S. J. TAOAND J. H. GREEN
882 it is small. If Ear= 0, then D(HaB-BH3) = 38.5 kcal and will be reduced by 2Earif E,,r # 0. It is reasonable to assume 0 5 Ear 5 2 kcal and thus 34 5 D(HaBBHa) 5 38 kcal. To place this determination in perspective, Figure 11 shows the values of b, expected for critical energies corresponding to D(HaB-BH3) values of 28.4, 35.0, and 59.0 kcal. Our data for the homogeneous reaction are also shown. Additional support for our value of the diborane bond energy is obtained by noting that the magnitude of the inverse isotope effect expected for the homogeneous reaction depends on the critical energy. Figure 12 shows this dependence, and we have indicated the expected isotope effects corresponding to values of D(H3B-BH3) of 28.4, 35.0, and 59.0 kcal. Although the measured isotope effect suffers from considerable scatter, it appears good enough to exclude the high value for D(HaBBHa). If one accepts the hypothesis concerning the surface reaction, a value for D(H3B-BH3) can also be calculated from these data. The activation energy for this reaction is a “high-pressure” value and is slightly lower than
the true value due to the weak surface interaction. Once again making the approximation that the reverse reaction has negligible activation energy, a value of D(HaB-BH3) of 36 kcal/mol is obtained. Besides the assumption concerning Earabove there are a number of other sources of error which we have estimated as follows. By comparison with the CHaNC the estimated error in the calculation of the absolute rate is about a factor of 2 in the rate or 1kcal in EBf. The measurement of the area of the reactor exit orifice is probably good to 20% or 0.5 kcal in Eaf. The uncertainty in temperature gives an error of 0.6 kcal in E,’ and the random error in the measurement of b, yields an error of 0.4 kcal in E,’. We conclude that D(H3B-BHa) is 36 f 3 kcal.
Acknowledgments. This work was supported by National Science Foundation Grant, XSF-GP-6820. G. AI. acknowledges his support as a National Science Foundation Predoctoral Fellow since 1965. The discussions with B. S. Rabinovitch are gratefully acknowledged.
Positronium Interactions in Aqueous Oxyacids and Hydrogen Compounds1 by S. J. Tao and J. H. Green New England Institute f o r Medical Research, Ridgefield, Connecticut
(Received August 1 2 , 1 9 6 8 )
The lifetimes of positrons in the oxyacid-water systems, H3P04,HzSO4, HC104, ”08, and water, and in the hydrogen compound-water systems, HCl, HF, “3, HzO2,and water, were determined. The short lifetime component ( T I ) , the long lifetime component ( 7 2 ) , and the intensity (12)of the long lifetime component were derived from the composite lifetime data. The connection between changes in 12,the solution composition, and hot radical reactions is discussed. Data are discussed in terms of a proposed oxidation of positronium (Ps) by H+ and of possible chemical reactions leading to compounds of Ps and some estimates of bond energies are made: PsO (2.2 0.5 eV), PsOH ( 0, the intensity of the second component will be reduced according to the value of the threshold if the reaction rate is fast.g The lower the threshold the more the intensity of the second component is reduced. Such reactions can occur in a solution when Ps is hot, Le., with more energy than the threshold, since the excess energy can be easily carried away by a third body. This is just the case observed here, where there is not much change in r2 in the range concerned. The values of DAB for (H2P08-0)-, (HSOrO)-, and (NO2-0)are known,l7 but the value of DPAfor PsO is unknown. However, we can estimate the bond strength of PsO approximately by the following empirical method. The values of DA are plotted against the corresponding values of I2 in the flat region of the curve (Figure 2) as shown in Figure 3. It is found, a8 IZ approaches zero, that the extrapolated value of DAis 2.2 eV, which
O-'
,5
0.1
0.2 0.3 Concentration m.f.
0.4
Figure 4. Lifetime and intensity of the second component, in lifetime spectra for positron annihilation in &02-&0.
The intensity levels off at a value of 3.5% at an HzO2 concentration of 0.2 mf. This may be explained if the bond strength of Ps-OH is less than 1.5 eV, the reaction
PS
+ Ha02 +PsOH + OH
(16) R. E. Green and R. E. Bell, Can. J. Phys., 35, 398 (1957).
'e ?4 Figure 3.
