J . Phys. Chem. 1989, 93, 2683-2688
2683
Photoconductivity of Anthracene in Liquid Hydrocarbons David W. Tweeten and Sanford Lipsky* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: September 8, 1988)
The photocurrent from anthracene in 2,2,4-trimethylpentane, 2,2-dimethylbutane, cyclohexane, cyclopentane, and tetramethylsilane has been studied as a function of excitation energy from the ionization threshold to the onset of strong solvent absorption. In the case of 2,2,4-trimethylpentane (isooctane), the dependence of the photocurrent on the magnitude of an externally applied electric field was additionally studied in order to separately evaluate the effect of excitation energy on the electron ejection probability and on the geminate ion pair escape probability. The effect of excitation energy on the quenching by n-perfluorohexane of the anthracene photocurrent in isooctane is also reported.
Introduction The photoconductivity of an aromatic solute in a liquid hydrocarbon exhibits a strong dependence on the nature of the hydrocarbon solvent.’J Both the energy threshold for photocurrent and the subsequent shape of the photocurrent spectrum are importantly altered by what would otherwise appear to be relatively minor changes in the nature of the solvent. For example, in neopentane, the photocurrent from anthracene onsets at eexc = 6.18 eV and then increases with increasing eCXC with an easily discernible structure consisting of at least four shoulders between 6.4 and 7.0 eV.Z At higher eoxc, light absorption by neopentane becomes too severe for reliable correction. On the other hand, in n-pentane, the photocurrent threshold lies -0.36 eV to higher energies (at 6.54 eV), and now as text increases the photocurrent simply monotonically rises without any semblance of structure to about 7.1 eV where again the solvent absorption becomes too severe.2 The effect of the solvent on the photocurrent threshold derives ultimately from its electronic polarization about the ion pair. The contribution to the total polarization energy from the positive ion, although relatively large in magnitude, carries little solvent variability. On the other hand, the polarization energy deriving from the electron (which is essentially the negative of the ”vertical” electron affinity of the solvent) appears to be very sensitive to molecular structure and accommodates almost all of the threshold shifting from one solvent to the next.3 The effect of the solvent on the structure of the photocurrent spectrum is less well understood. Holroyd et aL2 have noted that for anthracene in neopentane (and for azulene and methylnaphthalene as well) the photocurrent structure corresponds closely to the positions of relatively sharp Rydberg transitions in the vapor phase and have suggested that their manifestation in neopentane and their absence in n-pentane are ultimately tied to differences in the mobility of the electron in these solvents. The argument follows essentially that of Fermi’s4 to explain the broadening of the spectral lines of high-lying Rydberg states of atoms by perturbers with large scattering amplitudes for slow electrons. By linking the electron’s mobility in the solvent to the electronsolvent scattering amplitude, the argument for observation of the Rydberg transitions in neopentane and for their obscuration in n-pentane is made on the basis of a ca. 500-fold smaller electron mobility in n-pentane. To further support this, they note that, with nperfluorohexane added to anthracene (or benzanthracene) in neopentane, the photocurrent is quenched with an efficiency whose wavelength dependence exhibits a similar structure to that observed in the photocurrent spectrum.2 The implication is that the photocurrent quenching will be maximal when a Rydberg state of anthracene is populated. Such a state, it is presumed, will transfer (1) Bottcher, E. H.; Schmidt, W. F. Proc. Tihany Symp. Radiat. Chem. 1982, 421. (2) Holroyd, R. A.; Preses, J. M.; Bottcher, E. H.; Schmidt, W. F. J . Phys. Chem. 1984, 88,744. (3) Holroyd, R. A.; Preses, J. M.; Zevos, N. J . Chem. Phys. 1983, 79, 483. (4) Fermi, E. Nuovo Cimento 1934, 11, 157.
