4236
J. Phys. Chem. 1994,98, 4236-4242
Dynamics of Spin-Polarized Photoelectrons in Rubidium-Tetrahydrofuran Solutions Vladimir Rozenshtein, Cil Zilber, and Haim Levanon' Department of Physical Chemistry and the Farkas Center for Light- Induced Processes and Department of Organic Chemistry, The Hebrew University of Jerusalem, Jerusalem 91 904, Israel Received: December 15, 1993; In Final Form: February I I , 19940
We present a Fourier transform EPR study of photoexcited rubidium-tetrahydrofuran solutions (Rb/THF), in the absence and presence of thecomplexing chelate 222 cryptand (Kp), Rb/THF/Kp. The temporal behavior of the EPR signals is interpreted in terms of two components participating in the complex processes, i.e., the spin-polarized photoelectrons and the solvated electrons that are coupled to the alkali-metal cations and, when present, to the cryptand molecules. The spin polarization mechanism is due to the radical pair mechanism, which is induced by charge transfer to solvent as a result of the photoabsorption. Spin relaxation times, measured directly in these systems, are discussed in terms of a site-exchange narrowing mechanism and a spin-rotation coupling mechanism in Rb/THF solutions and by collision-induced electron transfer in Rb/THF/Kp solutions.
I. Introduction Spin-polarized photoelectrons generated by photoexcitation of ether solutions containing alkali metals were first discovered by Glarum and Marshall.' In subsequent studies, chemically induced dynamicelectronpolarization (CIDEP) effects were also found in pure alkali-metal/tetrahydrofuran(THF) systems and in solutions containing different chelating agents, such as crown ethers and cryptands (Kp)." Although the propertiesof alkalimetal solutions at equilibrium are well understood, no coherent studies have been carried out to establish the exact nature of the electron-like species in photoexcited systems or their spin relaxation and spin polarization mechanisms as a function of temperature, chelate concentration, and solvent. Such studies, fortunately, can be accomplished by employing fast time-resolved EPR spectroscopy that became available in recent years. The purpose of this study is to report on the spin polarization and relaxation effects of photoexcited rubidium-tetrahydrofuran solutions in the absence and presence of the chelate Kp: Rb/ THF and Rb/THF/Kp, respectively. On the basis of the results and analysis, we provide a unified presentation of the spin dynamics and the molecular structure of the participating species. As will be shown, the magnetic effects of the quasi-free electrons that participate in the photochemical reactions are unique cases in which the spin polarization development and its relaxation can be observed in a singleexperiment. These goals were accomplished by employing pulsed EPR spectroscopy (Fourier transform, FT) with high sensitivity, covering a time regime spanning from nanoseconds to hundreds of microseconds. This time scale corresponds to the time evolution of the spin polarization and to the spin relaxation times, T I and Tz.'J
Td, between the two p u l w is tuneable. The minimum time between two successive spectra is 10 ns, and the initial spectrum was taken at Td = 24 ns. The FID dead time is 130 ns, but with the application of the linear prediction singular value decomposition (LPSVD) routine, the FIDs within the dead time could be reconstru~ted.~sThe spectra of the solvated electrons in thermal equilibrium were used as references for phasecorrection of the spin-polarized spectra. The light pulse repetition rate of 20 Hz was found to be sufficiently slow to restore the initial conditions after each pulse. Rb/THF solutions were prepared by well-established p r O C t d ~ r e s , ~and ~ J ~222 cryptand (Aldrich Chemicals)was used without further purification. Tempcratures between 147 and 297 K were monitored by a Bruker cryostat, and the g factors were measured with DPPH as a standard.
