1188
J. Phys. Chern. 1980, 84, 1186-1189 W. Doidissen, G. Bakaie, and W. F. Schmidt, J. Nectrostatics, 7, 247 (1979). R. D. Goodwin, H. M. Rcder, and G. C. Straty, Nati. Bur. Stand. Tech Note, No. 684 (1976). W. Pfeiffer, 2. Angew. Pbys., 32, 265 (1971). D. L. Pulfrey, J . Sci. Instrum., Ser. 2 , 2 , 503 (1969). W. Pfeiffer, Thesis, Darmstadt, 1970. R. W. Gallant, “Physical Properties of Hydrocarbons”, Vol. 1, Gulf Publication Co. Houston, 1970. N. Gee and G. R. Freeman, Cbem. Pbys. Lett., 60, 439 (1979). T. Kimura and K. Fueki, J. Chem. Phys., 86, 366 (1977). W. Tauchert, H. Jungblut, and W. F. Schmldt, Can. J. Cbem., 55, 1860 (1977). S. Noda and L. Kevan, J. Cbem. Phys., 61, 2467 (1974). Y. Yamaguchi, T. Nakajima, and M. Nishikawa, J. Cbem. Pbys., 71, 550 (1979). 0. Bakale, W. Tauchert, and W. F. Schmidt, J. Chem. Phys., 83, 4470 (1975). W. F. Schmidt in “Electron-Solventand Anion-Solvent Interactions”, L. Kevan and B. Webster, Ed., Elsevler Scientific, Amsterdam, 1976, p 247. J. A. Jahnke, L. Meyer, and S. A. Rice, Pbys. Rev. A, 3, 734 (1971). J. M. L. Engels and A. J. M. Kimmenade, Cbem. Pbys. Lett., 48, 451 (1977).
(32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48)
J. P. Dodelet and G. R. Freeman, Can. J. Chem., 55, 2264 (1976). N. E. Cippoiini and A. 0. Alien, J. Cbem. Phys., 67, 131 (1977). J. Lekner, Pbys. Left., 27A, 341 (1968). N. E. Cippoilni, R. A. Holroyd, and M. Nishikawa, J . Chem. Pbys., in press. J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids”, Wiiey, New York, 1954. “Landolt-Bornstein, Zahlenwerte und Funktionen”, Bd. I, 6. Auflage, Springer-Verlag, Berlin, 1950. P. A. Egelstaff, “An Introduction to the Liquid State”, Academic Press, New York, 1967, p 200. J. Lekner, and A. R. Bishop, Phil. Mag., 27, 297 (1973). W. Shsckley, Bell Syst. Tech. J., 30, 990 (1951). T. L. Cotbell and J. C. Walker, Trans. Fara&ySoc., 81, 1585 (1985). D. L. McCorkle, L. 0. Christophorou, D. V. Maxey, and J. G. Carter, J. Pbys. B , 11, 3067 (1978). 8. Huber, Z . Naturforscb. A , 24, 578 (1969). W. Doldissen, Thesis Free University of Berlin, 1980. L. 0. Christophorou and D. L. McCorkle, Can. J. Cbem., 55, 1876 (1977). J. Bardeen and W. Shockley, Pbys. Rev., 80, 72 (1950). I. Adamczewski, “Ionlzatkn, Conductivity and Breakdownin Dielectric Liquids”, Taylor and Francis, London, 1969. J. P. Dodelet and G. R. Freeman, Can. J. Cbem., 55, 2264 (1977).
Mobilities of Solvated Electrons in Polar Solvents from Scavenging Rate Constants J. A. Delalre,“ M. 0. Delcourt, and J. Belloni Laboratoire de Physico-Cbimie des Rayonnements (associ6 au CNRS), Universit6 de Paris-Sud, Brit 350, 9 1405 Orsay Cedex, France (Received July l7? 1979) Publication costs assisted by Laboratoire de Pbysico-Chlmie des Rayonnements, Orsay
Rate constants k , for the reaction of solvated electrons (e;) with biphenyl have been determined at room temperature by fast spectrophotometric detection after pulse radiolysis. In various solvents where both k, and mobilities of e; (he)are known, it has been checked that the scavenging reaction with biphenyl is diffusion controlled. Then the Smoluchowski equation may be used to determine pe from k , in solventa where conductivity measurements are difficult due to a high intrinsic conductance. Mobilities of e; have been derived in various solvents, including ethers (diethyl ether, 1,2-dimethoxyethane), amines (ethylamine, n-propylamine, ethylenediamine, hydrazine), and amides (hexamethylphosphorictriamide). The values of pe so obtained are compared with those from the literature. For example, there is a significant discrepancy between our values and those for HMPT, n-butylamine,and tert-butylaminedetermined by pulse conductivity in the microsecond time range, and this discrepancy is discussed. The value of pe in ethylenediamine is larger by a factor of 4 than that of p(Na-). Finally, a rough correlation exists between ps and the energy at the absorption maximum of e; (Emm).
