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Lawrence J. Bartal and Hans J. Ache
Reactions of Carbonium Ions with Positronium Atoms in Solutions‘ Lawrence J. Bartal and Hans J. Ache* Department of Chemistry, Virginia Polytechnic lnstitute and State University, Blacksburg, Virginia 24061 (Received April 5 , 7973)
The reactions of Ps atoms with carbonium ions obtained by dissolving triphenylmethanol, pentaphenylcyclopentadienol, pentaphenylcyclopentadiene, or trichloromethylmesitylene in H2S04 or CH2Cl2 saturated with BF3 were studied and the rate constants measured. The results suggest that these carbonium ions are highly reactive toward Ps atoms and that their interaction may be diffusion controlled. The most likely type of interaction between these ions and Ps seems to be an electron transfer reaction leading to the corresponding organic radical and free positron.
Introduction Positrons emitted in the radioactive decay of certain nuclides can pair with a n electron through an electrostatic attraction forming a hydrogen-like system called positronium (Ps). Two states can be observed, singlet (spins antiparallel) or para-positronium and triplet (spins parallel) or ortho-positronium. The annihilation lifetimes of o-Ps andp-Ps are 140 and 0.125 nsec, respectively. The average lifetime of free 0-Ps, ie., 140 nsec, is relatively long, but only a small fraction of all 0-Ps atoms reaches this age in condensed matter, since the positrons can enter into a series of reactions with the substrate, all of which lead to a characteristic decrease in their average lifetime. These include (1) annihilation of Ps with “foreign” electrons on collision with substrate molecules (pick-off annihilation), (2) ortho-para conversion, under the influence of paramagnetic particles, a spin conversion from ortho to para can occur, and (3) chemical reactions of Ps addition, substitution, oxidation, compound formation. Thus, although the lifetime of the Ps is clearly too short for any kind of conventional product analysis, the lifetime and decay mechanism of the Ps depend on its chemical environment, which will have changed when the Ps has undergone a chemical reaction and consequently the progress of a Ps reaction can be recognized by changes in the average annihilation lifetime and decay characteristics of the Ps species. (Because of the extremely short intrinsic lifetime of the p-Ps only the reactions of the longer-lived o-Ps can be followed by lifetime measurements.) Since it is experimentally possible to distinguish between the various types of interactions between Ps and substrate positron annihilation techniques have been SUCcessfully employed for the study of the chemical and physical properties of a number of compounds. Positronium lifetime measurements allow a n easy and accurate access to the rate constants for the interactions of thermal o-positronium atoms with a variety of compounds and thus represent a very useful tool not only for the study of the reactivity of these compounds toward Ps atoms,2 but also for the evaluation of their electron donor -acceptor properties in general.3-5 Previous work2 36-15 in aqueous solutions of inorganic ions has shown that one of the major types of interaction between the solute and Ps is the electron transfer from Ps to the solute species resulting in the oxidation of the PS atom to give a free positron. The Journal of Physicai Chemistry, Vol. 77,
No. 17, 1973
It appeared that several factors govern the rate of the redox process; the most significant parameter, however, being the free energy changes involved in the electron transfer process. In view of these results it seemed interesting to investigate the possibility of electron transfer between organic ions such as carbonium ions and Ps, and to assess the controlling parameters of this process. This was attempted by measuring the positron lifetime spectra of a group of diamagnetic organic molecules such as triphenylmethanol, pentaphenylcyclopentadiene, pentaphenylcyclopentadienol, and trichloromethylmesitylene in various solvents. All of these compounds are known to form carbonium ions in acidic media.16 Thus the observed changes in their reactivity toward Ps upon replacing solvent such as benzene by H2SO4 should reflect the enhanced ability of carbonium ions to accept an electron from the. Ps . For comparison a series of experiments was carried out with m-dinitrobenzene which does not form a carbonium ion under these experimental conditions but reacts with thermal Ps. An interpretation of the observed results has been attempted. Experimental Section Purity and Source of Reagents. Benzene was of spectrophotometric grade from Mallinckrodt; research grade CH2C12 was obtained from Phillips; H2S04 was of Baker analytical grade; BF3 was of Matheson pure grade. Triphenylmethanol was purchased from Eastman Kodak. Trichloromethylmesitylene was prepared by using the procedure described by Hart and Fish.17 Pentaphenylcyclopentadienol was obtained following the method outlined by Ziegler and Schnell.18 Pentaphenylcyclopentadiene was prepared by reducing the bromopentaphenylcyclopentadiene with NaBH4 using standard procedures. Bromopentaphenylcyclopentadiene was obtained by the reaction of HBr with pentaphenylcyclopentadienol. Preparation of Samples. Specially designed sample vials for the concentration studies (cylindrical glass tubes 100 mm long and 10 mm i.d.) were filled with 0.5 ml of the pure solvent or solvent mixture to which was added about 5 pCi of carrier-free 22Na (obtained from ICN) as NaC1. These samples were subsequently brought to the appropriate solute concentrations by adding known amounts of