-
III. Phenomenological Description of the Experiments General Model. Laser excitation of Rb/THF or Rb/THF/ Kp solutions results in emissive EPR signals, which decay either to zero intensity or to absorption mode signals in thermal equilibrium. Typical photoinduced timedependent spectra of different systems are shown in Figures 1 and 2. To interpret the spin-polarized spectra, we start with the reaction scheme that describesthe dissolution of the alkali metal in different solvents:9
+ M, M (solid) F? M+, + eVs
2M (solid) F? M+,
II. Experimental Section
(1)
(2)
(4)
In solvents such as ammonia, certain primary amines, hexamethylphosphoramide,and ethers, the reactions of the solvated electrons and metal ions with the solvent molecules are sufficiently slow, to yield relatively stable solutions that last for hours and days.9-12 Thus, all experiments reported here were carried out using THF solutions. EPR experiments were performed with a pulsed EPR spectrometer (Bruker ESP 380) interfaced to a pu1sedNd:YAG laser (Continuum 661-2D), as described in detail elsewhere.13J4 FTEPR spectra were obtained with a pulse sequence that consisted of a light pulse (532 nm, 12-11s duration and energy up to -0.2 J/pulse) followed by a microwave pulse, where the delay time, -
~~
~
~~
Abtract published in Aduunce ACS Abstracts, April 1, 1994.
0022-3654/94/2098-4236S04.50/0 ._ ., . I
I
-
-
where M+, and M; are the alkali-metal cation and anion, respectively, (Mte-,) and (M+,,M-,) are the loose ion pairs, Me, is the tight ion pair or the gas-phase-likeatom, which exhibits hyperfineinteractions, and the subscript s stands for the solvated species. In high-dielectric solvents (c > 25) the alkali metals are extremely soluble. Hence, in ammonia, reaction 3 is shifted to the rigl1t,18,'~such that the anions escape detection. In solvents of low dielectric constant (e < 25), including THF, both the Q 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994 4237
Spin-Polarized Photoelectrons in Rb-THF
halide anions,2* have no vacant orbitals to retain an electron. Therefore, the transition should involve the electron transfer from the anion to the surrounding solvent molecules. Photoexcitation of the ion pair (M+,S,M-) initiates the spin polarization and relaxation processes in the following order:
-
hu CTTS (a)
h
y
(M+,S,M-)
X
(b)
'(M+,e-,,S,M*)
I
I
I
I
I
-15
40
4
0
5
10
m-I Figure 1. FT-EPRspectra of e-p in photoexcited Rb/THF solutions,vs thedelaytime,Td,betweenthelaserpulse(X= 532nm)andthemicrowave pulses at 167 K.
b
a
-1
Figure 2. (a) Same as in Figure 1, but for Rb/THF/Kp solutions at 167 K and [Kp]= 10-2 M (these spectra are denoted as + e-,); (b)
FT-EPRspectra, x"(e-,,), after the eubtraction: ~ " ( e + - ~e-,) - x"(e-,);
see text. Off-resonanceconditions were chosen to assure that artifacts do not affect the spectra.
metal anions and the solvated electrons are detectable, and the formationof ion pairs (M+,,e-,) and (M+B,M-s)proceedspreferably via eqs 4 and 6. The additioq of chelates, e+, crown ethers or cryptands, stronglyenhancesthe metal solubilityvia the reaction20 M+
+ Kp a (M+,Kp)
(7)
It is the van der Waals forces that are responsible for the contact between the cation and the oxygen atoms of the Kp." This selective complexation shifts equilibria 1-3 to the right, leaving the outer s orbital of the cation shielded from the electron. The optical spectra of alkali-metal solutions consist of two bands, attributed to (1) the anion, M-, and the ion pair (M+,,M-,) and (2) the solvated electron, e-,, and the ion pair (M+,,e-,).9JO The former absorption depends on the metal, whereas the latter is independent of the metal and appears in the infrared region. The maximum absorption of Rb- is at X = 900 nm with AX112 = 400 nm,21 allowing photoexcitation at 532 nm. The relatively low absorbance at this wavelength is compensated by the high intensity of the laser pulses of -0.2 J/pulse. Presently, it is well established that M- is indeed a metal anion with two electrons in the outer s ~ r b i t a l and ~ ~ -that ~ ~its optical spectrum is due to a chargatransfer-to-solvent (CTTS) mechanism.2427 This mechanism is operative because the alkali-metal anions, similar to the
