), J. Chem. Phys., 75, 2265 (1981). While the time scales for these reorganizational motions are crudely ‘scaled” by dielectric relaxation times, the exothermicity of the hydration reaction sets the two processes apart. In a future paper (ref 12), it will be shown that in the case relevant to the 6,2-TNS work, where the activation barrier is low and the exothermicity is high, negative entropy factors slow down the hydration rates. The prefactor in the Arrhenius equation can be a few orders of magnitude smaller than that for dielectric relaxation, which is accompanied by a positive entropy of activation. Some of our views are seen to overlap those expressed in the Discussion section of the HKR paper cited above. However, all the above cited electron trapping work was carried out at a single temperature where it is not possible to separate enthalpic from entropic effects.
+ ki)y
(1 1)
The quantities s ( t ) and s’(t) are time-dependent production rates of A* and A*-Q by the light source. The exact solution to these coupled rate equations was presented in earlier ~ o r k ~ , ~ ’
where 2xj = (ko
+ k1 + k2 + k2’) + (-l)i(l + 4’y)1/2(kl- ko + k2’Kj = k2 + (ko - Ai). Fj =
(Aj
k2)
- ko - k2) / kl
7 = k2k2//(kl - ko
(6)
[kctl
[k,’]
A-Q
Moore et al.
+ k2’ - k J 2
+
+
p ( 0 ) = s(0) s’(0) is the combined concentration, [A*], [A*-.Qlo = x ( 0 ) + y(O), at t = 0 of the “unquenched” and the “quenched” probes, and a = s’(O)/p(O) is the fraction of p(0) that has been excited to the state A*-Q at t = 0. In an early paper by Weller,25 an expression was given for fluorescence quantum yields in the presence of quenchers. The Appendix of a recent paper by Eftink and Ghiron26contains a more detailed derivation of the classical photochemical quenching equations and shows that Weller’s expression is a special case of a more general result. In earlier ~ o r k , ~using . ~ ’ the linear theory (eq 10 and 1l ) , we also derived an equation for relative quantum yields
where a’, important at high quencher concentrations, is the fractional production rate of the “quenched species”, A*.-Q, under steady-state conditions and the r superscripts refer to radiative rates. Comparing2I eq 14 with the Eftink and Ghiron expression shows theirs to be a special case of this general linear result with a’ set equal to zero. However, all of these previously published quantum yield expressions are based on the linear theory and will almost certainly break down as the quencher concentration increases. For the purposes of this work, such results are not useful, since we will wish to vary quencher concentration (Le., the concentration of water) over the entire range 0-100%. Previous s t u d i e ~ ,using ~ . ~ solvents having a low concentration of water in alcohol, have suggested that for 6,2-TNS single water molecules have no effect on the photophysics. In this case, the linear theory certainly does not apply. Some sort of compound or cooperative effect involving more than a single water molecule is required for electron ionization. Thus, the linear kinetics scheme is not expected to give an accurate picture of the 6,2-TNS decay in aqueous media. We have gone over this scheme because its foundations are familiar, and it is a good embarkation point, describing the correct kinetics except for compound effects when more than one quencher molecule participates at the active quenching site. IV. Theory for Compound Quenching
To study the kinetics when more than a single quencher molecule plays a role, a one-dimensional random walk (25) A. Weller, Prog. React. Kine?., 1, 129 (1961). (26) M. R. Eftink and C. A. Ghiron, Anal. Biochem., 114, 199 (1981).
The Journal of Physical Chemistry, Vol. 89, No. 17, 1985 3651
Hydration Dynamics of Electrons with a trap ("gambler's ruin" problem) is used. The following scheme
constitute the critical size, there are five different excited-state configurations (p = 1, 2, 3, 4, 5) plus the ground-state trap, giving N = 6. The reaction rate matrix becomes J,,
A
A"Q
A..Q2
A..Q3
0
0
A..Q,
depicts the case where up to four quencher molecules can act on the excited molecule A*. This scheme, suitably modified for different numbers of quencher molecules and for different types of cooperativity, is general, extending photochemical quenching theory beyond the Stern-Volmer limit. (An example, different from the one required here, but one that should have wide application, is where there are n neighbor sites, with the probability of quenching in any given configuration being proportional to the fraction of these sites occupied by quencher molecules. Methods such as these, which often require computer calculations, should be able to describe photochemical quenching data outside the usual low-concentration regimes where Stern-Volmer quenching applies.) Application to the specific case of 6,2-TNS probe molecules will now be made. Using four quencher molecules as an example, we can treat cooperative quenching of 6,2-TNS by water molecules within the above random walk framework. Each step in the random walk process corresponds to one solvent exchange, k,, k,' (2 In I5 ) . The ground state behaves as a trap in a pulsed light experiment, since decay into the ground state is irreversible except when photons are present. Since there is no change in the absorption spectrum of 6,2-TNS when the solvent is changed from pure alcohol to pure water, all ground-state configurations A-Q, (0 I n I4) are assumed equivalent, their concentrations being determined by the volume fraction of the quencher. The configuration A*-Q4 decays with the rate constant k , = kJV k,. In the case of 6,2-TNS, as for this is taken to be the "saturation value", further addition of quenchers, in a second coordination shell, for example, being taken to have negligible effect on the decay of A*. More will be said about this point later. The rate constant k , is therefore equal to the decay rate of 6,2T N S in pure water. All other configurations A*.-Q, (0 In I 3) are assumed to decay with rate parameters ko, kJ, k t l and kJ1'. These parameters are taken to be weighted averages of ko in pure alcohol and korVin pure H20. It is assumed that no electron formation is possible from these configurations of "subcritical" size. Since the values of the various k{s for 6,2-TNS are relatively small, the configurations A*.-Q, (0 In I3) are more likely to undergo solvent exchange than decay to the ground state. Configurations will therefore randomly proceed back and forth along the solvent-exchange chain, undergoing occasional decay through one of the ko processes. When they reach the configuration of "critical size", four water molecules in this example, they have a high probability of decaying to the ground state through the kl process. Random walk problems are conveniently solved by the probability matrix m e t h ~ d . ~ 'An . ~ ~incremental unit of time At is taken to be the step time. An off-diagonal element Jp4 @, q = 1, 2, 3, ...) of the reaction rate matrix R gives the probability that configuration A*--QP (p = n + 1) will change to configuration A*-.Qq ( q = p f 1) after time At. Special off-diagonal elements Kp represent the probability during this time that the configuration A*-Qp decays to the ground state. A diagonal element A , represents the probability that the pth configuration does not change during At. The reaction rate matrix R is therefore a square matrix whose order N is equal to the number of excited-state configurations plus one. For example, if four water molecules
+
(27) L. Takacs, 'Stochastic Processes-Problems and Solutions", Methuen, London, 1960, Chapter 1 . The dimensionality of the mathematics has, of course, nothing to do with the dimensionality of the physical system that it describes. (28) E. Parzen, "Modern Probability Theory and Its Applications", Wiley, New York, 1960, pp 136 et seq.
where Jppl and Jpgtl are, respectively, the probabilities that during time At a water molecule in the active coordination shell is replaced by an ethanol molecule, and vice versa. The J elements are thus analogous to k2 and k i of the linear quenching theory. Also, referring to the above rate scheme, one has
K1 = koAt
(16)
K2 = kJAt
(17)
K3 = k0"At
(18)
K4 = ktlIAt
(19)
KS = k1At
(20)
Since Appis the probability that the initial configuration remains unchanged during At
A , = 1 - Jp,p-1 - Jpp+l - Kp
(21)
remembering that At must be chosen small enough so that, for all off-diagonal elements, Rp4