Empirical relationship between the values
The Journal of Physical Chemistry
of DABand
12.
(17) These values have been taken from the thermochemical bond energies ( E ) given by T. Strengths of Chemical Bonds," Butterworth and 1958, rather than the bond dissociation energies, is listed e l ~ e w h e r e . ~The P-0, 9-0, and K-0 '~156, 104, and 53 kcal/mol, respectively.
best estimates of L. Cottrell, "The Co. Ltd., London, and a compilation bond energies are
887
POSITRONIUM INTERACTIONS IN AQUEOUS OXYACIDS is responsible for the reduction of I2, and the pick-off or conversion quenching rate of positronium in pure H202is greater than that in pure HzO. Referring to Figure 3, a rough extrapolation from the values of D A B and I2 for HzO and HzOz, gives the value of the bond strength of Ps-OH as 1.3 eV. This is much lower than the value of 4.8 eV for H-OH. If the greater quenching effect on the annihilation lifetime r2is considered to be wholly due to pick-off, the pick-off quenching cross section of HzOs is estimated to be 1.0 X cm2. The decrease of I z , as the acid concentration increases beyond 0.7 mf for both H3POrH20 and the H~SOK-HZO systems, can be also partly attributed to the formation of PsOH by such reactions as
PS+ HO-POaHz
-4
PsOH
+ POaHt
In mixtures of such high acid concentrations most of the acid exists as free acid rather than ions. The bond strength between the HO radical and the center atom of the free acid is expected to be weaker than the bond strength of the 0 atom and the center atom of the ions of the corresponding acid, which in turn reduces the threshold energy of the double-decomposition reaction. The positronium formation fraction may also be reduced because the ionization potentials of these acids are expected to be higher. 4.4. Hydrogen Compounds. The Ps formation gaps and the Ps compound formation gaps for simple hydrogen compounds of carbon (CH,) , nitrogen (NHs), oxygen (HzO), fluorine (HF), and chlorine
*":I
H20
5
(HC1) are shown in Figure 5, where the values of 2.9 and 2.0 eV are adopted as the bond strengths of PsF and PsC1. The estimate for PsCl depends primarily on the observations of TaoIs on annihilation rates of positrons in C12 and Ar-C12 gas mixtures. The resonance annihilation of Ps was attributed to the reaction Ps Cl2 + PsCl C1. This reaction occurs only when Ps has energies above thermal, This is in agreement with the fact that from the concentration of Clz in the Ar-C1z mixture in which the second shoulder just appears, the resonance annihilation energy was estimated reasonably as 0.5 eV, not far above thermal energies. The dissociation energy of C12 is 2.5 eV and the bond strength of PsCl is then about 2.0eV. This estimate is supported by the theoretical value, 1.55 eV, calculated by Simon~.'~ An estimate of the bond strength in PsF is obtained by noting that, when a hydrogen atom in benzene is replaced by fluorine, the value of I2 is reduced from 40 to 27%.20 Since the ionization potential of benzene is close to that of fluorobenzene, the reduction in I2 is most probably due to the formation of PsF by the reaction CeH5F Ps + PsF CsH5. From the shape of the empirical curves (Figure 2) the relation between threshold energy for Ps compound formation and the value of I2 can be roughly determined. The threshold energy for formation of PsF by the above reaction is thus estimated as 3.0 eV. The dissociation energy of H F is 5.9 eV and therefore 2.9 eV is a fair estimate of the bond strength of PsF. The error in the bond strengths so far estimated should be about 1 eV. Bond strengths of HsC-Ps or HtN-Ps should approach zero. From the above data, the intensities of the second component for the pure compounds should decrease in the order CH,, "3, H20, and HC1 provided that the positronium formation fractions are approximately the same. The positron annihilation lifetimes and the intensity of the long component in condensed methane, CH,, are not known but the values for n-pentane and n-hexane have been measured*O to be 7 2 = 4.0 and 3.8 nsec, and IZ = 39 and 40% respectively. The high values of I2 are due to the lower ionization potentials, e.g., 10.9 eV for n-hexane, and essentially to the negligible Ps compound formation gap. The positron annihilation lifetime 7 2 and the intensity IZ of the long component in pure condensed NH,, HF, and HC1 at room temperature are not available. If their values in dilute water solutions can be used as an indication HzO,HF, (Table V) , the intensities, Iz,for C5H12, "a, and HC1 just follow a decreasing order. (The particularly low value of IZ in HF-HzO systems of higher HF concentrations may be due to the high ionization