Introduction When low-energy electrons are injected into a liquid, they generally become solvated and can be evidenced by several techniques, mainly by absorption spectra, conductimetry, and scavenging experiments. The properties of solvated electrons (e;) vary greatly with the nature of the solvent, and these studies have received considerable attention in the recent years. Among them, the mobility (p,) seems to be a very interesting property. Its experimental determination carried out mainly in hydrocarbons’ gives information on the nature of the interaction between the solvent and the electron and on the mechanism of electron transport. Furthermore, the value of pe is needed to calculate diffusion-controlled rate constants between e,- and neutral or charged s01utes~--~ or to introduce physical parameters such as diffusion coefficients in models which are developed at present in order to explain primary radiation effeck5p6 Some solvents (NH,, amines, ethers) have the property of dissolving alkali metals and of giving e;. Conductivity measurements can be made in principle by conventional However, due to the formation of ion pairs or anions, the limiting equivalent conductance depends on
the nature of the metal,g10 except for ammonia.’l For most of the liquids, transient pulses of photons or electrons have to be used, and conductivity measurements involve different methods, namely, “time-of-flight” measurement or determination of transient currents.12 Due to the fact that pure solvents of low intrinsic conductivity have to be used, we know many values of pe in hydrocarbons,l and the variations of pe with the length of the carbon chain or with the sphericity of the molecule have been disc~ssed.’~-~~ As for polar solvents, except for ethers,16 there are few determinations of pe in alcohols,17J8amines,18 and water.lg Since many difficulties are present in conductivity measurements of pe in polar solvents, we examined whether the determination of diffusion-controlled rate constants can lead to reliable values of pe.
Experimental Section The pulse-radiolysis setup has been described earlier.20 A 600-keV Febetron 706 accelerator with a pulse width of 3 ns was used as the electron source, and it was associated with a spectrophotometric detection system having a whole risetime of 3.7 ns. Most of the rate constants measure-
0022-3654/80/2084-1186$01.0010@ 1980 American Chemical Society
The Journal of Physical Chemistty, Vol. 84, No. 10, 1980
Solvated Electrons in Polar Solvents
TABLE I: Scavenging Rate Constants, Mobilities, and E,
for Solvated Electrons at Room Temperature fie,
solvent hydrocarbons cyclohexane n-hexane ethers diethyl ether
DME THF
e
viscosity, CP ksa, L mol-' s-'
2 2
0.326
4.4 7.2 7.4
0.23 0.455 0.461
amines tert-butylamine n-butylamine n-propylamine ethylamine ethylenediamine alcoholis ethanol methanol ammonia HMPT
5.0 5.0 5.5 7 14
0.46
25 33 17 30
1.08 0.54 0.13 3.6
hydrazine
54
0.97
water
78
0.89
1187
cm'
V-I
s-'
scavengingb
conductivity
2.6 x 10'2d 7.7 x 10"d
2.4 x 'IO-' 8 x lo-'
3.5 x 10"Q 9 x 10-2Q
1.2 x 10°C 1.1 x 1O"f 1.1 x l o l ' g 1.2 x 10"(P)h
1.2 x IO+ 1.1x :to1.1x :to-*
5.1 x 10-3'
--
3.0 x 10-3'
Emax,eV
-.