I.sc (4
3(M+,e-p,S,M*) (8)
where S is the solvent or the complexing chelate, (M+,S,M-) stands for the solvated ion pair (M+,,M-,), and e-p is the photoelectron generated by the photoexcitation. Thus, the initial photochemical act results in the radical pair, l(SC,M*), where SO-stands for an electron bound to the original solvation shell of the parent anion (eq 8a). The radicals formed in the solvent cage, namely e-p and M', may either recombine or create their own solvation shells (eq 8b). The competition between these two routes is the reason for the low quantum yield of the radical pair W),(M+,e-p,s,M.). After light absorption the ejected electron forms the ion pair (M+,e-,), which exists in two forms that are in equilibrium, i.e., the loose (1) and tight (t) ion pairs: M'
-1
-
M+, '(So-, Me)*
(M+,e-,),
+ (M+,e-,),
(9)
The loose ion pair features a very weak hyperfine coupling (hfc) constant, whereas the tight species should exhibit an appreciable hfc value, Ahfc. For rapid jumps between these two states, such that T M A M < ~1 (where T M is the residence time of the electron on the metal in the tight ion pair in eq 9), a single EPR resonance will be observed, which is a time average signal of both species.29 In the case of potassium, the tight ion pair, (K+,C~)~, Ahfc = 30 G a t room temperature,2 and the single EPR line pattern requires a jump rate >lo* s-1 between the two structural states of eq 9. The above considerations indicate that the light absorption process inevitably leads to the formation of RPs consisting of M' and e-, and/or its ion pair forms (eq 9). Therefore, the RP polarization should be associated with these pairs. As already mentioned, theemissivepolarized single line spectrum (g = 2.0023 f 0.0002), observed for all Rb/THF solutions, is attributed to the quasi-free electrons or the ion pairs (M+, cP). The gfactor of Rb' is equal to 1.999 f 0.002;2930+31 therefore, Ag = g, - gRb = 0.0033 > 0 for the RP, which is responsible for the spin polarization development. We assume that only the radical pair mechanism (RPM) is operative, having (M+,e-,) and M' as the RP constituents. Before further elaboration, we should indicate that in all experiments the Rb radicals escape EPR detection, probably due to a short T2, which is within the dead time of the EPR detection (-100 ns).I4 The rapid CTTS and ISC processes (eq-8) must be completed within the time period of the laser pulses so that the constituents of the triplet RP can separate. For the polarization development, both the magnetic, BM, and the exchange, J , interactions are required. The former is essential for the S-TO mixing, while the latter rephases the spins, causing the spin polarization effects32 When the exchange interaction is very large (close interdistance between radicals), no spin polarization is observed (region I in Figure 31, while at large separation, where the exchange interaction disappears (regions IV in Figure 3), spin polarization cannot be developed. Therefore,the effectiveexchangeinteraction lies in the range 1012 > J > 108 rad/s.33 Since the exchange integral is reduced by an order of magnitude for -1-A increase in interradical distance, the effective range of this interaction is operative over a separation distance of -4 A only (region I1 in Figure 3). According to the CIDEP rules,33 the spin-polarized radicals must originate from the triplet precursor, )(M+,cp,S,M'), which is generated via the ISC route (eq 8c).
Rozenshtein et al.
4238 The Journal of Physical Chemistry, Vol. 98, No. 16, 1994
Figure 3. Singlet and triplet (TO)energy levels of the RPs as a function of the distance between ita constituents. The differentzones describe the behaviorof the RPs at the specifeddistanceregions: (I) strong reencounter depolarization region; (11) reencounters at a separation distance of R,, resulting in the spin polarization; (111) simultaneous action of both magnetic and exchange interactions, where Ro is the initial separation distance; (IV)STo mixing region.