+
+
+
+
0 Figure 6. Pa compound formation gap for CH4, and HCl.
"3,
HzO,HF,
(18) 9. J. Tao, Phys. Rev. Lett., 14, 935 (1965). (19) L. Simons, P h y s . Rev., 90, 165 (1953). (20) 9. J. Tao and J. W. Lee, unpublished data. Volume 75, Number 4 April 1989
888
S. J. TAOAND J. H. GREEN
potential of H F and the stable associated HF system, which in turn considerably reduce the positronium formation fraction.) 4.6. Pick-of Quenching and TZ. In the oxyacids, except "03, positrons have a longer lifetime R than in water. (However, even in highly concentrated "03 the value of T~ is still about 1nsec.) This indicates that the effect of oxidation on Ps is negligible after Ps has slowed down below the threshold energy and become thermalized. Only pick-off still remains effective at thermal energies. The longer lifetime of 72,or lower pick-off quenching rate, for oxyacids is mainly due to their low molar density. For instance, the pick-off quenching cross section for H2SO4 was calculated to be 4.0 X 10"' cm2 which is greater rather than smaller than that of water, 2.3 X cm2. The low quenching rates of hydrocarbons are also due to their low molar densities, e.g., 0.00767 M/cm3 for nhexane, compared with that of water 0.0556 M/cma. Only the low quenching rate of H F can be attributed to a lower pick-off quenching cross section instead of low molar density. Since H F has a very high ionization potential, its low Ps pick-off quenching cross section is expected.21 The values of T~ for oxyacid mixtures agrees well with the formulaQ 1 + [(WBPAhpqB P XpqA
hpq
PA
1
- 1)/WAPBbqAk
+ C(WB/WA) - I l x
where Xpq is the pick-off quenching rate of the mixture; the densities of A, B, and their mixture are PA, PB, and p, respectively; the molecular weights are WA and WB; pick-off quenching rates of pure A and B are hpqA and hpqB and x is the mole fraction. A plot for the H2S04-H20system, where pick-off quenching rates of 0.556 X lo8sec-l (TZ = 1.8 nsec) and 0.333 X lo9 sec-1 ( T ~= 3.0 nsec) are used for pure HzO and HzSO4is shown in Figure 6, as an example. This relationship fits the experimental data better than a simpler relationship based on density variations. (Also see Figure 7.) 4.6. Formation of PsSOs. In the H2S04-SOa system, excess SOs both strongly quenches I2 and slightly in-
O .5
m.f H2S04
0
q
1.0 m.f.
Figure 6. The values of A2 for H2SO4-H2O system. The solid line represents the theoretical curve for two pick-off quenching agents. The J O U T n d of Physical Chemistry
.30
A HF
I
1
1
1
j
1
.5 Concentration m.f. Figure 7. Values of A2 and l a for NHrH20, HF-HsO, and HCIHe0 systems.
creases the annihilation rate, 7 2 (Table 11). The bond strength O-SO2 in 803 is about 3.5 eV, not small enough to be supposed to lead to quenching of Ps by formation of PsO. Therefore, an alternative explanation is required. It seems more reasonable to attribute the change in I 2 and T~ to formation of PsSOs by the reactions Ps so3 3 PsSOs which may occur at thermal energies. However, in the HsPOrPzOs system (Table I) the annihilation rate increases considerably with increasing P206concentration, while 1 2 remains quite high (n is more than halved at 0.74 mf PzOr while I2 falls only from 18 to 1501,). This is interpreted to mean that P206 quenches Ps mainly by pick-off rather than by oxidation or compound formation. This is in agreement with the general chemical behavior of SO8 and PtOb
+
5.
.604
J
4
.60
Conclusion
Here we would like to point out once more that the explanations given in the previous sections are tentative. However, no matter how tentative these explanations 'are, the experimental results strongly support two important aspects in the theory of positronium annihilation. First, a considerable part of the Ps atoms annihilate before thermalization, and the average energy at their annihilation may be of the magnitude of 1 eV. Second, since Ps annihilates during slowing down, it undergoes many hot radical reactions with the medium. (21) I). C. Liu and W. K. Roberts, Phys. Rev.. 130, 2322 (1963).