2061
Reactions of Carbonium Ions with Ps Atoms the individual compound either in the solid form or in the form of a highly concentrated solution, so that only minor volume changes occurred. Before the start of the lifetime measurements each sample vial was thoroughly degassed and sealed under vacuum. The lifetime measurements were generally carried out a t room temperature; the lowtemperature measurements in the case of pentaphenylcyclopentadienol in CHzClz or in BF3-CHzC12 solutions were carried out in a specially designed dewar a t -60". In the latter case the sample was saturated with BF3. Whenever the nature of the ions required the exclusion of oxygen, the samples were prepared in an argon atmosphere. Carbonium lon Concentration, It was assumed that in H2S04 or BF3-CH2C12 solution in each case complete ionization of the solute species occurred. Thus the concentration of the added compound was substituted in eq 1 for the calculation of the rate constants. Since only small amounts were added the possible errors due to incomplete dissociation or rearrangement of the carbonium ions in SOlution would be relatively small and probably within the experimental error inherent to the applied technique. Replacement of concentrated HzS04 by more a dilute HzSO4 solution, as in the case of the triphenylmethylene carbonium ion study, may result in the re-formation of the precursor alcohols and a lower carbonium ion concentration. However, calculations based upon the spectrophotometric datalls reveal that even using 54% H2S04 solutions, the carbonium concentration is -86% of the original alcohol concentration. Further calculations show that the uncertainty arising from the assumption that the carbonium concentration is equal to the concentration of the dissolved alcohol are well within the intrinsic uncertainty of the calculated rate constants. Thus the approximation of cation concentration seems to be valid. Positron Lifetime Measurements. The lifetime measurements followed the standard procedure using delayed coincidence techniques as previously described.12.20 By applying constant fraction timing discrimination an optimum resolving time of 0.35 nsec was achieved, as characterized by the full-width at half-maximum of the prompt spectrum of a 6OCo source. The data obtained in the delayed coincidence spectrum were fitted by the method of least squares to determine the annihilation lifetimes. The lifetime spectra were decomposed into two or three components. The decomposition into two compounds resulted, however, in a better fit to the experimental curves. Consequently, it was concluded that the results can be best described by a two-component analysis. The calculations were performed on an IBM 370/ASP computer using computational methods developed by Cumming21 or Tao.22 The intensities were calculated by normalizing the areas under each of the components to that of the entire distribution. The intensity is then given by the ratio of the area of eaich component to that of the total area under the distribution curve. Correction for the small amount of positron annihilation occurring in the walls of the sample vials was made. As a standard procedure the lifetime spectrum of the pure solvent or mixture of solvent and BF3 was measured before the solute was added and thus T~~~~ determined which was substituted in eq 1.
Results The reaction rate constants for the interactions between thermalized IPS atoms and diamagnetic organic com-
i
I
0.05
0.10
F 2
d 5 2L 0 Y f n + A
3 4
1.10
1.05
SOLUTE CONC. (MOLE /LITER)
Figure 1. Relative positron annihilation rates (Xsolv f K[solute]/ plotted as a function of solute concentration in (Ad) sohtions of triphenylmethanol in).( 96% H2S04, ( A ) 57% H2S04, Xsolv)
and (0)benzene at room temperature. pounds, such as triphenylmethanol, pentaphenylcyclopentadiene, pentaphenylcyclopentadienol, trichloromethylmesitylene, and m-dinitrobenzene, dissolved in benzene, BF3-CHzC1, or HzS04, were determined in the usual way by measuring the positron lifetime spectra in these solutions. It has previously been shown that the reaction rate constants, K , are related to the average 1ifetime2J2J3 of thermal Ps atoms, as represented by the lifetime of the long-lived component, 7 2 = 1/X2, in the positron lifetime spectra by the following equation
where ~~~1~ is the lifetime of the long-lived component in the positron time spectra with no solute present; [solute] is the solute concentration; X2 and Xsolv are the observed annihilation rates of the thermal Ps atoms in solution or pure solvent, respectively. The results of these measurements are shown in Figures 1-4, where the relative changes in the observed annihilation rates of the thermal Ps atoms in the various solutions are plotted as a function of solute concentration.