0022-3654/89/2093-2683$01.50/0
an electron to n-perfluorohexane to produce a geminate ion pair with a separation distance smaller (and, therefore, with smaller espace probability) than is produced at other excitation energies by the simple ejection of an electron and its subsequent “epithermal” scavenging by the perfluorocarbon.’S2 The possible involvement in solute photoionization of a metastable, Rydberg-like precursor state to the geminate ion pair had been earlier considered by Wu and Lipsky5 to accommodate their results on the quenching by electron scavengers of recombination fluorescence. It had been noted that solute fluorescence was quenched for excitation energies both above and below the photoionization threshold but always more severely above the threshold. An analysis of this “enhanced” quenching indicated that its dependence on quencher concentration was more similar to what would be expected for the quenching of an exponentially decaying excited state than to what had been reported in radiation chemical studies for product formation from scavenging of electrons undergoing decay due to geminate recombination. However, more recent analyses of the radiation studies (including new measurements on the quenching of high-energy-induced recombination f l ~ o r e s c e n c e )indicate ~*~ that the photoionization and radiation measurements are not necessarily incompatible and, accordingly, the Wu and Lipsky datas can no longer be considered to mandate the postulation of a metastable precursor state. Also, steady-state measurements on the quenching of photocurrent from TMPD in hydrocarbon solvents appear not to require the introduction of such states for their analysis’ nor do picosecond measurements on charge recombination in liquid n-hexane provide any evidence for their existence.’ On the other hand, very recent work on the effect of electric field strength, of excitation energy, and of electron scavengers on the photocurrent from neat liquid hydrocarbonsI0 has been interpreted to implicate the importance of such states, as of course, too, have the aforementioned studies on the general shape of the anthracene photocurrent Thus, the question of the existence of such metastable states and of their participation in the photoionization process must be considered as still unresolved. In the present study we have reinvestigated the photocurrent spectrum of anthracene. We report here measurements of the photocurrent as a function of excitation energy in a variety of hydrocarbon solvents in some of which the effects of applied electric field strength and of added electron scavengers have been additionally examined. The field strength dependence provides information separately on the contributions to the overall photocurrent yield from the quantum yield for electron ejection and from the probability for the subsequent escape of the geminate ion pair. The sdvent dependence and scavenger studies have ( 5 ) Wu, K. C.; Lipsky, S. J . Chem. Phys. 1977, 66,5614. (6) Choi, H. T.; Wu, K. C.; Lipsky, S. Radiat. Phys. Chem. 1983,21,95. (7) Choi, H.T.; Haglund, J. A.; Lipsky, S. J. Phys. Chem. 1983, 87, 1583. (8) Lee, K.; Lipsky, S.J . Phys. Chem. 1982, 86, 1985. (9) Braun, C. L.; Scott, T. W. J . Phys. Chem. 1983,87, 4776. Scott, T. W.; Braun, C. L. Can. J . Chem. 1985, 63, 228. (10) Casanovas, J.; Guelfucci, J. P.; Terrissol, M. Radiat. Phys. Chem. 1988, 32, 361.
0 1989 American Chemical Societv
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The Journal of Physical Chemistry, Vol. 93, No. 6, 1989
Tweeten and Lipsky
permitted us to explore explanations for the photocurrent spectra alternative to those based on the Rydberg state hypothesis.
Experimental Section Light from an Hamamatsu, 30-W, D2 discharge lamp was dispersed through a McPherson 218 (0.3 m) monochromator operating at a band-pass of 0.8 nm and continuously N2 flushed. The light exiting from the monochromator was focused between the electrodes of the photoconductivity cell by a LiF lens. The cell consisted of two stainless steel electrodes (with 2.2 X 1.27 cm2 polished surfaces), each attached to a Ceramiseal connector soldered to a flange and assembled to a stainless steel body through an indium O-ring. One of the electrodes was spring-loaded and insulated against the cell body by a Macor ring. The other electrode was rigidly mounted. The electrode spacing was 0.037 cm and obtained by insertion of quartz spacers between the electrodes. The leading edge of both electrodes was pressed firmly against a 0.16-cm-thick Suprasil quartz window which was attached to the cell body through an indium O-ring. The photocurrent was measured with a digital electrometer (Keithley 617) which was interfaced to an IBM-PC. Photocurrent spectra were obtained by scanning the monochromator at rates sufficiently slow to accommodate the 0.32 s/reading analog-todigital conversion rate of the electrometer. A BASIC language program was written to store and subsequently manipulate the data obtained on successive sweeps of the spectrum. To obtain a