distance R, (region I1 and eqs 12b and 13a). As stated above, accordingto the CIDEP rules with a triplet precursor, the polarized radicals are characterized by net emissive polarization for the electrons and net absorptive polarization for the alkali-metal atoms. Part of the separatedRPs either can be in spin equilibrium without leaving region IV or can undergo reencounters at distances with large J (region I), thus resulting in depolarization of the radi~als.3~The final processes (eq 14) are the spin-lattice relaxation of the polarized species. At the initial separation distance, &, J(&) I2Aw while at the reencounter point, R,, J(R,) > 2Aw. (Aw is the difference in the resonance frequencies of the RP constituents.) The separation and reencounter processes are relatively and therefore, the characteristic time of the polarization development should be determined by %TO mixing time. This is the time where the interdistance between the RP constituents changes from & to R,, which is in the order of A d . In our case, where the Zeeman contributionto the mixing rate is probably dominant (Aw = 1/2AgflB),the polarization rise time, T&, is in the order of Aw-1 = 50 ns. Khtics and CIDEP. If we denote the upper and lower spin populations as n, and ng, respectively, and the concentration of the triplet precursor 3(M+,e-p,S,M*)as nplthe time evolution of the population is described by the coupled differential equations:
The polarization effects and spectral evolution will be discussed in terms of reactions 10-14 and Figure 3.
-
initial separation (a)
3(M+,e-p,S,M')
-
S-TO mixing, J # 0 (b)
3( M+,e-p...s...M')
li3( M+,e-p,,l...S...M'poI)
(10)
-
initial separation (a)
3(M+,e-p,S,M')
3(M+ - ...S...M') ,e P
S-Tomixing, diffusion, J = 0 (b) --B
..... .....
l ~ ~ ( M + , e -S~ M') (12)
dn,/dt = kkanp - (n, - n:)/Tl
(15)
dn,/dt = k,8np - (5- n:)/TI
(16)
dnp/dt = -khnp
(17)
where n,O and neo are the population at thermal equilibrium, kk= and kkB are the population buildup rate constants (eqs 12 and 13), and k k = k d a + kkb. In eqs 15 and 16 we assume that the polarization development can be described by first-order processes. This is a simplified approach, but it agrem well with the experimental kinetics in short times. In fact, by employing the Noyes reencounter diffusion mechanism,35 the kinetics of RP polarization cannot be described analytically, and numerical methods are required.32 However, it is physically obvious that the rise time should be proportionalto the phase correlation time, Tz,and inversely proportionalto mutual diffusion coefficient, D, of the RP constituents. Therefore, at high vismitia at low temperatures, the polarizationbuildup is relatively slow as indeed previously confirmed by Eliav and Freed6and by this study (Table 1). An EPR signal is proportional to the population difference An = ng - n,, and the polarization is defined as33 P = (ne - n,)/(n,
relaxation, TI,,TIN
(M+,e-,),]
and Mepol
---+
(M+,e-,),and
M', (14)
where "pol" stands for the spin-polarized species. The polarization starts when the magnetic and exchange interactions act simultaneously,as the radicals first separate via stages 10a and 10b in region I11 of Figure 3. The initial polarization (PO) in stages 10a and 10b is produced over a short time interval with a fraction of radical pairs. These polarized radicals diffuse apart according to the process described in eq 11. The unpolarized radical pairs separate into region IV, where the singlet, S,and the triplet, TO,states are degenerate, and J = 0. Therefore, processes 10 and 11 are responsible for the initial polarization, PO,which can be detected immediately after the laser pulse (see section IV). The main contribution to the polarization results from the sequential processes, namely, the initial separation (region 111) followed by diffusion (region IV) and subsequently a fast reencounter process, at a separation
+ na) = An/n
0:
Z
(18)
where n = n, + ng is the overall spin concentration (in the present case it is kept constant as the photoelectrons are not involved in chemical reactions) and l i s the EPR signal intensity. Hence, by solving eqs 15-17 the polarization, due to the reencounter mechanism (excluding the time evolution of the initial polarization) can be expressed by P
a
An a Z = {(kfiwg-k,")/(kh T I )- exp(-kkf)]
+ TI-')]n:(exp(-t/
+ Ano(l - exp(-t/T,))
(19)
where At+ = ngO- n,O and npois the initial concentrationof triplet RPs formed via ISC (eq 8c). Two cases will be considered: (1) Short times, Le., t