0.54h 0.605h 0.59
2.0 x 10-3s 2.7 x 10-3s 1.54
1.85 X 10"' 1.45 X 10"" 1.80 x 10'0'
1.3 X YO-' 1.4 X YO-* 1.4 x 10-3
4.3 x iogd 1.3 x i o 9 j 8 x 10'0k 4 x 10'0C 3 x 1 O l o (A)' 1.7 X lolorn 2.2 x 10'On 7 x 1090 1.2 x 10'OP
8 x 10-3 3.65 x 10-3
0.635w 0.917% 2.6 x 5.9 x 1 0 - ~ t 1.8 x 5.5 x 10-45
1.3 x 1.0-3
1.77y 1.97y 0.73' 0.55'3aa 1.03n
2.0 x
1.73bb
This The solute is biphenyl except when indicated P for pyrene, A for anthracene. From eq 1)taking R , = 5 A . work. Reference 26. f Reference 23. g Reference 27. Reference 28. Reference 22. I Reference 29. Reference Reference 21. Reference 32. O Reference 33. P Reference 34. Reference 13. ' Reference 30. Reference 31. Reference 11. " Reference 19. Reference 35. Reference 36. Y Reference 16. Reference 18. Reference 17. References 38 and 39. Oa Reference 40. b b Reference 2. 37.
'
Q
'
ments were made at 900 or lo00 rim. At these wavelengths, the initial optical density of solvated electrons in most of the solvents which we studied was rather high (0.2 < OD < 0.7). The purification of hydrazine,21 amines,22and 1,2-dimethoxyethaine (DME)23has been described in former studies on these solvents. Diethyl ether was purified in the same way as DME.% Hexamethylphosphoric triamide (HMPT) was distilled with lithium aluminum hydride (2.5 g in 400 mL) under vacuum. The middle fraction of the distillate was stored under nitrogen and outgassed in the pulse radiolysis cell. The concentrations of biphenyl (Ph,) (in the range IO4 to 2-3 X mol L-l) were measured from their absorption spectra by means of an adjacent optical cell (optical length 1mm). The extinction coefficient of Ph2 was determined by former calibration in each solvent.
Results and Discussion Determination of the Scavenging Rate Constants. Scavenging rate constants of e; with aromatic solutes are known to be very high. It has already been shown that in hydrocarbons the reactivity of the electron toward the scavengers differs significantly from one solvent to another. Except for solvents where p e is very high (neopentane, tetramethyl~ilane),~~ the absolute rate constants k, of the fastest scavenging reactions depend very little upon the nature of the r ~ a v e n g e r .Since ~ ~ ~biphenyl ~~ is one of the most typical solutes, it has been chosen in this study. When both k, and pe are known, we can check whether the Smoluchowski equation for diffusion-controlled reactions holds:
NA k, = 47rR,(De iDphz)-
103 In (1)R, is the reaction radius, De and Dphz are the diffusion coefficients of the solvated electron and the neutral biphenyl molecule, and NA is Avogadro's number. The
diffusion coefficient De is related to the mobility p e by the Nernst-Einstein equation
with k is the Boltzmann constant, T the absolute temperature, and e the electronic charge. The diffusion parameter DPhzcan be neglected in solvents where De and consequently pe is high ( p e > 5 X cm2 V-' ). Equation 1then reduces to (3)
When applying this equation to n-hexane (see Table I) with R, = 5 A (a reasonable value for the sum of e; and Phz radii), there is good agreement between the calculated and measured values of pes Thus, the scavenging reaction can be considered as diffusion controlled in n-hexane. Since in ammonia kg3O and pel1are determined with good accuracy (see Table I), the slight difference between the two determinations of p e in this solvent is relevant to the fact that the reaction is not exactly diffusion controlled. However, this reaction is usually considered close to the diffusion limit.4 Then it will be assumed below that eq 1and 2 give the correct order of magnitude of pe when k , can be determined. Since Ph2 has been used in our previous studies to determine the radiation yield of e;, k, has been already given for hydrazine,21ethylamine,22n-propylamine,22ethylenediamine,22and DMESz3In this work, we have measured k , in diethyl ether and HMPT (see Table I). The vdue in diethyl ether is comparable with those previously determined in other ethers23v27p28 and the values obtained in HMPT for two different scavengers are of the same order of magnitude. The scavenging reaction was studied by examining the decay of e; at 800 < X < 1000 nm or, in some cases, the corresponding increases of Ph2- at 410 or 640 nm, which
1108
The Journal of Physical Chemistry, Vol. 84, No. 10, 1980
Delaire, Delcourt, and Belloni
13 10
Id2 P
'v)
r
i
11 = 10 7%
4
Iv)
Y
TIME (nanoscccmdsl
3
10 10
Flgure 1. Decay of e[ at 900 nm in biphenyl solutions of n-propylamine: mol L-'; (A)[Ph,] = 1.25 X lo3 mol L-'. Inset shows the observed pseudefiist-order rate constant vs. Ph2 concentratlon.