photocurrent spectrum, the measured electrometer signal must be corrected both for the wavelength dependence of the lamp intensity and for contributions from " d a r k current. The lamp spectrum was obtained by monitoring the front face fluorescence intensity from the anthracene in the same cell as was used for the photocurrent measurement. The anthracene concentration was sufficient to completely absorb the incident light. The fluorescence was viewed by an EM1 6256 S photomultiplier in conjunction with an interference filter peaking at the maximum of the anthracene emission. Dark current consisted of high-frequency noise spikes superimposed on a relatively stable dc level. To reduce the magnitude and frequency of the noise spikes, the stainless steel electrodes were polished to optical flatness and solutions were admitted to the cell through a 0.2-pm pore size filter (Millex-FG, Millipore) to remove dust. Additionally, both the dark dc level and the noise spikes were reduced by applying an electric field of strength equal to the maximum to be employed in the experiment for a prior period of at least 24 h. Anthracene (Aldrich, 99.9%) and 9-methylanthracene (Eastman) were used without further purification. 2,2,4-Trimethylpentane (Aldrich, 99%), 2,2-dimethylbutane (Aldrich, 98%), tetramethylsilane (Aldrich, 99.9%), cyclopentane (Mat heson Coleman and Bell), cyclohexane (Fisher, Certified ACS Spectranalyzed), and n-pentane (Burdick and Jackson) were purified by passage through activated silica gel and stored over molecular sieves (4 A). n-Perfluorohexane (kindly donated by 3M) was distilled before using. All solutions were perpared at concentrations close to their solubility limits at 25 OC M) and deoxygenated by bubbling with N I . Unless otherwise specified, the photocurrent spectra were measured at a field strength of 3.0 kV/cm. Absorption spectra were measured on a Cary 15 spectrophotometer which, with N, flushing, permits reliable operation to 170 nm. Results Figure 1 shows plots of the photocurrent from anthracene in 2,2,4-trimethylpentane (uncorrected for wavelength variation of the lamp intensity) vs excitation wavelength at two electric field strengths of 5.7 (Figure 1A) and 35.0 kV/cm (Figure 1B). The observed structure is the same as that previously reported by Holroyd et aL2 A careful inspection of the two plots shows that the structure is less pronounced at the higher field strength. Figure 2 shows a typical plot of the photocurrent, J , at ,,A, = 194.8 nm as a function of electric field strength, E , and normalized to its linearly extrapolated value at E = 0 (i.e.. J o ) by using the
165
175
185
195
205
A (nm) Figure 1. Photocurrent from anthracene in isooctane vs excitation wavelength at an applied electric field of 5.7 kV/cm (A) and 35 kV/cm (B).
3.0
2.0
I
.o
0
IO
2 0
E
3 0
40
(KV/cm)
Figure 2. Photocurrent ( J ) normalized to zero electric field ( J o ) vs electric field strength ( E ) for anthracene in isooctane at A ; 194.8 nm. The insert shows high field behavior ( E -25-40 kV/cm) of J / J o for the three wavelengths of 192.4, 194.8, and 190.0 nm (in the order of decreasing J / J o ) , with solid lines representing fits to eq 7 using?./ = 0.471. 0.440, and 0.412 nm-', respectively.
least-squares slope of 5.65 X cm/V obtained from the first four experimental points. The Onsager prediction for this limiting slope at 22 OC is 5.75 X cm/V ( = e 3 / 2 t k 2 pwhere e is the electron charge, k is the Boltzmann constant, T is the absolute temperature, and t = 1.936 is the isooctane dielectric constant at 22 "C). The good agreement in slopes suggests that there are no appreciable losses in photocurrent due to "homogeneous" ionic recombinations at these field strengths. Plots similar to that in Figure 2 were obtained at 41 other excitation wavelengths from ,,A, = 178 to 198 nm with similarly good agreement (i,e, within 2%) between limiting experimental and Onsager-predicted slopes. From the field dependence of J it is possible to extract both the average initial range of the ejected electron and its ejection probability. The procedure for this has been previously discussed by Choi et al." and is briefly reviewed here. For a spherically symmetrical initial distribution of geminate ion pair separation distances that is uninfluenced by the presence of an externally applied electric field, the average geminate ion pair escape probability, (pest), can be written as
( 1 1) Choi, H.T.; Sethi, D. S.; Braun, C. L. J . Chem. Phys. 1982, 77,6027.
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2685 5
0'
80
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0
A
O ooo@%o
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,
,
,
,
,
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I90
180
A
175
165
2 00
185
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(nm)
Figure 3. (A) Electron thermalization range ( r ) as a function of excitation wavelength for anthracene in isooctane. (B) Electron ejection probability & as a function of excitation wavelength for anthracene in
isooctane.