+
X~X,I, = (hsolv K[solutel)/X,~, ( 21 They all exhibit, with the exception of the m-dinitrobenzene system, one common feature, namely, the drastic (linear) increase in the annihilation rate with solute concentration (over a solute concentration ranging from 0 to -0.1 M in CH2C12, when a Lewis acid such as BF3 is present, or in HzSO4 solution. Only slight differences in the rate constant are observed in acidic solutions of triphenylmethanol when concentrated H2S04 (96%) is replaced by a more dilute aqueous HzS04 acid concentration (57%). The rate constant increases from 0.60 X 109 M - 1 sec-1 observed in the former solution to about 0.70 X l o 9 M-1 sec-1 in the more dilute acid.23 Slightly greater rate constants were observed for the other systems: pentaphenylcyclopentadiene in 96% The Journal of Physical Chemistry, Vol. 77, No. 17, 1973
-
2062
Lawrence J. Bartal and Hans J. Ache
phpJph
Ph
1.20
Ph
Ph or
C
H
I
I
W
1.20
Ph
IN H,SO, Ph
K : 1.006x
1.15
lo9
3
0
1.10
4
1.05
x
IN BENZENE
I .oo
1.00 IN B E N Z E N E
K*CI.OX IO' LltOr/Mole sec I
0.05
0.I
SOLUTE CONC. ( M O L E I L I T E R )
Relative positron annihilation rates (Xsolv + K[solute])/ Xsolv plotted as a function of solute concentration in ( M ) solutions of pentaphenylcyclopentadiene in ( 0 ) 96% H2S04 and ( 0 )benzene at room temperature. Figure 2.
1.30
I
I
0.05 0.10 SOLUTE CONC. (MOLEILITER)
+
Figure
4. Relative positron annihilation rates (Xsolv K[solute])/ Xsolv plotted as function of solute concentration ( M ) in soh100% H2S04 and ( 0 ) tions of trichloromethylmesitylene in ).(
benzene at room temDerature.
I
SOLUTE PENTAPHENYLCYCLOPENTAOIENOL
1.25
0 [Ph,COM]
(-60' Cl
1.20
3 0
(ROOM TEMP.)
Liler/Mole sec
1.15 [Ph3C+]
UJ
x 1.10 I 0.01 0.10 SOLUTE CONC. (MOLE/LITER)
I .05
Figure 5. / * / / P O vs. solute concentration in solutions of triphenylmethanol in ( 0 )96% H2S04, ( A ) 57% H2S04, and (0)benzene at room temperature.
A IN CH,CI,
I .oc 0 IN B E N Z E N E K < IO' Liter/Molssec.
0.05
"A
0.10
+
Figure 3. Relative positron annihilation rates (hsolv K[solute])/ Xsolv plotted as function of solute concentration ( M ) in SOIUtions of pentaphenylcyclopentadienol in ( 0 ) 96% H2S04 and ( 0 ) benzene at room temperature and ( A ) CHzCI2 (+10?'0 BF3)
and ( A )CH2CIz at -60". HzS04, 1.01 x 109; and pentaphenylcyclopentadienol in 96% HzS04, 1.08 X 109; in BFs-CH2C12 (at -60"), 2.23 X 109; and trichloromethylmesitylene in 100% HzS04, 1.13 The Journal of Physical Chemistry, Vol. 77, No. 17, 1973
x 109. All rate constants are quoted in units of M-1 sec-1 at 25", if not otherwise indicated. The experimental error is in each case 10-15%. On the other hand, practically no change of A2 was observed if these organic compounds were dissolved in benzene or as in the case of pentaphenylcyclopentadienol in CH2C12, Le., the rate constants remain well below the detectable limit of 107 M - 1 sec-l. The results are summarized in Table I, where also the viscosities of the solutions are listed. From Figures 5-8, where the relative changes of the intensity 1 2 of the long-lived component in the positron time spectra, I2/120, I20 being the intensity observed with no solute present, are plotted as a function of solute concen-
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Reactions of Carbonium ions with Ps Atoms TABLE I: Rate Constants lor the Ps Interaction with Various Carbonium Ions in Solution -
Rate constant, Soiute
Solvent
Viscosity of solution, CP
M-l