889
ABSOLUTEINTENSITY OF THIN-FILM CeHds) Some of the possible reactions may become the dominant ones and most of these reactions do possess a threshold energy. Therefore, the resultant annihilation lifetime spectrum may not necessarily fit a simple multiexponential decay scheme. If we apply the “free volume” theory proposed by Brandt, et ~ 1 . t~o 2molecular ~ liquids and aqueous solutions, we shall find that the distortion of the electronic wave function of the positronium atom is small, about a few per cent.2s This implies that thermalized positronium occupies a cavity of relatively large size. Consequently, positronium is expected to behave as an atom in liquids, However, the penetration of the total positronium wave function into the barrier of the cavity is sufficiently large to alter the lifetime of positronium significantly. This is the contribution of the “pick-off” quenching. The deep penetration of positronium wave functions into neighboring molecules implies that activation energy for most of the positronium reactions is negligible. This also explains why the rates of the positronium reactions are very fast provided energy conservation is satisfied. This, in turn, further supports our theory that the change of intensity IZis mainly
due to a chemical reaction. From such an elementary theory we are able t o give reasonable explanations for some hot Ps reactions in certain aqueous solutions and obtain valuable estimates of some Ps bond strengths. A recent investigation by Hsu and Wu2*has indicated a method of measuring kinetic energy involved in positronium annihilation. This will enable us to measure an important unknown parameter involved in positronium reactions, the energy possessed by positronium when it annihilates, It is hoped that these measurements and this report will serve as a stimulant for further understanding of positronium chemistry. Aclcnowledgments. Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grants No. 62-398, 961-65, and 1195-67, and by the U. S. Atomic Energy Commission, Grant No. AT(30-1) 3661. We are grateful to J. Bell for technical assistance. (22) W. Brandt, 8 . Berko, and W. W. Walker, Phys. Rev., 120, 1289 (1960). (23) 9.J. Tao, unpublished data. (24) F. H. Hsu and 0 . 9. Wu. Phys. Rev. Lett., 18, 889 (1967).
Absolute Intensity of Thin-Film CaHe(s)from Reflectance and Transmittance near 680 Cm-1 by Donald E. Glover and J. Leland Hollenberg Department of Chemistry, Universitg of Redlands, Redlands, California 08NS
(Received August 19, 1088)
The infrared reflectance and transmittance spectra of the ~ 1 (a*,,) 1 fundamental of CeHe(s) for thin films have been measured. Optical expressions for the reflectance and transmittance of thin films have been used to calculate the refractive index n and the absorption index IC. Integration of IC over the band gives an absolute intensity r = 11.7 f 1.3 cm2 mmol-1, which is about 36% lower than the apparent absorption intensity of 15.9. Comparison to results of other workers is made.
I n a preliminary report,l we have described the observation of very significant reflection from a thin-film sample of crystalline benzene. Because reflection losses from thin films have previously been ignored, or their importance indicated theoretically,2 the need for direct experimental data is apparent. Moreover, the influence of intermolecular coupling and medium effects on intensities in condensed phases cannot be determined until accuracy of measurement is improved. With the purpose of obtaining the absolute intensity free from possible reflection errors, the reflectance and transmitfundamental of CsHa in the tance spectra of the v11 (ha) solid phase near 680 cm-I were analyzed. Both the experimental procedures and calculations are described here in detail.
Experimental Procedure Reagent grade benzene which had repeatedly been frozen and pumped under high vacuum was stored over molecular sieve in a glass sample tube attached t o the line. A cross section of the conventional dewar cold cell used to form the sample is shown in Figure 1. The copper frame holding the AgCl substrate makes good thermal contact with a coolant chamber above. Temperatures were measured with copper-constantan thermocouples. Although other workers have reported (1) J. L. Hollenberg and D. E. Glover, J . Phys. Chem., 71, 1644 (1967) (2) S. Maeda and P. N. Schatz, J. Chem. Phvs., 35, 1617 (1961); S. Maeda, G.Thyagarajan, and P. N. Schatz, ibid., 39, 3474 (1963); K. Kozima, W. Suetaka, and P. N. Schatz, J. Opt. Soc. Amer., 56, 181 (1966). Volume Y$, Number 4 April 1969