195
205
(nm)
Figure 4. Photocurrent spectra (corrected for incident light intensity) for anthracene in (A) isooctane and (B) 2,2-dimethylbutane. 5,
I
I
wheref(r) is the radial probability density for an ion pair separation distance of r and pes, is the geminate ion pair escape probability for this separation distance. From a variety of photoionization experiments,8*11,12fr) has been shown to be. reasonably well represented by an exponential function, i.e.
where y acts as an unspecified fitting parameter equal to 3 / ( r ) where ( r ) is the average range of the ejected electron. The escape probability, pes,, can be developed as a power series in E of the form pesc =
e-lClr( 1
+ aE + bE2 + cE3 + ...)
(3)
where r, = e2/ckT, a = erC/2kT,b = ( a 2 / 3 ) ( 1 - 2r/rc), c = ( a 3 / 3 ) (1 - 6r/rc + 6(r/rc)2)and where terms of order higher than cubic in E are negligible at the highest field strengths that were practical to use in our experiments (due to rapidly increasing dark current with increasing E ) . Since the measured photocurrent, J , will be proportional to ( p e s , ) (at least when there is negligible "homogeneous" ion recombination- and this is guaranteed by the aforementioned good agreement between the experimental and theoretically expected limiting slopes of J / J o and (pec)/(pec)o, respectively, vs E ) , it follows that the parameter y (and, therefore ( r ) ) can be obtained at each &, by a least-squares fit of J/Jo to ( p w ) / ( p W ) @ The insert in Figure 2 presents the high-field behavior of J / J o for three exciting wavelengths 192.4, 194.8, and 190.0 nm. These are displayed simply to give an indication of the nature of the effect of changing wavelength. In each case the solid line represents the fit to the Onsager theory with y = 0.471, 0.440, and 0.412 nm-] for 192.4, 194.8, and 190.0 nm, respectively. With y known, the absolute value of pes, is calculated via eq 1-3, and the ratio of this to J (suitability corrected for the lamp spectrum) gives relative values of the electron ejection probability &, as a function of A e x v The solid line in Figure 2 is a typical fit of J / J o to its theoretically predicted dependence on E using the exponential probability density of eq 2 with y = 4.40 X lo6 cm-'. Similarly good fits were obtained at other .,A,, Plots of ( r ) ( = 3 / y ) and of @* vs ,,A, are shown in Figure 3A,B for anthracene in isooctane. The quality of this procedure for extracting ( r ) and & depends im(12) Lee, K.; Lipsky, S. J . Phys. Chem. 1984, 88, 4251.
165
185
I75
A
195
205
(nm)
Figure 5. Photocurrent spectra (corrected for incident light intensity) for anthracene in (A) cyclopentane and (B) cyclohexane.
portantly on the sensitivity of ( ~ ~ ) / (to p( r ~) . This ) ~ sensitivity increases as E increases, at least until very high fields are achieved. Our limitation to fields not larger than -40 kV/cm for anthracene in isooctane (due to increasing dark current) is mainly responsible for some of the scatter in Figure 3A,B. Nevertheless, it is clear that there is structure in ( r ) and perhaps also, but much less well-defined, in &. On the other hand, with n-pentane as a solvent, the photocurrent from anthracene was so slight that even at 20 kV/cm the dark current was too large to allow accurate subtraction. Accordingly, the range of E was now too small for reliable extraction of ( r ) and &. The effect of different solvents on the photocurrent spectrum of anthracene is displayed in Figures 4-6. The spectra shown here have been corrected for the wavelength variation of the lamp intensity by taking the ratio of the measured photocurrent to the measured intensity of anthracene fluorescence. The rapid falloff in J o n the short-wavelength side of the maximum is due to the onset there of strong solvent absorption. This tends to reduce the penetration depth of the exciting light which leads both to more ion pairs being formed in the fringe field of the electrodes and to an increasing rate of "homogeneous" ion recombination. Both
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The Journal of Physical Chemistry, Vol. 93, No. 6, 1989
TABLE I: Electron Mobilities
( p ) , Conduction
solvent tetrameth ylsilane neopentane 2,2,4,4-tetramethylpentane 2,2-dimethylbutane isooctane cyclopentane cyclohexane n-pentane
Tweeten and Lipsky
Band Energies (V,,), and Photocurrent Thresholds ( I , ) of Anthracene in Various Solvents w,
VO
cm2/(V s) 100" 7OC 24d 12'
eV -0.55' -0.43' -0.33' -0.20b -0.249 -0.19' +0.01b +O.OO'
5.6 1.lC 0.26 0.19
1
I , (predicted)! eV 5.89 6.03 6.03 6.22 6.14 6.18 6.34 6.44
Idexpt), eV this work other work 5.90 5.87h 6.18' 6.07h 6.17 6.17 6.14h 6.17 6.17 6.38 6.54'
"Reference 17. *Reference 15. cReference 18. dReference 19. CReference20. 'Reference 21. EReference 16. *Reference 3. 'Reference 13.