(0) pure solvent; (0)[Ph,] = 2 X
are the absorption maxima of P h ~ . In ~ lwhatever solvent studied, the optical density never decreases to zero after the fast decay period of e;# The residual optical density (OD,) may be either a consequence of the equilibrium evidenced in tetramethyl~ilane~~ and ammonia30
+
e,- Ph2 PhL (4) or a result of the overlap of e; and Phf absorption spectra. Because the ratio OD,(900 nm)/OD,(640 nm) is independent of concentrations, we discarded the first hypothesis, Therefore OD, is the absorbance of Ph2-, the spectrum of which extends in the infrared beyond lo00 nm (see Figure 2 of ref 21 or ref 41). Hence the decay signal is analyzed in terms of pseudo-first-order kinetics by means of the difference OD - OD, (see Figure 1). Another difficulty in determining k , arises from the fact that the decay of e; is fast in pure solvents (the total lifetime of ;e is 200 ns in diethyl ether and 1 ps in npropylamine). Thus the reactions of e; with radiolytical species are not negligible with respect to the scavenging reaction. This is illustrated for n-propylamine in Figure 1,where a pure pseudo-first-order decay is only observed for the highest concentration studied ([Ph,] = 1.25 X low3 mol L-l). Nevertheless, the decay at long times follows pseudo-first-order kinetics. The observed rate constant kObdis plotted against Ph2 concentration (insert of Figure 1) and the second-order rate constant k , is deduced: k, = 1.35 X 10" L moll1 s-l in n-propylamine.22 The values of k , determined in various polar solvents are listed in Table I. Experimental mobilities are also included for sake of comparison with the values deduced from k,, as explained below. Mobilities Deduced from Scavenging Rate Constants. In Figure 2, the rate constant k , calculated according to eq 1 has been plotted against mobility for two different values of the reaction radius: R, = 5 A (upper curve) and R, = 3 A (lower curve). DPhzwas obtained with the Stokes-Einstein with a radius 3 %, for Phz and a mean viscosity of 0.5 cP. Thus these curves lead to the highest value for k,, i.e., the rate constant for diffusioncontrolled reactions. The fact that, in some solvents, experimental points are below the shaded region between both curves simply indicates that the reaction is somewhat slower than diffusion controlled. In the framework of Noyes's treatment of chemical rate we can express the experimental rate constant k , by the following equation: _1 -- -1 1 (5) ks
kdiff
+ -k c
I
10-
I 0-3
10-2 MOBILITY OF e;
I
1
(~t-n%'-~~'-~.l)
-.
Figure 2. Scavenging rate constant vs. mobility of e The curves are calculated according to eq 1 and 2, with R, = 5 (upper curve) and R, = 3 A (lower curve). Mobilttles corresponding to open circles are underestimated (see text).
1
where kdiff is given by eq 1 and k , is the activation rate constant, Le., the rate constant which would apply if diffusion of the reactive species was extremely fast. The limiting case of k , 00 corresponds to diffusion control and then gives the calculated curves of Figure 2. Except for methanol, the experimental rate constants given here never differ from the calculated one by more than a factor 3. The experimental points which are above the shaded region are not so easy to interprete. If we assume that the experimental values of k, and p e for THF, (C2H&0, and HMPT are correct, we have to consider the eventuality of tunneling to obtain rate constants higher than the diffusion limit. However, we have rejected this explanation because it appears valid only for some solvents. More likely, the experimental values of pa from conductivity measurements have been underestimated and must be reexamined. Underestimations may arise from different reasons, mainly the relatively long response time of detection systems (100 ns in ref 16, 500 ns in ref 18), the interference of other radiolytically charged species, and the possibility of ion pairing. The low value of pe found in HMPTl8 has already been discussed.31 The values of p e deduced from the experimental k , and the upper curve of Figure 2 are given in Table I. In ethanol, methanol, and water, as k , becomes less dependent upon p e , the calculated values of p e are not given. If one considers the experimentalpoints of Figure 2, it seems that the scavenging reaction is not diffusion controlled in methanol, unless the only determination of k , in this solvent would be in error by defect. The absolute values of p e must reflect the mechanism of electron transport. As suggested previously12J3J6the electron can move as a free particle when it is outside a trapping site and it can move as an ion when inside this site. It has already been suggestedle that, owing to the low mobilities of e; in water, alcohols, and ammonia, the mechanism of electron transport looks like ion migration in these solvents, i.e., the electron moves together with the solvation shell. In contrast, the mechanism in ethers was assumed to be intermediate between an ionlike and a quasi-free-electron displacement.le The values of pe determined in this work for ethers and amines confirm the last model. Indeed, pe/pNa* = 18.9 and 23.5 in DME and
-
Solvated Electrons In Polar Solvents
The Journal of Physical Chemistry, Vol. 84, No.
and R. 0 . Brown, Adv. Chem. Phys., 31, 329 (1975). E. J. Hart and M. Anbar, “The HydratedElectron”, Wiley, New York, 1970 (3) L. M. Perkey and Farhataziz, Int. J. Radiat. Phys. Chem., 7, 719 (1975). (4) U. Schindewolf and P. Wunschel, Can. J. Chem., 55, 2159 (1977). (5) J. Belloni, F. Billlau, P. Cordier, J. A. Delaire, M. 0. Delcourt, and M. Magat, Faraday DISCUSS.,Chem. Soc., 63, 58 (1977). (6) K. M. Hong and J. Noolandi, J . Chem. Phys., 88, 5163 (1978). (7) C. A. Kraus, J . Am. Chem. Soc., 43, 749 (1921). (8) R. R. Dewald and J. L. Dye, J. Phys. Chem., 88, 128 (1964). (9) R. R. Dewald and K. W. Browall, J . Phys. Chem., 74, 129 (1970). (10) J. L. Dye, “Electrons in Fluids”, Colloque Weyl 111, J. Jortner and N. R. Kestner, Ed., Springer-Verlag, West Berlln, 1973, p 77. (11) R. R. DewaM and J. H. Roberts, J. phys. Chem., 72, 4224 (1968). (12) W. F. Schmidt and A. 0. Allen, J. Chem. Phys., 52, 4788 (1970). (13) R. M. Minday, L. D. Schmidt, and H. T. Davls, J . Chem. Phys., 54, 3112 (1971). (14) J. P. Dodelet, K. Shinsaka, and 0. R. Freeman, J. Chem. phys:.,59, 1293 (1973). (15) L. Nyikos, E. ZBdor, and R. Schiller, 4th International Symposium of Radiation Chemistry, Keszthely, Hungary, 1976. (16) J.P. Dodelet and G. R. Freeman, Can. J. Chem., 53, 1263 (1975). (17) P. Fowles, Trans. Faraday SOC.,67, 428 (1971). (18) A. V. Vannikov, E. I.Mal’tzev, V. I. Zolotarevski, and A. V. Ruidnev, Int. J. Radiat. Phys. Chem., 4, 135 (1972). (19) K. H. Schmidt and W. L. Buck, Science, 151, 70 (1966). (20) J. Belloni, F. Bllllau, P. Cordier, J. A. Delaire, and M. 0. Delcourt, J. Phys. Chem., 82, 532 (1978). (21) J. A. Delalre, P. Cordier, J. Belloni, F. Billiau, and M. 0. Delcourt, J . Phys. Chem., 80, 1687 (1976). (22) J. A. Delaire and J. R. Bazouln, Can. J . Chem., 57, 2013 (1979). (23) F. Bllliau, J. Belloni, J. A. Dehire, and M. 0. Delcourt, J. Chim. mys., 78, 1059 (1979). (24) A. 0. Allen and R. A. Holroyd, J. Phys. Chem., 78, 796 (1974). (25) J. H. Baxendale, C. Bell, and P. Wardman, J. Chem. Soc., Faraday Trans. I , 89, 776 (1973). (26) G. Beck and J. K. Thomas, J . Chem. Phys., 57, 3649 (1972). (27) 8. Bockrath and L. M. Dorfman, J. Phys. Chem., 77, 1002 (1973). (28) F. Y. Jou and L. M. Dorfman, J. Chem. Phys., 58, 4715 (1973). (29) A. K. Pikaev, G. K. SiMskaya. and S.A. KabakcM, Dokl. M a d . ,&uk. SSSR,198, 1374 (1971). (30) Farhatazlz and L. M. Perkey, J . Phys. Chem., 80, 122 (1976). (31) E. A. Shaede, L. M. Dorfman, 0. J. Flynn, and D. C. Walker, Can. J . Chem.. 51, 3905 (1973). (32) W. A. Seddon, J. W. Fletcher, and F. C. Sopchyshyn, Can. J . C k m . , 54, 2807 (1976). (33) J. H. Fendler, H. A. Gillls, and N. V. Klassen, J. Chem. Soc., Faraday Trans. I , 70, 145 (1974). (34) K. Sehested and E. J. Hart. J. Phvs. Chem.. 79. 