W
0.4 -
0
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a
0.3
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0.2
-
0.1
-
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s:m
w
C
f
175
Y
7
11 I
165
( 175
185
i
185
195
205
215
225
A (nm) Figure 7 . Absorption spectrum of anthracene (3.4 X lo4 M) in isooctane covering the spectral region of the third (So S,) and fourth (So S,) transitions. Cell length is 0.05 cm.
-
-
i e
1 195
205
215
A (nm) Figure 6. Photocurrent spectra (corrected for incident light intensity) for anthracene in (A) tetramethylsilane and (B) n-pentane.
of these effects tend to reduce J below the value expected from the product of & with (pest). As can be noted from Figures 4-6, both the photocurrent threshold and the shape of the photocurrent spectrum are importantly influenced by the nature of the solvent as was initially reported by Holroyd et aL2 Table I lists for each of the solvents studied the photocurrent threshold, I,, found experimentally. These thresholds were determined by a power law plot as in Holroyd et aL3with the power P = 5 / 2 . These are compared with thresholds found by other workers3J3and those predicted from the gas-phase ionization potential of anthracene ( I , = 7.43 eV)I4 and the sum of the solvent polarization energies of the positive ion ( P + )and of the electron ( V0),15J6Le., via I , = I* vo P+ (4)
+ +
n c .& C
a L
3 7
A (nm) Figure 8. Photocurrent from 9-methylanthracene in isooctane vs excitation wavelength.
U
0 Y 7 b
0 Y
7
Values of P+ have been scaled to that of anthracene in isooctane (P+ = -1.05 eV)3 assuming the validity of the Born equation p
+-;:( :) --I--
where R is the ionic radius assumed independent of the nature of the solvent. For subsequent discussion, the electron's mobility, cl,17-21 is also listed in Table I for each of the solvents studied. (13) Bottcher, E. H. Ph.D. Thesis, Free University of Berlin, 1983. (14) Klasinc, L.; KovaE, B.; Giisten, H. Pure Appl. Chem. 1983.55, 289. Schmidt, W. J . Chem. Phys. 1977, 66, 828. (1 5 ) Allen, A. 0. Drift Mobilities and Conduction Band Energies of Excess Electrons in Dielectric Liquids. Natl. Stand. Re$ Date Ser. (US., Natl. Bur. Stand.) 1976, NSRDS-NBS-58. (16) Holroyd, R. A.; Tames, S.;Kennedy, A. J . Chem. Phys. 1975, 79, 2857. (17) Cipollini, N. E.; Allen, A. 0. J . Chem. Phys. 1977, 67, 131. (18) Schmidt, W. F.; Allen, A. 0. J . Chem. Phys. 1970,52, 4788. (19) Dodelet. J.-P.; Freeman, G. R. Can. J . Chem. 1972, 50, 2667.
0
0.I
0.2
0.3
CdM) Figure 9. Quenching of photocurrent from anthracene in isooctane by n-perfluorohexane at excitation wavelengths of 180 ( O ) , 185 (e),and 190 ( 8 )nm.
The electronic absorption spectrum of anthracene in isooctane covering the spectral region of the third and fourth transitions (Le., So S3and So S,) is displayed in Figure 7. Aside from
-
-
(20) Ddelet, J.-P.; Shinaska, K.; Freeman, G . R. Can. J . Chem. 1976,54, 714. (21) Nyikos, L.; Zador, E.; Schiller, R. In Proceedings of 4th Tihany Symposium on Radiation Chemistry; Hedvig, P., Schiller, R., Eds.; Publishing House of the Hungarian Academy of Sciences: Budapest, 1977; p 179.