1639 (1975). (35) W. A. seddon, J. W. Fletcher, and F. C.Sopchyshyn, Can. J. Chem:, 56, 839 (1978). (36)J. L. Dye, M. G. De Backer, and L. M. Dorfman, J . Chem. Phys., 52, 6251 (1970). (37) M. C. Sauer, Jr., S.Arai, and L. M. Dorfman, J . Chem. Phys., 42, 708 (1965). (38) J. Belloni and J. Fradin de h RenaudiBre, Nature(London),232, 173 (1971). (39) Farbtazlz, L. M. Perkey, and R. R. Hentz, J. chem. Phys., 80, 4383 (1974). (40) J. M. Brooks and R. R. Dewak!, J. Phys. Chem., 72, 2655 (1968). (41) 0. J. Hoytinck, Chem. Phys. Lett., 26, 318 (1974). (42) J. M. Warman, M. P. De Haas, E. ZBdor, and A. Hummel, Chem. Phys. Lett., 35, 383 (1975). (43) R. A. Robkrson and R. H. Stokes, “Electrolyte Sotutions”, Butterwlwths, London, 1959, p 44. (44) R. M. Noyes, Prog. React. Kinet., 1, 129 (1961). (45) C. Carvajal, K. J. Tolle, J. Smid, and M. Szwarc, J. Am. Chem. Soc., 80, 5059 (1968). (2)
I
0
O
as
10 EHAX(N
-
15
~
2D
Flgure 3. Mobilaies of electron vs. energy at the absorption maximum. The open points are for mobilities from scavenging, and the closed ones are for mobilities from conductivity.
TMF (with pNa+= 5.8 X loT4and 4.68 X cm2 V-l s-l in DME and THF, re~pectively~~), and p , / p ~ a= 4.2 in cm2 V-l s - ~ ) . ~ J O ethylenediamine (phi; = 3.3 X The mechanism of electron transport is not easily correlated with ithe nature of the interaction of the electron with its solvation shell. In other words, there is no simple relation between pe and the energy of the optical absorption maximu.m (Emm) of e;. Nevertheless, high mobility electrons are (consideredto be in weak interaction with the solvent and, as a first approximation, have low E,=. The plot of correlated values of pe and E , (Figure 3) show that this trend is respected as far as the values of pe calculated above are considered. If we assume that E,, is close to 0.6 eV in n-butylamine and tert-butylamine, and if we consider the earlier mobility data,lbtheir representative points in Figure 3 would be lower than those of the amine series. So the values of pe determined in ref 18 again seem doubtful. In conclusion, determination of wavenging rate constants prove to be a convenient means to determine pe in polar liquids. If the scavenging reaction is not exactly diffusion controlled, only a lower limit of pUeis obtained (unless a tunneling effect is occurring). The value of pe from conductivity measurements may be easily underestimated and then found lower than the above limit. Acknowledgment. The. authors are grateful to Dr. J. Drouin from Laboratoire des Carbocycles for distillation of HMPT.
References and Notes (1) (a) H. T. Davis, L. D. Schmklt, and R. G. Brown, ”Electrons in Flulds”, Colloque Weyl 111, J. Jortner and N. R. Kestner, Ed., Springer-Vetlag, West Berlin, 1973, p 393 and references therein. (b) H. T. Davis
IO, 1980 1189
L
~