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2687
Photoconductivity of Anthracene in Liquid Hydrocarbons
1
2.5
1
I
I
,
;I
1 I
0'5
i
J
I
1
170
180
190
200
A (nm) Figure 10. Quenching of photocurrent from anthracene in isooctane by n-perfluorohexane vs excitation wavelength at cq = 0.10 M.
small dispersion shifts, the spectra obtained in other solvents was the same as that shown in Figure 7. No evidence for any of the vapor-phase Rydberg transitions22 was detected in any of the liquid-phase absorption spectra. For comparison with the photocurrent from anthracene in isooctane as displayed in Figure 1, we show in Figure 8 some preliminary results for 9-methylanthracene in isooctane. In Figure 9, the effect of n-perfluorohexane to quench the photocurrent from anthracene in isooctance is indicated by a plot of the ratio of the photocurrent in the absence of n-perfluorohexane, J(O), to that at a concentration cq, J(cq),vs cq at representative excitation wavelengths of 180, 185, and 190 nm. Figure 10 indicates the wavelength dependence of this quenching effect by a plot of J(O)/J(c,) at cq = 0.10 M.
Discussion A comparison of Figure 3A and Figure 4A shows that the structure in ( r ) and in J are reasonably well coincident. That the ( r ) structure is not artifactual is supported by the following considerations. From eq 1-3 and by use of the integral representation of the modified Bessed function,23i.e.
with P2/4 = yr,, the ratio ( p , ) / ( ~ , ) ~ can be written (to terms cubic in E ) as a function of P as
where a = erC/2kT,rc = e 2 / t k T (=292 A), and (pes,)o = ( P / 2)jK3(P)is the escape probability at E = 0.24 An analysis of eq 7 indicates that for E between 1 and 10 kV/cm, and ( r ) between -60 and 80 A (which is the range over which structure in ( r ) is displayed in Figure 3A), ( p e s c ) / ( p e s c ) o is linearly correlated to E with a correlation coefficient of at least 0.99998, intercepts of -0.99-1.00, and slopes between 5.9 X and 5.7 X IOT5 cm/V. These slopes lie very close to the Onsager limiting slope of a = 5.8 X cm/V and also to the experimental slopes of J vs E of (5.7 f 0.10) X cm/V, thus tending to support our procedure for extrapolating to Jo. Also, the analysis of eq 7 indicates that, for E between 10 and 40 kV/cm, ( p m c ) / ( p w ) o will be concave upward or downward as a function of E depending on whether ( r ) is less than or greater than -70 A and that this concavity will be adequately large so that, at fields (22) Koch, E. E.; Otto. A.; Radler, R. Chem. Phys. Left. 1973, 21, 501. (23) Erdilyi, A., Ed. Tables of Integral Transforms, Bateman Manuscript Project; McGraw-Hill: New York, 1954; Vol. 1, p 146. (24) Replacing eq 2 by a more general distribution function, i.e.,flr) = [r"+)/(n2)!]r"e'r, eq 7 is easily generalized with the replacement of K3, K4. and 4 by K,+,,Kn+4,and K,+, and (p,),, becomes [@/2]"+'[2/(n
+
2) !I Kn+3,
E 2 2 0 kV/cm, changes in ( r ) by only a few percent (which is the variability responsible for the structure in Figure 3A) will lead to easily distinguishable changes in the ratio of ( p e s , ) / (pesc)o. Finally, it should be noted that our procedure for extracting ( r ) as a function of A,, involves the simple fitting of J / J o ( E ( p e s c ) / ( p m c ) o to ) eq 7 and makes no direct use of the magnitude of J nor its inherent variability with A,,. In contrast to ( r ) ,the structure in & as displayed in Figure 3B is much less certain. To obtain &, ( p s c ) is first calculated by using the values of ( r ) generated by the procedure outlined above and then J is divided by (p,). Since J, of course, is already structured, it follows that even if q5* were independent of A,, a structured ratio of J / (pes,) could be artifactually generated via the introduction of errors into (p,) by small uncertainties in ( r ) . The structure exhibited in Figure 3B (which tends to be anticoincident with that in J) we attribute largely to this effect. However, the general shape of $J*(Le., relatively constant between 186 and 198 nm and then rising rapidly at &,
